Quantum thermocouples: nonlocal conversion and control of heat in nanostructures

TL;DR

This work surveys multiterminal quantum thermoelectric transport in nanoscale conductors, emphasizing phase-coherent and interacting regimes that enable nonlocal conversion of heat to electrical power or cooling. It organizes the landscape into noninteracting and interacting models, including resonant tunneling, phonon/photon coupling, edge-state transport, and Coulomb-coupled quantum dots, while addressing phase coherence, dephasing, and nonequilibrium states as key design factors. It highlights concrete proposals and experiments for quantum heat engines, absorption refrigerators, heat circulators, and thermal transistors, including autonomous information-enabled perspectives. Overall, the paper demonstrates how spectral engineering and controlled interactions can realize efficient, tunable heat-to-work conversion and active heat management at the nanoscale, with implications for on-chip quantum technologies and foundational quantum thermodynamics.

Abstract

Nanoscale conductors are interesting for thermoelectrics because of their particular spectral features connecting separated heat and particle currents. Multiterminal devices in the quantum regime benefit from phase-coherent phenomena, which turns the thermoelectric effect nonlocal, and from tunable single-particle interactions. This way one can define quantum thermocouples which convert an injected heat current into useful power in an isothermal conductor, or work as refrigerators. Additionally, efficient heat management devices can be defined. We review recent theoretical and experimental progress in the research of multiterminal thermal and thermoelectric quantum transport leading to proposals of autonomous quantum heat engines and thermal devices.

Figures (6)

• Figure 1: (a) Macroscopic thermocouple. The central region of a conductor otherwise at a temperature $T_C$ is in contact with a heat source at temperature $T_H$ for which reason it reaches a local equilibrium at temperature $T_M$. Electron-hole excitations generate a thermovoltage when separated by p and n junctions. (b) Onsager coefficients $O=O_{ii}$ of a two-terminal resonant-tunneling barrier when sweeping the resonance energy $\varepsilon$ across the electrochemical potential $\mu$, with rates $\Gamma_{1}=\Gamma_{2}=k_\text{B}T$, cf. Eq. \ref{['eq:lorentz']}. The thermal conductance in the absence of particle current, $\tilde{K}=K-LM/G$ is plotted as a red dashed line. (c) Quantum thermocouple. An isothermal conductor is formed by terminals L and R. It is connected to heat sources (labeled H and C) via a mesoscopic region (dashed circle) where the electron phase coherence is preserved. Nonlocal transport $I_L=-I_R$ is a consequence of the (interference) properties of scattering in the mesoscopic region.
• Figure 2: (a) Inelastic-scattering junction, with the region in contact with the heat source sandwiched between two scattering regions ${\cal S}_{\alpha}$, $\alpha=1,2$, which connect it with the conductor terminals $L$ and $R$. (b) Resonant tunneling barriers introduce Lorentzian-shaped filters ${\cal T}_{\alpha}(E)$ that filter the transported electrons. Resonances can be tuned with gate voltages $V_{g\alpha}$. Those below (over) the electrochemical potential induce transport from hot to cold (from cold to hot) regions. (c) A finite power $P$ is generated in asymmetric configurations by generating a current through a load resistor closing the circuit. Here $R_{load}\gg R_K$, with resonances of width $\Gamma_1=\unit[0.2]{meV}$, $\Gamma_1=\unit[0.1]{meV}$, $T=\unit[175]{mK}$, $\Delta T=\unit[5]{mK}$, and being $R_K=h/e^2\approx\unit[25.813]{k\Omega}$ the von Klitzing resistance.
• Figure 3: Phase coherent coupling to the heat source. (a) A scanning probe tip injects heat at a given position $x$ between two scattering regions ${\cal S}_{\alpha}$, $\alpha=1,2$, separated by a distance $d$. (b) Extrinsic thermoelectric response of a conductor consisting on a single energy-independent scatterer, ${\cal S}_1$, with transmission probability ${\cal T}_1=0.3$ and ${\cal S}_2=\mathbb{1}$: the interference of multiple reflections between the scatterer and the tip generates a finite current (here, $T_H=1.5T$, the conduction band bottom is $U_0=-50k_\text{B}T$, and the tip is maximally coupled, $\epsilon=1/2$, see Ref. extrinsic for details). (c) Transmission probabilities between the different terminals when the two scatterers are double quantum dots with transparencies $3.1k_\text{B}T$, interdot coupling $2.1k_\text{B}T$ and splitting $11.7k_\text{B}T$, with the tip with transmission $\epsilon=0.4$ at $x=6.2l_0$, being $d=6.4l_0$ and $l_0=\hbar/\sqrt{8mk_\text{B}T}$, with the electron mass $m$balduque_coherent_2024.
• Figure 4: Three terminal quantum Hall conductor. (a) In the absence of backscattering, heat flows from the hot probe terminal into the next terminal along the chiral propagation of electrons, with no average currents $I_i=0$. (b) A scatterer mixing edge channels is able to generate a thermoelectric response. (c) A nonthermal reservoir injects electrons in one of the channels with a nonequilibrium distribution $f_{neq}(E)$ able to generate a finite current even if $I_{neq}=J_{neq}=0$.
• Figure 5: Nonlocal thermoelectrics mediated by interactions. (a) The heat injection is mediated by the Coulomb interaction, $U$, of electrons in capacitively coupled conductors. The coupling of the nanostructure to the $L$ and $R$ reservoirs needs to be energy-dependent and inversion asymmetric. (b) Sequence leading to a finite zero-voltage current with quantum dots with asymmetric tunneling rates $\Gamma_{n}^i$. (c) Phonon assisted tunneling between two quantum dots provides the energy, $\hbar\omega_p\approx\varepsilon_R-\varepsilon_L\gg\lambda$ to overcome an energy gap, where $\lambda$ is the interdot coupling, and $\Gamma$ are the tunneling rates for coupling with the reservoirs. The splitting of the quantum dot levels introduce all the required broken symmetries naturally.