The form of energy termed heat that typically derives from lattice vibrations, i.e., phonons, is usually considered as waste energy and, moreover, deleterious to information processing. However, in this Colloquium, an attempt is made to rebut this common view: By use of tailored models it is demonstrated that phonons can be manipulated similarly to electrons and photons, thus enabling controlled heat transport. Moreover, it is explained that phonons can be put to beneficial use to carry and process information. In the first part ways are presented to control heat transport and to process information for physical systems which are driven by a temperature bias. In particular, a toolkit of familiar electronic analogs for use of phononics is put forward, i.e., phononic devices are described which act as thermal diodes, thermal transistors, thermal logic gates, and thermal memories. These concepts are then put to work to transport, control, and rectify heat in physically realistic nanosystems by devising practical designs of hybrid nanostructures that permit the operation of functional phononic devices; the first experimental realizations are also reported. Next, richer possibilities to manipulate heat flow by use of time-varying thermal bath temperatures or various other external fields are discussed. These give rise to many intriguing phononic nonequilibrium phenomena such as, for example, the directed shuttling of heat, geometrical phase-induced heat pumping, or the phonon Hall effect, which may all find their way into operation with electronic analogs.

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Colloquium : Phononics: Manipulating heat flow with electronic analogs and beyond

CuO nanostructures: Synthesis, characterization, growth mechanisms, fundamental properties, and applications

Understanding energy dissipation and transport in nanoscale structures is of great importance for the design of energy-efficient circuits and energy-conversion systems. This is also a rich domain for fundamental discoveries at the intersection of electron, lattice (phonon), and optical (photon) interactions. This review presents recent progress in understanding and manipulation of energy dissipation and transport in nanoscale solid-state structures. First, the landscape of power usage from nanoscale transistors (∼10−8 W) to massive data centers (∼109 W) is surveyed. Then, focus is given to energy dissipation in nanoscale circuits, silicon transistors, carbon nanostructures, and semiconductor nanowires. Concepts of steady-state and transient thermal transport are also reviewed in the context of nanoscale devices with sub-nanosecond switching times. Finally, recent directions regarding energy transport are reviewed, including electrical and thermal conductivity of nanostructures, thermal rectification, and the role of ubiquitous material interfaces. 
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Energy dissipation and transport in nanoscale devices

This review presents an overview of the thermal properties of mesoscopic structures. The discussion is based on the concept of electron energy distribution, and, in particular, on controlling and probing it. The temperature of an electron gas is determined by this distribution: refrigeration is equivalent to narrowing it, and thermometry is probing its convolution with a function characterizing the measuring device. Temperature exists, strictly speaking, only in quasiequilibrium in which the distribution follows the Fermi-Dirac form. Interesting nonequilibrium deviations can occur due to slow relaxation rates of the electrons, e.g., among themselves or with lattice phonons. Observation and applications of nonequilibrium phenomena are also discussed. The focus in this paper is at low temperatures, primarily below $4\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, where physical phenomena on mesoscopic scales and hybrid combinations of various types of materials, e.g., superconductors, normal metals, insulators, and doped semiconductors, open up a rich variety of device concepts. This review starts with an introduction to theoretical concepts and experimental results on thermal properties of mesoscopic structures. Then thermometry and refrigeration are examined with an emphasis on experiments. An immediate application of solid-state refrigeration and thermometry is in ultrasensitive radiation detection, which is discussed in depth. This review concludes with a summary of pertinent fabrication methods of presented devices.

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Opportunities for mesoscopics in thermometry and refrigeration: Physics and applications

Microwave photonics with superconducting quantum circuits

A clever experiment that makes use of two metallic islands connected by superconducting leads now confirms that thermal conduction by photons is limited by the same quantum value. Although the result is mainly of fundamental importance, there are implications for the design of bolometers, detectors of far-infrared light that are used in astrophysical studies, and electronic micro-refrigerators. The thermal conductance of a single channel is limited by its unique quantum value GQ, as was shown theoretically1 in 1983. This result closely resembles the well-known quantization of electrical conductance in ballistic one-dimensional conductors2,3. Interestingly, all particles—irrespective of whether they are bosons or fermions—have the same quantized thermal conductance4,5 when they are confined within dimensions that are small compared to their characteristic wavelength. The single-mode heat conductance is particularly relevant in nanostructures. Quantized heat transport through submicrometre dielectric wires by phonons has been observed6, and it has been predicted to influence cooling of electrons in metals at very low temperatures due to electromagnetic radiation7. Here we report experimental results showing that at low temperatures heat is transferred by photon radiation, when electron–phonon8 as well as normal electronic heat conduction is frozen out. We study heat exchange between two small pieces of normal metal, connected to each other only via superconducting leads, which are ideal insulators against conventional thermal conduction. Each superconducting lead is interrupted by a switch of electromagnetic (photon) radiation in the form of a DC-SQUID (a superconducting loop with two Josephson tunnel junctions). We find that the thermal conductance between the two metal islands mediated by photons indeed approaches the expected quantum limit of GQ at low temperatures. Our observation has practical implications—for example, for the performance and design of ultra-sensitive bolometers (detectors of far-infrared light) and electronic micro-refrigerators9, whose operation is largely dependent on weak thermal coupling between the device and its environment.

Single-mode heat conduction by photons

We investigate hysteresis in the transport properties of superconductor-normal-metal-superconductor (S-N-S) junctions at low temperatures by measuring directly the electron temperature in the normal metal. Our results demonstrate unambiguously that the hysteresis results from an increase of the normal-metal electron temperature once the junction switches to the resistive state. In our geometry, the electron temperature increase is governed by the thermal resistance of the superconducting electrodes of the junction.

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Origin of hysteresis in a proximity josephson junction

The basis of synchronous manipulation of individual electrons in solid-state devices was laid by the rise of single electronics about two decades ago1,2,3. Ultrasmall structures in a low-temperature environment form an ideal domain for addressing electrons one by one. In the so-called metrological triangle, voltage from the Josephson effect and resistance from the quantum Hall effect would be tested against current via Ohm’s law for a consistency check of the fundamental constants of nature, ℏ and e (ref. 4). Several attempts to create a metrological current source that would comply with the demanding criteria of extreme accuracy, high yield and implementation with not too many control parameters have been reported5,6,7,8,9,10,11. Here, we propose and prove the unexpected concept of a hybrid normal-metal–superconductor turnstile in the form of a one-island single-electron transistor with one gate, which demonstrates robust current plateaux at multiple levels of e f at frequency f.

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Hybrid single-electron transistor as a source of quantized electric current

A superconductor with a gap in the density of states or a quantum dot with discrete energy levels is a central building block in realizing an electronic on-chip cooler. They can work as energy filters, allowing only hot quasiparticles to tunnel out from the electrode to be cooled. This principle has been employed experimentally since the early 1990s in investigations and demonstrations of micrometre-scale coolers at sub-kelvin temperatures. In this paper, we review the basic experimental conditions in realizing the coolers and the main practical issues that are known to limit their performance. We give an update of experiments performed on cryogenic micrometre-scale coolers in the past five years.

https://iopscience.iop.org/article/10.1088/0034-4885/75/4/046501/pdf

Micrometre-scale refrigerators

We demonstrate radio-frequency thermometry on a micrometer-sized metallic island below 100 mK. Our device is based on a normal-metal-insulator-superconductor tunnel junction coupled to a resonator with transmission readout. In the first generation of the device, we achieve 90 mu K/root Hz noise-equivalent temperature with 10 MHz bandwidth. We measure the thermal relaxation time of the electron gas in the island, which we find to be of the order of 100 mu s. Such a calorimetric detector, upon optimization, can be seamlessly integrated into superconducting circuits, with immediate applications in quantum-thermodynamics experiments down to single quanta of energy.

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Matthias Meschke

Papers

Single-mode heat conduction by photons

Origin of hysteresis in a proximity josephson junction

Hybrid single-electron transistor as a source of quantized electric current

Micrometre-scale refrigerators

Fast Electron Thermometry for Ultrasensitive Calorimetric Detection