Disorder in interacting quasi-one-dimensional systems: flat and dispersive bands

TL;DR

This study uses density-matrix renormalization group methods to analyze how flat and dispersive bands influence the superconductor-insulator transition in disordered quasi-one-dimensional systems, revealing the role of disorder symmetry and band structure.

Contribution

It provides a comparative analysis of SIT in flat versus dispersive bands, highlighting the impact of disorder symmetry and the critical disorder amplitude in these systems.

Findings

Flat-band models show a non-zero critical disorder for transition.

Disorder type determines whether transition involves singlet pairs or unpaired fermions.

No intermediate metallic phase observed in all models.

Abstract

We investigate the superconductor-insulator transition (SIT) in disordered quasi-one dimensional systems using the density-matrix renormalization group method. Focusing on the case of an interacting spinful Hamiltonian at quarter-filling, we contrast the differences arising in the SIT when the parent non-interacting model features either flat or dispersive bands. Furthermore, by comparing disorder distributions that preserve or not SU(2)-symmetry, we unveil the critical disorder amplitude that triggers insulating behavior. While scaling analysis suggests the transition to be of a Berezinskii-Kosterlitz-Thouless type for all models (two lattices and two disorder types), only in the flat-band model with Zeeman-like disorder the critical disorder is nonvanishing. In this sense, the flat-band structure does strengthen superconductivity. For both flat and dispersive band models, i) in the presence of SU(2)-symmetric random chemical potentials, the disorder-induced transition is from superconductor to insulator of singlet pairs; ii) for the Zeeman-type disorder, the transition is from superconductor to insulator of unpaired fermions. In all cases, our numerical results suggest no intermediate disorder-driven metallic phase.