Dimensional crossover in the quasi-one-dimensional superconductor Tl$_2$Mo$_6$Se$_6$

TL;DR

This paper reports the experimental observation of a dimensional crossover from 1D to 3D superconductivity in Tl$_2$Mo$_6$Se$_6$, revealing multiple fluctuating regimes and phase coherence development within the superconducting state.

Contribution

First experimental evidence of a 1D to 3D superconducting crossover in a homogeneous q1D superconductor, supported by magnetic and transport measurements.

Findings

Identification of multiple energy scales within the superconducting transition.

Observation of 1D pairing fluctuations, phase slips, and 3D phase fluctuations.

Quantitative agreement with a theoretical model for crossovers in q1D superconductors.

Abstract

Long-range order in quasi-one-dimensional (q1D) arrays of superconducting nanowires is established via a dimensional crossover from a fluctuating 1D regime to a phase-coherent 3D ground state. If a homogeneous crystalline superconductor exhibits sufficiently high uniaxial anisotropy, a similar 1D$\rightarrow$3D crossover has been predicted to occur, provided that single-particle hopping transverse to the 1D axis is absent in the normal state. Here we present magnetic penetration depth and electrical transport data in single crystals of q1D Tl$_2$Mo$_6$Se$_6$, which reveal a 1D$\rightarrow$3D superconducting dimensional crossover. Both experimental techniques uncover multiple energy scales within the superconducting transition, which describe a sequence of fluctuating regimes. As the temperature is reduced below $T_{ons}=$~6.7~K, 1D pairing fluctuations are replaced by 1D phase slips below $T_p\sim$~5.9~K. These give way to 3D phase fluctuations below $T_{ab}=$~4.9~K, prior to dimensional crossover at $T_{x2}\sim$~4.4~K. The electrical resistivity below $T_{ab}$ is quantitatively consistent with the establishment of phase coherence through gradual binding of Josephson vortex strings to form 3D loops. An anomalously low superfluid density persist down to $\sim$3~K before rising steeply --- in agreement with a theoretical model for crossovers in q1D superconductors, and suggesting that a small population of unbound, weakly-pinned vortices survives below the crossover. The observation of a dimensional crossover within the superconducting state has important consequences for the low-temperature normal state in Tl$_2$Mo$_6$Se$_6$ and similar q1D metals, which may exhibit one-dimensional behavior over far greater temperature ranges than band structure calculations suggest.