Competition and coexistence of superconductivity and nematic order in a two-dimensional electron gas with quadrupolar interactions

TL;DR

This paper explores how superconductivity and nematic order interact in a two-dimensional electron gas, revealing phase transitions and coexistence regimes influenced by interaction strengths and temperature.

Contribution

It introduces a minimal mean-field model capturing the competition and coexistence of superconductivity and nematic order with detailed phase diagrams.

Findings

Nematic order competes with d-wave superconductivity, causing a first-order transition.

Coexistence of s-wave superconductivity and nematic order results in an anisotropic Fermi surface.

Finite temperature interactions lead to regimes with multiple coexisting orders.

Abstract

We investigate the interplay between superconductivity and nematic order in a two-dimensional electron gas with competing pairing and quadrupolar forward-scattering interactions. The model includes both $s$-wave and $d$-wave superconducting channels. We compute the mean-field free energy density and determine the phase diagrams as functions of interaction strengths and temperature by solving a set of coupled self-consistent equations. At zero-temperature, we find that the nematic order competes strongly with $d$-wave superconductivity, leading to a direct first-order phase transition, while its interplay with $s$-wave pairing allows for a coexistence phase characterized by an anisotropic Fermi surface with a uniform superconducting gap. At finite-temperatures, quadrupolar interactions promote the emergence of additional superconducting components, giving rise to regimes where $s$-wave, $d$-wave, and nematic orders coexist. Our results highlight the role of symmetry and interaction strength in shaping the phase structure and provide a minimal framework to describe intertwined nematic and superconducting phases in correlated electron systems.