Connection between the semiconductor--superconductor transition and the spin-polarized superconducting phase in the honeycomb lattice

TL;DR

This paper explores how the semiconductor--superconductor transition in a honeycomb lattice is influenced by next-nearest-neighbor hopping and magnetic fields, revealing conditions for spin-polarized superconductivity and Lifshitz transitions.

Contribution

It demonstrates that NNN hopping and magnetic fields can tune the critical interaction and induce Lifshitz transitions, affecting the emergence of semiconducting and spin-polarized superconducting phases.

Findings

Critical NNN hopping value is one-third of nearest-neighbor hopping in weak coupling.

Lifshitz transition is induced by NNN hopping and magnetic field.

Sarma phase appears only within certain parameter ranges.

Abstract

The band structure of noninteracting fermions in the honeycomb lattice exhibits the Dirac cones at the corners of the Brillouin zone. As a consequence, fermions in this lattice manifest a semiconducting behavior below some critical value of the onsite attraction, $U_{c}$. However, above $U_{c}$, the superconducting phase can occur. We discuss an interplay between the semiconductor--superconductor transition and the possibility of realization of the spin-polarized superconductivity (the so-called Sarma phase). We show that the critical interaction can be tuned by the next-nearest-neighbor (NNN) hopping in the absence of the magnetic field. Moreover, a critical value of the NNN hopping exists, defining a range of parameters for which the semiconducting phase can emerge. In the weak coupling limit case, this quantum phase transition occurs for the absolute value of the NNN hopping equal to one third of the hopping between the nearest neighbors. Similarly, in the presence of the magnetic field, the Sarma phase can appear, but only in a range of parameters for which initially the semiconducting state is observed. Both of these aspects are attributed to the Lifshitz transition, which is induced by the NNN hopping as well as the external magnetic field.