Thermal fluctuations in superconducting phases with chiral $ d + id $ and $ s $ symmetry on a triangular lattice

TL;DR

This paper investigates thermal fluctuations in superconducting phases with extended s and chiral d+id symmetries on a triangular lattice, revealing phase diagrams and fluctuation behaviors relevant to topological states.

Contribution

It introduces a comprehensive analysis of thermal fluctuations in chiral d+id and extended s superconductors on a triangular lattice using functional integration, including phase diagrams and fluctuation distributions.

Findings

Topologically trivial s-wave states at charge boundaries.

Chiral d+id superconducting state exists between trivial states.

Fluctuation distributions depend on temperature and carrier concentration.

Abstract

The behavior of thermal fluctuations of a superconducting order parameter with extended $ s $ and chiral $ d + id $ symmetry is investigated. The study is carried out on a triangular lattice within the framework of the quasi-two-dimensional single-band model with attraction between electrons at neighboring sites. The method of consistent consideration of the order parameter fluctuations and the charge carrier scattering by fluctuations of coupled electron pairs, based on the theory of functional integration is used. The distribution functions of the phase fluctuation probabilities depending on temperature and charge carrier concentration are obtained. The temperature dependences of the amplitudes of the averaged superconducting order parameter are calculated. A phase diagram of superconducting states is constructed for the entire range of variation in the charge carrier concentration $ 0 <n <2 $. Near the boundaries of this range, topologically trivial superconducting states with extended $ s $ symmetry are realized, while a superconducting state with topologically nontrivial chiral $ d + id $ symmetry is realized between them. The calculated anomalous self-energies are compared with the experimental ones obtained using machine learning techniques.