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

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

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

“…Calculations of the TI C 1 (12) were carried out in the range of concentrations where the superconducting phase of the system under consideration has a d + id type of symmetry (α = 2π/3). For example, figure 1 shows a phase diagram of the dependence of the order parameter on the electron concentration at a value of the interelectronic attraction parameter [19]). In the concentration range where the superconducting phase has a generalized s symmetry (α = 0), from the explicit expression for C 1 (12) it follows that C 1 = 0 for any temperatures and system parameters (see appendix B).…”

“….⟩ is carried out with the distribution function of phase fluctuations, which is determined from a self-consistent system of equations. This system of equations is formed by the condition of the minimum thermodynamic potential together with the equations for the chemical potential, the distribution function of phase fluctuations and the self-energy part of the one-electron Green's function [19,23]. The numerical solution of this system of equations makes it possible to determine the superconducting properties of the system under consideration, taking into account thermal fluctuations.…”

“…The main purpose of this work is to study the effect of thermal fluctuations on the TI. It should be noted that although the work is not aimed at describing real superconductors, the considered Hamiltonian and the chosen parameters were used by us earlier to describe layered compounds with a triangular lattice, such as Na x CoO 2 • yH 2 O sodium cobaltites intercalated with water [19]. In addition, this Hamiltonian was considered in the study of nonequilibrium topological phase transitions without taking into account both quantum and thermal fluctuations in recent work [20].…”

“…In addition, this Hamiltonian was considered in the study of nonequilibrium topological phase transitions without taking into account both quantum and thermal fluctuations in recent work [20]. The largest part of the phase diagram (the dependence of the average order parameter on the electron concentration, see figure 1) of such a model is occupied by a superconducting region with chiral d + id symmetry and nontrivial topology (C 1 = −2) [21], on both concentration sides of which superconducting states with extended s symmetry with trivial topology (C 1 = 0) [19] are realized. Note that taking into account strong correlations does not lead to suppression of the d + id superconducting phase [22].…”