We consider a quantum Hall system with an antidot acting as an energy dependent scatterer. In the purely charge case, we find deviations from the Wiedemann-Franz law that take place in the nonlinear regime of transport. We also discuss Peltier effects beyond linear response and describe both effects using magnetic-field asymmetric transport coefficients. For the spin case such as that arising along the helical edge states of a two-dimensional topological insulator, we investigate the generation of spin currents as a result of applied voltage and temperature differences in samples attached to ferromagnetic leads. We find that in the parallel configuration the spin current can be tuned with the leads' polarization even in the linear regime of transport. In contrast, for antiparallel magnetizations the spin currents has a strict nonlinear dependence on the applied fields.
The thermoelectric properties of a three-terminal quantum Hall conductor are investigated. We identify a contribution to the thermoelectric response that relies on the chirality of the carrier motion rather than on spatial asymmetries. The Onsager matrix becomes maximally asymmetric with configurations where either the Seebeck or the Peltier coefficients are zero while the other one remains finite. Reversing the magnetic field direction exchanges these effects, which originate from the chiral nature of the quantum Hall edge states. The possibility to generate spin-polarized currents in quantum…
The possibility of using quantum Hall systems for thermoelectric energy conversion is investigated. It is shown that the massive degeneracy and the metallicity of a partially-filled Landau level enable thermoelectric cooling and power generation with unprecedented efficiency at low temperature. The figure of merit is explicitly derived for a transverse thermoelectric device using the $ν=0$ quantum Hall state of Dirac materials at charge neutrality, where due to electron-hole symmetry electrical Hall effect vanishes but thermoelectric Hall effect peaks.
A three-terminal conductor presents peculiar thermoelectric and thermal properties in the quantum Hall regime: it can behave as a symmetric rectifier and as an ideal thermal diode. These properties rely on the coherent propagation along chiral edge channels. We investigate the effect of breaking the coherent propagation by the introduction of a probe terminal. It is shown that chiral effects not only survive the presence of incoherence but they can even improve the thermoelectric performance in the totally incoherent regime.
We study the linear thermoelectric response of a quantum dot embedded in a constriction of a quantum Hall bar with fractional filling factors nu=1/m within Laughlin series. We calculate the figure of merit ZT for the maximum efficiency at a fixed temperature difference. We find a significant enhancement of this quantity in the fractional filling in relation to the integer-filling case, which is a direct consequence of the fractionalization of the electron in the fractional quantum Hall state. We present simple theoretical expressions for the Onsager coefficients at low temperatures, which expl…
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）
We study the thermoelectric properties of a Kramers pair of helical edge states of the quantum spin Hall effect coupled to a nanomagnet with a component of the magnetization perpendicular to the direction of the spin-orbit interaction of the host. We show that the transmission function of this structure has the desired qualities for optimal thermoelectric performance in the quantum coherent regime. For a single magnetic domain there is a power generation close to the optimal bound. In a configuration with two magnetic domains with different orientations, pronounced peaks in the transmission fu…
In this paper, we present the theoretical predication of a thermospin Hall effect, in which a transverse spin current can be generated in semiconductors in the presence of spin-orbit coupling by a frequency-dependent longitudinal temperature gradient. Because of the thermoelectric effect, there is no net charge current but there is a heat flow from the hot side to the cold side. We perform the theoretical calculation of dynamical thermospin Hall conductivity in a two-dimensional Rashba spintronic system. It has been shown that the direct interband optical transition dominates the ordering and …
We have considered the response at two energies corresponding to two plateaus in the quantum Hall effect. Since the thermoelectric power involves the derivative of conductivity with respect to energy, we introduce the concept of a line width and hence an activation energy. We then use the Hall conductivity to define the thermoelectric power at the centre of two plateaus, which is found to vary monotonically as T^2 at low temperatures with fixed magnetic field. At elivated temperatures, the thermoelectric power varies as T(exp-Δ/k_BT).
Detailed measurements of the longitudinal thermopower of two-dimensional electrons in the first excited Landau level are reported. Clear signatures of numerous fractional quantized Hall states, including those at $ν= 5/2$ and 7/3, are observed in the magnetic field and temperature dependence of the thermopower. An abrupt collapse of the thermopower is observed below about $T= 40$ mK at those filling factors where re-entrant insulating electronic states have been observed in conventional resistive transport studies. The thermopower observed at $ν= 5/2$ is discussed in the context of recent theo…
Interference represents one of the most striking manifestation of quantum physics in low-dimensional systems. Despite evidences of quantum interference in charge transport have been known for a long time, only recently signatures of interference induced thermal properties have been reported, paving the way for the phase-coherent manipulation of heat in mesoscopic devices. In this work we show that anomalous thermoelectric properties and efficient heat rectification can be achieved by exploiting the phase-coherent edge states of quantum Hall systems. By considering a tunneling geometry with mul…
The high-magnetic-field thermoelectric effect in nodal-line semimetals with straight nodal lines was investigated. Three-dimensional (3D) Dirac/Weyl semimetals exhibit constant thermoelectric Hall conductivity at the high-magnetic-field quantum limit, resulting in a boundless linear increase of Seebeck coefficient. This is known as the quantized thermoelectric Hall effect (QTHE), and is expected to lead to high-performance thermoelectricity at low temperatures. Here, in addition to Dirac/Weyl semimetals, we demonstrated that 3D semimetals with straight nodal lines can also exhibit the QTHE und…
Thermoelectric transport of two-dimensional quantum spin Hall systems are theoretically studied in narrow ribbon geometry. We find that at high temperature electrons in the bulk states dominate. By lowering temperature, the "perfectly conducting" edge channels becomes dominant, and a bulk-to-edge crossover occurs. Correspondingly, by lowering temperature, the figure of merit first decreases and then will increase again due to edge-state-dominated thermoelectric transport.
Thermoelectrics are promising by directly generating electricity from waste heat. However, (sub-)room-temperature thermoelectrics have been a long-standing challenge due to vanishing electronic entropy at low temperatures. Topological materials offer a new avenue for energy harvesting applications. Recent theories predicted that topological semimetals at the quantum limit can lead to a large, non-saturating thermopower and a quantized thermoelectric Hall conductivity approaching a universal value. Here, we experimentally demonstrate the non-saturating thermopower and quantized thermoelectric H…
Heat transport in the quantum Hall regime is investigated using micron-scale heaters and thermometers positioned along the edge of a millimeter-scale two dimensional electron system (2DES). The heaters rely on localized current injection into the 2DES, while the thermometers are based on the thermoelectric effect. In the $ν= 1$ integer quantized Hall state, a thermoelectric signal appears at an edge thermometer only when it is "downstream," in the sense of electronic edge transport, from the heater. When the distance between the heater and the thermometer is increased, the thermoelectric signa…
We study thermoelectric transport properties of fractional quantum Hall systems based on exact diagonalization calculation. Based on the relation between thermoelectric response and thermal entropy, we demonstrate that thermoelectric Hall conductivity $α_{xy}$ has powerlaw scaling $α_{xy} \propto T^η$ for gapless composite Fermi-liquid states at filling number $ν=1/2$ and $1/4$ at low temperature ($T$), with exponent $η\sim 0.5$ distinctly different from Fermi liquids. The powerlaw scaling remains unchanged for different forms of interaction including Coulomb and short-range ones, demonstratin…
We performed electric and thermoelectric transport measurements of bilayer graphene in a magnetic field up to 15 Tesla. The transverse thermoelectric conductivity $\rmα_{xy}$, determined from four transport coefficients, attains a peak value of $\rmα_{xy, peak}$ whenever chemical potential lies in the center of a Landau level. The temperature dependence of $\rmα_{xy, peak}$ is dictated by the disorder width $\rm W_L$. For $\rm k_BT/W_L\leq$0.2, $\rmα_{xy, peak}$ is nominally linear in temperature, which gives $\rmα_{xy,peak}/T=0.19 \pm 0.03 n A/K^2$ independent of the magnetic field, temperatu…
For the fractional quantum Hall states on a finite disc, we study the thermoelectric transport properties under the influence of an edge and its reconstruction. In a recent study on a torus [Phys. Rev. B 101, 241101 (2020)], Sheng and Fu found a universal non-Fermi liquid power-law scaling of the thermoelectric conductivity $α_{xy} \propto T^η$ for the gapless composite Fermi-liquid state. The exponent $η\sim 0.5$ appears an independence of the filling factors and the details of the interactions. In the presence of an edge, we find the properties of the edge spectrum dominants the low-temperat…
The thermoelectric Hall effect is the generation of a transverse heat current upon applying an electric field in the presence of a magnetic field. Here we demonstrate that the thermoelectric Hall conductivity $α_{xy}$ in the three-dimensional Dirac semimetal ZrTe$_5$ acquires a robust plateau in the extreme quantum limit of magnetic field. The plateau value is independent of the field strength, disorder strength, carrier concentration, or carrier sign. We explain this plateau theoretically and show that it is a unique signature of three-dimensional Dirac or Weyl electrons in the extreme quantu…
We measure the thermoelectric response of Corbino structures in the quantum Hall effect regime and compare it with a theoretical analysis. The measured thermoelectric voltages are qualitatively and quantitatively simulated based upon the independent measurement of the conductivity indicating that they originate predominantly from the electron diffusion. Electron-phonon interaction does not lead to a phonon-drag contribution in contrast to earlier Hall-bar experiments. This implies a description of the Onsager coefficients on the basis of a single transmission function, from which both thermovo…
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.
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…
We have investigated the spatial distribution of the electron temperature generated in a two-dimensional electron system (2DES) subjected to a perpendicular magnetic field. We measure thermoelectric voltages between Ohmic contacts located at the end of the voltage-probe arms of a Hall bar fabricated from a GaAs/AlGaAs 2DES wafer, immersed in the mixing chamber of a dilution refrigerator held at 20 mK. Magneto-oscillations due to the Landau quantization are examined for the thermoelectric voltages between the contact pairs straddling the main bar (arrangement to measure the transverse component…
The thermoelectric properties of a three terminal quantum spin Hall (QSH) sample are examined. Inherent helicity of the QSH sample helps to generate a large charge power efficiently. Along with charge the system can be designed to work as a highly efficient spin heat engine too. The advantage of a helical over a chiral sample is that, while a multiterminal quantum Hall sample can only work as a quantum heat engine due to broken time reversal(TR) symmetry, a multiterminal QSH system can work effectively both as a charge/spin heat engine as well as a charge/spin refrigerator as TR symmetry is pr…
We investigate thermoelectric transport through interfaces with inelastic scatterings by developing a quantum theory, which has been extensively validated by existing theories. We find that under temperature bias, while a two-terminal conductor-insulator interface behaves only as a thermal resistor, a three-terminal conductor-insulator-conductor interface can function as an electricity generator caused by phonon-mediated electron scatterings with heat-charge current separation. Unlike conventional thermoelectrics which is a property of a bulk caused by the Seebeck effect, this thermoelectric b…
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…
The quantum Hall effect in a 2D electron system expresses a topological invariant, leading to a quantized conductivity. The thermal Hall and thermoelectric Nernst conductances in two dimensions are also reported to be quantized in specific systems. However, a comprehensive study of these quantities within one formalism for quantum Hall systems is so far elusive. In this work, we investigate the Hall, thermal Hall, and Nernst effects analytically and numerically in 2D and 3D. In addition to the quantized values for the Hall and thermal Hall conductances in two dimensions, we also find quasi-qua…
We calculate the thermoelectric response coefficients of three-dimensional Dirac or Weyl semimetals as a function of magnetic field, temperature, and Fermi energy. We focus in particular on the thermoelectric Hall coefficient $α_{xy}$ and the Seebeck coefficient $S_{xx}$, which are well-defined even in the dissipationless limit. We contrast the behaviors of $α_{xy}$ and $S_{xx}$ with those of traditional Schrödinger particle systems, such as doped semiconductors. Strikingly, we find that for Dirac materials $α_{xy}$ acquires a constant, quantized value at sufficiently large magnetic field, whi…
Using the conformal field theory approach to the thermoelectric characteristics of fractional quantum Hall states, previously developed in Nucl. Phys. B 894 (2015) 284, we show that the thermoelectric power factor of Coulomb-blockaded islands, realized by point contacts in Fabry--Pérot interferometers in the $\mathbb{Z}_k$ parafermion Hall states, could give reliable signatures for distinguishing the topological orders of different quantum Hall states having identical electric properties. For example, while the conductance peak patterns in the Coulomb blockade regime for such states are practi…
The ν=5/2 anti-Pfaffian state and the ν=2/3 state are believed to have an edge composed of counter-propagating charge and neutral modes. This situation allows the generation of a pure thermal bias between two composite edge states across a quantum point contact (QPC) as was experimentally established in Nature 466, 585 (2010). We show that replacing the QPC by a quantum dot provides a natural way for detecting the neutral modes via the finite current generated by the thermoelectric response of the dot. We also show that the degeneracies of the dot spectrum, dictated by the conformal field theo…
We show that it is possible and rather efficient to compute at non-zero temperature the thermoelectric characteristics of Coulomb blockaded fractional quantum Hall islands, formed by two quantum point contacts inside of a Fabry-Perot interferometer, using the conformal field theory partition functions for the chiral edge excitations. The oscillations of the thermopower with the variation of the gate voltage as well as the corresponding figure-of-merit and power factors, provide finer spectroscopic tools which are sensitive to the neutral multiplicities in the partition functions and could be u…
We investigate the thermoelectric properties of electrons at the interface of oxide heterostructure and in the presence of a multiferroic oxide with spiral spin order. We find there is no (spin) Hall current generated by the temperature gradient. A Seebeck effect is however present. Due to the magnetoelectric coupling, the charge and thermal conductivities are electrically controllable via the spin spiral helicity. Moreover, the thermopower exhibits a sign change when tuning electro-statically the carrier density.
We consider a Josephson junction hosting a Kramers pair of helical edge states of a quantum spin Hall bar in contact with a normal-metal probe. In this hybrid system, the orbital phase induced by a small magnetic field threading the junction known as Doppler shift (DS), combines with the conventional Josephson phase difference and originates an effect akin to a Zeeman field in the spectrum. As a consequence, when a temperature bias is applied to the superconducting terminals, a thermoelectric current is established in the normal probe. We argue that this purely non-local thermoelectric effect …
Using the explicit rational conformal field theory partition functions for the ${\mathbb Z}_k$ parafermion quantum Hall states on a disk we compute numerically the thermoelectric power factor for Coulomb-blockaded islands at finite temperature. We demonstrate that the power factor is rather sensitive to the neutral degrees of freedom and could eventually be used to distinguish experimentally between different quantum Hall states having identical electric properties. This might help us to confirm whether non-Abelian quasiparticles, such as the Fibonacci anyons, are indeed present in the experim…
We analyze the thermoelectric cooling properties of a Corbino device in the quantum Hall regime on the basis of experimental data of electrical conductance. We focus on the cooling power and the coefficient of performance within and beyond linear response. Thermovoltage measurements in this device reported in {\em Phys. Rev. Applied, {\bf 14} 034019 (2020)} indicated that the transport takes place in the diffusive regime, without signatures of effects due to the electron-phonon interaction in a wide range of temperatures and filling factors. In this regime, the heat and charge currents by elec…
Hamiltonian systems can be classified into ten classes, in terms of the presence or absence of time-reversal symmetry, particle-hole symmetry and sublattice/chiral symmetry. We construct a quantum coherent scattering theory of linear transport for coupled electric, heat and spin transport; including the effect of Andreev reflection from superconductors. We derive a complete list of the Onsager reciprocity relations between transport coefficients for coupled electric, spin, thermoelectric and spin caloritronic effects. We apply these to all ten symmetry classes, paying special attention to spec…
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…
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.
The mechanism of the anomalous Hall transport phenomena, if it is of the intrinsic or extrinsic origin, has been controversial. We present a unified theory of them for ferromagnetic metals with dilute impurities at the zero temperature, in terms of a quantum transport theory with the self-consistent T-matrix approximation. With the Fermi energy E_F and the spin-orbit interaction energy E_{SO} being fixed (E_F > E_{SO}), three regimes are found as a function of the scattering rate \hbar/τ. (i) In the superclean case \hbar/τ< u_{imp} E_{SO}D, the skew scattering from the vertex correction domina…
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…
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…
Considering metallic films at room temperature, we present the first theoretical study of the spin Nernst and thermal Edelstein effects which takes into account dynamical spin-orbit coupling, i.e., direct spin-orbit coupling with the vibrating lattice (phonons) and impurities. This gives rise to two novel processes, namely a dynamical Elliott-Yafet spin relaxation and a dynamical side-jump mechanism. Both are the high-temperature counterparts of the well-known $T = 0$ Elliott-Yafet and side-jump, central to the current understanding of the spin Hall, spin Nernst and Edelstein effects at low $T…
Application of sufficient lateral current to a heavy metal (HM) can switch the perpendicular magnetization orientation of adjacent ferromagnetic layer (FM) through spin-orbit torques (SOTs). The choice of the HM and its arrangement plays a major role for the SOT induced magnetization switching in magnetic heterostructures. Here, in asymmetric Pt/Co/Pt heterostructures, anti-damping (AD) SOT prevails. Ta addition to this stack (Ta/Pt/Co/Pt) give rise to several compelling effects viz. competing spin currents (due to opposite spin-Hall angles of adjacent Ta and Pt layers), significant AD-SOT, th…
We compute the intrinsic contributions to the Berry-phase mediated anomalous Hall and Nernst effects in electron- and hole-doped semiconductors in the presence of an in-plane magnetic field as well as Rashba and Dresselhaus spin orbit couplings. For both systems we find that the regime of chemical potential which supports the topological superconducting state in the presence of superconducting proximity effect can be characterized by plateaus in the topological Hall and Nernst coefficients flanked by well-defined peaks marking the emergence of the topological regime. The plateaus arise from a …
We establish a theory of optimal efficiency and power for three-terminal thermoelectric engines which have two independent output electric currents and one input heat current. This set-up goes beyond the conventional heat engines with only one output electric current. For such a set-up, we derive the optimal efficiency and power and their trade-off for three-terminal heat engines with and without time-reversal symmetry. The formalism goes beyond the known optimal efficiency and power for systems with or without time-reversal symmetry, showing interesting features that have not been revealed be…
The thermoelectric voltage of a quantum dot connected to leads is calculated using the scattering R-matrix method. Our approach takes into account a temperature gradient between the contacts beyond the linear regime. We obtain sign changes of the thermopower when varying the temperature or the chemical potential around the resonances. The influence of the coupling strength of the contacts and of the thermoelectric field on the thermoelectric voltage is discussed.
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 analyze thermally induced spin and charge transport in HgTe/CdTe quantum wells on the basis of the numerical non-equilibrium Green's function technique in the linear response regime. In the topologically non-trivial regime, we find a clear signature of the gap of the edge states due to their finite overlap from opposite sample boundaries -- both in the charge Seebeck and spin Nernst signal. We are able to fully understand the physical origin of the thermoelectric transport signatures of edge and bulk states based on simple analytical models. Interestingly, we derive that the spin Nernst sig…
We numerically study the electrical and thermoelectric transport properties in phosphorene in the presence of both a magnetic field and disorder. The quantized Hall conductivity is similar to that of a conventional two-dimensional electron gas, but the positions of all the Hall plateaus shift to the left due to the spectral asymmetry, in agreement with the experimental observations. The thermoelectric conductivity and Nernst signal exhibit remarkable anisotropy, and the thermopower is nearly isotropic. When a bias voltage is applied between top and bottom layers of phosphorene, both thermopowe…
Quantization of the magneto-thermoelectric transport is studied when an external d.c. magnetic field is applied to the C/N-knot formed as crossing between a narrow stripe of conducting atomic monolayer C on the one hand and metal stripe N on the other hand. The temperature gradient in C is created by injecting the non-equilibrium electrons, holes and phonons from the heater H thereby directing them toward the C/N-knot. A non-linear coupling between electron states of the C/N-knot counter electrodes causes splitting of the heat flow into several fractions owing to the Lorentz force acting in th…
