Nature Physics

Published by Springer Nature

Online ISSN: 1745-2481


Print ISSN: 1745-2473


Figure 2: Representative snapshots of the trajectory followed by villin headpiece from the pre-folded intermediate to the native state, with labels corresponding to the discussion in the text. Protein coloring runs blue to red from N terminus to C terminus; the crystal structure is shown as a transparent gray cartoon for comparison. Reprinted from Biophysical Journal 97; Peter L. Freddolino and Klaus Schulten; Common structural transitions in explicit-solvent simulations of villin headpiece folding; 2338-2347; Copyright 2009, with permission from Elsevier.
Figure 4: Directionality of hydrogen bonding in folding simulations. a) Illustration of the hydrogen-acceptor-acceptor antecedent angle Ψ in a protein backbone hydrogen bond. b) Normalized histogram of Ψ angles present in MD simulations of a misfolded helical state (Helix) or the native state (Sheet) of the WW domain (39). A survey of the PDB indicated that both should peak between 155 and 160 degrees (80). Part (b) reprinted from supplementary material of Biophysical Journal 96; Peter L. Freddolino, Sanghyun Park, BenoˆıtBenoˆıt Roux, and Klaus Schulten; Force field bias in protein folding simulations; 3772-3780; Copyright 2009, with permission from Elsevier.
Challenges in protein folding simulations: Timescale, representation, and analysis. Nature Physics, 6, 751
  • Article
  • Full-text available

October 2010


830 Reads

Peter L Freddolino


Christopher B Harrison



Klaus Schulten
Experimental studies of protein folding processes are frequently hampered by the fact that only low resolution structural data can be obtained with sufficient temporal resolution. Molecular dynamics simulations offer a complementary approach, providing extremely high resolution spatial and temporal data on folding processes. The effectiveness of such simulations is currently hampered by continuing questions regarding the ability of molecular dynamics force fields to reproduce the true potential energy surfaces of proteins, and ongoing difficulties with obtaining sufficient sampling to meaningfully comment on folding mechanisms. We review recent progress in the simulation of three common model systems for protein folding, and discuss how recent advances in technology and theory are allowing protein folding simulations to address their current shortcomings.

Figure 1: The M2S–S2M pulse sequence, all pulses are resonant with the 13C Larmor frequency. a, Magnetization to singlet spin order (M2S) sequence, the first part is equivalent to a CPMG sequence with each echo pulse composed of a [90018090900]φ composite pulse unit with an overall phase increment φ = [0022…]. The interpulse delay is determined to be around 2.46 ms. The CPMG sequence is followed by another 90° pulse with a 90° phase shift compared with the first 90°. Then a second multiple echo sequence with half as many pulses ( ) is preceded by a 1/(4Jcc) delay. Inset, Structure of DEO–13C2, dissolved in DMSO-d6 (stars indicate 13C atoms). The concentration of DEO–13C2 is around 2 M. b, Complete M2S–S2M sequence. A gradient is added right after the M2S sequence to suppress the single-quantum coherence generated by M2S, a variable waiting time τr is followed by another 90° pulse and a gradient to suppress recovered IZ magnetization during τr. Then the time-reversed M2S (S2M) converts the singlet state population back to magnetization. A final 90° pulse tips down the bulk magnetization for detection.
Figure 3: Single scan 13C spectra of DEO–13C2 acquired after the CPMG part of the M2S sequence. a,b, Consistent pertubation in 13C spectra in experiment (a) and simulation (b) after the CPMG sequence with the same interpulse delay (4.92 ms) and with various numbers of echo pulses (n1); maximum conversion in the singlet–triplet subspace occurs after 45 echo pulses, middle row of b, which is the spectrum after a perfect conversion from carbon triplet to singlet (see the text). c,d, Consistent pertubation in 13C spectra in experiment (c) and simulation (d) after the CPMG sequence with the same number of echo pulses (n1 = 45) and various interpulse delays (τ = 2, 4.92 or 16 ms). Minimum perturbation can be observed with 2 or 16 ms interpulse delays.
Figure 4: DEO 13C signal from the M2S–τr–S2M sequence decays as a function of the waiting time τr. a–c, Signal intensity is normalized against the full thermal polarized magnetization in all cases (simulation at thermal condition (a), experiment at thermal condition (b) and natural logarithm of DNP-hyperpolarized signal (c)), all estimations include a 95% confidence interval. In a, a rotational correlation time of 40 ps is assumed, corresponding to a T1 of 17 s in a 360 MHz B0 field. The singlet signal decays with a lifetime TS of 116.8±7.4 s. In b,  T1 of 13C2-DEO is measured to be 22.2±0.6 s in a Bruker 360 MHz magnet, the sample is dissolved with DMSO-d6. The singlet signal decays with a lifetime TS of 50.6±2.1 s. In c, the hyperpolarized singlet signal is acquired in a 7 T (300 MHz) Bruker MRI scanner and plotted on a semilog scale. A TS of 41.4±3.2 s is obtained compared with a T1 of 23±0.6 s.
Accessing long-lived nuclear singlet states between chemically equivalent spins without breaking symmetry

November 2012


318 Reads

Long-lived nuclear spin states could greatly enhance the applicability of hyperpolarized nuclear magnetic resonance. Using singlet states between inequivalent spin pairs has been shown to extend the signal lifetime by more than an order of magnitude compared to the spin lattice relaxation time (T 1), but they have to be prevented from evolving into other states. In the most interesting case the singlet is between chemically equivalent spins, as it can then be inherently an eigenstate. However this presents major challenges in the conversion from bulk magnetization to singlet. In the only case demonstrated so far, a reversible chemical reaction to break symmetry was required. Here we present a pulse sequence technique that interconverts between singlet spin order and bulk magnetization without breaking the symmetry of the spin system. This technique is independent of field strength and is applicable to a broad range of molecules.

Figure 1: Schematic model of adaptive feedback systems. a, The three-node feedback topology and its general adaptive behaviour. The inhibitory effect of the input is chosen arbitrarily and does not affect any of the conclusions in this paper. b–e, Examples of sensory adaptive networks with highlighted key negative feedback loops. b, E. coli chemotaxis: association of ligand to methyl-accepting chemotaxis protein (MCP) induces the methyltransferase (CheR)/methylesterase (CheB) to add/remove methyl-groups to/from MCP respectively to counteract the influence of ligand binding. c, Osmotic sensing in yeast: hyperosmotic shock deactivates the osmosensor Sln1p to Sln1, which stops the multi-step phospho-relay and activates the high osmolarity glycerol (HOG1) pathway to restore cell turgidity and eventually enhance the phosphorylation of Sln1 back to active Sln1p. d, Olfactory sensing in mammalian neurons: odorant binding induces activation of adenylyl cyclase (AC) causing the inbound calcium (Ca2+) flux, and calmodulin (CaM) interacts with enriched calcium to form Ca-CaM and activate AC phosphorylase calmodulin kinase II (CAMKII) that eventually phosphorylates and deactivates AC. e, Light sensing in mammalian neurons: light activates the G-protein coupled receptor (photon-sensor) that decreases the cellular level of cyclic guanosine monophosphate (cGMP) and inhibits the inbound calcium (Ca2+) flux, which eventually turns on the octopus rhodopsin kinase (ORK) to phosphorylate and deactivate the photon-sensor. The key high-energy biomolecules are labelled in red.
Figure 2: Energetics and kinetics of adaptation. a, An effective potential, obtained by averaging over the fast activity variation, is shown for the equilibrium model (β=0)and the non-equilibrium models (β>0). For β>βc, the state at m=m* changes from being unstable to stable. b, The steady-state probability density P(a,m) (colour plot) and the phase-space fluxes (Ja,Jm) (vector field) are shown for the equilibrium model (β=0). The fluxes vanish Ja=Jm=0 everywhere and P(a,m) is centred at the corners of the phase space. c, In the non-equilibrium fully adaptive model (β=1), the non-zero fluxes form a vortex (cycle) around the peak of P(a,m). The peak of P(a,m) has a fixed value of activity and a value of m that is small for low background signal (left panel) and high for high background signal (right panel). d, In the equilibrium model (left panel), the system always moves downhill (green arrows) to its lowest energy state; in the non-equilibrium adaptive model (right panel), external energy (W) is consumed to push the system uphill (red arrows) to maintain it near the cross-over point of the active and inactive states.
Figure 3: The E. coli chemotaxis adaptation. a, The schematics of the E. coli chemoreceptor adaptation process. The red and blue cycles represent the receptor methylation–demethylation cycles for low and high attractant concentrations respectively, analogous to the flux cycles shown in d. b, The energy dissipation ΔW≡&Wdot;kR−1 per unit of time (kR−1) (solid lines) and the normalized adaptation error ε/ε0(dotted lines) versus the parameter γ for different values of ligand concentration s. ε0≡ε(γ=1). c, The adaptation error versus energy dissipation for different values of background ligand concentration s. Solid lines from bottom to top represent log10(s/KI)=1.2,1.0,0.5,−3.0; dashed lines from bottom to top represent log10(s/KI)=3,3.5,4,6. KI is the dissociation constant for the inactive receptor. εc is the saturation error at , ΔWc is defined as the ΔW value when ε=0.99εc. d, The prefactor α in the error–energy relationship and its dependence on the methyl modification rates kR and kB.
Figure 4: The cost–performance relationship. a, Adaptive accuracy versus energy cost for over 10,000 different models (represented by open circles) with random choices of parameters. log10γ is randomly picked from [0,−10], log10τa is randomly picked from [−3,3], ΔE(0) and −ΔE(m0)are randomly picked from [11,22]kT, log10(s/KI) is randomly picked from [−10,10]. The best performance line is outlined. The case for Tar is shown (dashed line) with the available energies in SAM and ATP (both at 20% efficiency) marked. b, The responses to a step stimulus (from s=0 to s=10KI) at t=1 for the equilibrium model (black), and non-equilibrium models driven by ATP (red line) and SAM (blue line) at 20% efficiency.
Figure 5: Adaptation dynamics of starving E. coli cells. a, Response of E. coli cells to successive addition and removal of a saturating stimulus (50 μM MeAsp) over a 7 h period in a medium without nutrition (stimulus time series shown at top). Changes in kinase activity were measured using a FRET reporter based on a YFP fusion to the chemotaxis response regulator CheY and a CFP fusion to its phosphatase CheZ. The grey line is the monitored ratio of YFP to CFP fluorescence. The baseline YFP/CFP ratio at zero FRET is shown by the black dashed line. The black solid line indicates the adapted activity without any stimuli. The drift in the zero-FRET baseline is primarily due to the differences in the photobleaching kinetics of YFP and CFP. The inset plot shows the normalized FRET signal in response to 50 μM MeAsp addition at 1,442 s (blue), 10,761 s (red) and 23,468 s (black), as indicated by arrows of the same colours in the main plot. The response amplitude weakens as cells de-energize. Adaptation takes longer, but activity always returns to its pre-stimulus level with high accuracy. b, The adaptation half-time, defined as the time needed to recover half of the maximum response on MeAsp addition, increases by a factor of about three (from ~ 130 s to ~ 410 s). c, The relative adaptation accuracy remains unchanged (~  95%). The symbols in b and c are from measurements and the red lines are a guide for the eye.
The energy-speed-accuracy tradeoff in sensory adaptation

May 2012


550 Reads

Ganhui Lan


Pablo Sartori


Silke Neumann




Yuhai Tu
Adaptation is the essential process by which an organism becomes better suited to its environment. The benefits of adaptation are well documented, but the cost it incurs remains poorly understood. Here, by analysing a stochastic model of a minimum feedback network underlying many sensory adaptation systems, we show that adaptive processes are necessarily dissipative, and continuous energy consumption is required to stabilize the adapted state. Our study reveals a general relation among energy dissipation rate, adaptation speed and the maximum adaptation accuracy. This energy-speed-accuracy relation is tested in the Escherichia coli chemosensory system, which exhibits near-perfect chemoreceptor adaptation. We identify key requirements for the underlying biochemical network to achieve accurate adaptation with a given energy budget. Moreover, direct measurements confirm the prediction that adaptation slows down as cells gradually de-energize in a nutrient-poor medium without compromising adaptation accuracy. Our work provides a general framework to study cost-performance tradeoffs for cellular regulatory functions and information processing.

Figure 1: Thin actin protrusions emerge from dendritic actin networks.a, Phase-contrast and spinning–disc confocal images of membrane (green) and actin (red) show multiple protrusions in the lumen of a GUV. Overlay of the fluorescence images confirms that the membrane protrusions are supported by actin filaments. Scale bar, 5 m. b, Localization of AF555 actin and AF488 capping protein (CP) fluorescence in thin actin filament protrusions shows that filament barbed ends are concentrated at the tip of the protrusions. Scale bar, 10 m. c, Localization of actin, Arp2/3 complex and capping protein along thin actin filament protrusions. The normalized Arp2/3 complex (n=4) and capping protein (n=3) traces were divided by the normalized actin (n=7) line scans. d, Elongation of a thin protrusion visualized by phase-contrast microscopy. A second, independent protrusion enters the field at 10 min and crosses the path of the protrusion that is tracked (red arrows). Scale bar, 3 m. The length of the protrusion was tracked through time showing that growth initially occurs quickly but slows down over time. Inset: Kymograph of fluorescently labelled membrane.
Figure 2: Elongation of a thin actin filament protrusion by polymerization proximal to the membrane.a, Laser scanning confocal images of fluorescence recovery of a photobleached region along a protrusion. The red arrow denotes the tip of the protrusion. Scale bar, 1 m. b, Trajectories of positions along the photobleached protrusion. Blue circles mark the tip of the filopodium-like protrusion. Black circles (white on the image) mark the edge of the photobleached spot that is proximal to the tip. Red circles mark the edge of the photobleached spot that is distal to the tip.
Figure 3: Role of membrane in formation of thin actin filament protrusions.a, The total energy associated with membrane deformation and filament bending is calculated for two actin filaments anchored 100 nm below the membrane with protrusion length L-L0 and separation D. The lightly shaded region under the curve represents the set of thermodynamically accessible states that will lead to filament bundling by the membrane. The darkly shaded region represents a subset of these states that are kinetically accessible, determined by the branching distance of 100 nm (ref. 1). Inset schematic diagrams represent the merged and unmerged states (not to scale). b, Stability of thin actin filament protrusions against Euler buckling. Left: A schematic diagram illustrates a straight protrusion, the total energy of which is due to the membrane tube. Right: A hypothetical situation in which the filaments buckle under the load of the membrane, where buckling is energetically unfavourable (see text). c, Model of membrane-induced formation of a thin actin filament protrusion. Left: Small-amplitude local deformations of the membrane arise as actin filaments polymerize against the membrane (black arrows). Deformations that are within the range of attraction are able to merge to create a larger deformation that gathers extra filaments (curly brackets). Middle: Deformations that fail to gather extra filaments are stalled and diminish (grey arrows). Right: After bundling enough filaments to overcome the membrane resistance to tube formation, a 'proto-filopodium' can elongate without further physical constraint.
Membrane-induced bundling of actin filaments

August 2008


187 Reads

Dynamic interplay between the plasma membrane and underlying cytoskeleton is essential for cellular shape change. Spatial organization of actin filaments, whose growth generates membrane deformations during motility 1, phagocytosis 2, endocytosis 3, and cytokinesis 4, is mediated by specific protein-protein interactions that branch, crosslink, and bundle filaments into networks that interact with the membrane. Although membrane curvature has been found to influence binding of proteins with curvature-sensitive domains 5, the direct effect of membrane elasticity on cytoskeletal network organization is not clear. Here we show through in vitro reconstitution and elastic modeling that a lipid bilayer can drive the emergence of bundled actin filament protrusions from branched actin filament networks, thus playing a role normally attributed to actin-binding proteins. Formation of these filopodium-like protrusions with only a minimal set of purified proteins points to an active participation of the membrane in organizing actin filaments at the plasma membrane. In this way, elastic interactions between the membrane and cytoskeleton can cooperate with accessory proteins to drive cellular shape change.

Figure 1: Elastomeric components for autonomously controlled microfluidic devices.a, A three-layer composite of the check-valve and switch-valve. b, Cross-section schematic of the check-valve and switch-valve in both the open and closed state based on differential pressure. c, Corresponding component state symbol of the check-valve and switch-valve. Conducting current/flow is shown as solid lines and non-conducting current/flow is shown as dotted lines. d, The diode and p-channel JFET transistor shown as analogous electronic components to the check-valve and switch-valve, respectively.
Figure 2: Interactive elastomeric components for oscillatory switching.a, Comparison between a microfluidic oscillator and an electronic oscillator. The two states of a microfluidic oscillator automatically produce an alternating output flow between two distinct solutions being simultaneously infused at a constant rate. b, Graph of both the simulated and experimental data for the oscillator’s switching frequency for various flow rates within its operating range. The error bars represent the standard deviations from three measurements taken at each flow rate. c, Graph of pressure oscillations at solution inlets for an infusion rate of 10 μl min−1.
Figure 3: Microfluidic-oscillator control of flow in a subordinate fluid circuit.a, Fluid-circuit diagram for state 1 of a microfluidic oscillator providing input signals (red and green solutions) to a subordinate fluid circuit that distributes the flow of two solutions (yellow and blue) to four outlets. b, Actual images of both states for the fluid circuit with an infusion rate of 100 μl min−1 that oscillates at 1 Hz.
Integrated Elastomeric Components for Autonomous Regulation of Sequential and Oscillatory Flow Switching in Microfluidic Devices

June 2010


988 Reads

A critical need for enhancing usability and capabilities of microfluidic technologies is the development of standardized, scalable, and versatile control systems1,2. Electronically controlled valves and pumps typically used for dynamic flow regulation, although useful, can limit convenience, scalability, and robustness3-5. This shortcoming has motivated development of device-embedded non-electrical flow-control systems. Existing approaches to regulate operation timing on-chip, however, still require external signals such as timed generation of fluid flow, bubbles, liquid plugs or droplets, or an alteration of chemical compositions or temperature6-16. Here, we describe a strategy to provide device-embedded flow switching and clocking functions. Physical gaps and cavities interconnected by holes are fabricated into a three-layer elastomer structure to form networks of fluidic gates that can spontaneously generate cascading and oscillatory flow output using only a constant flow of Newtonian fluids as the device input. The resulting microfluidic substrate architecture is simple, scalable, and should be applicable to various materials. This flow-powered fluidic gating scheme brings the autonomous signal processing ability of microelectronic circuits to microfluidics where there is the added diversity in current information of having distinct chemical or particulate species and richness in current operation of having chemical reactions and physical interactions.

Classes of complex networks defined by role-to-role connectivity profiles

February 2007


314 Reads

In physical, biological, technological and social systems, interactions between units give rise to intricate networks. These-typically non-trivial-structures, in turn, critically affect the dynamics and properties of the system. The focus of most current research on complex networks is, still, on global network properties. A caveat of this approach is that the relevance of global properties hinges on the premise that networks are homogeneous, whereas most real-world networks have a markedly modular structure. Here, we report that networks with different functions, including the Internet, metabolic, air transportation and protein interaction networks, have distinct patterns of connections among nodes with different roles, and that, as a consequence, complex networks can be classified into two distinct functional classes on the basis of their link type frequency. Importantly, we demonstrate that these structural features cannot be captured by means of often studied global properties.

Self-organized criticality occurs in non-conservative neuronal networks during Up states

October 2010


83 Reads

During sleep, under anesthesia and in vitro, cortical neurons in sensory, motor, association and executive areas fluctuate between Up and Down states (UDS) characterized by distinct membrane potentials and spike rates [1, 2, 3, 4, 5]. Another phenomenon observed in preparations similar to those that exhibit UDS, such as anesthetized rats [6], brain slices and cultures devoid of sensory input [7], as well as awake monkey cortex [8] is self-organized criticality (SOC). This is characterized by activity “avalanches” whose size distributions obey a power law with critical exponent of about −32 and branching parameter near unity. Recent work has demonstrated SOC in conservative neuronal network models [9, 10], however critical behavior breaks down when biologically realistic non-conservatism is introduced [9]. We here report robust SOC behavior in networks of non-conservative leaky integrate-and-fire neurons with short-term synaptic depression. We show analytically and numerically that these networks typically have 2 stable activity levels corresponding to Up and Down states, that the networks switch spontaneously between them, and that Up states are critical and Down states are subcritical.

Phase transitions in contagion processes mediated by recurrent mobility patterns

July 2011


396 Reads

Human mobility and activity patterns mediate contagion on many levels, including: spatial spread of infectious diseases, diffusion of rumors, and emergence of consensus. These patterns however are often dominated by specific locations and recurrent flows and poorly modeled by the random diffusive dynamics generally used to study them. Here we develop a theoretical framework to analyze contagion within a network of locations where individuals recall their geographic origins. We find a phase transition between a regime in which the contagion affects a large fraction of the system and one in which only a small fraction is affected. This transition cannot be uncovered by continuous models due to the stochastic features of the contagion process and defines an invasion threshold that depends on mobility parameters, providing guidance for controlling contagion spread by constraining mobility processes. We recover the threshold behavior by analyzing diffusion processes mediated by real human commuting data.

Figure 3: Propagation of perturbations.a, The propagation to distant nodes is governed by the structure of g(f−1(x)) through the leading terms of equation (7), which determine the dissipation rate, β, in equation (12). b, Conservative dynamics: if the leading term in equation (7) is m0≠0 we have β = 0, predicting a conservative propagation, in which perturbations penetrate the network without loss. As a result Γ(l) = 1 (equation (12)) and P(G)~G−2 (equation (13)). We predict that  and  are in this class, as confirmed by results in a1,a2 and d1,d2. c, Dissipative dynamics: if the leading terms in equation (7) are g(f−1(x))~b0+xm1 we have β = m1>0 in equation (12), leading to a dissipative propagation, in which perturbations decay exponentially with network distance. As a result, P(G)~G−ν (equation (13)), where 1<ν<2 (equation (14)). For  and  we predict β = 1 and hence ν = 3/2, in perfect agreement with the results of a3,a4 and d3,d4.
Fig. 4. Cascade sizes
Figure 5: Uncovering the dynamical universality class from empirical data.Human dynamics: we constructed Gij from the correlations in the usage patterns of users in an email network48 (Supplementary Section SVIII.A). a1, The stability versus ki follows Si~kiδ with δ = 2.4±0.2, predicting heterogeneous stability (the solid line indicates a slope of δ = 2.4). a2, As expected for heterogeneous stability, the system features a fat-tailed P(S). b1,b2, The local impact versus ki follows Ii~kiφ with φ = 2.1±0.1, predicting heterogeneous impact with a fat-tailed P(I). c1, The correlation function Γ(l) does not decay, indicating conservative dynamics. c2, As expected for conservative dynamics, P(G)~G−ν with ν = 2. d1,d2, From the measured β and φ we predict ω = 2.1 in equation (15) and hence expect a fat-tailed P(C). As β = 0 we also expect that P(C)~P(I). Indeed, we find that P(C)~C−1.5 and P(I)~I−1.5, in agreement with the prediction for a scale-free network (Supplementary Section SVII.E). For large ki the cascades saturate owing to the finite size of the network (N = 2,668). Cellular dynamics: to test our predictions for a biological system we collected perturbation data in which 55 yeast genes were perturbed, measuring their impact on the rest of the 6,222 genes, giving rise to a 6,222×55 correlation matrix, Gij (ref. 49). Lacking the wiring diagram we could not measure δ, φ, β and ω directly. Yet, we can identify the universality class by measuring P(I), P(S), P(G) and P(C), which do not require knowledge of the underlying topology (Supplementary Section SVIII.B). e–h,  P(S) indicates uniform stability (δ = 0; e); P(I) indicates heterogeneous impact (φ≠0), in which P(I)~I−1 (f); P(G) has ν = 2, indicating conservative dynamics (β = 0; g); from the inferred values of φ and β we predict ω>0, foreseeing heterogeneous cascades, a prediction supported by the fat-tailed P(C)~C−1 (h). As β = 0, we expect that cascade heterogeneity is driven by the local dynamics, also supported by the fact that P(C)~P(I).
Universality in network dynamics

November 2013


642 Reads

The art of network science lies in our ability to unify our understanding of structure and function. On the one hand predicting the dynamical behavior of the system from its topological structure, and on the other hand elucidating the topological structure from dynamical measurements. Here we present a formalism, which through a set of scaling laws enables us to peek into the dynamical mechanism characterizing the pairwise interactions in a network. We find that these scaling laws, described by three empirically accessible exponents, are an intrinsic property of the system's dynamics, and can thus provide insights into the type of interactions governing them - providing a theory for dynamical inference. Additionally, this formalism is useful for topological inference, translating dynamical measurements into prediction of network links. This prediction is of crucial importance in biology, as currently only a small fraction of the network links has been verified, hindering progress in drug development and mechanistic predictions.

Figure 1: Disordered free-energy profiles showing the free-energy cost of rearranging a region with Nc compact particles and Nf stringy particles.The transition state separating the unreconfigured state (Nc=Nf=0) from the final state where stable reconfigurations are possible (coloured yellow) determines the barrier to reconfiguration. The upper left panel shows the fluctuation-free profile whereas the others demonstrate three possible realizations of the fluctuations. In the upper-right-panel situation compact reconfiguration is required to overcome the free-energy barrier. For the two other realizations the fluctuations yield stable (yellow) regions along the vertical axis, enabling string-like reconfiguration, which accounts for the secondary relaxation.
Figure 2: Activation-barrier distribution for free-energy barriers governing relaxation events in supercooled liquids.Different curves represent different temperatures (measured by the configurational entropy sc), increasing from near the glass-transition temperature to just above the dynamical-crossover temperature. The arrows indicate the typical relaxation times predicted from the fuzzy-sphere model without fluctuations. The top panel corresponds to a rather strong liquid with small fluctuations, ΔCP≈1 kB per bead. The bottom panel corresponds to a fragile liquid with larger fluctuations, ΔCP=3 kB per bead. In this figure we have used the continuous approximation of Fin as discussed in the text.
FIG. 3.
FIG. 4. Activation barrier distribution for fragile liquids with ΔC P ≈ 3k B per bead. See figure 3 for details.
FIG. 5.
Erratum: A universal origin for secondary relaxations in supercooled liquids and structural glasses

November 2009


108 Reads

Supercooled liquids and glasses show a range of relaxation times. Nearly all glass-forming liquids show secondary relaxations, high-frequency dynamical modes of structural reconfiguration seemingly distinct from the primary alpha relaxations. We show that accounting for driving-force fluctuations and the diversity of reconfiguring shapes in the random first-order transition theory yields a new dynamical process that shares many of the features ascribed to secondary relaxations. Whereas primary relaxation takes place through activated events involving compact regions, secondary relaxation is governed by more ramified, string-like or percolation-like clusters of particles. These secondary relaxations generate a low free-energy tail on the distribution of activation barriers, which becomes more prominent with increasing temperature. The activation barrier distributions of the two processes merge near the dynamical-crossover temperature Tc, where the secondary process ultimately becomes the dominant mode of structural relaxation. These string-like reconfigurations are seen to smooth the transition at Tc between high-temperature collisional dynamics and activated events.

Figure 1: Actomyosin stress-fibre alignment in hMSCs sparsely plated on 2D substrates of different elasticities. a–c, hMSCs immunostained for myosin NMMIIa 24 h after plating on elastic substrates with Young’s moduli Em of 1 (a), 11 (b) and 34 kPa (c). Images are the most representative cells of the mean values obtained for cell area A, aspect ratio of long to short axis r and stress-fibre order parameter S=cos2θ, where θ is the angle between each stress fibre in the cell and the long axis of the fitted ellipse. d–f, The respective orientational plots, where the different orientations of myosin filaments are depicted with different colours. The dark grey dashed ellipses are calculated from the moments up to the second order and represent the cell shape in terms of area and long and short axes, and the red line indicates the mean orientation of the stress fibres as determined by the anisotropic filter algorithm. χ is the angle between the mean stress-fibre orientation and the principal axis of the ellipse. From symmetry considerations, we need consider only the absolute value of χ between 0 and π/2; thus, a completely random distribution has an average χ=π/4. Values given for r and S are the mean values of at least 60 cells per condition. All scale bars represent 50 μm.
Figure 2: Cell adhesion and polarization represented by a 1D spring model. Springs with constants kc and km represent the elasticity of the cell and matrix respectively. Elastic morphological changes on cell adhesion (a–b) are represented here by a change in the cellular spring length Δlc=[kc/(kc+km)]Δlc0 This triggers an internal feedback mechanism (b–c) that results in an enhancement of the active forces (see equation (2)), and to a further change in cell length as given by equation (1).
Figure 3: Cell polarization as a function of the ratio of Young’s modulus of the matrix, Em, and the cell, Ec, in both our 2D and 3D models. The plots are shown for different values of the cellular aspect ratio, r. a,b, The normalized average dipole elements pzza (solid lines) and pxxa (dashed lines) corresponding to the forces in the directions that are respectively parallel ( ) and perpendicular ( ) to the long axis of the cell (dark grey: r=5, light grey: r=2) for our 3D (a) and 2D (b) models. c,d, The calculated orientational order parameter of the stress fibres that is given by the normalized difference (pzza−pxxa)/p for our 3D (c) and 2D (d) models. The colour coding indicates the aspect ratio. In this plot, the Poisson ratio of the matrix and the cellular domain are taken to be νm=0.45 and νc=0.3 and the magnitude of the polarizability is α=3.
Figure 4: The effect of axial cell elongation on stress-fibre polarization and experimental values of the order parameter S for different elastic substrates. a, A calculation of the 2D order parameter as a function of the matrix rigidity, for two cases: the cell spreads isotropically on the substrate, η=0 (black curve); the cell spreads anisotropically on the substrate, η=1 (grey curve), see the text. The two illustrations left of the curves show top views over the cell, before (shown as blank) and after (shown as shaded) cell spreading. In the asymmetric spreading case, r corresponds to the cell shape in an infinitely rigid matrix. For both curves we used r=2,α=2 and Poisson ratios as in . b, The experimental values of the stress-fibre order parameter, S=cos2θ, 24 h after plating the cells, for the three groups of cells (of aspect ratios r=1.5,2.5,3.5) as a function of Young’s modulus of the matrix, Em;θ is the angle between each stress fibre in the cell and the long axis of the fitted ellipse. Within each of the different groups, S is maximal for Em=11 kPa and generally increases with aspect ratio r, in agreement with our theoretical predictions. The error bars denote the standard error of the mean and theory curves (dotted lines) calculated from the simplified expansion of S (Supplementary Information) are shown to guide the eye.
Optimal matrix rigidity for stress-fibre polarization in stem cells

June 2010


444 Reads

The shape and differentiation of human mesenchymal stem cells is especially sensitive to the rigidity of their environment; the physical mechanisms involved are unknown. A theoretical model and experiments demonstrate here that the polarization/alignment of stress-fibers within stem cells is a non-monotonic function of matrix rigidity. We treat the cell as an active elastic inclusion in a surrounding matrix whose polarizability, unlike dead matter, depends on the feedback of cellular forces that develop in response to matrix stresses. The theory correctly predicts the monotonic increase of the cellular forces with the matrix rigidity and the alignment of stress-fibers parallel to the long axis of cells. We show that the anisotropy of this alignment depends non-monotonically on matrix rigidity and demonstrate it experimentally by quantifying the orientational distribution of stress-fibers in stem cells. These findings offer a first physical insight for the dependence of stem cell differentiation on tissue elasticity.

Figure 4: Effect of a phase ring on X-ray fluorescence imaging properties.a, Computed PSF comparison with and without a phase ring in a linear and logarithmic scale. Inset: The objective transmission profile of the respective pupil functions. b,c, Experimental gold X-ray fluorescence signal of a Siemens star test pattern with (b) and without (c) a phase ring present.
Figure 5: Freshwater flagellate Cryptomonas.a, Scanning Zernike with absorption as inset. b,c, X-ray fluorescence of phosphorus (b) and sulphur (c). Magnified subregions in a and b are scaled separately from the main image to highlight features. The flagella (whiplike appendages) outside the cell are pointed out by a dashed ellipse in a and c.
Zernike phase contrast in scanning microscopy with X-rays

November 2010


228 Reads

Scanning X-ray microscopy focuses radiation to a small spot and probes the sample by raster scanning. It allows information to be obtained from secondary signals such as X-ray fluorescence, which yields an elemental mapping of the sample not available in full-field imaging. The analysis and interpretation from these secondary signals can be considerably enhanced if these data are coupled with structural information from transmission imaging. However, absorption often is negligible and phase contrast has not been easily available. Originally introduced with visible light, Zernike phase contrast(1) is a well-established technique in full-field X-ray microscopes for visualization of weakly absorbing samples(2-7). On the basis of reciprocity, we demonstrate the implementation of Zernike phase contrast in scanning X-ray microscopy, revealing structural detail simultaneously with hard-X-ray trace-element measurements. The method is straightforward to implement without significant influence on the resolution of the fluorescence images and delivers complementary information. We show images of biological specimens that clearly demonstrate the advantage of correlating morphology with elemental information.

Collective strong coupling with ion Coulomb crystals in an optical cavity

July 2009


61 Reads

Cavity Quantum Electrodynamics (CQED) is an attractive platform for the realization of efficient light-matter quantum interfaces at the single photon level. Such interfaces are key elements for the development of quantum information and communication science due to the need for swapping information between flying and stationary qubits. Here, we report on the first CQED demonstration of collective strong coupling between atomic ions in a solid in the form of an ion Coulomb crystal and an optical field.

Figure 2: Long-time confinement of antihydrogen. a, Antihydrogen trapping rate (the number of trapped antihydrogen atoms per attempt), as a function of confinement time. An antihydrogen detection efficiency of 0.57±0.06, derived from an independent calibration, is assumed. The error bars represent uncertainties from counting statistics only (propagated from the square root of the observed event numbers). Scatter within subsets of the data indicates the presence of a systematic uncertainty at the level of ±0.2 in the trapping rate, which is not explicitly included; this does not affect our conclusions, or our claims of statistical significance. b, The statistical significance of the observed signal against the (cosmic-ray) background-only hypothesis, expressed in terms of the number of Gaussian standard deviations for a one-sided limit. The point for 0.4 s ( 20 σ) is off scale, and is thus not shown.
Figure 3: Antihydrogen annihilation patterns and comparisons with simulations. a, Time t and axial z  distribution of annihilations on release of antihydrogen from the magnetic trap for different confinement times (see legend), and comparison with simulation (grey dots). The simulation includes the effects of the annihilation-detection z -position resolution (~5 mm) and the detection efficiency as a function of z, both determined from a dedicated detector Monte Carlo study. b, Comparison of the t  distributions between the data (red circles with error bars), and simulations of trapped antihydrogen with various initial energy distributions (histograms). The error bars for the data represent the counting error (vertical) and the bin size (horizontal). Our time resolution is much less than 1 ms. The blue filled histogram represents our standard simulation, whose detailed dynamics are presented in . See b for the corresponding energy distribution. c, Comparison of the data with the standard simulation, shown on a log scale. d, Comparison of the annihilation position z between the data (red circles with error bars) and various simulations (histograms). The vertical error bars represent counting statistics whereas the horizontal ones represent the bin size of 25 mm. The same colour code as used in b applies. e, Predicted z  distribution for an anisotropic energy distribution with an axial energy of ~1 mK and a radial energy of ~0.5 K (red), compared with that of the standard (isotropic) energy distribution (blue filled histogram), suggesting the possibility of direction-sensitive determination of antihydrogen energies (see the text).
Figure 4: Dynamics of trapped antihydrogen from the standard simulation. a, Blue dots: A scatter plot of the initial antihydrogen kinetic energy E versus the time t at which the atom collides with the trap walls, providing the mapping between t and E in our measurements. Energies are given in units of temperature. Red lines: The time evolution of the axial trap well depth Dax (solid) and of the radial well depth Drad (dashed), which decay with time constants of ~9 ms and ~4.5 ms, respectively, after the release is initiated. b, Filled histogram: Distribution of the initial kinetic energy of trapped antihydrogen. The vertical dashed line represents our trap depth of 0.54 K, above which the population is quasi-trapped. Green line: Power law showing E1/2 associated with the tail of a Maxwell–Boltzmann distribution. Red histogram: Distribution of antihydrogen kinetic energy Ef at the time of annihilation on the trap walls. c, Scatter plot showing the axial and radial components of the initial antihydrogen kinetic energies versus the annihilation time t. Blue dots show the radial energy Erad=(1/2)mH(vx2+vy2), and red dots show the axial energy Eax=(1/2)mHvz2, where vx,vy and vz are and components of the velocity, respectively, and mH is the mass of the antihydrogen atom. d, Axial and radial components of the initial antihydrogen kinetic energies versus annihilation position, z. The same colour scheme as in c applies.
Confinement of antihydrogen for 1000 seconds

April 2011


376 Reads

Atoms made of a particle and an antiparticle are unstable, usually surviving less than a microsecond. Antihydrogen, made entirely of antiparticles, is believed to be stable, and it is this longevity that holds the promise of precision studies of matter-antimatter symmetry. We have recently demonstrated trapping of antihydrogen atoms by releasing them after a confinement time of 172 ms. A critical question for future studies is: how long can anti-atoms be trapped? Here we report the observation of anti-atom confinement for 1000 s, extending our earlier results by nearly four orders of magnitude. Our calculations indicate that most of the trapped anti-atoms reach the ground state. Further, we report the first measurement of the energy distribution of trapped antihydrogen which, coupled with detailed comparisons with simulations, provides a key tool for the systematic investigation of trapping dynamics. These advances open up a range of experimental possibilities, including precision studies of CPT symmetry and cooling to temperatures where gravitational effects could become apparent.

Figure 1: The p-value for the background-only hypothesis as a function of the Higgs boson mass hypothesis for both the observed data (obs.) and pseudo-data constructed using the median expectation for the standard model Higgs boson after the signal-plus-background fit to the data (exp.). To help visualize the results, smooth lines connect the points at which the probabilities are evaluated. The H ττ analysis results are broken down into a contribution from VH ττ categories, which share the production process with the analysis, and another contribution with all other H ττ event categories. For every mass hypothesis tested, the non-fermionic decay contributions are taken to be those of the standard model Higgs boson with a mass of 125 GeV. Non-fermionic decays are considered as part of the background and consequently do not contribute to the measurement.
Figure 2: Scan of the profile likelihood as a function of the signal strength relative to the expectation for the production and decay of a standard model Higgs boson, μ, for mH = 125 GeV. The statistical significance against the background-only (μ = 0) hypothesis is shown for the two channels and their combination. By definition, the expectation for the standard model Higgs boson with a mass of 125 GeV is μ = 1. The non-fermionic decay contributions expected for the standard model Higgs boson with a mass of 125 GeV are considered as part of the background and therefore not scaled with μ.
Evidence for the direct decay of the 125 GeV Higgs boson to fermions

January 2014


343 Reads

The discovery of a new boson with a mass of approximately 125 GeV in 2012 at the LHC has heralded a new era in understanding the nature of electroweak symmetry breaking and possibly completing the standard model of particle physics. Since the first observation in decays to gamma gamma, WW, and ZZ boson pairs, an extensive set of measurements of the mass and couplings to W and Z bosons, as well as multiple tests of the spin-parity quantum numbers, have revealed that the properties of the new boson are consistent with those of the long-sought agent responsible for electroweak symmetry breaking. An important open question is whether the new particle also couples to fermions, and in particular to down-type fermions, since the current measurements mainly constrain the couplings to the up-type top quark. Determination of the couplings to down-type fermions requires direct measurement of the corresponding Higgs boson decays, as recently reported by the CMS experiment in the study of Higgs decays to bottom quarks and tau leptons. In this paper we report the combination of these two channels which results, for the first time, in strong evidence for the direct coupling of the 125 GeV Higgs boson to down-type fermions, with an observed significance of 3.8 standard deviations, when 4.4 are expected.

Figure 1: Nanotube double dot with integrated charge sensor.a, Scanning electron micrograph (with false colour) of a device similar to the measured 12C and 13C devices. The carbon nanotube (not visible) runs horizontally under the four Pd contacts (red). Top-gates (blue) create voltage-tunable tunnel barriers enabling the formation of a single or double quantum dot between contacts 1 and 2. Plunger gates L and R (green) control the occupancy of the double dot. A separate single dot contacted by Pd contacts 3 and 4 is controlled with gate plunger gate S (grey) and is capacitively coupled to the double dot by a coupling wire (orange). b, Current through the double dot, Idd, (colour scale) with the top-gates configured to form a large single dot. c, When carriers beneath the middle gate, M, are depleted, Idd shows typical double-dot transport behaviour, demarcating the honeycomb charge stability pattern. d, Within certain gate voltage ranges, honeycomb cells with larger addition energy and fourfold periodicity (outlined with dashed lines) indicate the filling of spin and orbital states in shells. Source–drain bias is -1.0 mV for b–d.
Electron-nuclear interaction in 13C nanotube double quantum dots

November 2008


85 Reads

For coherent electron spins, hyperfine coupling to nuclei in the host material can either be a dominant source of unwanted spin decoherence or, if controlled effectively, a resource allowing storage and retrieval of quantum information. To investigate the effect of a controllable nuclear environment on the evolution of confined electron spins, we have fabricated and measured gate-defined double quantum dots with integrated charge sensors made from single-walled carbon nanotubes with a variable concentration of 13C (nuclear spin I=1/2) among the majority zero-nuclear-spin 12C atoms. Spin-sensitive transport in double-dot devices grown using methane with the natural abundance (~ 1%) of 13C is compared with similar devices grown using an enhanced (~99%) concentration of 13C. We observe strong isotope effects in spin-blockaded transport, and from the dependence on external magnetic field, estimate the hyperfine coupling in 13C nanotubes to be on the order of 100 micro-eV, two orders of magnitude larger than anticipated theoretically. 13C-enhanced nanotubes are an interesting new system for spin-based quantum information processing and memory, with nuclei that are strongly coupled to gate-controlled electrons, differ from nuclei in the substrate, are naturally confined to one dimension, lack quadrupolar coupling, and have a readily controllable concentration from less than one to 10^5 per electron.

Many-body Landau-Zener dynamics in coupled 1D Bose liquids

March 2010


110 Reads

The Landau-Zener model of a quantum mechanical two-level system driven with a linearly time dependent detuning has served over decades as a textbook paradigm of quantum dynamics. In their seminal work [L. D. Landau, Physik. Z. Sowjet. 2, 46 (1932); C. Zener, Proc. Royal Soc. London 137, 696 (1932)], Landau and Zener derived a non-perturbative prediction for the transition probability between two states, which often serves as a reference point for the analysis of more complex systems. A particularly intriguing question is whether that framework can be extended to describe many-body quantum dynamics. Here we report an experimental and theoretical study of a system of ultracold atoms, offering a direct many-body generalization of the Landau-Zener problem. In a system of pairwise tunnel-coupled 1D Bose liquids we show how tuning the correlations of the 1D gases, the tunnel coupling between the tubes and the inter-tube interactions strongly modify the original Landau-Zener picture. The results are explained using a mean-field description of the inter-tube condensate wave-function, coupled to the low-energy phonons of the 1D Bose liquid.

Non-Abelian statistics and topological quantum information processing in 1D wire networks

June 2010


146 Reads

Topological quantum computation provides an elegant way around decoherence, as one encodes quantum information in a non-local fashion that the environment finds difficult to corrupt. Here we establish that one of the key operations---braiding of non-Abelian anyons---can be implemented in one-dimensional semiconductor wire networks. Previous work [Lutchyn et al., arXiv:1002.4033 and Oreg et al., arXiv:1003.1145] provided a recipe for driving semiconducting wires into a topological phase supporting long-sought particles known as Majorana fermions that can store topologically protected quantum information. Majorana fermions in this setting can be transported, created, and fused by applying locally tunable gates to the wire. More importantly, we show that networks of such wires allow braiding of Majorana fermions and that they exhibit non-Abelian statistics like vortices in a p+ip superconductor. We propose experimental setups that enable the Majorana fusion rules to be probed, along with networks that allow for efficient exchange of arbitrary numbers of Majorana fermions. This work paves a new path forward in topological quantum computation that benefits from physical transparency and experimental realism.

A polynomial-time algorithm for the ground state of 1D gapped local Hamiltonians

July 2013


51 Reads

Computing ground states of local Hamiltonians is a fundamental problem in condensed matter physics. We give the first randomized polynomial-time algorithm for finding ground states of gapped one-dimensional Hamiltonians: it outputs an (inverse-polynomial) approximation, expressed as a matrix product state (MPS) of polynomial bond dimension. The algorithm combines many ingredients, including recently discovered structural features of gapped 1D systems, convex programming, insights from classical algorithms for 1D satisfiability, and new techniques for manipulating and bounding the complexity of MPS. Our result provides one of the first major classes of Hamiltonians for which computing ground states is provably tractable despite the exponential nature of the objects involved.

Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas

January 2011


89 Reads

The problem of how complex quantum systems eventually come to rest lies at the heart of statistical mechanics. The maximum entropy principle put forward in 1957 by E. T. Jaynes suggests what quantum states one should expect in equilibrium but does not hint as to how closed quantum many-body systems dynamically equilibrate. A number of theoretical and numerical studies accumulate evidence that under specific conditions quantum many-body models can relax to a situation that locally or with respect to certain observables appears as if the entire system had relaxed to a maximum entropy state. In this work, we report the experimental observation of the non-equilibrium dynamics of a density wave of ultracold bosonic atoms in an optical lattice in the regime of strong correlations. Using an optical superlattice, we are able to prepare the system in a well-known initial state with high fidelity. We then follow the dynamical evolution of the system in terms of quasi-local densities, currents, and coherences. Numerical studies based on the time-dependent density-matrix renormalization group method are in an excellent quantitative agreement with the experimental data. For very long times, all three local observables show a fast relaxation to equilibrium values compatible with those expected for a global maximum entropy state. We find this relaxation of the quasi-local densities and currents to initially follow a power-law with an exponent being significantly larger than for free or hardcore bosons. For intermediate times the system fulfills the promise of being a dynamical quantum simulator, in that the controlled dynamics runs for longer times than present classical algorithms based on matrix product states can efficiently keep track of.

Enhancement of long range correlations in a 2D vortex lattice by incommensurate 1D disorder potential

October 2014


122 Reads

Long range correlations in two-dimensional (2D) systems are significantly altered by disorder potentials. Theory has predicted the existence of disorder induced phenomena such as Anderson localization and the emergence of novel glass and insulating phases as the Bose glass. More recently, it has been shown that disorder breaking the 2D continuous symmetry, such as a one dimensional (1D) modulation, can enhance long range correlations. Experimentally, developments in quantum gases have allowed the observation of a wealth of phenomena induced by the competition between interaction and disorder. However, there are no experiments exploring the effect of symmetry-breaking disorder. Here, we create a 2D vortex lattice at 0.1 K in a superconducting thin film with a well-defined 1D thickness modulation and track the field induced modification using scanning tunneling microscopy. We find that the 1D modulation becomes incommensurate to the vortex lattice and drives an order-disorder transition, behaving as a scale-invariant disorder potential. We show that the transition occurs in two steps and is mediated by the proliferation of topological defects. We find that critical exponents determining the loss of positional and orientational order are far above theoretical expectations for scale-invariant disorder and follow instead the critical behaviour which describes dislocation unbinding melting. Our data show for the first time that randomness disorders a 2D crystal, and evidence enhanced long range correlations in presence of a 1D modulation demonstrating the transformation induced by symmetry breaking disorder in interactions and the critical behaviour of the transition.

Figure 1: Manifestation of carbon 1s binding-energy variations in individual X-ray photoemission spectra.a, Schematic of the graphene lattice and the experimental geometry. b–f, C 1s photoemission spectra taken at a photon energy of 400 eV, for fixed polar emission angles θ in each panel but at different azimuthal emission angles φ. The spectra are all normalized to the same height and shown as a group plot, such that binding-energy variations become evident. The first and last spectrum in a range of azimuthal angles φ is indicated by a thicker line. g, Comparison of the spectrum taken at θ=0° and one taken at 25°. The lines are the fits through the data points using the line-shape parameters described in the Supplementary Information. h, C 1s binding energy required to obtain a good fit for the curves shown above (markers) as well as for the entire azimuthal range measured (lines). The green horizontal line marks the binding energy at normal emission. The binding-energy uncertainty is smaller than 10 meV. i, Intensity variation of the C 1s peak as a function of azimuthal angle. The curves are shifted vertically for clarity.
Figure 3: Calculated C 1s binding-energy variation and interference-induced modulations of the photoemission intensity.a, Tight-binding calculation for a σ-type band formed from the C 1s core states in graphene. The bonding (blue) and antibonding (red) bands are degenerate at and show the highest splitting at . The choice of tight-binding parameters was guided by the experimentally observed binding-energy modulations. The inset shows the Brillouin zone of graphene. b,c, Calculated photoemission intensity from all of the antibonding (b) and bonding (c) states. The greyscale is chosen such that bright corresponds to high intensity. The green crosses mark the reciprocal lattice of graphene and the green hexagon the first Brillouin zone. d, All-electron ab initio calculation of the C 1s dispersion. e–g, Calculated photoemission intensity from the states in the binding-energy windows indicated by the small circles in a. Note the similarity of the emission pattern from the bonding states in e with the positions of maximum binding energy in the right panel of .
Band dispersion in the deep 1s core level of graphene

January 2010


159 Reads

Chemical bonding in molecules and solids arises from the overlap of valence electron wave functions, forming extended molecular orbitals and dispersing Bloch states, respectively. Core electrons with high binding energies, on the other hand, are localized to their respective atoms and their wave functions do not overlap significantly. Here we report the observation of band formation and considerable dispersion (up to 60 meV) in the $1s$ core level of the carbon atoms forming graphene, despite the high C $1s$ binding energy of $\approx$ 284 eV. Due to a Young's double slit-like interference effect, a situation arises in which only the bonding or only the anti-bonding states is observed for a given photoemission geometry. Comment: 12 pages, 3 figures, including supplementary material

Figure 1: Suppression of the charge density wave in 1T-TiSe2 with temperature and pressure. a, Scans through the charge density wave (CDW) ordering vector showing suppression of CDW correlations with increasing pressure for (H, 1/2, 1/2). b, Small, residual CDW correlations observed in the normal state, both at high and low pressure. c, Pressure-dependence of the ratio TCDW/I(0), or the Landau coupling constant g, which in McMillan’s picture is proportional to the CDW coupling constant. d, Phase boundary delineating the ordered and disordered phases in the pressure–temperature plane. The TCDW values from ref. 1 are shown for comparison (the grey dashed line is an interpolation of the data). The points were found to fit well to a single power law over the entire region, TCDW(P) = T0|1−P/Pc|β, with β = 0.87±0.08 (black dashed line), identifying the location of the quantum critical point at Pc = 5.1±0.2 GPa. Error bars on the temperature values represent the difference in reading between the cryostat cold finger and the top of the pressure cell. Error bars on the pressure values were determined by the energy resolution of the spectrometer used to monitor the ruby fluorescence lines. The range of fits consistent with these error bars were used to determine the error bars on β and Pc.
Figure 2: Summary pressure–temperature phase diagram of TiSe2. a, Broad phase diagram showing charge density wave (CDW) ordered, normal state and superconducting phase boundaries. The green colour scale indicates the integrated intensity of CDW correlations, including both the C and IC components. The superconducting TSC value, reproduced from (ref. 1) has been exaggerated by a factor of five for visibility. Points where the precise commensurability was measured are labelled C, I or C/I, indicating commensurate, incommensurate or coexistence, respectively. b, Zoom-in on the region exhibiting the transition between commensurate and incommensurate order (grey dashed rectangle in a).
Emergence of charge density wave domain walls above the superconducting dome in 1T-TiSe2

September 2013


783 Reads

Superconductivity (SC) in so-called "unconventional superconductors" is nearly always found in the vicinity of another ordered state, such as antiferromagnetism, charge density wave (CDW), or stripe order. This suggests a fundamental connection between SC and fluctuations in some other order parameter. To better understand this connection, we used high-pressure x-ray scattering to directly study the CDW order in the layered dichalcogenide TiSe2, which was previously shown to exhibit SC when the CDW is suppressed by pressure [1] or intercalation of Cu atoms [2]. We succeeded in suppressing the CDW fully to zero temperature, establishing for the first time the existence of a quantum critical point (QCP) at Pc = 5.1 +/- 0.2 GPa, which is more than 1 GPa beyond the end of the SC region. Unexpectedly, at P = 3 GPa we observed a reentrant, weakly first order, incommensurate phase, indicating the presence of a Lifshitz tricritical point somewhere above the superconducting dome. Our study suggests that SC in TiSe2 may not be connected to the QCP itself, but to the formation of CDW domain walls.

Anisotropic Impurity-States, Quasiparticle Scattering and Nematic Transport in Underdoped Ca(Fe1-xCox)2As2

November 2012


91 Reads

Iron-based high temperature superconductivity develops when the `parent' antiferromagnetic/orthorhombic phase is suppressed, typically by introduction of dopant atoms. But their impact on atomic-scale electronic structure, while in theory quite complex, is unknown experimentally. What is known is that a strong transport anisotropy with its resistivity maximum along the crystal b-axis, develops with increasing concentration of dopant atoms; this `nematicity' vanishes when the `parent' phase disappears near the maximum superconducting Tc. The interplay between the electronic structure surrounding each dopant atom, quasiparticle scattering therefrom, and the transport nematicity has therefore become a pivotal focus of research into these materials. Here, by directly visualizing the atomic-scale electronic structure, we show that substituting Co for Fe atoms in underdoped Ca(Fe1-xCox)2As2 generates a dense population of identical anisotropic impurity states. Each is ~8 Fe-Fe unit cells in length, and all are distributed randomly but aligned with the antiferromagnetic a-axis. By imaging their surrounding interference patterns, we further demonstrate that these impurity states scatter quasiparticles in a highly anisotropic manner, with the maximum scattering rate concentrated along the b-axis. These data provide direct support for the recent proposals that it is primarily anisotropic scattering by dopant-induced impurity states that generates the transport nematicity; they also yield simple explanations for the enhancement of the nematicity proportional to the dopant density and for the occurrence of the highest resistivity along the b-axis.

FIG. 3: (Tm,ν) melting curve of the electron solid in sample 2, a narrow QW of width 15 nm. Sample 2 has a tunable n=2.7-4×10 10 cm −2 and enters an electron solid phase at ν< 0.3.
Melting of a 2D Quantum Electron Solid in High Magnetic Field

May 2006


48 Reads

The melting temperature ($T_m$) of a solid is generally determined by the pressure applied to it, or indirectly by its density ($n$) through the equation of state. This remains true even for helium solids\cite{wilk:67}, where quantum effects often lead to unusual properties\cite{ekim:04}. In this letter we present experimental evidence to show that for a two dimensional (2D) solid formed by electrons in a semiconductor sample under a strong perpendicular magnetic field\cite{shay:97} ($B$), the $T_m$ is not controlled by $n$, but effectively by the \textit{quantum correlation} between the electrons through the Landau level filling factor $\nu$=$nh/eB$. Such melting behavior, different from that of all other known solids (including a classical 2D electron solid at zero magnetic field\cite{grim:79}), attests to the quantum nature of the magnetic field induced electron solid. Moreover, we found the $T_m$ to increase with the strength of the sample-dependent disorder that pins the electron solid.

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