We derive the low-temperature behavior of the Casimir-Polder free energy for a polarizable atom interacting with graphene sheet which possesses the nonzero energy gap $Δ$ and chemical potential $μ$. The response of graphene to the electromagnetic field is described by means of the polarization tensor in the framework of Dirac model on the basis of first principles of thermal quantum field theory in the Matsubara formulation. It is shown that the thermal correction to the Casimir-Polder energy consists of three contributions. The first of them is determined by the Matsubara summation using the polarization tensor defined at zero temperature, whereas the second and third contributions are caused by an explicit temperature dependence of the polarization tensor and originate from the zero-frequency Matsubara term and the sum of all Matsubara terms with nonzero frequencies, respectively. The asymptotic behavior for each of the three contributions at low temperature is found analytically for any value of the energy gap and chemical potential. According to our results, the Nernst heat theorem for the Casimir-Polder free energy and entropy is satisfied for both $Δ> 2μ$ and $Δ< 2μ$. We also reveal an entropic anomaly arising in the case $Δ= 2μ$. The obtained results are discussed in connection with the long-standing fundamental problem in Casimir physics regarding the proper description of the dielectric response of matter to the electromagnetic field.
We study electronic transport in graphene under the influence of a transversal magnetic field $\f{B}(\f{r})=B(x)\f{e}_z$ with the asymptotics $B(x\to\pm\infty)=\pm B_0$, which could be realized via a folded graphene sheet in a constant magnetic field, for example. By solving the effective Dirac equation, we find robust modes with a finite energy gap which propagate along the fold -- where particles and holes move in opposite directions. Exciting these particle-hole pairs with incident photons would then generate a nearly perfect charge separation and thus a strong magneto-thermoelectric (Nerns…
We find analytic asymptotic expressions at low temperature for the Casimir free energy, entropy and pressure of two parallel graphene sheets in the framework of the Lifshitz theory. The reflection coefficients of electromagnetic waves on graphene are described on the basis of first principles of quantum electrodynamics at nonzero temperature using the polarization tensor in (2+1)-dimensional space-time. The leading contributions to the Casimir entropy and to the thermal corrections to the Casimir energy and pressure are given by the thermal correction to the polarization tensor at nonzero Mats…
We find the low-temperature behavior of the Casimir-Polder free energy and entropy for an atom interacting with real graphene sheet possessing nonzero energy gap and chemical potential. Employing the formalism of the polarization tensor, it is shown that the Casimir-Polder entropy goes to zero by the power law with vanishing temperature, i.e., the Nernst heat theorem is satisfied. This result is discussed in connection with the problems connected with account of free charge carriers in the Lifshitz theory.
Cyclotron resonance of a Landau-quantized graphene can absorb significant amount of infrared light. However, application of this phenomenon to the photodetector had been limited due to the lack of efficient photon to charge conversion scheme. Here, we demonstrate the detection of cyclotron resonance in a partially metal-masked monolayer graphene two-terminal device using photo-Nernst effect. Due to the presence of the mask, incident infrared light is irradiated on only one-half of the graphene channel. This partial irradiation creates a temperature gradient perpendicular to the graphene channe…
We consider intrinsic contributions to the spin Hall and spin Nernst effects in a bilayer graphene. The relevant electronic spectrum is obtained from the tight binding Hamiltonian, which also includes the intrinsic spin-orbit interaction. The corresponding spin Hall and spin Nernst conductivities are compared with those obtained from effective Hamiltonians appropriate for states in the vicinity of the Fermi level of a neutral bilayer graphene. Both conductivities are determined within the linear response theory and Green function formalism. The influence of an external voltage between the two …
The derivation for the transport coefficients of an electron system in the presence of temperature gradient and the electric and magnetic fields are presented. The Nernst conductivity and the transverse thermoelectric power of the Dirac fermions in graphene under charged impurity scatterings and weak magnetic field are calculated on basis of the self-consistent Born approximation. The result is compared with so far the available experimental data.
We report measurements of the thermopower $S$ and Nernst signal $S_{yx}$ in graphene in a magnetic field $H$. Both quantities show strong quantum oscillations vs. the gate voltage $V_g$. Our measurements for Landau Levels of index $n\ne 0$ are in quantitative agreement with the edge-current model of Girvin and Jonson (GJ). The inferred off-diagonal thermoelectric conductivity $α_{yx}$ comes close to the quantum of Amps per Kelvin. At the Dirac point ($n=0$), however, the width of the peak in $α_{yx}$ is very narrow. We discuss features of the thermoelectric response at the Dirac point includin…
Photocurrent measurements provide a powerful means of studying the spatially resolved optoelectronic and electrical properties of a material or device. Generally speaking there are two classes of mechanism for photocurrent generation: those involving separation of electrons and holes, and thermoelectric effects driven by electron temperature gradients. Here we introduce a new member in the latter class: the photo-Nernst effect. In graphene devices in a perpendicular magnetic field we observe photocurrent generated uniformly along the free edges, with opposite sign at opposite edges. The signal…
Van Hove singularity-driven giant Nernst signal in twisted double bilayer graphene
Indian Institute of Science（印度科学研究所）；Tel-Aviv University（特拉维夫大学）；The Ohio State University（俄亥俄州立大学）；Weizmann Institute of Science（魏茨曼科学研究所）；National Institute of Material Science（国家材料研究所）；Tata Institute of Fundamental Research（塔塔基础研究所）
The thermoelectric power, including the Nernst and Seebeck effects, in graphene nanoribbon is studied. By using the non-equilibrium Green function combining with the tight-binding Hamiltonian, the Nernst and Seebeck coefficients are obtained. Due to the electron-hole symmetry, the Nernst coefficient is an even function of the Fermi energy while the Seebeck coefficient is an odd function regardless of the magnetic field. In the presence of a strong magnetic field, the Nernst and Seebeck coefficients are almost independent of the chirality and width of the nanoribbon, and they show peaks when th…
The reflectivity properties of graphene with nonzero mass-gap parameter are investigated in the framework of Dirac model using the polarization tensor in (2+1)-dimensional space-time. For this purpose, a more simple explicit representation for the polarization tensor along the real frequency axis is found. The approximate analytic expressions for the polarization tensor and for the reflectivities of graphene are obtained in different frequency regions at any temperature. We show that the nonzero mass-gap parameter has a profound effect on the reflectivity of graphene. Specifically, at zero tem…
We consider Berry phase mediated Nernst effect in silicene. The low energy band structure of silicene consists of two valleys near the Dirac points, similar to graphene. The low energy transport properties of the quasiparticles can be described as Berry phase dependent phenomena. By contrast to graphene, silicene has strong spin-orbit interaction leading to opening of the gap in the energy spectrum and spin-splitting of the bands in each valley. If an electric field is applied perpendicular to the silicene sheet, it allows tunability of the gap. \ We show that this results in Berry-phase-suppo…
Large Nernst effect in chemically derived multilayer graphene at millitesla magnetic fields
Moscow Institute of Physics and Technology（莫斯科物理技术学院）；Joint-Stock Company ”Skanda Rus”（斯坎达鲁斯股份公司）；National Research Nuclear University “MEPhI”（国立核研究大学“莫斯科工程物理学院”）；Institute of Microelectronics Technology and High Purity Materials, Russian Academy of Sciences（俄罗斯科学院微电子技术与高纯材料研究所）
We analyze the thermoelectric response of Dirac and Weyl semimetals using the semiclassical approach, focusing on the extrinsic contributions due to skew-scattering and side jump. Our results apply to linear response Nernst effect in ferromagnetic Dirac materials such as Fe$_3$Sn$_2$, Weyl semimetal Co$_3$Sn$_2$S$_2$ and to second order response of monolayer graphene on hBN with trigonal warping. Our analysis indicates that the extrinsic contributions can be a significant component of anomalous Nernst response and used to explain an enhanced thermoelectric response.
Nernst effect, the transverse voltage generated by a longitudinal thermal gradient in presence of magnetic field has recently emerged as a very sensitive, yet poorly understood, probe of electron organization in solids. Here we report on an experiment on graphite, a macroscopic stack of graphene layers, which establishes a fundamental link between dimensionality of an electronic system and its Nernst response. In sharp contrast with single-layer graphene, the Nernst signal sharply peaks whenever a Landau level meets the Fermi level. This points to the degrees of freedom provided by finite inte…
Using the Matsubara Green function formalism we calculate the temperature dependence of spin Hall and spin Nernst conductivities of a two-dimensional electron gas with Rashba spin-orbit interaction in the linear response regime. In the case of spin Nernst effect we also include the contribution from spin-resolved orbital magnetization, which assures correct behavior of the spin Nernst conductivity in the zero-temperature limit. Analytical formulas for the spin Hall and spin Nernst conductivities are derived in some specific situations. Using the Ioffe-Regel localization criterion, we have also…
We consider the anomalous thermoelectric transport in gapped single and bilayer graphene where the gap may be due to broken inversion symmetry. In the presence of the gap, non-trivial Berry phase effects can be shown to mediate a transverse thermoelectric voltage in response to an applied temperature gradient even in the absence of a perpendicular magnetic field. This spontaneous, anomalous Nernst effect is nonzero for non-uniform chemical potential in the two inequivalent valleys in the graphene band structure. Conversely, the Nernst response can be used to create a valley-index polarization …
The spin Nernst effect is a phenomenon in which the spin current flows perpendicular to a temperature gradient. Similar to the spin Hall effect, this phenomenon also causes spin accumulation at the boundaries. Here, we study the spin response to the gradient of the temperature gradient with the use of Green's functions. Our formalism predicts physically observable spin accumulation without the ambiguity regarding the definition of the spin current or the magnetization correction. We prove the generalized Mott relation between the electric and thermal responses assuming the presence of time-rev…
The complete theory of electrical conductivity of graphene at arbitrary temperature is developed with taken into account mass-gap parameter and chemical potential. Both the in-plane and out-of-plane conductivities of graphene are expressed via the components of the polarization tensor in (2+1)-dimensional space-time analytically continued to the real frequency axis. Simple analytic expressions for both the real and imaginary parts of the conductivity of graphene are obtained at zero and nonzero temperature. They demonstrate an interesting interplay depending on the values of mass gap and chemi…
The thermal free energy and pressure of dispersion interaction between two graphene sheets described by the Dirac model are calculated using the Lifshitz formula with reflection coefficients expressed via the polarization tensor. The obtained results for a pristine graphene are found to be in agreement with computations using Coulomb coupling between density fluctuations. For a graphene with nonzero mass gap parameter a qualitatively different behavior for the free energy and pressure is obtained. The Lifshitz formula with reflection coefficients expressed via the polarization tensor is used a…
We theoretically study the thermoelectric transport properties of strained HgTe in the topological insulator phase. We developed a model for the system using a Dirac Hamiltonian including the effect of strain induced by the interface between HgTe and the CdTe substrate. The conductivity tensor was explored assuming the electrons are scattered by charge impurities, while the thermopower tensor was addressed using the Mott relation. Seebeck and Nernst responses exhibit remarkable enhancements in comparison with other two-dimensional Dirac materials, such as graphene, germanane, prosphorene and s…
We consider the Nernst-Ettingshausen (NE) effect in the presence of semiclassically strong magnetic fields for a quasi-two dimensional system with a parabolic or linear dispersion of carriers. We show that the occurring giant oscillations of the NE coefficient are coherent with the recent experimental observation in graphene, graphite and bismuth. In the 2D case we find the exact shape of these oscillations and show that their magnitude decreases/increases with enhancement of the Fermi energy for Dirac fermions/normal carriers. With a crossover to 3D spectrum the phase of oscillations shifts, …
We report a thermoelectric study of graphene in both zero and applied magnetic fields. As a direct consequence of the linear dispersion of massless particles, we find that the Seebeck coefficient Sxx diverges with 1 /, where n2D is the carrier density. We observe a very large Nernst signal Sxy (~ 50 uV/K at 8 T) at the Dirac point, and an oscillatory dependence of both Sxx and Sxy on n2D at low temperatures. Our results underscore the anomalous thermoelectric transport in graphene, which may be used as a highly sensitive probe for impurity bands near the Dirac point.
Thermoelectric power (TEP) is measured in bilayer graphene for various temperatures and charge-carrier densities. At low temperatures, measured TEP well follows the semiclassical Mott formula with a hyperbolic dispersion relation. TEP for a high carrier density shows a linear temperature dependence, which demonstrates a weak electron-phonon interaction in the bilayer graphene. For a low carrier density, a deviation from the Mott relation is observed at high temperatures and is attributed to the low Fermi temperature in the bilayer graphene. Oscillating TEP and the Nernst effect for varying car…
In van der Waals heterostructures, the periodic potential from the Moiré superlattice can be used as a control knob to modulate the electronic structure of the constituent materials. Here we present a nanoscale angle-resolved photoemission spectroscopy (Nano-ARPES) study of transferred graphene/h-BN heterostructures with two different stacking angles of 2.4° and 4.3° respectively. Our measurements reveal six replicas of graphene Dirac cones at the superlattice Brillouin zone (SBZ) centers. The size of the SBZ and its relative rotation angle to the graphene BZ are in good agreement with Moiré s…
We find that the empirical relation between the longitudinal and Hall resistivities (i.e. Rxx and Rxy) and its counterpart between the Seebeck and Nernst coefficients (i.e. Sxx and Sxy), both originally discovered in two-dimensional electron gases, hold remarkably well for graphene in the quantum transport regime except near the Dirac point. The validity of the relations is cross-examined by independently varying the magnetic field and the carrier density in graphene. We demonstrate that the pre-factor, α_s, does not depend on carrier density in graphene. By tuning the carrier mobility therefo…
We present a formalism based on first principles of quantum electrodynamics at nonzero temperature which permits to calculate the Casimir-Polder interaction between an atom and a graphene sheet with arbitrary mass gap and chemical potential, including graphene-coated substrates. The free energy and force of the Casimir-Polder interaction are expressed via the polarization tensor of graphene in (2+1)-dimensional space-time in the framework of the Dirac model. The obtained expressions are used to investigate the influence of the chemical potential of graphene on the Casimir-Polder interaction. C…
We study the DC transport of finite graphene samples with random gap. Using Dirac fermions to describe the low-energy physics near the Dirac point, we employ a generalized Drude form for the conductivity. The latter is constant for a vanishing average gap but always decreases with increasing sample size for a nonzero average gap. The asymptotic conductivity of the infinite sample is either nonzero if the average gap is smaller than a critical value or zero otherwise. Our results are in agreement with recent numerical calculations of Bardarson et al..
Quantum oscillations of metallic systems at low temperatures is one of the key rules to experimentally access their electronic properties, such as energy spectrum, scattering mechanisms, geometry of Fermi surface and many other features. The importance of these knowledge is enormous, since from these a thorough understanding of anomalous Hall effect, thermopower and Nernst coefficients, just to name a few, is possible; and from those knowledge, a plenty of applications arise as emerging technologies. In this direction, the present contribution focus on a complete description of quantum capacit…
We present the results of an experiment on measuring the gradient of the Casimir force between an Au-coated hollow glass microsphere and graphene-coated fused silica plate by means of a modified atomic force microscope cantilever based technique operated in the dynamic regime. These measurements were performed in high vacuum at room temperature. The energy gap and the concentration of impurities in the graphene sample used have been measured utilizing scanning tunnelling spectroscopy and Raman spectroscopy, respectively. The measurement results for the gradients of the Casimir force are found …
The analytical expressions for both diagonal and off-diagonal ac and dc conductivities of graphene placed in an external magnetic field are derived. These conductivities exhibit rather unusual behavior as functions of frequency, chemical potential and applied field which is caused by the fact that the quasiparticle excitations in graphene are Dirac-like. One of the most striking effects observed in graphene is the odd integer quantum Hall effect. We argue that it is caused by the anomalous properties of the Dirac quasiparticles from the lowest Landau level. Other quantities such as Hall angle …
We report precision measurements of the gradient of the Casimir force between an Au-coated sphere and graphene sheet deposited on a silica plate. The measurement data are compared with exact theory using the polarization tensor found in the framework of the Dirac model including effects of the nonzero chemical potential and energy gap of the graphene sample with no fitting parameters. The very good agreement between experiment and theory demonstrates the unusually big thermal effect at separations below 1 mum which has never been observed for conventional 3D materials. Thus, it is confirmed ex…
We numerically study the thermoelectric transports of Dirac fermions in graphene in the presence of a strong magnetic field and disorder. We find that the thermoelectric transport coefficients demonstrate universal behavior depending on the ratio between the temperature and the width of the disorder-broadened Landau levels(LLs). The transverse thermoelectric conductivity $α_{xy}$ reaches a universal quantum value at the center of each LL in the high temperature regime, and it has a linear temperature dependence at low temperatures. The calculated Nernst signal has a peak at the central LL with…
It is known that fluctuations in the electrostatic potential allow for metallic conduction (nonzero conductivity in the limit of an infinite system) if the carriers form a single species of massless two-dimensional Dirac fermions. A nonzero uniform mass $\bar{M}$ opens up an excitation gap, localizing all states at the Dirac point of charge neutrality. Here we investigate numerically whether fluctuations $δM \gg \bar{M} \neq 0$ in the mass can have a similar effect as potential fluctuations, allowing for metallic conduction at the Dirac point. Our negative conclusion confirms earlier expectati…
Understanding magnetoresistance, the change in electrical resistance upon an external magnetic field, at the atomic level is of great interest both fundamentally and technologically. Graphene and other two-dimensional layered materials provide an unprecedented opportunity to explore magnetoresistance at its nascent stage of structural formation. Here, we report an extremely large local magnetoresistance of ~ 2,000% at 400 K and a non-local magnetoresistance of > 90,000% in 9 T at 300 K in few-layer graphene/boron-nitride heterostructures. The local magnetoresistance is understood to arise from…
We solve Dirac-Bogoliubov-De-Gennes (DBdG) equation in a superconductor-normal graphene superconductor (SGS) junction with Corbino disk structure to investigate the Josephson current through this junction. We find that the critical current $I_c$ has a nonzero value at Dirac point in which the concentration of the carriers is zero. We show this nonzero critical current depends on the system geometry and it decreases monotonically to zero by increasing the ratio of the outer to inner radii of the Corbino disk ($R_2/R_1$), while in the limit of $R_2/R_1 \rightarrow 1$ it scales like a diffusive C…
We study graphene with an adsorbed spin texture, where the localized spins create a periodic magnetic flux. The latter produces gaps in the graphene spectrum and breaks the valley symmetry. The resulting effective electronic model, which is similar to Haldane's periodic flux model, allows us to tune the gap of one valley independently from that of the other valley. This leads to the formation of two Hall plateaux and a quantum Hall transition. We discuss the density of states, optical longitudinal and Hall conductivities for nonzero frequencies and nonzero temperatures. A robust logarithmic si…
We study magic angle graphene in the presence of both strain and particle-hole symmetry breaking due to non-local inter-layer tunneling. We perform a self-consistent Hartree-Fock study that incorporates these effects alongside realistic interaction and substrate potentials, and explore a comprehensive set of competing orders including those that break translational symmetry at arbitrary wavevectors. We find that at all non-zero integer fillings very small strains, comparable to those measured in scanning tunneling experiments, stabilize a fundamentally new type of time-reversal symmetric and s…
The electrical conductivity of graphene with a nonzero mass-gap parameter is investigated starting from the first principles of quantum electrodynamics in (2+1)-dimensional space-time at any temperature. The formalism of the polarization tensor defined over the entire plane of complex frequency is used. At zero temperature we reproduce the results for both real and imaginary parts of the conductivity, obtained previously in the local approximation, and generalize them taking into account the effects of nonlocality. At nonzero temperature the exact analytic expressions for real and imaginary pa…
Graphene/hBN heterostructure based Valley transistor: Dynamic Control of valley current in synchronized nonzero voltages, within the time-dependent regime
We have investigated the transmission in monolayer graphene barrier at nonzero angle of incidence. Taking the influence of parallel wave vector into account, the transmission as the function of incidence energy has a gap due to the evanescent waves in two cases of Klein tunneling and classical motion. The modulation of the transmission gap by the incidence angle, the height, and width of potential barrier may lead to potential applications in graphene-based electronic devices.
Spin Hall effect due to random Rashba spin-orbit coupling in the two-dimensional honeycomb lattice of carbon atoms (graphene) is considered theoretically. Using the Green function method and diagrammatic technique we show that fluctuations of the Rashba interaction around zero average value give rise to nonzero spin Hall conductivity. Generally, the conductivity is not universal, but depends on the ratio of the total momentum and spin-flip relaxation rates.
In the context of the low energy effective theory, the exact Landau level spectrum of quasiparticles in twisted bilayer graphene with small twist angle is analytically obtained by spheroidal eigenvalues. We analyze the dependence of the Landau levels on the twist angle to find the points, where the two-fold degeneracy for twist angles is lifted in the nonzero modes and below/above which massive/massless fermion pictures become valid. In the perpendicular magnetic field of 10\,T, the degeneracy is removed at $θ_{\rm deg}\sim 3^\circ$ %angles around 3 degrees for a few low levels, specifically, …
The Casimir effect in graphene systems is reviewed with emphasis made on the large thermal correction to the Casimir force predicted at short separations between the test bodies. The computational results for the Casimir pressure and for the thermal correction are presented for both pristine graphene and real graphene sheets, which possess nonzero energy gap and chemical potential, obtained by means of exact polarization tensor. Two experiments on measuring the gradient of the Casimir force between an Au-coated sphere and graphene- coated substrates performed by using a modified atomic force m…
We study conductance and adiabatic pumped charge and spin currents in a graphene quantum pump with Corbino geometry in the presence of an applied perpendicular magnetic field. The pump is driven by the periodic and out of phase modulations of the magnetic field and an electrostatic potential applied to the ring area of the pump. We show that the Zeeman splitting, despite of its smallness, can suppress the conductance oscillations at the zero doping and in a threshold value for the flux piercing the ring area which depends on the inner lead radius and thus on the flux penetrating in it. Moreove…
We find that the Casimir pressure in peptide films deposited on metallic substrates is always repulsive which makes these films less stable. It is shown that by adding a graphene sheet on top of peptide film one can change the sign of the Casimir pressure by making it attractive. For this purpose, the formalism of the Lifshitz theory is extended to the case when the film and substrate materials are described by the frequency-dependent dielectric permittivities, whereas the response of graphene to the electromagnetic field is governed by the polarization tensor in (2+1)-dimensional space-time f…
Using a semiclassical Boltzmann transport equation (BTE) approach, we derive analytical expressions for electric and thermoelectric transport coefficients of graphene in the presence and absence of a magnetic field. Scattering due to acoustic phonons, charged impurities and vacancies are considered in the model. Seebeck ($S_{xx}$) and Nernst ($N$) coefficients have been evaluated as functions of carrier density, temperature, scatterer concentration, magnetic field and induced band gap, and the results are compared with experimental data. $S_{xx}$ is an odd function of Fermi energy while $N$ is…
We investigate the reflectance of a dielectric plate coated with a graphene sheet which possesses the nonzero energy gap and chemical potential at any temperature. The general formalism for the reflectance using the polarization tensor is presented in the framework of Dirac model. It allows calculation of the reflectivity properties for any material plate coated with real graphene sheet on the basis offirst principles of quantum electrodynamics. Numerical computations of the reflectance are performed for the graphene-coated SiO$_2$ plate at room, liquid-nitrogen, and liquid-helium temperatures…
A close study is made of the static structure factor for graphene in a magnetic field at integer filling factors nu, with focus on revealing possible signatures of "relativistic" quantum field theory in the low-energy physics of graphene. It is pointed out, in particular, that for graphene even the vacuum state has a nonzero density spectral weight, which, together with the structure factor for all nu, grows significantly with increasing wave vector; such unusual features of density correlations are a "relativistic" effect deriving from massless Dirac quasiparticles in graphene. Remarkably it …
Using the Green function formalism we calculate a current-induced spin polarization of weakly magnetized graphene with Rashba spin-orbit interaction. In a general case, all components of the current-induced spin polarization are nonzero, contrary to the nonmagnetic limit, where the only nonvanishing component of spin polarization is that in the graphene plane and normal to electric field. When the induced spin polarization is exchange-coupled to the magnetization, it exerts a spin-orbit torque on the latter. Using the Green function method we have derived some analytical formulas for the spin …
