Aspects of Unconventional Transport and Quasiparticles in Condensed Matter Systems

Abstract

Transport in condensed matter system serve as one of the main properties for characterizing its phases and topological properties. A cornerstone in the theoretical efforts in transport is the Boltzmann transport equation (BTE), which describes the low frequency responses of weakly correlated systems through distribution functions of particle-like carriers. The BTE is extremely successful in describing transports in classical systems where the collision is largely uncorrelated and the quasiparticles wave lengths are significantly less than the mean free path. However, such major assumptions made by the Boltzmann transport does not hold in many aspects of modern condensed matter systems. Examples of such scenarios include quantum ballistic transport on the edge of a quantum Hall system, variable-range hopping in an Anderson localized system, and transport above the Mott-Ioeffe-Regel limit in bad metals. In this thesis, we discuss three example systems that exhibit transport properties beyond the conventional Boltzmann framework. First, we will introduce a new family of systems for Majorana zero mode that does not require an external magnetic field. Our proposal is based on a planar Josephson junction setup with a quasi two dimensional spin-orbit coupled electron gas and the usual role of the magnetic field that breaks the time reversal symmetry is taken by three phase biased superconductors. This idea is then simulated with HgTe as the two dimensional material together with realistic parameters. Our result demonstrates a large parameter regime of Majorana zero mode and a topological gap at the order of the superconducting gap. In the second part, we will discuss the physics of plasmonic mode in a Josephson junction chain in its insulating regime. Utilizing the Luther-Emery point of the sine-Gordon model, the polarizability can then be interpreted by the responses of soliton and anti-soliton pairs. we consider the system in both the clean limit and with disorder. Our theory suggests the existence of coherent phase mode in the insulating regime and provides a natural explanation for the frequency-dependent broadening of such a mode. The results is consistent with the recent experiments on the reflection spectrum of Josephson junction chains. Finally, we will look into the problem of Planckian thermal diffusion bound where a mechanism for sub-Planckian thermal diffusion is introduced. We will study a lattice system with large degrees of freedom per unit cell but has limited channel for heat conduction. In the highly-nonlinear regime, the thermal diffusivity can be solved accurately through applications of fluctuation-dissipation theorem. Through numerical simulations, our proposal demonstrate a modification of the lower bound to $D_P/N$ , where $D_P$ is the Planckian diffusivity and $N$ is the per-unit-cell degrees of freedom.