Superconducting order parameter in aperiodic binary systems

Abstract

Recent discovery of the superconducting ground state in systems lacking perfect periodicity but with long-range ordering has opened up an exciting new avenue for superconductivity based on aperiodic systems. In this work, we explore the scope by theoretically investigating the behavior of the superconducting order parameter (OP) in aperiodic binary systems (ABSs), both Fibonacci and non-Fibonacci type, based on the attractive Hubbard model. We begin with one-dimensional toy model, and for the generality of our findings, we extend our analysis to two-dimensional ABSs. Remarkably, despite the increased dimensionality, the qualitative features of the OP remain largely preserved. By systematically analyzing models generated through various growth rules, we elucidate the influence of aperiodicity on the OP amplitudes and how it evolves towards the periodic limit with the change in the structural pattern. We study the evolution of the OP with respect to the temperature, strength of the interaction, and nearest-neighbor hopping amplitude. Our numerical analysis identifies the most favorable ABS and parameter regime that support enhanced onsite pairing amplitudes. Additionally, we provide a comparative analysis of the superconducting transition temperatures across the range of aperiodic configurations. To gain further insight into these systems, we compute key thermodynamic quantities: the entropy and electronic specific heat, and examine their dependence on the underlying structural sequences. This analysis enables us to determine which ABSs are most conducive to Cooper pair formation.

21 pages, 21 figures; Published version