Possible anomalous Doppler shift effect in superconductor Sr$_{2}$RuO$_{4}$

TL;DR

This paper investigates how the Doppler shift affects surface states and thermal conductivity in Sr$_2$RuO$_4$, revealing a crossover from 2D to 1D behavior and a dominant two-fold symmetry in thermal conductivity oscillations.

Contribution

It models the $eta$ bands of Sr$_2$RuO$_4$ to show how hybridization influences oscillation symmetry, providing insights into the superconducting gap structure.

Findings

Oscillation exhibits 2D to 1D crossover with hybridization strength.

Thermal conductivity shows dominant two-fold symmetry in the crossover regime.

Four-fold symmetry component is barely detectable in the observed regime.

Abstract

The effect of the Doppler shift is studied in a model for the $\alpha$-$\beta$ bands of Sr$_2$RuO$_4$ consisting of two hybridized 1D bands. Assuming a superconducting gap with nodes in the diagonal directions, we examine the oscillation of the surface density of states and the thermal conductivity under a rotating magnetic field. Upon varying the strength of the hybridization, the oscillation in these quantities is found to exhibit 2D to 1D crossover. In the crossover regime, which corresponds to the actual Sr$_2$RuO$_4$, the thermal conductivity exhibits a two-fold-symmetry oscillation, while the four-fold-symmetry component in the oscillation is barely detectable.