The time-dependent thermopower is analyzed through an interacting quantum dot coupled to a time-dependent gate voltage and under the influence of an external magnetic field using the Keldysh nonequilibrium Green's function formalism. Formal expressions of the electrical and thermal conductances, thermopower, and thermoelectrical figure of merit are obtained. The influence of the magnetic field on the displacement current and the heat current is studied. Results show that although applying time-dependent gate voltage results in the enhancement of the Seebeck coefficient, the electron-electron interaction gives rise to a significant reduction in the thermopower. The reason for why applying time dependent gate voltage results in the enhancement of the thermopower is also analyzed.
We investigate the electrical conductance and thermopower of a quantum dot tunnel coupled to external leads described by an extension of the Anderson impurity model which takes into account the assisted hopping processes, i.e., the occupancy-dependence of the tunneling amplitudes. We provide analytical understanding based on scaling arguments and the Schrieffer-Wolff transformation, corroborated by detailed numerical calculations using the numerical renormalization group (NRG) method. The assisted hopping modifies the coupling to the two-particle state, which shifts the Kondo exchange coupling…
We derive formal expressions of time-dependent energy and heat currents through a nanoscopic device using the Keldysh nonequilibrium Green function technique. Numerical results are reported for a metal/dot/metal junction where the dot level energy is abruptly changed by a step-shaped voltage pulse. Analytical linear responses are obtained for the time-dependent thermoelectric coefficients. We show that the Seebeck coefficient can be enhanced in the transient regime up to an amount (here rising 40%) controlled by both the dot energy and the height of the voltage step.
We study the electric and thermoelectric transport properties of correlated quantum dots coupled to two ferromagnetic leads and one superconducting electrode. Transport through such hybrid devices depends on the interplay of ferromagnetic-contact induced exchange field, superconducting proximity effect and correlations leading to the Kondo effect. We consider the limit of large superconducting gap. The system can be then modeled by an effective Hamiltonian with a particle-non-conserving term describing the creation and annihilation of Cooper pairs. By means of the full density-matrix numerical…
Quantum dots are an important model system for thermoelectric phenomena, and may be used to enhance the thermal-to-electric energy conversion efficiency in functional materials. It is therefore important to obtain a detailed understanding of a quantum-dot's thermopower as a function of the Fermi energy. However, so far it has proven difficult to take effects of co-tunnelling into account in the interpretation of experimental data. Here we show that a single-electron tunnelling model, using knowledge of the dot's electrical conductance which in fact includes all-order co-tunneling effects, pred…
Using analytical arguments and the numerical renormalization group method we investigate the spin-thermopower of a quantum dot in a magnetic field. In the particle-hole symmetric situation the temperature difference applied across the dot drives a pure spin current without accompanying charge current. For temperatures and fields at or above the Kondo temperature, but of the same order of magnitude, the spin-Seebeck coefficient is large, of the order of k_B/e. Via a mapping, we relate the spin-Seebeck coefficient to the charge-Seebeck coefficient of a negative-U quantum dot where the correspond…
We use a many-body rate-equation approach to calculate the thermopower of a quantum dot in the presence of an exchange interaction. At temperatures much smaller than the single-particle level spacing, the known quantum jumps (discontinuities) in the thermopower are split by the exchange interaction. The origin and nature of the splitting are elucidated with a simple physical argument based on the nature of the intermediate excited state in the sequential tunneling approach. We show that this splitting is sensitive to the number parity of electrons in the dot and the dot's ground-state spin. Th…
We investigate the finite-frequency thermal transport through a quantum dot subject to strong interactions, by providing an exact, nonperturbative formalism that allows us to carry out a systematic analysis of the thermopower at any frequency. Special emphasis is put on the dc and high-frequency limits. We demonstrate that, in the Kondo regime, the ac thermopower is characterized by a universal function that we determine numerically.
We discuss the thermoelectrical properties of nanowires hosting Majorana edge states. For a Majorana nanowire directly coupled to two normal reservoirs the thermopower always vanishes regardeless of the value of the Majorana hybridization. This situation changes drastically if we insert a quantum dot. Then, the dot Majorana side coupled system exhibits a different behavior for the thermopower depending on the Majorana hybridization parameter. Thermopower reverses its sign when the half fermionic state is fully developed. As long as the hybridization becomes finite the Seebeck coefficient behav…
We study the response of the thermopower of a quantum dot in the Kondo regime to sinusoidal displacement of the dot energy level via a gate voltage using time dependent non-crossing approximation and linear response Onsager relations. Instantaneous thermopower begins to exhibit complex fluctuations when the driving amplitude is increased at constant driving frequency. We also find that the time averaged thermopower decreases steadily until it saturates at constant driving amplitude as a function of inverse driving frequency. On the other hand, time averaged thermopower is found to be quite sen…
Signatures of the Kondo effect in the electrical conductance of strongly correlated quantum dots are well understood both experimentally and theoretically, while those in the thermopower have been the subject of recent interest. Here, we extend theoretical work [T. A. Costi, Phys. Rev. B {\bf 100}, 161106(R) (2019)] on the field-dependent thermopower of such systems, and carry out calculations in order to address a recent experiment on the field dependent thermoelectric response of Kondo-correlated quantum dots [A. Svilans {\em et al.,} Phys. Rev. Lett. {\bf 121}, 206801 (2018)]. In addition t…
We study a system composed of a quantum dot in contact with ferromagnetic leads, held at different temperatures. Spin analogues to the thermopower and thermoelectric figures of merit are defined and studied as a function of junction parameters. It is shown that in contrast to bulk ferromagnets, the spin thermopower coefficient in a junction can be as large as the Seebeck coefficient, resulting in a large spin figure of merit. In addition, it is demonstrated that the junction can be tuned to supply only spin current but no charge current. We also discuss experimental systems where our predictio…
Recent experiments have measured the signatures of the Kondo effect in the zero-field thermopower of strongly correlated quantum dots [Svilans {\em et al.,} Phys. Rev. Lett. {\bf 121}, 206801 (2018); Dutta {\em et al.,} Nano Lett. {\bf 19}, 506 (2019)]. They confirm the predicted Kondo-induced sign change in the thermopower, upon increasing the temperature through a gate-voltage dependent value $T_{1}\gtrsim T_{\rm K}$, where $T_{\rm K}$ is the Kondo temperature. Here, we use the numerical renormalization group (NRG) method to investigate the effect of a finite magnetic field $B$ on the thermo…
We investigate the time evolution of the thermopower in a vibrating quantum dot suddenly shifted into the Kondo regime via a gate voltage by adopting the time-dependent non-crossing approximation and linear response Onsager relations. Behaviour of the instantaneous thermopower is studied for a range of temperatures both in zero and strong electron-phonon coupling. We argue that inverse of the saturation value of decay time of thermopower to its steady state value might be an alternative tool in determination of the Kondo temperature and the value of the electron-phonon coupling strength.
Interference effects in quantum dots between different transport channels can lead to a strong suppression of conductance, which cuts like a canyon through the common conductance plot [Phys. Rev. Lett. 104, 186804 (2010)]. In the present work, we consider the thermoelectric transport properties of the canyon of conductance suppression using the second-order von Neumann approach. We observe a characteristic signal for the zeros of the thermopower. This demonstrates that thermoelectric measurements are an interesting complimentary tool to study complex phenomena for transport through confined sy…
We derive the statistics of the time-delay matrix (energy derivative of the scattering matrix) in an ensemble of superconducting quantum dots with chaotic scattering (Andreev billiards), coupled ballistically to $M$ conducting modes (electron-hole modes in a normal metal or Majorana edge modes in a superconductor). As a first application we calculate the density of states $ρ_0$ at the Fermi level. The ensemble average $\langleρ_0\rangle=δ_0^{-1}M[\max(0,M+2α/β)]^{-1}$ deviates from the bulk value $1/δ_0$ by an amount depending on the Altland-Zirnbauer symmetry indices $α,β$. The divergent aver…
We investigate the conductance and thermopower of massless Dirac fermions through a quantum dot using a pseudogap Anderson model in the non-crossing approximation. When the Fermi level is at the Dirac point, the conductance has a cusp where the thermopower changes its sign. When the Fermi level is away from the Dirac point, the Kondo temperature illustrates a quantum impurity transition between an asymmetric strong coupling Kondo state and a localized moment state. The conductance shows a peak near this transition and reaches the unitary limit at low temperatures. The magnitude of the thermopo…
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…
We report a numerical renormalization-group study of the thermoelectric effect in the single-electron transistor (SET) and side-coupled geometries. As expected, the computed thermal conductance and thermopower curves show signatures of the Kondo effect and of Fano interference. The thermopower curves are also affected by particle-hole asymmetry.
We study the thermoelectric transport through a single-level quantum dot (QD) coupled to two normal metallic leads and side-coupled to Majorana bound state (MBS). The Coulomb interaction in QD is considered. To investigate only the influence of MBS on thermoelectric transport, we focus on the relatively high temperature region ($T\gg T_K$), where Kondo effect does not appear. The electric and thermal conductance and thermopower as a function of gate voltage (i.e. QD level) are completely different whether the coupling between MBSs is zero or not. When the coupling between MBSs is finite, all t…
Mesoscopic circuit elements such as quantum dots and quantum point contacts (QPCs) offer a uniquely controllable platform for engineering complex quantum devices, whose tunability makes them ideal for generating and investigating interacting quantum systems. However, the conductance measurements commonly employed in mesoscopics experiments are poorly suited to discerning correlated phenomena from those of single-particle origin. Here, we introduce non-equilibrium thermopower measurements as a novel approach to probing the local density of states (LDOS), offering an energy-resolved readout of m…
The thermoelectric effects in three-terminal structures with a quantum dot are considered. We propose the experimentally consistent protocol for determination of the transport coefficients in terms of the local and non-local conductances and thermopowers that can be measured in two steps, applying the `four probe technique'. This proposal is compared with other approaches discussed so far in the literature. As an example we study in detail the thermopower induced by the superconducting electrode in a subgap regime which might be useful for analysis of novel hybrid devices.
The effect of electron-phonon coupling on transport through a pair of strongly correlated quantum dots embedded in the Aharonov-Bohm ring is considered in the mean field slave boson Kotliar-Ruckenstein approach. It is shown that coupling with phonons opens transport gap in the region of double occupancy. Low-bias conductance and thermopower provide information on electron-phonon coupling strength.
Interacting Tomonaga-Lüttinger liquid with impurity for interaction constant $K = 1/2$: Thermopower investigation, entropy variation and heat capacity densities associated with thermoelectric particle transport
University of Bouira（布依拉大学）；Higher Normal School of Bouzareah, University of Bouira（布扎雷亚高等师范学院，布依拉大学）
We investigate thermoelectric properties of correlated quantum dots and molecules, described by a single level Anderson model coupled to conduction electron leads, by using Wilson's numerical renormalization group method. In the Kondo regime, the thermopower, $S(T)$, exhibits two sign changes, at temperatures $T=T_{1}$ and $T=T_{2}>T_{1}$. We find that $T_{2}$ is of order the level width $Γ$ and $T_{1}> T_{p}\approx T_{K}$, where $T_{p}$ is the position of the Kondo induced peak in the thermopower and $T_{K}$ is the Kondo scale. No sign change is found outside the Kondo regime, or, for weak co…
Thermoelectric transport phenomena in a single-level quantum dot coupled to ferromagnetic leads are considered theoretically in the Kondo regime. The dot is described by the Anderson model with Rashba type spin-orbit interaction. The finite-U mean field slave boson technique is used to describe the transport characteristics, like heat conductance, thermopower, thermoelectric efficiency (figure of merit). The role of quantum interference effects in thermoelectric parameters is also analyzed.
We report thermopower ($S$) and electrical resistivity ($ρ_{2DES}$) measurements in low-density (10$^{14}$ m$^{-2}$), mesoscopic two-dimensional electron systems (2DESs) in GaAs/AlGaAs heterostructures at sub-Kelvin temperatures. We observe at temperatures $\lesssim$ 0.7 K a linearly growing $S$ as a function of temperature indicating metal-like behaviour. Interestingly this metallicity is not Drude-like, showing several unusual characteristics: i) the magnitude of $S$ exceeds the Mott prediction valid for non-interacting metallic 2DESs at similar carrier densities by over two orders of magnit…
We discuss out-of-equilibrium population imbalances between different orbital states due to applied thermal gradients. This purely thermoelectric orbital effect appears quite generically in nanostructures with a pseudospin degree of freedom. We establish an orbital Seebeck coefficient that characterizes the induced orbital bias in response to a temperature difference between reservoirs coupled to a quantum conductor. We analyze a two-terminal strongly interacting quantum dot with two orbital states and find that the orbital thermopower acts as an excellent tool to describe the transition betwe…
We present thermopower $S$ and resistance $R$ measurements on GaAs-based mesoscopic two-dimensional electron gases (2DEGs) as functions of the electron density $n_s$. At high $n_s$ we observe good agreement between the measured $S$ and $S_{\rm{MOTT}}$, the Mott prediction for a non-interacting metal. As $n_s$ is lowered, we observe a crossover from Mott-like behaviour to that where $S$ shows strong oscillations and even sign changes. Remarkably, there are absolutely no features in $R$ corresponding to those in $S$. In fact, $R$ is devoid of even any universal conductance fluctuations. A statis…
We investigate the thermoelectric properties of a quantum dot coupled to ferromagnetic and superconducting electrodes. The combination of spin polarized tunneling at the ferromagnetic-quantum dot interface and the application of an external magnetic field that Zeeman splits the dot energy level leads to large values of the thermopower (Seebeck coefficient). Importantly, the thermopower can be tuned with an external gate voltage connected to the dot. We compute the figure of merit that measures the efficiency of thermoelectric conversion and find that it attains high values. We discuss the diff…
We study transport properties of weakly interacting spinless electrons in one-dimensional single channel quantum wires. The effects of interaction manifest as three-particle collisions due to the severe constraints imposed by the conservation laws on the two-body processes. We focus on short wires where the effects of equilibration on the distribution function can be neglected and collision integral can be treated in perturbation theory. We find that interaction-induced corrections to conductance and thermopower rely on the scattering processes that change number of right- and left-moving elec…
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…
Using the slave boson Kotliar-Ruckenstein approach (SBMFA) for N level Anderson model, we compare fully symmetric SU(N) Kondo resonances occurring for spin and orbital conserving tunneling with many-body resonances for the dot with broken symmetry caused by spin, orbital or full spin-orbital mixing. As a result of interorbital or spin flip processes new interference paths emerge, which manifests in the occurrence of antibonding Dicke like and bonding Kondo like resonances. The analytical expressions for linear conductances and linear temperature thermopower coefficient for arbitrary N are foun…
Using the Keldysh Green function technique, we calculate the finite-frequency correlator between the electrical current and the heat current flowing through a quantum dot connected to reservoirs. At equilibrium, we find that this quantity, called mixed noise, is linked to the thermoelectric ac-conductance by the fluctuation-dissipation theorem. Out-of-equilibrium, we discuss its spectrum and find evidence of the close relationship between the mixed noise and the thermopower. We study the spectral coherence and identify the conditions to have a strong correlation between the electrical and heat…
Thermoelectric effects through a serial double quantum dot system weakly coupled to ferromagnetic leads are analyzed. Formal expressions of electrical conductance, thermal conductance, and thermal coefficient are obtained by means of Hubbard operators. The results show that although the thermopower is independent of the polarization of the leads, the figure of merit is reduced by an increase of polarization. The influences of temperature and interdot tunneling on the figure of merit are also investigated, and it is observed that increase of the interdot tunneling strength results in reduction …
We study thermoelectric currents of neutral, fermionic atoms flowing through a mesoscopic channel connecting a hot and a cold reservoir across the superfluid transition. The thermoelectric response results from a competition between density-driven diffusion from the cold to the hot reservoir and the channel favoring transport of energetic particles from hot to cold. We control the relative strength of both contributions to the thermoelectric response using an external optical potential in a nearly non-interacting and a strongly-interacting system. Without interactions, the magnitude of the par…
A detailed investigation of the non-equilibrium steady-state electric and thermoelectric transport properties of a quantum dot coupled to the normal metallic and s-wave superconducting reservoirs (N-QD-S) are provided within the Coulomb blockade regime. Using non-equilibrium Keldysh Green's function formalism, initially, various model parameter dependence of thermoelectric transport properties are analysed within the linear response regime. It is observed that the single-particle tunnelling close to the superconducting gap edge can generate a relatively large thermopower and figure of merit. M…
We consider a single level quantum dot interacting with a phonon mode and weakly coupled to metallic leads which are subjected to a time dependent gate voltage. Electrical conductance, thermopower, and figure of merit are investigated in detail using a Tien-Gordon-type rate equation. In the presence of the microwave field, the electrical conductance exhibits extra peaks whose height is controlled by the magnitude of the microwave field. Furthermore, the oscillation of the thermopower increases in the presence of the time-dependent gate voltage or the electron-phonon interaction. Influence of t…
