Quantum Smectic and Supersolid Order in Helium Films and Vortex Arrays

TL;DR

This paper explores quantum smectic and supersolid phases in helium films and vortex arrays, revealing stable ordered states, phase transitions, and unique transport properties in layered superconductor and helium systems.

Contribution

It introduces a theoretical framework for quantum smectic and supersolid order in helium films and vortex arrays, highlighting stability and phase behavior under various conditions.

Findings

Stable smectic order in layered superconductors and helium films.

Presence of nonzero superfluid density and propagating third sound modes.

Permeation modes cause small resistivity and finite tilt modulus.

Abstract

A flux liquid can condense into a smectic crystal in a pure layered superconductor with the magnetic field oriented nearly parallel to the layers. Similar order can arise in low temperature $^4$He films with a highly anisotropic periodic substrate potential. If the smectic order is commensurate with the layering, this periodic array is {\sl stable} to quenched random point--like disorder. By tilting and adjusting the magnitude of the applied field, both incommensurate and tilted smectic and crystalline phases are found for vortex arrays. Related variations are possible by changing the chemical potential in the helium system. We discuss transport near the second order smectic freezing transition, and show that permeation modes in superconductors lead to a small non--zero resistivity and a large but finite tilt modulus in the smectic crystal. In helium films, the theory predicts a nonzero superfluid density and propagating third sound modes, showing that the quantum smectic is always simultaneously crystalline and superfluid.