Experimental consequences of $p_z$-wave spin triplet superconductivity in A$_2$Cr$_3$As$_3$

TL;DR

This paper theoretically investigates the experimental signatures of $p_z$-wave triplet superconductivity in A$_2$Cr$_3$As$_3$, revealing characteristic power-law behaviors and anisotropic properties consistent with experiments.

Contribution

It provides a detailed theoretical analysis of $p_z$-wave pairing effects on observable properties, supporting the triplet pairing hypothesis in A$_2$Cr$_3$As$_3$.

Findings

Power-law behaviors in specific heat, superfluid density, Knight shift, and spin relaxation rate at low temperatures.

Anisotropic superfluid density with in-plane $ ho_ ho o T$ and out-of-plane $ ho_ot o T^3$.

Consistency of the $p_z$-wave pairing state with experimental upper critical field measurements.

Abstract

The experimental observable properties of the triplet $p_z$-wave pairing state, proposed by Wu {\em et al.} [arXiv:1503.06707] in quasi-one dimensional A$_2$Cr$_3$As$_3$ materials, are theoretically investigated. This pairing state is characterized by the line nodes on the $k_z=0$ plane on the Fermi surfaces. Based on the three-band tight binding model, we obtain the specific heat, superfluid density, Knight shift and spin relaxation rate and find that all these properties at low temperature ($T\ll T_c$) show powerlaw behaviors and are consistent available experiments. Particularly, the superfluid density determined by the $p_z$-wave pairing state in this quasi-one dimensional system is anisotropic: the in-plane superfluid density varies as $\Delta\rho_{\parallel}\sim T$ but the out-plane one varies as $\Delta\rho_{\perp}\sim T^3$ at low temperature. The anisotropic upper critical field reported in experiment is consistent with the $S_z=0$ (i.e., $(\uparrow\downarrow+\downarrow\uparrow)$) $p_z$-wave pairing state. We also suggest the phase-sensitive dc-SQUID measurements to pin down the triplet $p_z$-wave pairing state.