Lifshitz transition in dirty nematic superconductor

TL;DR

This paper investigates how the Lifshitz transition from closed to open Fermi surfaces affects nematic superconductivity in dirty topological insulators, revealing impacts on critical temperature, disorder susceptibility, phase competition, and Meissner current anisotropy.

Contribution

It provides a theoretical analysis of the Lifshitz transition's effects on nematic superconductivity, including critical temperature, phase competition, and magnetic response, in disordered topological insulators.

Findings

Open Fermi surface lowers critical temperature and increases disorder susceptibility.

Lifshitz transition enhances anisotropy of Meissner currents.

Disorder suppresses superconducting density more than critical temperature.

Abstract

We study the effects of the Lifshitz transition from closed to open Fermi surface in dirty topological insulators with the nematic superconductivity near the critical temperature. We solve linearized Gor'kov equations and find that the nematic superconductor with an open Fermi surface has a lower critical temperature and more susceptible to the disorder than the superconductor with the closed Fermi surface. We propose that correspondence between the critical temperature and stability against the disorder is the general feature of the superconductivity. We investigate the effects of the Lifshitz transition on the competition between superconducting phases in a topological insulator. Open Fermi surface is beneficial for the nematic order parameter $\Delta_4$ in competition with orbital-triplet $\Delta_2$ and disfavors nematic state over the s-wave order parameter. We study Meissner currents in both clean and dirty limits. We found that transition from closed to open Fermi surface increases anisotropy of Meissner currents. Finite disorder suppresses superconducting density stronger than critical temperature. We compare our results with the existing experimental data.