Effect of thermal fuctuations on the nontrivial topology of the d+id superconducting phase

TL;DR

This paper investigates how thermal fluctuations influence the topological properties of a d+id superconducting phase in a quasi-two-dimensional system, using a self-consistent functional-integral approach to account for temperature effects.

Contribution

It introduces a new method to calculate the topological index considering thermal fluctuations, revealing their impact on the topological phase stability.

Findings

Thermal fluctuations do not alter the topological properties of the system.

The topological index remains close to -2 over an expanded temperature range due to thermal effects.

Increasing effective attraction extends the temperature region with nontrivial topology.

Abstract

The behavior of the topological index, characterizing the properties of superconducting phases of quasi-two-dimensional systems with nontrivial topology, is investigated depending on the temperature and parameters of the effective non-Hermitian Hamiltonian. For this purpose, a method of calculating the topological index, based on a self-consistent functional-integral theory, is proposed. The method makes it possible to take into account thermal fluctuations and study the behavior of the topological index as a function of temperature and Hamiltonian parameters. The chiral d+id superconducting phase of a quasi-two-dimensional model with effective attraction between the electrons located at the nearest sites of a triangular lattice is considered. It is shown that the characteristic features in the energy dependence of the self-energy part, which arise when thermal fluctuations are taken into account, have a structure that does not lead to a change in the topological properties of the system. It is found that thermal fluctuations, as well as an increase in effective attraction in this system, contribute to the expansion of the temperature region, in which the value of the topological index is close to the integer C1=-2.