Quantum oscillation in band insulators and properties of non-equilibrium steady states in disordered insulators

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PhD; 2023; Department of Physics

Starting with the experiment on Kondo insulator SmB6 , which shows 1/B-periodic oscillations despite the absence of gapless electronic excitations in bulk, the candidate insulators showing quantum oscillation (QO) are on the rise. But this is contrary to our conventional understanding that we need a Fermi surface to have QO. So an obvious question to ask is, ‘How can insulators show QO?’. If there is QO, then which physical quantities show QO, and what is the physical reason behind their origin? In the absence of a Fermi surface, what determines the frequency of these QO? In search of answers, we revisit recently proposed theories for this phenomenon, focusing on a minimal model of an insulator with a hybridization gap between two opposite-parity light and heavy mass bands with an inverted band structure. We show that there are characteristic differences between the QO frequencies in the magnetization and the low-energy density of states (LE-DOS) of these insulators, in marked contrast with metals where all observables exhibit oscillations at the same frequency. The temperature dependence of the amplitudes of the magnetization and DOS oscillations are also qualitatively different and show marked deviations from the Lifshitz-Kosevich form well-known in metals. The interplay of disorder and interactions in quantum systems can lead to several intriguing phenomena, amongst which many-body localization (MBL) has caught many physicists’ attention in recent times. In the second work, we investigate whether an MBL system undergoes a transition to a current-carrying non-equilibrium steady state under a drive and how the entanglement properties of the quantum states change across the transition. The drive is introduced by using a phenomenological non-Hermitian model. We also discuss the dynamics, entanglement growth, and long-time fate of a generic initial state under an appropriate time evolution of the system governed by the non-H ermitian Hamiltonian. Our study reveals rich entanglement structures of the eigenstates of the non-Hermitian Hamiltonian. We find the transition between current-carrying states with volume-law to area-law entanglement entropy as a function of disorder and the strength of the non-Hermitian term. In the third work, we take two 1D systems, namely the 1D Anderson model and Aubry-André-Harper model, that show the localization of single particle eigenstates depending on the strength of disorder and study it under a chemical potential drive. The drive is induced by connecting baths at different chemical potentials to the two edges of the system. We calculate the Green functions of the systems on the Keldysh contour that we use to calculate physical quantities like current and occupation of the non-equilibrium steady state. Our results can distinguish between the localized and delocalized phases in the non-interacting limit. In the presence of interaction, our systems can show MBL to a thermal phase transition. We end with a discussion on the possibility of probing this thermal to MBL phase boundary using dynamical mean field theory.