Universality of thermal transport in amorphous nanowires at low temperatures

Abstract

Thermal transport properties of amorphous materials at low temperatures are governed by the interaction between phonons and localized excitations referred to as tunneling two-level systems (TLSs). The temperature variation of the thermal conductivity of these amorphous materials is considered as universal and is characterized by a quadratic power law. This is well described by the phenomenological TLS model even though its microscopic explanation is still elusive. Here, by scaling down to the nanometer-scale amorphous systems much below the bulk phonon-TLS mean free path, we probe the robustness of that model in restricted geometry systems. Using very sensitive thermal conductance measurements, we demonstrate that the temperature dependence of the thermal conductance of silicon nitride nanostructures remains mostly quadratic independently of the nanowire section. It does not follow the cubic power law in temperature as expected in a Casimir-Ziman regime of boundary-limited thermal transport. This shows a thermal transport counterintuitively dominated by phonon-TLS interactions and not by phonon boundary scattering in the nanowires. This could be ascribed to an unexpected high density of TLSs on the surfaces which still dominates the phonon diffusion processes at low temperatures and explains why the universal quadratic temperature dependence of thermal conductance still holds for amorphous nanowires. DOI: 10.1103/PhysRevB.95.165411 Amorphous materials may have significant dispersion in their chemical compositions or their physical structures at the microscopic level. However, at low temperatures, the behavior of the thermal properties of almost all amorphous materials is thought to be universal [1]. These common features include a nearly linear specific heat and a nearly quadratic thermal conductivity in temperature below a few kelvins. As thermal transport is concerned, this universality is not only qualitative but also quantitative; indeed the thermal conductivity of all amorphous materials lies within a factor of twenty in the same order of magnitude called the glassy range [2,3]. Despite much theoretical effort, this universality remains poorly understood and its true microscopic origin is still elusive. Nowadays, the most accepted model is based on the presence of tunneling twolevel systems (TLSs) involving tunneling between different equilibrium positions of an atom or group of atoms [4][5][6]. The scatterings of the phonons on these tunneling sites is assumed to be at the origin of the quadratic variation of thermal conductance in temperature. The phonon heat transport is then characterized by the phonon-TLS mean free path (MFP; the distance between two inelastic collisions), which is on the order of a few hundred micrometers.Phillips suggested that TLSs are likely to form in materials with an open structure and low-coordination regions, and are unlikely in highly dense amorphous systems [4]. Recent experiments give indication of the correlation between the low-density regions, the presence of nanovoid...

Heat conduction measurements in ballistic 1D phonon waveguides indicate breakdown of the thermal conductance quantization

“…This is illustrated in Fig. 3b , where the measurements are compared to the different expected regimes of heat conduction at low temperature: boundary-limited heat transport (the Casimir regime) characterized by a cubic behavior in temperature (black line), and the quantum limit of fully ballistic transport characterized by a linear regime (dark blue line) only when the transmission coefficients are equal to one; the light blue line is a simple quadratic fit likely to describe thermal transport in amorphous materials like SiN when phonons are predominantly scattered by two level systems (TLS) 34 – 38 ; in amorphous materials atoms or group of atoms may tunnel between two different equilibrium positions creating what is called a TLS. As it is shown in Fig.…”

“…However, this is not the only possible origin for this thermal resistance. It has been shown recently that, in amorphous nanostructures, the phonon-TLS scattering is the limiting mechanism for phonon transport in the diffusive regime 38 . As shown in Fig.…”

Colloquium: Quantum heat transport in condensed matter systems

“…Adapted from Leivo andPekola, 1998, andLeivo, 1999. temperatures of ∼0.1 K fall about 1 order of magnitude below the quantum value, and the temperature dependence of thermal conductance is close to T 2 . Tavakoli et al (2017Tavakoli et al ( , 2018 proposed nonballistic transmission in their bridges as the origin of their results. Finally, experiments by Zen et al (2014) demonstrated that thermal conductance can be strongly suppressed even in two dimensions with proper patterning of the membranes into a nanostructured periodic phononic crystal.…”

“…The latter experiment measuring the temperature of the GaAs platform in the middle using N-I-S tunnel junctions demonstrated Debye thermal conductance at T ≫ 100 mK but tended to follow the expected quantum thermal conductance at the lowest temperatures. In the more recent experiments by Tavakoli et al (2017Tavakoli et al ( , 2018 the measurement on submicronwide silicon nitride bridges was made differential in the sense that there was no need to add superconducting leads on these phonon-conducting legs. The results at the lowest κ ≃ 14.5T 1.98 mW m −1 K −1 for the full membrane and κ ≃ 1.58T 1.54 and 0.57T 1.37 mW m −1 K −1 for 25and 4-μm-wide bridges, respectively, where T is expressed in kelvins.…”

Colloquium: Quantum heat transport in condensed matter systems

“…The latter experiment measuring the temperature of the GaAs platform in the middle using NIS tunnel junctions demonstrated Debye thermal conductance at T 100 mK, but tended to follow the expected quantum thermal conductance at the lowest temperatures. In the more recent experiments by (Tavakoli et al, 2017(Tavakoli et al, , 2018 the measurement on sub-micron wide silicon nitride bridges was made differential in the sense that there was no need to add superconducting leads on these phonon-conducting legs. The results at the lowest temperatures of ∼ 0.1 K fall about one order of magnitude below the quantum value, and the temperature dependence of thermal conductance is close to T 2 .…”