We investigate the intrinsic linear and nonlinear ac orbital Hall (OH) conductivity in a two-dimensional system, arising from the transverse motion of electrons with finite orbital angular momentum in an applied electric field. Using the quantum kinetic approach, we show that the total OH conductivity comprises both interband and intraband contributions. However, the interband contribution dominates over the intraband in the high frequency regime. Our analysis predicts that the interband part of the linear OH conductivity is governed by the Fermi sea contribution. Meanwhile the nonlinear responses, including second harmonic and rectification effects, stem from the interplay between the Fermi sea and Fermi surface contributions. We find that the broken inversion symmetry in the system yields nonzero orbital angular momentum and consequently the orbital Hall response. In addition, the linear OH conductivity exhibits a resonant peak and a sign transition depending on the gap and Fermi energy values relative to the incident energy. Unlike the linear, the second harmonic OH conductivity shows two sign conversions as the incident energy approaches to the gap value and twice its value. These findings shed light on the modulation of field-driven orbital Hall conductivity with frequency, Fermi energy, and band gap.

To obtain the total response of the system, the effect of disorder cannot be neglected, as it introduces a new contribution (i.e., extrinsic) in the total response of the system. In the study of dynamical (AC) effects, the interband response exhibits an exotic resonance peak due to interband transitions. Herein, the dynamical interband response of the Dirac nodal line semimetal is investigated by using the quantum kinetic approach. The scattering-driven effect is analyzed under the first-order Born approximation (i.e., in the weak disorder limit) and reveals a resonance peak at (Formula presented.). In contrast, the field-driven intrinsic response peak depends on both the mass ((Formula presented.)) and chemical potential ((Formula presented.)). The results indicate that the total interband response of the 3D nodal line semimetals is mainly dominated by the disorder-induced contributions.

The anomalous Hall conductivity (AHC) in the nodal line semimetals (NLSMs) due to the presence of a symmetry-protected nodal ring adds complexity in the investigation of their transport properties. By employing quantum kinetic theory and considering the weak disorder limit, we analyze the intraband and interband parts of AHC in the tilted 3D Dirac NLSMs. Our findings reveal that the net anomalous response is mainly contributed by the interband part. Further, the latter part gives non zero results by breaking inversion symmetry via tilt. We observe that the competition between the tilt and the chemical potential emerges kinks at distinct characteristic frequencies in the intrinsic interband part of the anomalous conductivity. On the other hand, the disorder driven interband component of the conductivity exhibits a prominent peak at low chemical potential, followed by a sign change. Notably, the disorder or extrinsic contribution to the response dominates over the intrinsic interband contribution, making it a crucial factor for the study of the overall response of a three-dimensional system.

This paper extends the previous study on the electronic band structure of bilayer graphene (BG) under the influence of intrinsic spin–orbit interaction (ISOI), intralayer Rashba spin–orbit interactions (RSOI), and bias voltage (BV), where eigen values were calculated using the tight-binding (TB) approximation (van Gelderen and Smith, 2010). To better observe the effect of ISOI on band gap, we have increased its intensity beyond typical experimental values. Our results, evaluated at 200 K, 300 K, and 400 K, show that the application of BV and spin–orbit interactions significantly enhances thermoelectric performance, with the maximum electronic figure of merit reaching 0.47 when all interactions are present.

In this theoretical investigation, we analyze light-induced nonlinear spin Hall currents in a gated single-layer 1T ′ -WTe2, flowing transversely to the incident laser polarization direction. Our study encompasses the exploration of the second and third-order rectified spin Hall currents using an effective low-energy Hamiltonian and employing the Kubo’s formalism. We extend our analysis to a wide frequency range spanning both transparent and absorbing regimes, investigating the influence of light frequency below and above the optical band gap. Additionally, we investigate the influence of an out-of-plane gate potential on the system, disrupting inversion symmetry and effectively manipulating both the strength and sign of nonlinear spin Hall responses. We predict a pronounced third-order spin Hall current relative to its second-order counterpart. The predicted nonlinear spin currents show strong anisotropic dependence on the laser polarization angle. The outcomes of our study contribute to a generalized framework for nonlinear response theory within the spin channel will impact the development of emerging field of opto-spintronic.

We study the phenomenon of controlling the light by light known as the optical bistability for the two-dimensional tilted Dirac system. Using the Boltzmann approach under relaxation time approximation, we find that the optical bistability can be controlled by the nonlinear response of the system. For the prototype, we consider an inversion symmetry broken system. We find that the optical bistability associated with the nonlinear response is tunable with the strength of the tilt, gap and chemical potential. The resulting features suggest the inputs for the development of future-generation optical devices.

Using the Green’s function method, we investigate the effect of vacancies on conductance and local density of states (LDOS) in zigzag graphene nanoribbons within a symmetric and asymmetric potential wells. The results differ from ideal ribbons in that there are no conductance plateaus and a decline in conductance for varied N (number of atoms in the unit cell) and M (number of unit cells) values following vacancy incorporation. LDOS and conductance in symmetrical and asymmetrical circumstances are examined alongside vacancies and accordingly, they are affecting the respective edge states.

Nodal line semimetals, a class of topological quantum materials, exhibit a variety of novel phenomena due to their properties, such as bands touching on a one-dimensional line or a ring in the Brillouin zone and drumheadlike surface states. In addition, these semimetals are protected by the combined space-inversion and time-reversal (PT) symmetries. In this study, we investigate the longitudinal dc conductivity of the Dirac nodal line semimetals for the broken PT-symmetric system by the mass term. Here, using the quantum kinetic technique, we find the intrinsic (field-driven) and extrinsic (scattering-driven) contributions to the total dc conductivity due to interband effects. Interestingly, the resulting intrinsic conductivity is the Fermi-sea contribution, while the extrinsic stems from the Fermi-surface contribution. We show that at low chemical potential, the extrinsic part contributes more and dominates over the traditional Drude intraband term, while at the high chemical potential, the intrinsic conductivity contributes. Furthermore, the total dc response due to interband effects saturates at high chemical potential and its strength decreases with increasing mass value. Our findings suggest that the extrinsic contributions are rich enough to understand the overall feature of the response for the three-dimensional system.

The quantum kinetic framework provides a versatile method for investigating the dynamical optical and transport currents of crystalline solids. In this paper, starting from the density-matrix equations of motion, we present a general theoretical path to obtain the nonlinear optical response in an elegant and transparent manner. We devise an extensive kinetic theory that can be applied to materials with arbitrary band structures and captures intraband and interband coherence effects, finite Fermi surfaces, and disorder effects. We present a classification of the nonlinear optical currents arising from the interference of the interband and intraband components of the density matrix with distinct symmetry and quantum geometrical origin for each contribution. In this context, we report the following four primary findings: (i) The Fermi golden rule approach is insufficient to derive the correct expression for the injection current, a shortcoming that we remedy in our theory while associating the injection current with the intraband-interband contribution to the second-order density matrix. (ii) The interband-intraband contribution yields a resonant current that survives irrespective of any symmetry constraint in addition to the well-known anomalous nonlinear current (nonresonant), which requires time-reversal symmetry. (iii) Quite generally, the nonlinear current is significantly enhanced by contributions arising from the finite Fermi surface. (iv) The finite Fermi surface and Fermi sea additionally lead to sizable novel nonlinear effects via contributions we term double resonant and higher-order pole. We investigate such effects in sum frequency and difference frequency generation. As an illustration, we compute the nonlinear response of the topological antiferromagnet CuMnAs and thin film tilted Weyl semimetals as model systems dominated by interband coherence contributions. We find that the nonlinear response of CuMnAs is responsive to the direction of the finite magnetization field and the response of Weyl semimetal to the tilt. In addition, the choice of the polarization angle of the beam is crucial to have a nonlinear current in CuMnAs, while it is not the case for Weyl semimetals.

We investigate the second-order nonlinear electronic thermal transport induced by the temperature gradient. We develop the quantum kinetic theory framework to describe thermal transport in the presence of a temperature gradient. Using this, we predict an intrinsic scattering time-independent nonlinear thermal current in addition to the known extrinsic nonlinear Drude and Berry curvature dipole contributions. We show that the intrinsic thermal current is determined by the band geometric quantities and is nonzero only in systems in which both the space inversion and time-reversal symmetries are broken. We employ the developed theory to study the thermal response in tilted massive Dirac systems. We show that besides the different scattering time dependencies, the various current contributions have distinct temperature dependencies in the low-temperature limit. Our systematic and comprehensive theory for nonlinear thermal transport paves the way for future theoretical and experimental studies on intrinsic thermal responses.

Using a diagrammatic scheme, we study the acoustoelectric effects in two-dimensional (2D) hexagonal Dirac materials due to the sound-induced pseudogauge field. We analyze both uniform and spatially dispersive currents in response to copropagating and counterpropagating sound waves, respectively. In addition to the longitudinal acoustoelectric current, we obtain an exotic transverse charge current flowing perpendicular to the sound propagation direction owing to the interplay of transverse and longitudinal gauge field components jT∝ALAT∗. In contrast to the almost isotropic directional profile of the longitudinal uniform current, a highly anisotropic transverse component jT∼sin(6θ) is achieved that stems from the inherited threefold symmetry of the hexagonal lattice. However, both longitudinal and transverse parts of the dispersive current are predicted to be strongly anisotropic ∼sin2(3θ) or cos2(3θ). We quantitatively estimate the pseudogauge field contribution to the acoustoelectric current that can be probed in future experiments in graphene and other 2D hexagonal Dirac materials.

A single layer of the 1T′ phase of WTe2 provides a rich platform for exotic physical properties such as the nonlinear Hall effect and high-temperature quantum spin Hall transport. Utilizing a continuum model and the diagrammatic method, we calculate the second harmonic conductivity of monolayer 1T′-WTe2 modulated by an external vertical electric field and electron doping. We obtain a finite helicity and Faraday rotation for the second harmonic signal in response to linearly polarized incident light in the presence of time-reversal symmetry. The second harmonic signal's helicity is highly controllable by altering the bias potential and serves as an optical indicator of the nonlinear Hall current. Our study motivates future experimental investigation of the helicity spectroscopy of two-dimensional materials.

fter the publication of our paper, we became aware of a simultaneously experimental work by Zhao et al. [1], where the authors measured acoustoelectric effects and acoustically generated Hall voltage in graphene due to the sound-induced synthetic gauge fields that resemble our theoretical predictions.

Nonlinear responses are actively studied as probes of topology and band geometric properties of solids. Here, we show that second harmonic generation serves as a probe of the Berry curvature, quantum metric, and quantum geometric connection. We generalize the theory of second harmonic generation to include Fermi surface effects in metallic systems, and finite scattering timescale. In doped materials the Fermi surface and Fermi sea cause all second harmonic terms to exhibit resonances, and we identify two novel contributions to the second harmonic signal: a double resonance due to the Fermi surface and a higher-order pole due to the Fermi sea. We discuss experimental observation in the monolayer of time reversal symmetric Weyl semimetal WTe2 and the parity-time reversal symmetric topological antiferromagnet CuMnAs.

Irradiation of strong light on a material leads to numerous nonlinear effects that are essential to understand the physics of excited states of the system and optoelectronics. Here, we study the nonlinear thermoelectric effects due to the electric and thermal fields applied on a noncentrosymmetric system. The phenomenon arises on the Fermi surface with the transitions of electrons from the valence to conduction bands. We derive the formalism to investigate these effects and find that the nonlinearity in these effects, namely, nonlinear Seebeck and nonlinear Peltier effects, depends on the ratio of the nonlinear to linear conductivities. The theory is tested for a hexagonally warped and gapped topological insulator. Results show enhancement in the longitudinal and Hall effects on increasing the warping strength but show opposite behavior with the surface gap.

We demonstrate that the Berry curvature monopole of nonmagnetic two-dimensional spin-3/2 holes leads to a novel Hall effect linear in an applied in-plane magnetic field B. Remarkably, all scalar and spin-dependent disorder contributions vanish to leading order in B, while there is no Lorentz force and hence no ordinary Hall effect. This purely intrinsic phenomenon, which we term the anomalous planar Hall effect (APHE), provides a direct transport probe of the Berry curvature accessible in all p-type semiconductors. We discuss experimental setups for its measurement.

Motivated by recent experimental findings, we study the contribution of a quantum critical optical phonon branch to the thermal conductivity of a paraelectric system. We consider the proximity of the optical phonon branch to transverse acoustic phonon branch and calculate its contribution to the thermal conductivity within the Kubo formalism. We find a low temperature power law dependence of the thermal conductivity as T α , with 1 < α < 2, (lower than T 3 behavior) due to optical phonons near the quantum critical point. This result is in accord with the experimental findings and indicates the importance of quantum fluctuations in the thermal conduction in these materials.

Quantum spin Hall edges are envisaged as next-generation transistors, yet they exhibit dissipationless transport only over short distances. Here, we show that in a diffusive sample, where charge puddles with odd spin cause backscattering, a magnetic field drastically increases the mean free path and drives the system into the ballistic regime with a Landauer-Buttiker conductance. A strong nonlinear nonreciprocal current emerges in the diffusive regime with opposite signs on each edge, and vanishes in the ballistic limit. We discuss its detection in state-of-the-art experiments.

Topological edge states (TES) exhibit dissipationless transport, yet their dispersion has never been probed. Here we show that the nonlinear electrical response of ballistic TES ascertains the presence of symmetry breaking terms, such as deviations from nonlinearity and tilted spin quantization axes. The nonlinear response stems from discontinuities in the band occupation on either side of a Zeeman gap, and its direction is set by the spin orientation with respect to the Zeeman field. We determine the edge dispersion for several classes of TES and discuss experimental measurement.

The rectified non-linear response of a clean, time-reversal symmetric, undoped semiconductor to an ac electric field includes a well known intrinsic shift current. In a recent work we demonstrated that, when Kramers degeneracy is broken, a distinct second order rectified response appears due to Bloch state anomalous velocities in a system with an oscillating Fermi surface. This effect has been termed the resonant photovoltaic effect (RPE). It manifests itself as a resonant galvanic current peak at the interband absorption threshold in doped semiconductors or semimetals with approximate particle-hole symmetry. In this manuscript we present a detailed theory of this effect, and we evaluate the RPE for a model of the surface states of a magnetized topological insulator.

The rectified nonlinear response of a clean, time-reversal symmetric, undoped semiconductor to an ac electric field includes a well known intrinsic shift current. We show that when Kramers degeneracy is broken, a distinct second order rectified response appears due to Bloch state anomalous velocities in a system with an oscillating Fermi surface. This effect, which we refer to as the resonant photovoltaic effect, produces a resonant galvanic current peak at the interband absorption threshold in doped semiconductors or semimetals with approximate particle-hole symmetry. We evaluate the resonant photovoltaic effect for a model of the surface states of a magnetized topological insulator.

The Zeeman interaction is a quantum mechanical effect that underpins spin-based quantum devices such as spin qubits. Typically, identification of the Zeeman interaction needs a large out-of-plane magnetic field coupled with ultralow temperatures, which limits the practicality of spin-based devices. However, in two-dimensional (2D) semiconductor holes, the strong spin-orbit interaction causes the Zeeman interaction to couple the spin, the magnetic field, and the momentum, and has terms with different winding numbers. In this work, we demonstrate a physical mechanism by which the Zeeman terms can be detected in classical transport. The effect we predict is very strong, and tunable by means of both the density and the in-plane magnetic field. It is a direct signature of the topological properties of the 2D hole system, and a manifestation in classical transport of an effect stemming from relativistic quantum mechanics. We discuss experimental observation and implications for quantum technologies.

We report a comparative study of scattering rates which are calculated using different formalisms such as [P. B. Allen, Phys. Rev. B 3, 305 (1971); S. V. Shulga, D. V. Dolgov and E. G. Maksimov, Physica C 178, 266 (1991); B. Mitrović and M. A. Fiorucci, Phys. Rev. B 31, 2694 (1985); S. G. Sharapov and J. P. Carbotte, Phys. Rev. B 72, 134506 (2005)] and memory function formalism (MemF) [H. Mori, Prog. Theor. Phys. 33, 423 (1965)]. An advantage of this study is that it sheds light on the physical assumptions used in these formalisms. In this context, we consider a case of electron-phonon interaction and discuss frequency-and temperature-dependent behavior of scattering rates. Further, a comparative study of scattering rate proceeds for distinct phonon density of states (PDOS) and electron density of states (EDOS). From the detailed analysis, we observe that the MemF is the most general one and others are based on restrictive assumptions as discussed in this work.

We apply memory function formalism to investigate nonequilibrium electron relaxation in graphene. Within the premises of two-temperature model (TTM), explicit expressions of the imaginary part of the memory function or generalized Drude scattering rate (1/τ) are obtained. In the DC limit and in equilibrium case where electron temperature (Te) is equal to phonon temperature (T), we reproduce the known results (i.e., 1/τ T4 when T â‰BG and 1/τ T when T ≫ δBG, where δBG is the Bloch-Grüneisen temperature). We report several new results for 1/τ where TTe relevant in pump-probe spectroscopic experiments. In the finite-frequency regime we find that 1/τ ω2 when ω ωBG, and for ω = ωBG it is ω-independent. These results can be verified in a typical pump-probe experimental setting for graphene.

In this paper, we investigate the aspects of electron transport in the zigzag graphene nanoribbons (ZGNRs) using the nonequilibrium Green's function (NEGF) formalism. The latter is an esoteric tool in mesoscopic physics. It is used to perform an analysis of ZGNRs by considering potential well. Within this potential, the dependence of transmission coefficient, local density of states (LDOS) and electron transport properties on number of atoms per unit cell is discussed. It is observed that there is an increment in electron and thermal conductance with increasing number of atoms. In addition to these properties, the dependence of same is also studied in figure of merit. The results infer that the contribution of electrons to enhance the figure of merit is important above the crossover temperature.

We study the effect of the electron–phonon interaction on the finite frequency dependent electronic thermal conductivity of two dimensional graphene. We calculate it for various acoustic phonons present in graphene and characterized by different dispersion relations using the memory function approach. It is found that the electronic thermal conductivity κe(T) in the zero frequency limit follows different power law for the longitudinal/transverse and the flexural acoustic phonons. For the longitudinal/transverse phonons, κe(T)∼T−1 at the low temperature and saturates at the high temperature. These signatures qualitatively agree with the results calculated by solving the Boltzmann equation analytically and numerically. Similarly, for the flexural phonons, we find that κe(T) shows T1/2 law at the low temperature and then saturates at the high temperature. In the finite frequency regime, we observe that the real part of the electronic thermal conductivity, Re[κe(ω,T)] follows ω−2 behavior at the low frequency and becomes frequency independent at the high frequency.

We study the dynamical thermoelectric transport in metals subjected to the electron-impurity and the electron-phonon interactions using the memory function formalism. We introduce a generalized Drude form for the Seebeck coefficient in terms of thermoelectric memory function and calculate the latter in various temperature and frequency limits. In the zero frequency and high temperature limit, we find that our results are consistent with the experimental findings and with the traditional Boltzmann equation approach. In the low temperature limit, we find that the Seebeck coefficient is quadratic in temperature. In the finite frequency regime, we report new results: In the electron-phonon interaction case, we find that the Seebeck coefficient shows frequency independent behavior both in the high frequency regime (ω⪢ωD, where ωD is the Debye frequency) and in the low frequency regime (ω⪡ωD), whereas in the intermediate frequencies, it is a monotonically increasing function of frequency. In the case of the electron-impurity interaction, first it decays and then after passing through a minimum it increases with the increase in frequency and saturates at high frequencies.

The memory function formalism is an important tool to evaluate the frequency dependent electronic conductivity. It is previously used within some approximations in the case of electrons interacting with various other degrees of freedom in metals with great success. However, one needs to go beyond those approximations as the interaction strengths become stronger. In this work, we propose a systematic expansion of the memory function involving its various moments. We calculate the higher order contribution to the generalized Drude scattering rate in case of electron-impurity interactions. Further we compare our results with the results from previously studied lowest order calculations. We find larger contributions from the higher moments in the low frequency regime and also in the case of larger interaction strength.

An explicit perturbative computation of the Mori’s memory function was performed by Götzeand Wölfle (GW) to calculate generalized Drude scattering (GDS) rate for the case ofelectron-impurity and electron-phonon scattering in metals by assuming constant electronicdensity of states at the Fermi energy. In the present investigation, we go beyond thisassumption and extend the GW formalism to the case in which there is a gap around theFermi surface in electron density of states. The resulting GDS is compared with a recentone by Sharapov and Carbotte (SC) obtained through a different route. We find goodagreement between the two at finite frequencies. However, we find discrepancies in the dcscattering rate. These are due to a crucial assumption made in SC namely ω ≫ | Σ(ϵ+ ω) − Σ∗(ϵ)|. No such high frequency assumption is made in the memory functionbased technique.

The Mori's projection method, known as the memory function method, is an important theoretical formalism to study various transport coefficients. In the present work, we calculate the dynamical thermal conductivity in the case of metals using the memory function formalism. We introduce thermal memory functions for the first time and discuss the behavior of thermal conductivity in both the zero frequency limit and in the case of nonzero frequencies. We compare our results for the zero frequency case with the results obtained by the Bloch-Boltzmann kinetic approach and find that both approaches agree with each other. Motivated by some recent experimental advancements, we obtain several new results for the ac or the dynamical thermal conductivity.

Memory function formalism or projection operator technique is an extremely useful method to study the transport and optical properties of various condensed matter systems. A recent revival of its uses in various correlated electronic systems is being observed. It is being used and discussed in various contexts, ranging from nonequilibrium dynamics to the optical properties of various strongly correlated systems such as high temperature superconductors. However, a detailed discussion on this method, starting from its origin to its present day applications at one place is lacking. In this paper, we attempt a comprehensive review of the memory function approach focusing on its uses in studying the dynamics and the transport properties of correlated electronic systems.

The frequency dependent scattering rate of generalized Drude model contains important information on the electronic structure and on scattering mechanism. In the present investigation, we study the frequency dependent scattering rate of cuprates (Mitrović-Fiorucci/Sharapov-Carbotte scattering rate) in the pseudogap phase using the non-constant energy dependent Yang-Rice-Zhang (YRZ) density of states. First, with the energy dependent density of states, the scattering rate shows a depression at low energy coming from the opening of the pseudogap. Second, the evolution of 1/τ(ω,T) with temperature shows the observed increase in scattering rate with temperature at lower frequencies and the temperature independence of 1 /τ(ω) at higher frequencies. Third, the signature of the thresholds due to the boson density of states and to the electronic density of states are also observed. These signatures are qualitatively in accord with the experiments.