Hydrodynamics of a superfluid smectic

TL;DR

This paper analyzes the hydrodynamic modes of a superfluid smectic phase, revealing a second-sound mode at zero temperature linked to broken symmetries, with explicit velocity expressions based on system parameters.

Contribution

It provides the first detailed hydrodynamic description of a superfluid smectic phase, connecting broken symmetries to observable sound modes and deriving explicit velocity formulas.

Findings

Identification of a second-sound mode at zero temperature.

Derivation of explicit formulas for sound velocities.

Connection to supersolid and stripe phases in Bose gases.

Abstract

We determine the hydrodynamic modes of the superfluid analog of a smectic-A phase in liquid crystals, i.e., a state in which both gauge invariance and translational invariance along a single direction are spontaneously broken. Such a superfluid smectic provides an idealized description of the incommensurate supersolid state realized in Bose-Einstein condensates with strong dipolar interactions as well as of the stripe phase in Bose gases with spin-orbit coupling. We show that the presence of a finite normal fluid density in the ground state of these systems gives rise to a well-defined second-sound type mode even at zero temperature. It replaces the diffusive permeation mode of a normal smectic phase and is directly connected with the classic description of supersolids by Andreev and Lifshitz in terms of a propagating defect mode. An analytic expression is derived for the two sound velocities that appear in the longitudinal excitation spectrum. It only depends on the low-energy parameters associated with the two independent broken symmetries, which are the effective layer compression modulus and the superfluid fraction.