Correlation induced $d$-wave pairing in quantum dot square lattice

TL;DR

This paper investigates how electron-electron correlations in a quantum dot square lattice induce a $d$-wave paired state, revealing a transition to a Mott insulator and superconducting-like domes similar to cuprates.

Contribution

It introduces a detailed model of correlated electrons in quantum dot lattices and uncovers $d$-wave pairing and Mott insulating phases through advanced computational methods.

Findings

Identification of a transition from moderate to strong correlations.

Observation of a Mott insulator phase with antiferromagnetic order.

Discovery of a two-dome $d$-wave pairing structure near half-filling.

Abstract

We consider an electrostatically induced square lattice of quantum dots and study the role of electron-electron correlations in the resulting electronic features of the system. We utilize the Wannier functions methodology in order to construct Hamiltonian for interacting fermions and find that the change of the depth of the quantum dot confining potential results in a transition from a moderately-, to strong-correlated regime of the system. We obtain the approximate ground state by means of Variational Monte-Carlo method for a wide range of dopings. The values of microscopic parameters, charge gap as well as spin- and pair-correlation functions obtained in the strongly-correlated regime signify the presence of antiferromagnetic spin-ordering and the realization of the Mott insulator phase. Moreover, we report on a two dome structure of the emerging $d$-wave paired state residing on both sides of the half filled case. The obtained results are discussed in view of the well known families of unconventional superconducting materials such as copper based compounds.