Tero T. Heikkilä

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

Electron-phonon heat transfer in monolayer and bilayer graphene

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Microwave amplification with nanomechanical resonators

, 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.

Flat bands in topological media

We calculate the heat transfer between electrons to acoustic and optical phonons in monolayer and bilayer graphene (MLG and BLG) within the quasiequilibrium approximation. For acoustic phonons, we show how the temperature-power laws of the electron-phonon heat current for BLG differ from those previously derived for MLG and note that the high-temperature (neutral-regime) power laws for MLG and BLG are also different, with a weaker dependence on the electronic temperature in the latter. In the general case we evaluate the heat current numerically. We suggest that a measurement of the heat current could be used for an experimental determination of the electron-acoustic-phonon coupling constants, which are not accurately known. However, in a typical experiment heat dissipation by electrons at very low temperatures is dominated by diffusion and we estimate the crossover temperature at which acoustic-phonon coupling takes over in a sample with Joule heating. At even higher temperatures optical phonons begin to dominate. We study some examples of potentially relevant types of optical modes, including, in particular, the intrinsic in-plane modes and additionally the remote surface phonons of a possible dielectric substrate.

High-temperature surface superconductivity in topological flat-band systems

The sensitive measurement of electrical signals is at the heart of modern technology. According to the principles of quantum mechanics, any detector or amplifier necessarily adds a certain amount of noise to the signal, equal to at least the noise added by quantum fluctuations. This quantum limit of added noise has nearly been reached in superconducting devices that take advantage of nonlinearities in Josephson junctions. Here we introduce the concept of the amplification of microwave signals using mechanical oscillation, which seems likely to enable quantum-limited operation. We drive a nanomechanical resonator with a radiation pressure force, and provide an experimental demonstration and an analytical description of how a signal input to a microwave cavity induces coherent stimulated emission and, consequently, signal amplification. This generic scheme, which is based on two linear oscillators, has the advantage of being conceptually and practically simpler than the Josephson junction devices. In our device, we achieve signal amplification of 25 decibels with the addition of 20 quanta of noise, which is consistent with the expected amount of added noise. The generality of the model allows for realization in other physical systems as well, and we anticipate that near-quantum-limited mechanical microwave amplification will soon be feasible in various applications involving integrated electrical circuits.

Multimode circuit optomechanics near the quantum limit.

Topological media are systems whose properties are protected by topology and thus are robust to deformations of the system. In topological insulators and superconductors the bulk-surface and bulk-vortex correspondence gives rise to the gapless Weyl, Dirac or Majorana fermions on the surface of the system and inside vortex cores. Here we show that in gapless topological media, the bulk-surface and bulk-vortex correspondence is more effective: it produces topologically protected gapless fermions without dispersion—the fiat band. Fermion zero modes forming the flat band are localized on the surface of topological media with protected nodal lines [A. P. Schnyder and S. Ryu, Phys. Rev. B 84, 060504(R) (2011); T. T. Heikkil G. E. Volovik, JETP Lett. 93, 59 (2011)] and in the vortex core in systems with topologically protected Fermi points (Weyl points) [G. E. Volovik, JETP Lett. 93, 66 (2011)]. Flat band has an extremely singular density of states, and we show that this property may give rise in particular to surface superconductivity which could exist even at room temperature.

Dimensional crossover in topological matter: Evolution of the multiple Dirac point in the layered system to the flat band on the surface

We show that the topologically protected flat band emerging on a surface of a nodal fermionic system promotes the surface superconductivity due to an infinitely large density of states associated with the flat band. The critical temperature depends linearly on the pairing interaction and can be thus considerably higher than the exponentially small bulk critical temperature. We discuss an example of surface superconductivity in multilayered graphene with rhombohedral stacking.

Supercurrent-carrying density of states in diffusive mesoscopic Josephson weak links

The coupling of distinct systems underlies nearly all physical phenomena. A basic instance is that of interacting harmonic oscillators, giving rise to, for example, the phonon eigenmodes in a lattice. Of particular importance are the interactions in hybrid quantum systems, which can combine the benefits of each part in quantum technologies. Here we investigate a hybrid optomechanical system having three degrees of freedom, consisting of a microwave cavity and two micromechanical beams with closely spaced frequencies around 32 MHz and no direct interaction. We record the first evidence of tripartite optomechanical mixing, implying that the eigenmodes are combinations of one photonic and two phononic modes. We identify an asymmetric dark mode having a long lifetime. Simultaneously, we operate the nearly macroscopic mechanical modes close to the motional quantum ground state, down to 1.8 thermal quanta, achieved by back-action cooling. These results constitute an important advance towards engineering of entangled motional states.

Nexus and Dirac lines in topological materials

We consider the dimensional crossover in the topological matter, which involves the transformation of different types of topologically protected zeroes in the fermionic spectrum. In the considered case, the multiple Dirac (Fermi) point in quasi 2-dimensional system evolves into the flat band on the surface of the 3-dimensional system when the number of atomic layers increases. This is accompanied by formation of the spiral nodal lines in the bulk. We also discuss the topological quantum phase transition at which the surface flat band shrinks and changes its chirality, while the nodal spiral changes its helicity.

Cavity optomechanics mediated by a quantum two-level system

Recent experiments have demonstrated the nonequilibrium control of the supercurrent through diffusive phase-coherent normal-metal weak links. The experimental results have been accurately described by the quasiclassical Green’s-function technique in the Keldysh formalism. Taking into account the geometry of the structure, different energy scales, and the nonidealities at the interfaces allows us to obtain a quantitative agreement between the theory and the experimental results in both the amplitude and the phase dependence of the supercurrent, with no or very few fitting parameters. Here we discuss the most important factors involved with such comparisons: the ratio between the superconducting order parameter and the Thouless energy of the junction, the effect of additional wires on the weak link, and the effects due to imperfections, most notably due to the nonideal interfaces.