Zero temperature superconductor - edge metal - insulator transition in $2D$ bosonic systems

TL;DR

This paper explores phase transitions in a 2D bosonic system, revealing an edge metal phase with unique properties and connecting theoretical results to experimental STM observations on MoS2.

Contribution

It introduces a new phase called the edge metal in a 2D bosonic system and analyzes its properties and relation to experimental findings.

Findings

Identification of an edge metal phase with zero superfluid stiffness

Connection of theoretical phases to STM experiments on MoS2

Absence of a 2D metallic conductivity phase

Abstract

Motivated by the recent experimental observation of an intermediate bosonic metallic state in the two-dimensional superconductor-insulator transition at $T=0$, we study an extended Bose Hubbard model in the limit of large number of particles per site. Using a representation of this in terms of two coupled $XY$ models, we find, in addition to an insulating phase and a $(2+1)D$ superfluid phase, two other phases. One phase is a $2D$ superfluid phase where a crossover from $(2+1)D$ to $2D$ has taken place as a result of incipient charge ordering, signaled by $\theta$ disordering, and which is closely related to a supersolid phase. The other new phase is an edge metal state characterized by zero superfluid stiffness, zero charge ordering, and zero bulk compressibility. However, the edge compressibility of the system is nonzero. While we do not find any intermediate state with $2D$ metallic conductivity, we are able to connect these results to STM experiments on $\mathrm{MoS_2}$ showing brims of finite density of states around the entire edge of $2D$ $\mathrm{MoS_2}$ samples.