In a series of recent papers anomalous Hall and Nernst effects have been theoretically discussed in the non-linear regime and have seen some early success in experiments. In this paper, by utilizing the role of Berry curvature dipole, we derive the fundamental mathematical relations between the anomalous electric and thermoelectric transport coefficients in the non-linear regime. The formulae we derive replace the celebrated Wiedemann-Franz law and Mott relation of anomalous thermoelectric transport coefficients defined in the linear response regime. In addition to fundamental and testable new formulae, an important byproduct of this work is the prediction of nonlinear anomalous thermal Hall effect which can be observed in experiments.
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.
We develop a theory of Berry phase effect in anomalous transport in ferromagnets driven by statistical forces such as the gradient of temperature or chemical potential. Here a charge Hall current arises from the Berry phase correction to the orbital magnetization rather than from the anomalous velocity which does not exist in the absence of a mechanical force. A finite-temperature formula for the orbital magnetization is derived, which enables us to provide an explicit expression for the off-diagonal thermoelectric conductivity, to establish the Mott relation between the anomalous Nernst and H…
We present a microscopic theory of the magnetic quadrupole moment density $\mathcal{Q}_{ij}$ in periodic crystals with combined time reversal ($\mathcal{T}$) and inversion ($\mathcal{I}$) symmetry. We obtain a gauge-invariant expression with clear physical interpretation and demonstrate the typical behaviour of $\mathcal{Q}_{ij}$ in a minimal two-band model that hosts a tilted Dirac cone. We then show that $\mathcal{Q}_{ij}$ leads to an intrinsic nonlinear anomalous thermoelectric current. As an example, we calculate the nonlinear Nernst and Hall current in the loop-current model for cuprate s…
The spin momentum non-orthogonality in 3D topological insulators leads to modification of the spin texture and brings in an out-of-plane spin polarization component. Apart from spin texture, the anomalous thermoelectric properties of these materials are worth studying. In this paper, we have pointed out that the off resonant light used to irradiate the surface states, induces a gap, which becomes momentum dependent due to the presence of non-orthogonal terms in the Hamiltonian. Importantly, to maintain the off resonant condition of light, the momentum value should satisfy a bound. Furthermore,…
Decades of research on thermoelectrics stimulated by the fact that nano- and meso-scale thermoelectric transport could yield higher energy conversion efficiency and output power has recently uncovered a new direction on inelastic thermoelectric effects. We introduce the history, motivation, and perspectives on mesoscopic inelastic thermoelectric effects.
Anomalous thermoelectric and thermal Hall effects in irradiated altermagnets
School of Science, Jiangsu University of Science and Technology（江苏科技大学理学院）；State Key Laboratory of Quantum Functional Materials, Department of Physics, and Guangdong Basic Research Center of Excellence for Quantum Science, Southern University of Science and Technology (SUSTech)（南方科技大学量子功能材料国家重点实验室、物理系及广东省量子科学基础研究中心）；Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University（南洋理工大学物理与数学科学学院物理与应用物理系）
The thermoelectric transport coefficients are calculated in a generic lattice model of multi-Weyl semimetals with a broken time-reversal symmetry by using the Kubo's linear response theory. The contributions connected with the Berry curvature-induced electromagnetic orbital and heat magnetizations are systematically taken into account. It is shown that the thermoelectric transport is profoundly affected by the nontrivial topology of multi-Weyl semimetals. In particular, the calculation reveals a number of thermal coefficients of the topological origin which describe the anomalous Nernst and th…
Thermoelectric measurements have the potential to uncover the density of states of low-dimensional materials. Here, we present the anomalous thermoelectric behaviour of mono-layer graphene-nanowire (NW) heterostructures, showing large oscillations as a function of doping concentration. Our devices consist of InAs NW and graphene vertical heterostructures, which are electrically isolated by thin ($\sim$ 10nm) hexagonal boron nitride (hBN) layers. In contrast to conventional thermoelectric measurements, where a heater is placed on one side of a sample, we use the InAs NW (diameter $\sim 50$ nm) …
In the past decade, a new research frontier emerges at the interface between physics and renewable energy, termed as the inelastic thermoelectric effects where inelastic transport processes play a key role. The study of inelastic thermoelectric effects broadens our understanding of thermoelectric phenomena and provides new routes towards high-performance thermoelectric energy conversion. Here, we review the main progress in this field, with a particular focus on inelastic thermoelectric effects induced by the electron-phonon and electron-photon interactions. We introduce the motivations, the b…
Improving the thermoelectric figure of merit zT is one of the greatest challenges in material science. Recent discovery of topological insulators (TIs) offers new promise in this prospect. In this work, we demonstrate theoretically that zT is strongly size dependent in TI, and the size parameter can be tuned to enhance zT to be significantly greater than 1. Furthermore, we show that the life time of the edge states in TI is strongly energy dependent, leading to large and anomalous Seebeck effects with an opposite sign to the Hall effect. These striking properties make TIs the promising materia…
We study thermoelectric transport through double quantum dots system with spin-dependent interdot coupling and ferromagnetic electrodes by means of the non-equilibrium Green function in the linear response regime. It is found that the thermoelectric coefficients are strongly dependent on the splitting of interdot coupling, the relative magnetic configurations and the spin polarization of leads. In particular, the thermoelectric efficiency can achieve considerable value in parallel configuration when the effective interdot coupling and tunnel coupling between QDs and the leads for spin-down ele…
We study the effects caused by Rashba and Dresselhaus spin-orbit coupling over the thermoelectric transport properties of a single-electron transistor, viz., a quantum dot connected to one-dimensional leads. Using linear response theory and employing the numerical renormalization group method, we calculate the thermopower, electrical and thermal conductances, dimensionless thermoelectric figure of merit, and study the Wiedemann-Franz law, showing their temperature maps. Our results for all those properties indicate that spin-orbit coupling drives the system into the Kondo regime. We show that …
Nonlinear transport coefficients do not obey, in general, reciprocity relations. We here discuss the magnetic-field asymmetries that arise in thermoelectric and heat transport of mesoscopic systems. Based on a scattering theory of weakly nonlinear transport, we analyze the leading-order symmetry parameters in terms of the screening potential response to either voltage or temperature shifts. We apply our general results to a quantum Hall antidot system. Interestingly, we find that certain symmetry parameters show a dependence on the measurement configuration.
We study features of the thermoelectric transport through a Kitaev chain hosting Majorana bound states (MBS) at its ends. We describe the behavior of the Seebeck coefficient and the ZT figure of merit for two different configurations between MBS and normal current leads. We find an important violation of the Wiedemann-Franz law in one of these geometries, leading to sizeable values of the thermoelectric efficiency over a narrow window in chemical potential away from neutrality. These findings could lead to interesting thermoelectric-based MBSs detection devices, via measurements of the Seebeck…
The transport and thermoelectric properties of the interface between SrTiO$_3$ and a 26-monolayer thick LaAlO$_3$-layer grown at high oxygen-pressure have been investigated at temperatures from 4.2 K to 100 K and in magnetic fields up to 18 T. For $T>$ 4.2 K, two different electron-like charge carriers originating from two electron channels which contribute to transport are observed. We probe the contributions of a degenerate and a non-degenerate band to the thermoelectric power and develop a consistent model to describe the temperature dependence of the thermoelectric tensor. Anomalies in the…
We investigate the thermopower of a metal-molecule-metal junction taking into account thermal effects on the junction. Based on analytical expressions and numerical simulations we show that the thermoelectric potential reveals valuable information on the mechanisms controlling the electron transfer process, including coherent transmission and thermalized hopping. We also show that at high temperatures the position of the Fermi energy relative to the molecular states can be easily deduced from the thermoelectric potential. Standard current-voltage measurements are insensitive to this informatio…
Symmetry relations are manifestations of fundamental principles and constitute cornerstones of modern physics. An example are the Onsager relations between coefficients connecting thermodynamic fluxes and forces, central to transport theory and experiments. Initially formulated for classical systems, these reciprocity relations are also fulfilled in quantum conductors. Surprisingly, novel relations have been predicted specifically for thermoelectric transport. However, whereas these thermoelectric reciprocity relations have to date not been verified, they have been predicted to be sensitive to…
The Landauer approach to diffusive transport is mathematically related to the solution of the Boltzmann transport equation, and expressions for the thermoelectric parameters in both formalisms are presented. Quantum mechanical and semiclassical techniques to obtain from a full description of the bandstructure, E(k), the number of conducting channels in the Landauer approach or the transport distribution in the Boltzmann solution are developed and compared. Thermoelectric transport coefficients are evaluated from an atomistic level, full band description of a crystal. Several example calculatio…
The thermoelectric transport through a molecular bridge is discussed, with an emphasis on the effects of inelastic processes of the transport electrons caused by the coupling to the vibrational modes of the molecule. In particular it is found that when the molecule is strongly coupled to a thermal bath of its own, which may be at a temperature different from those of the electronic reservoirs, a heat current between the molecule and the electrons can be converted into electric current. Expressions for the transport coefficients governing this conversion and similar ones are derived, and a poss…
We investigate the influence of a quantized photon field on thermoelectric transport of electrons through a quantum wire embedded in a photon cavity. The quantum wire is connected to two electron reservoirs at different temperatures leading to a generation of a thermoelectric current. The transient thermoelectric current strongly depends on the photon energy and the number of photons initially in the cavity. Two different regimes are studied, off-resonant and resonant polarized fields, with photon energy smaller than, or equal to the energy spacing between some of the lowest states in the quan…
We numerically study the disorder effect on the thermoelectric and thermal transport for bilayer graphene under a strong perpendicular magnetic field. In the unbiased case, we find that the thermoelectric transport has similar properties as in the monolayer graphene, i.e., the Nernst signal has a peak at the central Landau level (LL) with the value of the order of $k_B/e$ and changes sign near other LLs while the thermopower has an opposite behavior. We attribute this to the coexistence of particle and hole LLs around the Dirac point. When a finite interlayer bias is applied and a band gap is …
A two-site nanostructure (e.g, a "molecule") bridging two conducting leads and connected to a phonon bath is considered. The two relevant levels closest to the Fermi energy are connected each to its lead. The leads have slightly different temperatures and chemical potentials and the nanos- tructure is also coupled to a thermal (third) phonon bath. The 3 x 3 linear transport ("Onsager") matrix is evaluated, along with the ensuing new figure of merit, and found to be very favorable for thermoelectric energy conversion.
In the present work, we theoretically analyze the steady-state thermoelectric transport through a single-molecule junction with a vibrating bridge. Thermally induced charge current in the system is explored using a nonequilibrium Green's functions formalism. We study combined effects of Coulomb interactions between charge carriers on the bridge and electron-phonon interactions on the thermocurrent beyond the linear response regime. It is shown that electron-vibron interactions may significantly affect both magnitude and direction of the thermocurrent, and vibrational signatures may appear.
We study thermoelectric transport through a coherent molecular conductor connected to two electron and two phonon baths using the nonequilibrium Green's function method. We focus on the mutual drag between electron and phonon transport as a result of `momentum' transfer, which happens only when there are at least two phonon degrees of freedom. After deriving expressions for the linear drag coefficients, obeying the Onsager relation, we further investigate their effect on nonequilibrium transport. We show that the drag effect is closely related to two other phenomena: (1) adiabatic charge pumpi…
Several small-bandgap semiconductors are now known to have protected metallic surface states as a consequence of the topology of the bulk electron wavefunctions. The known "topological insulators" with this behavior include the important thermoelectric materials Bi_2Te_3 and Bi_2Se_3, whose surfaces are observed in photoemission experiments to have an unusual electronic structure with a single Dirac cone. We study in-plane (i.e., horizontal) transport in thin films made of these materials. The surface states from top and bottom surfaces hybridize, and conventional diffusive transport predicts …
We investigate spin-dependent thermoelectric transport through a system of two coupled quantum dots attached to reservoirs of spin-polarized electrons. Generally, we focus on the strongly correlated regime of transport. To this end, a slave-boson method for finite $U$ is employed. Our main goal is to show that, apart from complex low-temperature physics, such a basic multilevel system provides a possibility to examine various quantum interference effects, with particular emphasis put on the influence of such phenomena on thermoelectric transport. Apart from the influence of interference effect…
Thermoelectric effects are more sensitive and promising probes to topological properties of emergent materials, but much less addressed compared to other physical properties. Zirconium pentatelluride (ZrTe$_{5}$) has inspired active investigations recently because of its multiple topological nature. We study the thermoelectric effects of ZrTe$_{5}$ in a magnetic field and find several anomalous behaviors. The Nernst response has a steplike profile near zero field when the charge carriers are electrons only, suggesting the anomalous Nernst effect arising from a nontrivial profile of Berry curva…
We show that coherent electron transport through zero-dimensional systems can be used to tailor the shape of the system's transmission function. This quantum-engineering approach can be used to enhance the performance of quantum dots or molecules in thermal-to-electric power conversion. Specifically, we show that electron interference in a two-level system can substantially improve the maximum thermoelectric power and the efficiency at maximum power by suppressing parasitic charge flow near the Fermi energy, and by reducing electronic heat conduction. We discuss possible realizations of this a…
The conductance and thermoelectric power (TEP) of graphene is simultaneously measured using microfabricated heater and thermometer electrodes. The sign of the TEP changes across the charge neutrality point as the majority carrier density switches from electron to hole. The gate dependent conductance and TEP exhibit a quantitative agreement with the semiclassical Mott relation. In the quantum Hall regime at high magnetic field, quantized thermopower and Nernst signals are observed and are also in agreement with the generalized Mott relation, except for strong deviations near the charge neutrali…
Quantum dots are useful model systems for studying quantum thermoelectric behavior because of their highly energy-dependent electron transport properties, which are tunable by electrostatic gating. As a result of this strong energy dependence, the thermoelectric response of quantum dots is expected to be nonlinear with respect to an applied thermal bias. However, until now this effect has been challenging to observe because, first, it is experimentally difficult to apply a sufficiently large thermal bias at the nanoscale and, second, it is difficult to distinguish thermal bias effects from pur…
We investigate thermoelectric efficiency of systems with broken time reversal symmetry under a three-terminal transport. Using a model of Aharonov-Bohm interferometer formed with three noninteracting quantum dots, we show that Carnot efficiency can be achieved when the thermopower is a symmetric function of the applied magnetic field. On the other hand, the maximal value of the efficiency at maximum power is obtained for asymmetric thermopower. Indeed, we show that Curzon-Ahlborn limit is exceeded within the linear response regime in our model. Moreover, we investigate thermoelectric efficienc…
The thermoelectric response of 80-nm-thick strained HgTe films of a three-dimensional topological insulator (3D TI) has been studied experimentally. An ambipolar thermopower is observed where the Fermi energy moves from conducting to the valence bulk band. The comparison between theory and experiment shows that the thermopower is mostly due to the phonon drag contribution. In the region where the 2D Dirac electrons coexist with bulk hole states, the Seebeck coefficient is modified due to 2D electron - 3D hole scattering.
We study nonlinear transport effects on the maximum efficiency and power for both inelastic and elastic thermoelectric generators. The former refers to phonon-assisted hopping in double quantum-dots, while the latter is represented by elastic tunneling through a single quantum-dot. We find that nonlinear thermoelectric transport can lead to enhanced efficiency and power for both types of devices. A comprehensive survey of various quantum-dot energy, temperature, and parasitic heat conduction reveals that the nonlinear transport induced improvements of the maximum efficiency and power are overa…
We investigate the thermoelectric properties of a T-shaped double quantum dot system described by a generalized Anderson Hamiltonian. The system's electrical conduction (G) and the fundamental thermoelectric parameters such as the Seebeck coefficient ($S$) and the thermal conductivity ($κ$), along with the system's thermoelectric figure of merit (ZT) are numerically estimated based on a Green's function formalism that includes contributions up to the Hartree-Fock level. Our results account for finite onsite Coulomb interaction terms in both component quantum dots and discuss various ways leadi…
We present first principles study of thermoelectric transport properties of sandwiched heterostructure of Graphene (G)/hexagonal Boron Nitride (BN)/G, based on Boltzmann transport theory for band electrons using the bandstructure calculated from the Density Functional Theory (DFT) based plane-wave method. Calculations were carried out for three, four and five BN layers sandwiched between Graphene layers with three different arrangements to obtain the Seebeck coefficient and Power factor in $T\sim 25-400$K range. Moreover, using Molecular Dynamics (MD) simulations with very large simulation cel…
Nonreciprocal transport phenomena indicate that the forward and backward flows differ, and are attributed to broken inversion symmetry. In this paper, we study the nonreciprocity of a thermal and thermoelectric transport of electronic systems resulting from inversion-symmetry-broken crystal structures. The nonlinear electric, thermoelectric, and thermal conductivities are derived up to the second order in an electric field and a temperature gradient by using the Boltzmann equation with the relaxation time approximation. All the second-order conductivities appearing in this paper are described …
Thermoelectric properties of a model Skyrmion crystal were theoretically investigated, and it was found that its large anomalous Hall conductivity, corresponding to large Chern numbers induced by its peculiar spin structure leads to a large transverse thermoelectric voltage through the anomalous Nernst effect. This implies the possibility of finding good thermoelectric materials among Skyrmion systems, and thus motivates our quests for them by means of the first-principles calculations as were employed here.
We investigate nonlinear transport properties of quantum conductors in response to both electrical and thermal driving forces. Within scattering approach, we determine the nonequilibrium screening potential of a generic mesoscopic system and find that its response is dictated by particle and entropic injectivities which describe the charge and entropy transfer during transport. We illustrate our model analyzing the voltage and thermal rectification of a resonant tunneling barrier. Importantly, we discuss interaction induced contributions to the thermopower in the presence of large temperature …
We consider thermoelectric transport properties of the edge states of a two dimensional topological insulator in a double quantum point contact geometry coupled to two thermally biased reservoirs. Both spin-preserving and spin-flipping tunneling processes between opposite edges are analyzed in the presence of electron-electron interactions. We demonstrate that the simultaneous presence of spin-flipping processes and interactions gives rise to a finite longitudinal spin current. Moreover, its sign and amplitude can be tuned by means of gate voltages with the possibility to generate a pure spin …
We perform an analytic calculation of thermoelectric transport coefficients for massless Dirac electrons using the approach based on the Kubo--Středa formula and generalized Mott's relation. The main focus of the letter is made on the properties of the Nernst coefficient in the vicinity of the Dirac point in quantum limit. We calculate magnetic field and temperature dependencies of the Nernst coefficient and compare our results with recent experiments in $α$-(BEDT-TTF)$_{2}$I$_{3}$ organic conductor. We argue that the Zeeman splitting is important to understand the experimental data at high ma…
In this note we summarize our recent results for the temperature dependence of transport coefficients of metallic films in the presence of spin-orbit coupling. Our focus is on (i) the spin Nernst and the thermal Edelstein effects, and (ii) the phonon skew scattering contribution to the spin Hall conductivity, which is relevant for the temperature dependence of the spin Hall angle. Depending on the parameters, the latter is expected to show a non-monotonous behavior.
We review some of our recent experimental studies on low-carrier concentration, mesoscopic two-dimensional electron gases (m2DEGs). The m2DEGs show a range of striking characteristics including a complete avoidance of the strongly localised regime even when the electrical resistivity $ρ>> h/e^2$, giant thermoelectric response, and an apparent decoupling of charge and thermoelectric transport. We analyse the results and demonstrate that these observations can be explained based on the assumption that the charge carriers retain phase coherence over the m2DEG dimensions. Intriguingly, this would …
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.
The possibility of electrically exciting and detecting magnon currents in magnetic insulators has opened exciting perspectives for transporting spin information in electronic devices. However, the role of the magnetic field and the nonlocal thermal gradients on the magnon transport remain unclear. Here, by performing nonlocal harmonic voltage measurements, we investigate magnon transport in perpendicularly magnetized ultrathin Tm3Fe5O12 (TmIG) films coupled to Pt electrodes. We show that the first harmonic nonlocal voltage captures spin-driven magnon transport in TmIG, as expected, and the sec…
We have simultaneously measured conductance and thermoelectric power (TEP) of individual silicon and germanium/silicon core/shell nanowires in the field effect transistor device configuration. As the applied gate voltage changes, the TEP shows distinctly different behaviors while the electrical conductance exhibits the turn-off, subthreshold, and saturation regimes respectively. At room temperature, peak TEP value of $\sim 300 μ$V/K is observed in the subthreshold regime of the Si devices. The temperature dependence of the saturated TEP values are used to estimate the carrier doping of Si nano…
We present a comprehensive study of thermoelectric transport properties of a quantum nanoelectromechanical system (NEMS) described by a single-electron-transistor (SET) coupled to a quantum nanomechanical resonator (NR). The effects of a quantum NR on the electronic current are investigated with special emphasis on how the SET-NR coupling strength plays a role in such a NEMS. We find that the SET-NR coupling is not only able to suppress or enhance the thermoelectric current but can also switch its direction. The effect of the NR on the thermoelectric coefficients of the SET are studied and we …
Within the semiclassical Boltzmann transport theory, the formula for Seebeck coefficient $S$ is derived for an isotropic two-dimensional electron gas (2DEG) system that exhibits anomalous Hall effect (AHE) and anomalous Nernst effect (ANE) originating from Berry curvature on their bands. Deviation of $S$ from the value $S_0$ estimated neglecting Berry curvarture is computed for a special case of 2DEG with Zeeman and Rashba terms. The result shows that, under certain conditions the contribution of Berry curvature to Seebeck effect could be non-negligible. Further study is needed to clarify the …
We discuss the temperature-dependent thermoelectric transport properties of semiconductor nanostructures comprising a quantum dot coupled to quantum wires: the thermal dependence of the electrical conductance, thermal conductance, and thermopower. We explore the universality of the thermoelectric properties in the temperature range associated with the Kondo crossover. In this thermal range, general arguments indicate that any equilibrium property's temperature dependence should be a universal function of the ratio $T^{*}=T/T_{K}$, where $T_{K}$ is the Kondo temperature. Considering the particl…
