Surface State of Inter-orbital Pairing State in Sr$_2$RuO$_4$ Superconductor

TL;DR

This paper investigates the surface states of a proposed inter-orbital odd spin-triplet s-wave superconductor in Sr$_2$RuO$_4$, revealing chiral d-wave characteristics and robust zero-energy peaks in the local density of states.

Contribution

It demonstrates that the inter-orbital pairing transforms into a chiral d-wave state with distinctive surface states and analyzes their robustness against perturbations.

Findings

Surface states appear near zero energy due to chiral d-wave pairing.

Pseudo-Zeeman field causes band splitting of surface states, smaller than the gap.

Zero-energy LDOS peak is robust under various perturbations.

Abstract

We study the (001) surface state of a recently proposed $E_g$ symmetry inter-orbital-odd spin-triplet s-wave superconducting (SC) state in Sr$_2$RuO$_4$ (SRO). We confirm that this pair potential is transformed into a chiral $d$-wave pair potential and a pseudo-Zeeman field in the band basis for a low-energy range. Due to the chiral $d$-wave pair potential, the surface states appear near zero energy in the momentum range enclosed by the nodal lines of the chiral d-wave pair potential for each band at the (001) surface. Nevertheless, the pseudo-Zeeman field gives band splitting of the surface states, and its splitting energy is much smaller than the SC energy gap. The local density of states (LDOS) at the (001) surface of the SC state has a pronounced peak structure at zero energy due to the surface states near zero energy when the order of the resolution is lower than the splitting energy. This peak structure is robust under perturbations, such as an orbital Rashba coupling or an $E_u$ SC pair potential at the surface.