Jukka P. Pekola

Opportunities for mesoscopics in thermometry and refrigeration: Physics and applications

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

Efficient Peltier refrigeration by a pair of normal metal/insulator/superconductor junctions

4\phantom{\rule{0.3em}{0ex}}\mathrm{K}

Single-mode heat conduction by photons.

, 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.

Violation of the Wiedemann-Franz law in a single-electron transistor

We suggest and demonstrate in experiment that two normal metal/insulator/superconductor (NIS) tunnel junctions combined in series to form a symmetric SINIS structure can operate as an efficient Peltier refrigerator. Specifically, it is shown that the SINIS structure with normal‐state junction resistances 1.0 and 1.1 kΩ is capable of reaching a temperature of about 100 mK starting from 300 mK. We estimate the corresponding cooling power to be 1.5 pW per total junction area of 0.8 μm2 at T=300 mK.

Experimental realization of a Szilard engine with a single electron

The thermal conductance of a single channel is limited by its unique quantum value GQ, as was shown theoretically in 1983. This result closely resembles the well-known quantization of electrical conductance in ballistic one-dimensional conductors. Interestingly, all particles—irrespective of whether they are bosons or fermions—have the same quantized thermal conductance 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 observed, and it has been predicted to influence cooling of electrons in metals at very low temperatures due to electromagnetic radiation. Here we report experimental results showing that at low temperatures heat is transferred by photon radiation, when electron–phonon 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-refrigerators, whose operation is largely dependent on weak thermal coupling between the device and its environment.

Micrometre-scale refrigerators

We study the influence of Coulomb interaction on the thermoelectric transport coefficients for a metallic single-electron transistor. By performing a perturbation expansion up to second order in the tunnel-barrier conductance, we include sequential and cotunneling processes as well as quantum fluctuations that renormalize the charging energy and the tunnel conductance. We find that Coulomb interaction leads to a strong violation of the Wiedemann-Franz law: the Lorenz ratio becomes gate-voltage dependent for sequential tunneling, and is increased by a factor 9/5 in the cotunneling regime. Finally, we suggest a measurement scheme for an experimental realization.

Origin of Hysteresis in a Proximity Josephson Junction

Significance A Maxwell demon makes use of information to convert thermal energy of a reservoir into work. A quantitative example is a thought experiment known as a Szilard engine, which uses one bit of information about the position of a thermalized molecule in a box to extract kBT ln 2 of work. The second law of thermodynamics remains valid because, according to Landauer principle, erasure of the information dissipates at least the same amount of heat. Here, we present an experimental realization of a Maxwell demon similar to a Szilard engine, in the form of a single electron box. We provide, to our knowledge, the first demonstration of extracting nearly kBT ln 2 of work for one bit of information. The most succinct manifestation of the second law of thermodynamics is the limitation imposed by the Landauer principle on the amount of heat a Maxwell demon (MD) can convert into free energy per single bit of information obtained in a measurement. We propose and realize an electronic MD based on a single-electron box operated as a Szilard engine, where kBT ln 2 of heat is extracted from the reservoir at temperature T per one bit of created information. The information is encoded in the position of an extra electron in the box.

A superconducting antenna-coupled hot-spot microbolometer

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.

Environment-Assisted Tunneling as an Origin of the Dynes Density of States

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.

Heat transistor: Demonstration of gate-controlled electronic refrigeration

We report the electrical properties of an antenna-coupled niobium vacuum-bridge bolometer, operated at a temperature of 4.2 K, in which the thermal isolation is maximized by the vacuum gap between the bridge and the underlying silicon substrate. The device is voltage-biased, which results in a formation of a normal state region in the middle of the bridge. The device shows a current responsivity of −1430 A/W and an amplifier limited electrical noise equivalent power of 1.4×10−14 W/Hz.