Effect of thermal fluctuations on topological crossover in the chiral d+id superconducting phase

TL;DR

The paper investigates how finite-temperature thermal fluctuations influence the topological index $C_1$ of a chiral $d+id$ superconducting phase in a two-dimensional single-band model on a triangular lattice. It adopts a self-consistent functional-integral framework to include fluctuations in the Green's functions, yielding a temperature-dependent self-energy and a renormalized chemical potential $\mu^{*}$ that renormalizes the Fermi contour, with energy scales in units of the hopping $t$. The main finding is that thermal fluctuations broaden the temperature windows where $C_1$ remains near integer values, with stronger effects for the $C_1=4$ phase; when nodal points approach the Fermi contour, two regimes arise: weak renormalization ($V=2$) preserves a crossover to $C_1=1$, while strong renormalization ($V=4$) can drive a crossover to $C_1=-2$. The work also discusses implications for edge states under open boundaries via bulk-boundary correspondence and points to potential applications in quantum thermal electronics.

Abstract

The effect of thermal fluctuations on the temperature dependence of the topological index C1 of the chiral d+id superconducting phase of a two-dimensional single-band model on a triangular lattice is investigated. Thermal fluctuations are taken into account within the framework of the self-consistent functional-integral theory. It is established that when the nodal points are located far inside (outside) the Fermi contour of the normal phase, thermal fluctuations expand the relative temperature ranges in which the values of the topological index are close to integer values C1=4(-2). This expansion depends both on the value of the topological index and on the magnitude of the effective attraction between the electrons. However, as the nodal points approach the Fermi contour, topological crossovers to new C1 values are observed, which can persist over a wide temperature range. The nature and degree of influence of thermal fluctuations on these crossovers are established. It is assumed that the observed effects may also manifest in the edge state behavior of a similar system with open boundaries.

Figures (9)

• Figure 1: (Color online) The dependence of the topological index $C_1$ on temperature and chemical potential (phase diagram) in the HF approximation at the value of the interelectron attraction parameter $V=2$. The temperature of the superconducting transition $T_c$ is represented by a black line.
• Figure 2: (Color online) Temperature dependences of the topological index $C_{1}$ in the HF approximation for different values of the interelectron attraction parameter $V=2$ (dotted lines) and $V=4$ (solid lines).
• Figure 3: (Color online) Temperature dependences of the topological index $C_{1}$ in the HF approximation (dotted lines) and taking into account thermal fluctuations (solid lines) at the value of the interelectron attraction parameter $V=2$.
• Figure 4: (Color online) Temperature dependences of the topological index $C_{1}$ in the HF approximation (dotted lines) and taking into account thermal fluctuations (solid lines) at the value of the interelectron attraction parameter $V=4$.
• Figure 5: (Color online) The temperature behavior of the RMSF value of the superconducting order parameter at the value of the interelectron attraction parameter $V=2$.