Mesoscopic superconductivity in ultrasmall metallic grains

Abstract

Abstract.A nano-scale metallic grain (nanoparticle) with irregular boundaries in which the single-particle dynamics are chaotic is a zero-dimensional system described by the so-called universal Hamiltonian in the limit of a large number of electrons. The interaction part of this Hamiltonian includes a superconducting pairing term and a ferromagnetic exchange term. Spin-orbit scattering breaks spin symmetry and suppresses the exchange interaction term. Of particular interest is the fluctuation-dominated regime, typical of the smallest grains in the experiments, in which the bulk pairing gap is comparable to or smaller than the single-particle mean-level spacing, and the Bardeen-Cooper-Schrieffer (BCS) mean-field theory of superconductivity is no longer valid. Here we study the crossover between the BCS and fluctuation-dominated regimes in two limits. In the absence of spin-orbit scattering, the pairing and exchange interaction terms compete with each other. We describe the signatures of this competition in thermodynamic observables, the heat capacity and spin susceptibility. In the presence of strong spin-orbit scattering, the exchange interaction term can be ignored. We discuss how the magnetic-field response of discrete energy levels in such a nanoparticle is affected by pairing correlations. We identify signatures of pairing correlations in this response, which are detectable even in the fluctuation-dominated regime.

Pairing Hamiltonians of Nearest-Neighbor Interacting Superconducting Qubits on an IBM Quantum Computer

“…In the context of type-1 superconductors, pairing Hamiltonians like the BCS Hamiltonian [22] introduces complex long-range many-body interactions that are typically beyond the capabilities of classical computers to solve. Nonetheless, conducting extensive numerical simulations involving these pairing Hamiltonians holds significant value, both in advancing superconducting quantum computing technology and in conducting scientific inquiries into quantum systems within mesoscopic condensed matter, ultra-small metallic grains, and heavy nuclei [23]. An effort has been made to address this challenge through the proposal of a polynomial time quantum algorithm based on nuclear magnetic resonance (NMR) quantum computing [24].…”