Spin-polarized superconducting phase in semiconducting system with next-nearest-neighbor hopping on the honeycomb lattice

TL;DR

This paper investigates how next-nearest-neighbor hopping influences the superconducting phases in a honeycomb lattice Hubbard model, revealing a spin-polarized superconducting phase and a change in phase transition nature under magnetic fields.

Contribution

It demonstrates the impact of next-nearest-neighbor hopping on phase transition order and the emergence of spin-polarized superconductivity in the honeycomb lattice Hubbard model.

Findings

Transition changes from discontinuous to continuous with non-zero $t'$.

Spin-polarized superconducting phase appears at half-filling under magnetic field.

Behavior is linked to Dirac cones in the band structure.

Abstract

The particles in the honeycomb lattice with on-site $s$-wave pairing exhibit many interesting behaviors, which can be described in the framework of the Hubbard model. Among others, at the half-filling, some critical value $|U_c|$ of pairing interaction $U<0$ exists that, for $U<U_c$, the superconducting phase becomes unstable. Introduction of the nonzero hopping $t'$ between next-nearest-neighbor sites strongly modifies the physical properties of the system. Here, we discuss the behavior of the system for $t' \neq 0$ (at the ground state), where the hopping between next-nearest neighbors leads to change of the order of phase transition between superconducting and normal phases from discontinuous to continuous one in the external magnetic field $h$. We show that this behavior is strongly dependent on $t'$ and associated with the Dirac cones in the non-interacting band structure of the system. For non-zero magnetic field and for some range of $t'$, a spin-polarized superconducting phase occurs in the ground state phase diagram (only at the half-filling and for $h\neq 0$).