In this first part, I would like to discuss the effects of strong magnetic impurities on the edge transport of a quantum spin Hall insulator. The location of the impurity strongly influences its effects. When it is near to the edge of the system, antiresonance of the transmission for the edge states happens. The interaction effects will be also discussed based on the renormalization theory. In the second part, I will discuss transport properties and topological phase transition in 2D interacting disordered Chern insulator within the dynamical mean-field theory. The band inversion induced by the disorder and interaction and the delocalization effects induced by interaction are discussed. We found that the repulsive onsite interaction is really friendly to the topological phase in the disordered Chern insulator
A prime example of non-equilibrium or active environment is a biological cell. In order to understand in-vivo functioning of biomolecules such as proteins, chromatins, a description beyond equilibrium is absolutely necessary. In this context, biomolecules have been modeled as Rouse chains in Gaussian active bath [1, 2]. However, these non-equilibrium fluctuations in biological cells are non-Gaussian . This motivates us to take a Rouse chain subjected to a series of pulses of force with finite duration, mimicking run and tumble motion of a class of micro-organisms . Thus by construction, this active force is non-Gaussian. Our analytical calculations show that the mean square displacement (MSD) of chain center of mass grows faster, but chain reconfiguration is slower for short chains. The reconfiguration time of a chain with N monomers scales as N σ , where the exponent σ ≃ 1.6 − 2. The MSD of the tagged monomer in this active bath also shows superdiffusion at an intermediate time unlike a monomer of a Rouse chain. In addition, the chain swells. We compare this activity-induced swelling with that of a Rouse chain in a Gaussian active bath .  N. Samanta and R. Chakrabarti, J. Phys. A 49, 195601 (2016).  D. Osmanovi ́c and Y. Rabin, Soft Matter 13, 963 (2017).  O. Pohl, M. Hintsche, Z. Alirezaeizanjani, M. Seyrich, C. Beta, and H. Stark, PLoS Comp. Biol. 13, 1005329 (2017).  S. Chaki and R. Chakrabarti, J. Chem. Phys. 150, 094902 (2019).
I discuss the interplay between non-Fermi liquid behavior and superconductivity near a quantum-critical point (QCP) in a metal. It is widely thought that the tendency towards superconductivity and towards non-Fermi liquid behavior compete with each other, and if the pairing interaction is reduced below a certain threshold, the system displays a naked non-Fermi liquid QC behavior. I show that the situation is more complex. First, there is a difference between spin-triple and spin-singlet superconductivity. For spin-triplet pairing, thermal fluctuations are crucial and make superconducting transition first order. For spin-singlet pairing, they are essentially irrelevant, and the transition is second order. Second, I show that for spin-singlet pairing, there are multiple solutions with the same gap symmetry. For all solutions, except one, Tc vanishes when the pairing interaction drops below the threshold. For the one special solution, Tc remains finite even when the pairing interaction is arbitrary small, despite that there is no Cooper logarithm. I argue that superconductivity between this Tc and a lower T, when other solutions appear, is special, as it is entirely induced by fermions with the first Matsubara frequency. I show that this has specific implications for the observable quantities, such as the density of states and the spectral function.