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Magnetophonon Resonance on the phonon frequency difference in Quasi-Free-Standing Graphene
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Van der Waals materials and their heterostructures offer a versatile platform for studying a variety of quantum transport phenomena due to their unique crystalline properties and the exceptional ability in tuning their electronic spectrum. However, most experiments are limited to devices that have lateral dimensions of only a few micrometres. Here, we perform magnetotransport measurements on graphene/hexagonal boron-nitride Hall bars and show that wider devices reveal additional quantum effects. In devices wider than ten micrometres we observe distinct magnetoresistance oscillations that are caused by resonant scattering of Landau-quantised Dirac electrons by acoustic phonons in graphene. The study allows us to accurately determine graphene's low energy phonon dispersion curves and shows that transverse acoustic modes cause most of phonon scattering. Our work highlights the crucial importance of device width when probing quantum effects and also demonstrates a precise, spectroscopic method for studying electron-phonon interactions in van der Waals heterostructures.
The Monte Carlo simulation method is applied to study the relaxation of excited electrons in monolayer graphene. The presence of spin polarized background electrons population, with density corresponding to highly degenerate conditions is assumed. Formulas of electron-electron scattering rates, which properly account for electrons presence in two energetically degenerate, inequivalent valleys in this material are presented. The electron relaxation process can be divided into two phases: thermalization and cooling, which can be clearly distinguished when examining the standard deviation of electron energy distribution. The influence of the exchange effect in interactions between electrons with parallel spins is shown to be important only in transient conditions, especially during the thermalization phase.
We have investigated the disorder of epitaxial graphene close to the charge neutrality point (CNP) by various methods: i) at room temperature, by analyzing the dependence of the resistivity on the Hall coefficient ; ii) by fitting the temperature dependence of the Hall coefficient down to liquid helium temperature; iii) by fitting the magnetoresistances at low temperature. All methods converge to give a disorder amplitude of meV. Because of this relatively low disorder, close to the CNP, at low temperature, the sample resistivity does not exhibit the standard value but diverges. Moreover, the magnetoresistance curves have a unique ambipolar behavior, which has been systematically observed for all studied samples. This is a signature of both asymmetry in the density of states and in-plane charge transfer. The microscopic origin of this behavior cannot be unambiguously determined. However, we propose a model in which the SiC substrate steps qualitatively explain the ambipolar behavior.
Our low-temperature magneto-Raman scattering measurements performed on
graphene-like locations on the surface of bulk graphite reveal a new series of
magneto-phonon resonances involving both K-point and Gamma-point phonons. In
particular, we observe for the first time the resonant splitting of three
crossing excitation branches. We give a detailed theoretical analysis of these
new resonances. Our results highlight the role of combined excitations and the
importance of multi-phonon processes (from both K and Gamma points) for the
relaxation of hot carriers in graphene.
Raman spectroscopy is frequently used to study the properties of
epitaxial graphene grown on silicon carbide (SiC). In this work, we
present a confocal micro-Raman study of epitaxial graphene on SiC(0001)
in top-down geometry, i.e. in a geometry where both the primary laser
light beam as well as the back-scattered light is guided through the SiC
substrate. Compared to the conventional top-up configuration, in which
confocal micro-Raman spectra are measured from the air side, we observe
a significant intensity enhancement in top-down configuration,
indicating that most of the Raman-scattered light is emitted into the
SiC substrate. The intensity enhancement is explained in terms of dipole
radiation at a dielectric surface. The new technique opens the
possibility to probe graphene layers in devices where the graphene layer
is covered by non-transparent materials. We demonstrate this by
measuring gate-modulated Raman spectra of a top-gated epitaxial graphene
field effect device. Moreover, we show that these measurements enable us
to disentangle the effects of strain and charge on the positions of the
prominent Raman lines in epitaxial graphene on SiC.
We report the magnetoresistance (MR) in single-layer graphene field-effect transistors at different gate voltages. At low temperatures, the MR exhibits fluctuations at Dirac point, which is attributed to quantum interference effect. Apart from the Dirac point, the MR shows a linear behavior under the extreme quantum limit that is identified by Shubnikov-de Haas oscillations and quantum Hall effect. Our experimental results give a clear manifestation of the quantum linear MR. (C) 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4795149]
Effects of interactions with electrons on optical phonons are studied in an effective-mass approximation. The longitudinal mode with displacement in the axis direction is lowered in its frequency, while the transverse mode with displacement in the circumference direction is raised, in metallic nanotubes. The shifts are opposite but their absolute values are smaller in semiconducting nanotubes. Only the longitudinal mode has a considerable broadening in metallic nanotubes. In the presence of an Aharonov-Bohm magnetic flux, the broadening appears for the transverse mode and diverges when the induced gap becomes the same as the frequency of the optical phonon.
The frequency shift and broadening of long-wavelength optical phonons due to interactions with electrons are calculated in a monolayer graphene in magnetic fields. The broadening is resonantly enhanced and the frequency shift exhibits a rapid change when the phonon energy becomes the energy separation of Landau levels between which optical transitions are allowed.
We perform polarization-resolved Raman spectroscopy on graphene in magnetic fields up to 45 T. This reveals a filling-factor-dependent, multicomponent anticrossing structure of the Raman G peak, resulting from magnetophonon resonances between magnetoexcitons and E_{2g} phonons. This is explained with a model of Raman scattering taking into account the effects of spatially inhomogeneous carrier densities and strain. Random fluctuations of strain-induced pseudomagnetic fields lead to increased scattering intensity inside the anticrossing gap, consistent with the experiments.
Cyclotron resonance in highly doped graphene has been explored using infrared magnetotransmission. Contrary to previous work, which only focused on the magneto-optical properties of graphene in the quantum regime, here we study the quasiclassical response of this system. We show that it has a character of classical cyclotron resonance, with an energy which is linear in the applied magnetic field and with an effective cyclotron mass defined by the position of the Fermi level .
The conductivity describing magnetophonon resonances is calculated in monolayer graphene, with the Fermi level located near the Dirac point. Intervalley scattering due to zone-edge phonons gives dominant contribution to the conductivity compared to intravalley scattering due to zone-center optical phonons mainly because of lower frequency. Resonances are classified into three types, i.e., principal, symmetric, and asymmetric transitions. The magnetophonon oscillations due to the principal and symmetric transitions are periodic in inverse magnetic field, while those due to the asymmetric transitions are not precisely periodic. The amplitude of the oscillation is shown to be weakly dependent on magnetic field.
The experimental results obtained for the magnetotransport in pulsed magnetic fields in the InGaAs/InAlAs
double quantum well �DQW� structures of two different shapes of wells and different values of the electron
density are reported. The magnetophonon resonance �MPR� was observed for both types of structures within the temperature range 77–125 K. Four kinds of LO phonons are taken into account to interpret the MPR oscillations in the DQW and a method of the Landau level calculation in the DQW is elaborated for this aim. The peculiarity of the MPR in the DQW is the large number of the Landau levels caused by SAS splitting of the electron states �splitting on the symmetric and anti-symmetric states� and the large number of the phonon assistance electron transitions between Landau levels. The significant role of the carrier statistics is shown too. The behavior of the electron states in the DQWs at comparably high temperatures has been studied using the MPR. It is shown that the Huang and Manasreh �Manasreh �Phys. Rev. B 54, 2044 �1996�� model involving screening of exchange interaction is confirmed.
We perform Raman scattering experiments on natural graphite in magnetic
fields up to 45 T, observing a series of peaks due to interband electronic
excitations over a much broader magnetic field range than previously reported.
We also explore electron-phonon coupling in graphite via magnetophonon
resonances. The Raman G peak shifts and splits as a function of magnetic field,
due to the magnetically tuned coupling of the E2g optical phonons with the K-
and H-point inter-Landau-level excitations. The analysis of the observed
anticrossing behavior allows us to determine the electron-phonon coupling for
both K- and H-point carriers. In the highest field range (>35 T) the G peak
narrows due to suppression of electron-phonon interaction.
Magneto-Raman scattering experiments from the surface of graphite reveal
novel features associated to purely electronic excitations which are observed
in addition to phonon-mediated resonances. Graphene-like and graphite domains
are identified through experiments with spatial resolution
performed in magnetic fields up to 32T. Polarization resolved measurements
emphasize the characteristic selection rules for electronic transitions in
graphene. Graphene on graphite displays the unexpected hybridization between
optical phonon and symmetric across the Dirac point inter Landau level
transitions. The results open new experimental possibilities - to use light
scattering methods in studies of graphene under quantum Hall effect conditions.
We report on an investigation of quasi-free-standing graphene on 6H-SiC(0001)
which was prepared by intercalation of hydrogen under the buffer layer. Using
infrared absorption spectroscopy we prove that the SiC(0001) surface is
saturated with hydrogen. Raman spectra demonstrate the conversion of the buffer
layer into graphene which exhibits a slight tensile strain and short range
defects. The layers are hole doped (p = 5.0-6.5 x 10^12 cm^(-2)) with a carrier
mobility of 3,100 cm^2/Vs at room temperature. Compared to graphene on the
buffer layer a strongly reduced temperature dependence of the mobility is
observed for graphene on H-terminated SiC(0001)which justifies the term
"quasi-free-standing".
Coherent coupling of Dirac fermion magnetoexcitons with an optical phonon is observed in graphite as marked magnetic-field dependent splittings and anticrossing behavior of the two coupled modes. The sharp magnetophonon resonance occurs in regions of the graphite sample with properties of superior single-layer graphene having enhanced lifetimes of Dirac fermions. The greatly reduced carrier broadening to values below the graphene electron-phonon coupling constant explains the appearance of sharp resonances that reveal a fundamental interaction of Dirac fermions.
We have studied, both experimentally and theoretically, the change of the
so-called 2D band of the Raman scattering spectrum of graphene (the two-phonon
peak near 2700 cm-1) in an external magnetic field applied perpendicular to the
graphene crystal plane at liquid helium temperature. A shift to lower frequency
and broadening of this band is observed as the magnetic field is increased from
0 to 33 T. At fields up to 5--10 T the changes are quadratic in the field while
they become linear at higher magnetic fields. This effect is explained by the
curving of the quasiclassical trajectories of the photo-excited electrons and
holes in the magnetic field, which enables us (i) to extract the electron
inelastic scattering rate, and (ii) to conclude that electronic scattering
accounts for about half of the measured width of the 2D peak.
Magneto Raman scattering study of the E optical phonons in multi-layer
epitaxial graphene grown on a carbon face of SiC are presented. At 4.2K in
magnetic field up to 33 T, we observe a series of well pronounced avoided
crossings each time the optically active inter Landau level transition is tuned
in resonance with the E phonon excitation (at 196 meV). The width of the
phonon Raman scattering response also shows pronounced variations and is
enhanced in conditions of resonance. The experimental results are well
reproduced by a model that gives directly the strength of the electron-phonon
interaction.
We report on the temperature dependence of acoustic-phonon-induced resistance oscillations in very-high mobility two-dimensional electron systems. We observe that the temperature dependence is nonmonotonic and that higher order oscillations are best developed at progressively lower temperatures. Our analysis shows that, in contrast with the Shubnikov\char21{}de Haas effect, phonon-induced resistance oscillations are sensitive to electron-electron interactions modifying the single particle lifetime.
We find that the electronic dispersion in graphite gives rise to double resonant Raman scattering for excitation energies up to 5 eV. As we show, the curious excitation-energy dependence of the graphite D mode is due to this double resonant process resolving a long-standing problem in the literature and invalidating recent attempts to explain this phenomenon. Our calculation for the D-mode frequency shift ( 60{\mathrm{cm}}^{\ensuremath{-}1}/\mathrm{eV}) agrees well with the experimental value.
We report on a new class of magnetoresistance oscillations observed in a high-mobility two-dimensional electron gas (2DEG) in GaAs-Al(x)Ga(1--x)As heterostructures. Appearing in a weak magnetic field ( B < 0.3 T) and only in a narrow temperature range ( 2 K < T < 9 K), these oscillations are periodic in 1/B with a frequency proportional to the electron Fermi wave vector, k(F). We interpret the effect as a magnetophonon resonance of the 2DEG with leaky interface-acoustic phonon modes carrying a wave vector q = 2k(F). Calculations show a few branches of such modes existing on the GaAs-Al(x)Ga(1--)xAs interface, and their velocities are in quantitative agreement with the observation.
When electrons are confined in two-dimensional materials, quantum-mechanically enhanced transport phenomena such as the quantum Hall effect can be observed. Graphene, consisting of an isolated single atomic layer of graphite, is an ideal realization of such a two-dimensional system. However, its behaviour is expected to differ markedly from the well-studied case of quantum wells in conventional semiconductor interfaces. This difference arises from the unique electronic properties of graphene, which exhibits electron-hole degeneracy and vanishing carrier mass near the point of charge neutrality. Indeed, a distinctive half-integer quantum Hall effect has been predicted theoretically, as has the existence of a non-zero Berry's phase (a geometric quantum phase) of the electron wavefunction--a consequence of the exceptional topology of the graphene band structure. Recent advances in micromechanical extraction and fabrication techniques for graphite structures now permit such exotic two-dimensional electron systems to be probed experimentally. Here we report an experimental investigation of magneto-transport in a high-mobility single layer of graphene. Adjusting the chemical potential with the use of the electric field effect, we observe an unusual half-integer quantum Hall effect for both electron and hole carriers in graphene. The relevance of Berry's phase to these experiments is confirmed by magneto-oscillations. In addition to their purely scientific interest, these unusual quantum transport phenomena may lead to new applications in carbon-based electronic and magneto-electronic devices.
Graphene is the two-dimensional building block for carbon allotropes of every other dimensionality. We show that its electronic structure is captured in its Raman spectrum that clearly evolves with the number of layers. The D peak second order changes in shape, width, and position for an increasing number of layers, reflecting the change in the electron bands via a double resonant Raman process. The G peak slightly down-shifts. This allows unambiguous, high-throughput, nondestructive identification of graphene layers, which is critically lacking in this emerging research area.
Recently observed magnetophonon resonances in the magnetoresistance of graphene are investigated using the Kubo formalism. This analysis provides a quantitative fit to the magnetophonon resonances over a wide range of carrier densities. It demonstrates the predominance of carrier scattering by low-energy transverse acoustic (TA) mode phonons: the magnetophonon resonance amplitude is significantly stronger for the TA modes than for the longitudinal acoustic (LA) modes. We demonstrate that the LA and TA phonon speeds and the electron-phonon coupling strengths determined from the magnetophonon resonance measurements also provide an excellent fit to the measured dependence of the resistivity at zero magnetic field over a temperature range of 4–150 K. A semiclassical description of magnetophonon resonance in graphene is shown to provide a simple physical explanation for the dependence of the magneto-oscillation period on carrier density. The correspondence between the quantum calculation and the semiclassical model is discussed.
In this report, we demonstrate a complete Hall effect element that is based on quasi-free-standing monolayer
graphene synthesized on a semi-insulating on-axis Si-terminated 6H-SiC substrate in an epitaxial
Chemical Vapor Deposition process. The device offers the current-mode sensitivity of 87 V/AT and low excess noise (Hooge's parameter αH < 2 × 10−3) enabling room-temperature magnetic resolution of 650 nT/Hz0.5 at 10 Hz, 95 nT/Hz0.5 at 1 kHz, and 14 nT/Hz0.5 at 100 kHz at the total active area of 0.1275 mm2. The element is passivated with a silicone encapsulant to ensure its electrical stability and environmental resistance. Its processing cycle is suitable for large-scale commercial production and it is available in large quantities through a single growth run on an up to 4-in SiC wafer.
Many-body effects resulting from strong electron-electron and electron-phonon
interactions play a significant role in graphene physics. We report on their
manifestation in low B field magneto-phonon resonances in high quality
exfoliated single-layer and bilayer graphene encapsulated in hexagonal boron
nitride. These resonances allow us to extract characteristic effective Fermi
velocities, as high as m/s, for the observed "dressed"
Landau level transitions, as well as the broadening of the resonances, which
increases with Landau level index.
For the first time in a single experiment the magnetophonon resonances of three types of carriers in p-InSb are investigated: light holes (MPR1), heavy holes (MPRh), and electrons (MPRe). From the temperature shift of the ground series (most intensive ones) of MPR1 and MPRh the valence-band parameters of the band structure as function of temperature are calculated. The investigation completed allows for the first time to identify nonearlier observed two-phonon transitions in p-InSb, alongside with an additional series of peculiarities: a satellite of the main MPRh series peaks at weak magnetic fields. The comparison of MPRh of two samples with different mobilities of heavy holes lead to the observance of a distortion in the period of the transverse field of the main MPRh series in the sample of less mobility of heavy holes.
Erstmalig werden in einem Experiment die Magnetophononresonanz an drei Arten von Ladungsträgern in p-InSb untersucht: leichte Löcher (MPR1), schwere Löcher (MPRh) und Elektronen (MPRe). Aus der Temperaturverschiebung der Grundzustandsserien (die intensivste) von MPR1 und MPRh werden die Valenzparameter der Bandstruktur als Funktion der Temperatur berechnet. Die vollständige Untersuchung erlaubt erstmalig die Identifizierung der früher nicht beobachteten Zwei-Phasenübergänge in p-InSb zusammen mit einer zusätzlichen Reihe von Besonderheiten wie ein Satellit der MPRh-Hauptserienmaxima bei schwachen Magnetfeldern. Der Vergleich der MPRh zweier Proben mit unterschiedlicher Beweglichkeit der schweren Löcher führt zu einer Störung der Periode des transversalen Feldes der Haupt-MPRh-Serie in der Probe mit der geringeren Beweglichkeit der schweren Löcher.
We investigated the magnetotransport properties of a bilayer graphene
Hall bar sample epitaxially grown on Si-terminated silicon carbide.
Integer quantum Hall effect and weak localization effect were observed.
From the weak localization effect, the carrier scattering and phase
coherence were extracted. The extracted phase coherence length is 0.5
μm at 2 K, which is comparable with that of the exfoliated graphene.
The temperature dependence of the phase coherence rate shows that
electron-electron interaction is the main inelastic-scattering
factor and direct Coulomb interaction also exists. Compared with
exfoliated bilayer graphene, no sign of weak antilocalization was
observed at such high carrier concentration of 1013
cm-2 due to the strong intervally scattering. Both the
strong intervally scattering and Coulomb interaction of phase coherence
are due to the large amount of atomically sharp defects in epitaxial
graphene on Si-terminated SiC.
We present a first-principles study of the temperature- and density-dependent intrinsic electrical resistivity of graphene. We use density-functional theory and density-functional perturbation theory together with very accurate Wannier interpolations to compute all electronic and vibrational properties and electron-phonon coupling matrix elements; the phonon-limited resistivity is then calculated within a Boltzmann-transport approach. An effective tight-binding model, validated against first-principles results, is also used to study the role of electron-electron interactions at the level of many-body perturbation theory. The results found are in excellent agreement with recent experimental data on graphene samples at high carrier densities and elucidate the role of the different phonon modes in limiting electron mobility. Moreover, we find that the resistivity arising from scattering with transverse acoustic phonons is 2.5 times higher than that from longitudinal acoustic phonons. Last, high-energy, optical, and zone-boundary phonons contribute as much as acoustic phonons to the intrinsic electrical resistivity even at room temperature and become dominant at higher temperatures.
This article was written with the objective of developing, and illustrating, the principles and practice of the application of group theory methods to the analysis of the infra-red and Raman lattice optical processes in insulating crystals. The group theory methods have proven to be very powerful tools in the interpretation and prediction of optical processes. It is also our objective to make these methods as accessible, and transparent, and hence as widely used as possible.
We describe a mechanism in which low-energy phonons of the SiC/graphene
interface modify the separation between the buffer layer and the
graphene overlayer, resulting in a deformation potential and hence
charge carrier scattering. We determine this deformation potential ab
initio, and then calculate transport properties within the Boltzmann
formalism. Our results show (i) a remarkable decrease in the resistivity
(ρ) near the Dirac point with increasing temperature (T), (ii) a
linear increase of ρ with T away from the Dirac point, and (iii)
good agreement with experiment for low temperature to room temperature
change in resistivity for epitaxial graphene on the SiC Si face.
DOI:https://doi.org/10.1103/PhysRevLett.16.655
Recent Raman scattering studies in different types of graphene samples are reviewed here. We first discuss the first-order and the double resonance Raman scattering mechanisms in graphene, which give rise to the most prominent Raman features. The determination of the number of layers in few-layer graphene is discussed, giving special emphasis to the possibility of using Raman spectroscopy to distinguish a monolayer from few-layer graphene stacked in the Bernal (AB) configuration. Different types of graphene samples produced both by exfoliation and using epitaxial methods are described and their Raman spectra are compared with those of 3D crystalline graphite and turbostratic graphite, in which the layers are stacked with rotational disorder. We show that Resonance Raman studies, where the energy of the excitation laser line can be tuned continuously, can be used to probe electrons and phonons near the Dirac point of graphene and, in particular allowing a determination to be made of the tight-binding parameters for bilayer graphene. The special process of electron–phonon interaction that renormalizes the phonon energy giving rise to the Kohn anomaly is discussed, and is illustrated by gated experiments where the position of the Fermi level can be changed experimentally. Finally, we discuss the ability of distinguishing armchair and zig-zag edges by Raman spectroscopy and studies in graphene nanoribbons in which the Raman signal is enhanced due to resonance with singularities in the density of electronic states.
On the SiC(0001) surface (the silicon face of SiC), epitaxial graphene is obtained by sublimation of Si from the substrate. The graphene film is separated from the bulk by a carbon-rich interface layer (hereafter called the buffer layer) which in part covalently binds to the substrate. Its structural and electronic properties are currently under debate. In the present work we report scanning tunneling microscopy (STM) studies of the buffer layer and of quasi-free-standing monolayer graphene (QFMLG) that is obtained by decoupling the buffer layer from the SiC(0001) substrate by means of hydrogen intercalation. Atomic resolution STM images of the buffer layer reveal that, within the periodic structural corrugation of this interfacial layer, the arrangement of atoms is topologically identical to that of graphene. After hydrogen intercalation, we show that the resulting QFMLG is relieved from the periodic corrugation and presents no detectable defect sites.
We report the first observation of magnetophonon resonances in the two-dimensional electronic system in single interface GaAs-AlxGa1-xAs heterojunctions and heterojunction superlattices. They result from inelastic scattering between Landau levels with resonant absorption of LO phonons of GaAs and yield a polaron mass mp*=(0.077±0.004)me.
A systematic survey has been made with epitaxial films of n-type GaAs of the dependence of the position and amplitude of magnetophonon resistance oscillations on the experimental parameters of magnetic field, temperature and sample mobility. A number of corroborative experiments have also been performed with n-type InSb and InAs. With the magnetic field applied perpendicular to the current direction, a dependence of magnetophonon peak position on both temperature and mobility was found. A change in the curvature of the band edge can be deduced from the temperature dependence, and the low-frequency effective mass at the bottom of the conduction band of GaAs is found to be 00653m at 280 °K and 00675m at 70 °K. With InSb the band-edge mass of the electrons is found to be 00127m at 160 °K and 00134m at 60 °K. The dependence of the peak position on mobility is thought to be related to an expression describing the magnetic field dependence of the amplitude of the oscillatory terms. The amplitudes of the oscillatory terms do not depend on the mobility in a simple manner and appear to be a function of the number of ionized impurity sites rather than of the actual mobility of the sample.
When the magnetic field is applied parallel to the direction of current flow, resistance minima are always observed at magnetic fields close to the fields at which maxima are observed in the transverse orientation, but these minima cannot be used to determine band parameters as they are shifted with respect to the transverse maxima by amounts which can be as high as 16% in the case of InAs. Additional series of minima were observed at high temperatures with both GaAs and InAs in the longitudinal configuration. These extra series are attributed to the presence of indirect scattering processes involving two optical phonons.
Magnetophonon oscillations of the transverse magnetoresistance of Cd0.196Hg0.804Te due to two-phonon transitions have been investigated in magnetic fields from 1.4 to 6T. An abundance of peaks has been traced, only the part of which had been interpreted in Sheregii et al. (Pisma v JETF47, 613 (1988)) with using long-wave phonons. For the interpretation of all obtained peaks the short-wave phonons of both sublattices of HgTe-type and CdTe-type have been used. The frequencies of the extreme compounds HgTe (Kepa et al., Phys. Scripta25, 807 (1982)) and CdTe (Rowe et al., Phys. Rev.B10, 671 (1974)) have been accepted as initials. The shift for the given composition of solid alloy has been calculated pos the best concord of the experimental peaks with calculated positions in the magnetic field of the corresponding resonances.
We show how coupling to an Einstein phonon affects the absorption
peaks seen in the optical conductivity of graphene under a magnetic field B.
The energies and widths of the various lines are shifted, and additional peaks
arise in the spectrum. Some of these peaks are Holstein sidebands, resulting
from the transfer of spectral weight in each Landau level (LL) into
phonon-assisted peaks in the spectral function. Other additional absorption
peaks result from transitions involving split LLs, which occur when a LL falls
sufficiently close to a peak in the self-energy. We establish the selection
rules for the additional transitions and characterize the additional absorption
peaks. For finite chemical potential, spectral weight is asymmetrically
distributed about the Dirac point; we discuss how this causes an asymmetry in
the transitions due to left- and right-handed circularly polarized light and
therefore oscillatory behavior in the imaginary part of the off-diagonal Hall
conductivity. We also find that the semiclassical cyclotron resonance region is
renormalized by an effective-mass factor but is not directly affected by the
additional transitions. Last, we discuss how the additional transitions can
manifest in broadened, rather than split, absorption peaks due to large
scattering rates seen in experiment.
We calculate the density of states (DOS) in graphene for electrons coupled to
a phonon in an external magnetic field. We find that coupling to an Einstein
mode of frequency not only shifts and broadens the Landau levels
(LLs), but radically alters the DOS by introducing a new set of peaks at
energies , where is the energy of the nth LL. If one of
these new peaks lies sufficiently close to a LL, it causes the LL to split in
two; if the system contains an energy gap, a LL may be split in three. The new
peaks occur outside the interval , leaving the LLs in
that interval largely unaffected. If the chemical potential is greater than the
phonon frequency, the zeroth LL lies outside the interval and can be split,
eliminating its association with a single Dirac point. We find that coupling to
an extended phonon distribution such as a Lorentzian or Debye spectrum does not
qualitatively alter these results.
We present a Raman study of Ar(+)-bombarded graphene samples with increasing ion doses. This allows us to have a controlled, increasing, amount of defects. We find that the ratio between the D and G peak intensities, for a given defect density, strongly depends on the laser excitation energy. We quantify this effect and present a simple equation for the determination of the point defect density in graphene via Raman spectroscopy for any visible excitation energy. We note that, for all excitations, the D to G intensity ratio reaches a maximum for an interdefect distance ∼3 nm. Thus, a given ratio could correspond to two different defect densities, above or below the maximum. The analysis of the G peak width and its dispersion with excitation energy solves this ambiguity.
Surface-enhanced Raman scattering (SERS) exploits surface plasmons induced by the incident field in metallic nanostructures to significantly increase the Raman intensity. Graphene provides the ideal prototype two-dimensional (2d) test material to investigate SERS. Its Raman spectrum is well-known, graphene samples are entirely reproducible, height controllable down to the atomic scale, and can be made virtually defect-free. We report SERS from graphene, by depositing arrays of Au particles of well-defined dimensions on a graphene/SiO(2) (300 nm)/Si system. We detect significant enhancements at 633 nm. To elucidate the physics of SERS, we develop a quantitative analytical and numerical theory. The 2d nature of graphene allows for a closed-form description of the Raman enhancement, in agreement with experiments. We show that this scales with the nanoparticle cross section, the fourth power of the Mie enhancement, and is inversely proportional to the tenth power of the separation between graphene and the center of the nanoparticle. One important consequence is that metallic nanodisks are an ideal embodiment for SERS in 2d.
Epitaxial graphene films were grown in vacuo by silicon sublimation from the
(0001) and (000-1) faces of 4H- and 6H-SiC. Hall effect mobilities and sheet
carrier densities of the films were measured at 300 K and 77 K and the data
depended on the growth face. About 40% of the samples exhibited holes as the
dominant carrier, independent of face. Generally, mobilities increased with
decreasing carrier density, independent of carrier type and substrate polytype.
The contributions of scattering mechanisms to the conductivities of the films
are discussed. The results suggest that for near-intrinsic carrier densities at
300 K epitaxial graphene mobilities will be ~150,000 cm2V-1s-1 on the (000-1)
face and ~5,800 cm2V-1s-1 on the (0001) face.
Quasi-free-standing epitaxial graphene is obtained on SiC(0001) by hydrogen intercalation. The hydrogen moves between the (6 square root(3) x 6 square root(3))R30 degrees reconstructed initial carbon layer and the SiC substrate. The topmost Si atoms which for epitaxial graphene are covalently bound to this buffer layer, are now saturated by hydrogen bonds. The buffer layer is turned into a quasi-free-standing graphene monolayer with its typical linear pi bands. Similarly, epitaxial monolayer graphene turns into a decoupled bilayer. The intercalation is stable in air and can be reversed by annealing to around 900 degrees C.
We describe a peculiar fine structure acquired by the in-plane optical phonon at the Gamma point in graphene when it is brought into resonance with one of the inter-Landau-level transitions in this material. The effect is most pronounced when this lattice mode (associated with the G band in graphene Raman spectrum) is in resonance with inter-Landau-level transitions 0 --> +, 1 and -, 1 --> 0, at a magnetic field B{0} approximately 30 T. It can be used to measure the strength of the electron-phonon coupling directly, and its filling-factor dependence can be used experimentally to detect circularly polarized lattice vibrations.
Rotation and reflection symmetries impose that out-of-plane (flexural) phonons of freestanding graphene membranes have a quadratic dispersion at long wavelength and can be excited by charge carriers in pairs only. As a result, we find that flexural phonons dominate the phonon contribution to the resistivity rho below a crossover temperature T(x) where we obtain an anomalous temperature dependence rho proportional, variantT(5/2)lnT. The logarithmic factor arises from renormalizations of the flexural-phonon dispersion due to coupling between bending and stretching degrees of freedom of the membrane.