Josephson scanning tunneling spectroscopy in superconducting phases coexisting with pair-, charge- and spin-density-waves

TL;DR

This paper shows that spatial oscillations in superconducting coherence peaks, observed in various materials, can be explained by coexisting density-wave phases, and these oscillations can be visualized using Josephson scanning tunneling spectroscopy.

Contribution

It demonstrates how Josephson scanning tunneling spectroscopy can image spatial oscillations of the superconducting order parameter caused by coexisting density-wave phases in superconductors.

Findings

Spatial oscillations in coherence peaks are consistent with density-wave phases.

Oscillations of the order parameter can be imaged via critical Josephson current.

Relative phase shifts depend on the type of density wave (charge or spin).

Abstract

We demonstrate that the recent observations of spatial oscillations in the energy position of the superconducting coherence peaks in the cuprate, transition metal dichalcogenide, iron-based and heavy-fermion superconductors are consistent with the possible presence of a pair-, charge- or spin-density-wave phase. We show that for all three cases, the spatial oscillations of the superconducting order parameter, $\Delta({\bf r})$ can be imaged via the critical Josephson current, $I_c({\bf r})$ measured in Josephson scanning tunneling spectroscopy experiments. Finally, we show that the spatial oscillations of the density waves and of $\Delta({\bf r})$ exhibit relative phase shifts of $\Delta \phi = 0$ or $\pi$ for a charge-density wave, and $\Delta \phi =\pi/2$ for the spin-density wave.