Colloquium: Quantum heat transport in condensed matter systems

Abstract

In this Colloquium recent advances in the field of quantum heat transport are reviewed. This topic has been investigated theoretically for several decades, but only during the past twenty years have experiments on various mesoscopic systems become feasible. A summary of the theoretical basis for describing heat transport in one-dimensional channels is first provided. Then the main experimental investigations of quantized heat conductance due to phonons, photons, electrons, and anyons in such channels are presented. These experiments are important for understanding the fundamental processes that underly the concept of a heat conductance quantum for a single channel. Then an illustration on how one can control the quantum heat transport by means of electric and magnetic fields, and how such tunable heat currents can be useful in devices is given. This lays the basis for realizing various thermal device components such as quantum heat valves, rectifiers, heat engines, refrigerators, and calorimeters. Also of interest are fluctuations of quantum heat currents, both for fundamental reasons and for optimizing the most sensitive thermal detectors; at the end of the review the status of research on this intriguing topic is given.

Multi-particle scattering and breakdown of the Wiedemann-Franz law at a junction of N interacting quantum wires

“…Compared to the D N −1 FP, the D N FP is characterized by the center-of-mass field Φ defined in Eq. (34) satisfying Dirichlet, instead of Neumann, boundary conditions. Correspondingly, the charge conservation breaks down and the WFL can be violated, even though the corresponding FP can be fully described in terms of singleparticle scattering processes only.…”

“…An efficient mean to identify the system phases is by looking at the equilibrium charge and energy transport properties of the system under investigation (see, for instance, [34] for a review). These are typically not independent of each other: whenever an electronic system can be adiabatically deformed into a noninteracting Fermi gas, the ratio between the charge and the thermal conductance of the system are related by the Wiedemann-Franz law (WFL).…”

Tuning nonequilibrium heat current and two-photon statistics via composite qubit-resonator interaction

“…We should note that the dissipative composite qubitresonator model is more than a toy model. It can be experimentally realized in the superconducting quantum circuit platforms [43][44][45][46], where the transmon qubit is able to show both the longitudinal and transverse interactions with the microwave resonator, and the bosonic thermal bath is simulated by the LC circuit coupled to a metallic resistor. Hence, the heat energy naturally flows from the hot source to the cold drain under the temperature bias.…”

“…Recently, quantum thermal transport in cQED systems has attracted increasing attention, which leads to a flurry of valuable works [43][44][45][46][47]. Particularly, Pekola et al [43] experimentally detected heat flow in a hybrid quantum system comprising one transmon-qubit and two microwave resonators, of which the resonators are individually coupled to two metallic resistors, respectively.…”

A Cooper-Pair Box Coupled to Two Resonators: An Architecture for a Quantum Refrigerator

“…Furthermore, modern nanofabrication techniques allow the integration and characterization of superconducting qubits coupled to normal-metal dissipative elements [21], creating hybrid c-QED systems capable of probing thermal transport in quantum systems. Such systems differentiate themselves from previous attempts on quantum heat engines via their unambiguous implementation of thermal reservoirs, which naturally define the bath temperature, and possess a multitude of techniques for both primary and secondary thermometry [22,23].…”