Unconventional superconducting phases on a two-dimensional extended Hubbard model

TL;DR

This paper explores the phase diagram of a 2D extended Hubbard model, revealing various unconventional superconducting phases, including d-wave and p-wave pairings, with implications for realizing Majorana fermions in cold atom systems.

Contribution

It identifies new superconducting phases in the extended Hubbard model with specific interactions and fillings, expanding understanding of pairing mechanisms in 2D systems.

Findings

Charge-density-wave phase at half-filling transitions to d_{xy}-wave superconductivity away from half-filling.

Emergence of triplet (p_x + ip_y)-wave pairing when nesting is suppressed and with nearest-neighbor attraction.

Dominance of (p_x + ip_y)-wave superconductivity at low fillings with no nesting, suggesting potential for Majorana fermions.

Abstract

We study the phase diagram of the extended Hubbard model on a two-dimensional square lattice, including on-site (U) and nearest-neighbor (V) interactions, at weak couplings. We show that the charge-density-wave phase that is known to occur at half-filling when 4V > U gives way to a d_{xy} -wave superconducting instability away from half-filling, when the Fermi surface is not perfectly nested, and for sufficiently large repulsive and a range of on-site repulsive interaction. In addition, when nesting is further suppressed and in presence of a nearest-neighbor attraction, a triplet time-reversal breaking (p_x + ip_y)-wave pairing instability emerges, competing with the d_{x2+y2} pairing state that is known to dominate at fillings just slightly away from half. At even smaller fillings, where the Fermi surface no longer presents any nesting, the (p_x +ip_y)-wave superconducting phase dominates in the whole regime of on-site repulsions and nearest-neighbor attractions, while d_{xy}-pairing occurs in the presence of on-site attraction. Our results suggest that zero-energy Majorana fermions can be realized on a square lattice in the presence of a magnetic field. For a system of cold fermionic atoms on a two-dimensional square optical lattice, both an on-site repulsion and a nearest-neighbor attraction would be required, in addition to rotation of the system to create vortices. We discuss possible ways of experimentally engineering the required interaction terms in a cold atom system.