Publications (101)322.57 Total impact
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ABSTRACT: Recently it has been proposed that a unitary topological mirror symmetry can stabilize multiple zero energy Majorana fermion modes in one dimensional (1D) time reversal (TR) invariant topological superconductors. Here we establish an exact equivalence between 1D "topological mirror superconductivity" and chiral topological superconductivity in BDI class which can also stabilize multiple MajoranaKramers pairs in 1D TRinvariant topological superconductors. The equivalence proves that topological mirror superconductivity can be understood as chiral superconductivity in the BDI symmetry class coexisting with timereversal symmetry. Furthermore, we show that the mirror Berry phase coincides with the chiral winding invariant of the BDI symmetry class, which is independent of the presence of the timereversal symmetry. Thus, the timereversal invariant topological mirror superconducting state may be viewed as a special case of the BDI symmetry class in the wellknown AltlandZirnbauer periodic table of free fermionic phases. We illustrate the results with the examples of 1D spinorbit coupled quantum wires in the presence of nodeless s_{\pm} superconductivity and the recently discussed experimental system of ferromagnetic atom (Fe) chains embedded on a lead (Pb) superconductor.Physical Review B 07/2015; 92(4):045421. DOI:10.1103/PhysRevB.92.045421 · 3.74 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Weyl semimetals (WSM) are topologically protected three dimensional materials whose low energy excitations are linearly dispersing massless Dirac fermions, possessing a nontrivial Berry curvature. Using semiclassical Boltzmann dynamics in the relaxation time approximation for a lattice model of time reversal (TR) symmetry broken WSM, we compute both magnetic field dependent and anomalous contributions to the Nernst coefficient. In addition to the magnetic field dependent Nernst response, which is present in both Dirac and Weyl semimetals, we show that, contrary to previous reports, the TRbroken WSM also has an anomalous Nernst response due to a nonvanishing Berry curvature. We also compute the thermal conductivities of a WSM in the Nernst (${\nabla T} \perp \mathbf{B}$) and the longitudinal (${\nabla T} \parallel \mathbf{B}$) setup and confirm from our lattice model that in the parallel setup, the WiedemannFranz law is violated between the longitudinal thermal and electrical conductivities due to chiral anomaly.  [Show abstract] [Hide abstract]
ABSTRACT: A mechanism is proposed for the tantalizing evidence of polar Kerr effect in a class of high temperature superconductorsthe signs of the Kerr angle from two opposite faces of the same sample are identical and magnetic field training is nonexistent. The mechanism does not break global time reversal symmetry, as in an antiferromagnet, and results in zero Faraday effect. It is best understood in a phenomenological model of bilayer cuprates, such as YBCO, in which intrabilayer tunneling nucleates a chiral ddensity wave such that the individual layers have opposite chirality. Although specific to the chiral ddensity wave, the mechanism may be more general to any quasitwodimensional orbital antiferromagnet in which time reversal symmetry is broken in each plane, but not when averaged macroscopically.  [Show abstract] [Hide abstract]
ABSTRACT: Majorana fermion (MF) excitations in solid state system have nonAbelian statistics which is essential for topological quantum computation. Previous proposals to realize MF, however, generally requires finetuning of parameters. Here we explore a platform which avoids the finetuning problem, namely a ferromagnetic chain deposited on the surface of a spinorbit coupled swave superconductor. We show that it generically supports zeroenergy topological MF excitations near the two ends of the chain with minimal finetuning. Depending on the strength of the ferromagnetic moment in the chain, the number of MFs at each end, n, can be either one or two, and should be revealed by a robust zerobias peak (ZBP) of height 2 ne(2)/h in scanning tunneling microscopy (STM) measurements which would show strong (weak) signals at the ends (middle) of the chain. The role of an approximate chiral symmetry which gives an integer topological invariant to the system is discussed.Scientific Reports 03/2015; 5:8880. DOI:10.1038/srep08880 · 5.58 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Multiple zeroenergy Majorana fermions (MFs) with spatially overlapping wave functions can survive only if their splitting is prevented by an underlying symmetry. Here we show that, in quasionedimensional (Q1D) timereversalinvariant topological superconductors (class DIII), a realistic model for superconducting lithium molybdenum purple bronze ${(\mathrm{Li}}_{0.9}{\mathrm{Mo}}_{6}{\mathrm{O}}_{17})$ and certain families of organic superconductors, multiple MajoranaKramers pairs with strongly overlapping wave functions persist at zero energy even in the absence of an easily identifiable symmetry. We find that similar results hold in the case of Q1D semiconductorsuperconductor heterostructures (class D) with ${t}_{$\perp${}}$\ll${}t$, where ${t}_{$\perp${}}$ and $t$ are the transverse and longitudinal hoppings, respectively. Our results, explained in terms of special properties of the Hamiltonian and wave functions, underscore the importance of hidden accidental symmetries in topological superconductors.Physical Review B 03/2015; 91(12). DOI:10.1103/PhysRevB.91.121413 · 3.74 Impact Factor 
Article: Normal state Nernst effect from bidirectional bond density wave state in high T_c cuprates
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ABSTRACT: The role of charge order in the phase diagram of high temperature cuprate superconductors has been recently reemphasized by the experimental discovery of an incipient bidirectional charge density wave (CDW) phase in a class of underdoped cuprates. In a subset of the experiments, the CDW has been found to be accompanied by a dwave intraunitcell form factor, indicating modulation of charge density on the oxygen orbitals sandwiched between neighboring Cu atoms on the CuO planes (the socalled bonddensity wave (BDW) phase). Here we take a mean field Q_1=(2\pi/3,0) and Q_2=(0,2\pi/3) bidirectional BDW phase with a dwave form factor, which closely resembles the experimentally observed charge ordered states in underdoped cuprates, and calculate the Fermi surface topology and the resulting quasiparticle Nernst coefficient as a function of temperature and doping. We establish that, in the appropriate doping ranges where the low temperature phase (in the absence of superconductivity) is a BDW, the Fermi surface consists of an electron and a hole pocket, resulting in a low temperature negative Nernst coefficient as observed in experiments.  [Show abstract] [Hide abstract]
ABSTRACT: We show that certain singularities of the Hamiltonian in the complex wave vector space can be used to identify topological quantum phase transitions for $1D$ chiral topological superconductors/superfluids in the BDI class. These singularities fall into the category of the socalled exceptional points ($EP$'s) studied in the context of nonHermitian Hamiltonians describing open quantum systems. We also propose a generic formula in terms of the properties of the $EP$'s to quantify the exact number of Majorana zero modes in a particular chiral topological superconducting phase, given the values of the parameters appearing in the Hamiltonian. This formula serves as an alternative to the familiar integer ($\mathbb{Z}$) winding number invariant characterizing topological superconductor/superfluid phases in the chiral BDI class. 
Article: Magnetic field response and chiral symmetry of timereversalinvariant topological superconductors
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ABSTRACT: We study the magnetic field response of MajoranaKramers pairs of onedimensional timereversal (TR)invariant topological superconductors (class DIII) with or without a coexisting chirality symmetry. In addition to explaining the anomalous magnetic field response of all the DIII class topological superconducting systems proposed in the literature, we provide a realistic route to engineer a ``true'' TRinvariant topological superconductor, i.e., one whose pair of Majorana bound states at each end is split by an applied Zeeman field in arbitrary direction. We also prove that quite generally the splitting of the Majorana bound states in a timereversalinvariant topological superconductor by timereversal breaking fields is highly anisotropic in spin space.Physical Review B 12/2014; 90(24). DOI:10.1103/PhysRevB.90.245438 · 3.74 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The recent discovery of an incipient chargedensity wave (CDW) instability competing with superconductivity in a class of hightemperature cuprate superconductors has brought the role of charge order in the phase diagram of the cuprates under renewed focus. Here, we take a mean field ${Q}_{1}=(2$\pi${}/3,0)$ and ${Q}_{2}=(0,2$\pi${}/3)$ biaxial CDW state and calculate the Fermisurface topology and the resulting Hall and Seebeck coefficients as a function of temperature and hole doping. We establish that, in the appropriate doping ranges where the lowtemperature state (in the absence of superconductivity) is a CDW, the Fermi surface consists of electron pockets, resulting in the Hall and Seebeck coefficients becoming negative at low temperatures, as seen in experiments.Physical Review B 11/2014; 90(17). DOI:10.1103/PhysRevB.90.174503 · 3.74 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Motivated by a recent experiment in which zerobias peaks have been observed in scanning tunneling microscopy (STM) experiments performed on chains of magnetic atoms on a superconductor, we show, by generalizing earlier work, that a multichannel ferromagnetic wire deposited on a spinorbit coupled superconducting substrate can realize a nontrivial chiral topological superconducting state with Majorana bound states localized at the wire ends. The nontrivial topological state occurs for generic parameters requiring no fine tuning, at least for very large exchange spin splitting in the wire. We theoretically obtain the signatures which appear in the presence of an arbitrary number of Majorana modes in multiwire systems incorporating the role of finite temperature, finite potential barrier at the STM tip, and finite wire length. These signatures are presented in terms of spatial profiles of STM differential conductance which clearly reveal zero energy Majorana end modes and the prediction of a multiple Majorana based fractional Josephson effect. A critical comparison of our results with the experimental data shows a basic inconsistency in the interpretation of the Fe nanowire STM experiment in terms of Majorana zero modes in particular, the observation of the precise localization of the Majorana zero modes at the wire ends cannot be reconciled with the extremely small topological superconducting gap (and the associated extremely weak Majorana tunneling peak) observed simultaneously. Other than this rather disturbing basic incompatibility, for which we can offer no resolution at this stage, most other aspects of the experimental phenomenology are reasonably well explained by our theory.Physical Review B 10/2014; 91(9). DOI:10.1103/PhysRevB.91.094505 · 3.74 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We establish theoretically that a ferromagnetic wire deposited on the surface of a spinorbit coupled $s$wave superconductor generically supports zeroenergy topological Majorana fermion (MF) excitations near the two ends of the wire. Depending on the strength of the ferromagnetic moment in the wire, the number of MFs at each end, $n$, can be either one or two, and should be revealed by a robust zerobias peak (ZBP) of height $2ne^2/h$ in scanning tunneling microscopy (STM) measurements which would show strong (weak) signals at the ends (middle) of the wire. The underlying physics of this system, which is distinct from that of the wellstudied spinorbitcoupled semiconductorsuperconductor heterostructures in the presence of an applied magnetic field, is discussed in terms of a topological chiral symmetry in BDI class with an integer topological invariant. Our work introduces a new platform, namely a magnetic metalsuperconductor heterostructure, in the race for finding a Majoranacarrying topological superconductor.  [Show abstract] [Hide abstract]
ABSTRACT: We identify the dynamic chiral magnetic effect and the optical gyrotropy as the manifestations of the same physical phenomenon, namely the dynamic magnetoelectric effect. Therefore, the measurement of optical gyrotropy through Kerr effect is provides a confirmation of the existence of the dynamic chiral magnetic effect. We derive a general formula for the gyrotropic conductivity of a noncentrosymmetric metal in the high frequency limit, and apply our results to the special cases of inversion symmetry breaking Weyl semimetals and noncentrosymmetric cubic metals.  [Show abstract] [Hide abstract]
ABSTRACT: Multiple zeroenergy Majorana fermions (MFs) with spatially overlapping wave functions can survive only if their splitting is prevented by an underlying symmetry. Here we show that, in quasionedimensional (Q1D) time reversal invariant topological superconductors (class DIII), a realistic model for superconducting lithium molybdenum purple bronze and certain families of organic superconductors, multiple MajoranaKramers pairs with strongly overlapping wave functions persist at zero energy even in the absence of an easily identifiable symmetry. We find that similar results hold in the case of Q1D semiconductorsuperconductor heterostructures (class D) with transverse hopping t_{perp} much smaller than longitudinal hopping t_x. Our results, explained in terms of special properties of the Hamiltonian and wave functions, underscore the importance of hidden accidental symmetries in topological superconductors.  [Show abstract] [Hide abstract]
ABSTRACT: The recent discovery of an incipient charge density wave (CDW) instability competing with superconductivity in a class of high temperature cuprate superconductors has brought the role of charge order in the phase diagram of the cuprates under renewed focus. Here we take a mean field (Q = 2pi/3,2pi/3) CDW state and calculate the Fermi surface topology and the resulting Hall and Seebeck coefficients as a function of temperature and hole doping. We show that, in the appropriate doping ranges where the low temperature state (in the absence of superconductivity) is a CDW, the Fermi surface consists of electron pockets, resulting in the Hall and Seebeck coefficients becoming negative at low temperatures, as seen in experiments.  [Show abstract] [Hide abstract]
ABSTRACT: From a direct calculation of the anomalous Hall conductivity and an effective electromagnetic action obtained via Fujikawa's chiral rotation technique, we conclude that an axionic field theory with a nonquantized coefficient describes the electromagnetic response of the (3+1)dimensional Weyl semimetal. The coefficient is proportional to the momentum space separation of the Weyl nodes. Akin to the ChernSimons field theory of quantum Hall effect, the axion field theory violates gauge invariance in the presence of the boundary, which is cured by the chiral anomaly of the surface states via the CallanHarvey mechanism. This provides a unique solution for the radiatively induced CPTodd term in the electromagnetic polarization tensor of the Lorentz violating spinor electrodynamics, where the source of the Lorentz violation is a constant axial 4vector term for the Dirac fermion. A direct linear response calculation also establishes anomalous thermal Hall effect and a WiedemannFranz law, but thermal Hall conductivity does not directly follow from the well known formula for the gravitational chiral anomaly.Physical Review B 12/2013; 88(24):245107. DOI:10.1103/PhysRevB.88.245107 · 3.74 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We consider the quasionedimensional (quasi1D) system realized by an array of weakly coupled parallel onedimensional “tubes” in a twodimensional lattice which permits free motion of atoms in an axial direction in the presence of a Zeeman field, Rashba type spinorbit coupling (SOC), and an swave attractive interaction, while the radial motion is tightly confined. We solve the zerotemperature (T=0) Bogoliubovde Gennes (BdG) equations for the quasi1D Fermi gas with the dispersion modified by tunneling between the tubes and show that the T=0 phase diagram hosts the FuldeFerrellLarkinOvchinnikov (FFLO) phase with nonzero centerofmass momentum Cooper pairs for small values of the SOC while for larger values of the SOC and high Zeeman fields the uniform superfluid phase with zero centerofmass momentum Cooper pairs has an instability towards the topological uniform superfluid phase with Majorana fermions at the tube ends. Also, we show that tuning the twodimensional optical lattice strength in this model allows one to explore the crossover behaviors of the phases during the transition between the threedimensional and 1D systems and in general the FFLO (for small SOC) and the topological uniform superfluid phase (for large SOC) are favored as the system becomes more one dimensional. We also find evidence of the existence of a Zeemantuned topological quantum phase transition (TQPT) within the FFLO phase itself and, for large values of the Zeeman field and small SOC, the TQPT gives rise to a topologically distinct FFLO phase.Physical Review A 12/2013; 88(6):63601. DOI:10.1103/PhysRevA.88.063601 · 2.99 Impact Factor 
Article: Chiral magnetic effect of Weyl fermions and its applications to cubic noncentrosymmetric metals
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ABSTRACT: When the right and the left handed Weyl points are separated in energy, they give rise to a nondissipative charge current along the direction of a uniform applied magnetic field, even in the absence of an external electric field. This effect is known as the chiral magnetic effect and is a hallmark of the underlying chiral anomaly of the Weyl fermions. According to the linearized continuum theory of Weyl fermions, the induced current is proportional to the magnetic field strength and the energy separation with a universal coefficient $e^2/h^2$. By considering a generic tight binding model for the cubic noncentrosymmetric metals, we show that such a system naturally supports a set of Weyl points, which are separated in energies. We also show the existence of the chiral magnetic effect for generic band parameters, and recover the universal result of the continuum Weyl fermions for a restricted parameter regime. Therefore, cubic noncentrosymmetric metals can serve as suitable platforms for realizing Weyl fermions and the exotic chiral elctrodynamic phenomena, which have promising technological applications.  [Show abstract] [Hide abstract]
ABSTRACT: We show that onedimensional time reversal (TR) symmetric (class DIII) topological superconductors (TS) frequently possess a coexisting chiral symmetry allowing one to define an underlying integer chirality invariant. For unbroken TR and chirality invariance the parameter regimes for nontrivial values of the Z_2 DIIIinvariant and the Z chiral invariant coincide. However, broken TR may or may not be accompanied by broken chirality, and if chiral symmetry is unbroken, the pair of Majorana fermions (MFs) at a given end survives the loss of TR symmetry. Conversely, we show that broken chirality may or may not be accompanied by broken TR, and if TR is unbroken, the pair of MFs survives the loss of broken chirality. In addition to solving the outstanding problem of the anomalous magnetic field response of all the DIII class topological superconductors proposed in the literature so far, we also provide a realistic route to engineer a "true" TRinvariant TS, whose Majorana Kramer's pair at each end is split by an applied Zeeman field in arbitrary directions in spin space.  [Show abstract] [Hide abstract]
ABSTRACT: The realization of spinorbit coupling (SOC) in ultracold atomic gases has opened the door for observing Majorana fermions (MFs) in cold atom systems. We show that MFs exist in three dimensional (3D) fermionic optical lattices with strictly one dimensional (1D) SOC which has already been realized in experiments. The presence of an inplane Zeeman field drives the system from a BardeenCooperSchrieffer (BCS) superfluid to a FuldeFerrell (FF) superfluid phase. We find that both phases support multiple MFs at each end of quasione dimensional (quasi1D) optical lattices with a weak transverse tunneling. In the generalization to 3D, the multiple MFs form a zero energy flat band. Our results are useful to guide the experimentalists on searching for MFs in the context of ultracold fermionic atoms.  [Show abstract] [Hide abstract]
ABSTRACT: We show that the topologically trivial zero bias peak (ZBP) emerging in semiconductor Majorana wires due to soft confinement exhibits correlated splitting oscillations as function of the applied Zeeman field, similar to the correlated splitting of the Majorana ZBP. Also, we find that the presence of a strong impurity can effectively cut the wire in two and destroy the correlated splitting in both the trivial and the Majorana regimes. We identify a strong nonlocal effect that operates only in the topologically trivial regime and demonstrate that the dependence of the ZBP on the confining gate potential at the opposite end in Majorana wires with two normal metal endcontacts represents a powerful tool for discriminating between topologically trivial and nontrivial ZBPs.Physical Review B 10/2013; 89(22). DOI:10.1103/PhysRevB.89.220507 · 3.74 Impact Factor
Publication Stats
2k  Citations  
322.57  Total Impact Points  
Top Journals
Institutions

2007–2015

Clemson University
 Department of Physics and Astronomy
CEU, South Carolina, United States


2005–2015

University of Maryland, College Park
 • Department of Physics
 • Institute for Physical Science and Technology
CGS, Maryland, United States


2006

University of California, Santa Barbara
 Kavli Institute for Theoretical Physics
Santa Barbara, California, United States


2004

University of Oregon
 Department of Physics
Eugene, OR, United States


2001–2003

University of California, Los Angeles
 Department of Physics and Astronomy
Los Angeles, CA, United States
