Quantum phase transitions in superconducting arrays under external magnetic fields

TL;DR

This paper investigates zero-temperature quantum phase transitions in 2D superconducting arrays under magnetic fields, analyzing excitations, phase boundaries, and their relation to experimental observations and classical XY models.

Contribution

It provides a detailed analysis of phase boundaries influenced by magnetic frustration and suggests the superconductor-insulator transition may differ from the BKT type.

Findings

Phase boundaries depend strongly on magnetic frustration.

Comparison with experiments indicates a non-BKT transition.

Mapping to a 3D XY model reveals transition nature.

Abstract

We study the zero-temperature phase transitions of two-dimensional superconducting arrays with both the self- and the junction capacitances in the presence of external magnetic fields. We consider two kinds of excitations from the Mott insulating phase: charge-dipole excitations and single-charge excitations, and apply the second-order perturbation theory to find their energies. The resulting phase boundaries are found to depend strongly on the magnetic frustration, which measures the commensurate-incommensurate effects. Comparison of the obtained values with those in recent experiment suggests the possibility that the superconductor-insulator transition observed in experiment may not be of the Berezinskii-Kosterlitz-Thouless type. The system is also transformed to a classical three-dimensional XY model with the magnetic field in the time-direction; this allows the analogy to bulk superconductors, revealing the nature of the phase transitions.