Duality in 2+1D Quantum Elasticity: superconductivity and Quantum Nematic Order

TL;DR

This paper extends the 2D melting theory to 2+1D quantum systems, revealing dualities between quantum crystals, superfluids, and nematic orders, and providing new insights into the nature of superconductivity and quantum nematic phases.

Contribution

It introduces a duality framework for quantum elasticity in 2+1D, linking quantum crystals, superfluids, and nematic phases, and interprets topological order in quantum nematics.

Findings

Quantum crystal dualizes into superfluids or superconductors with nematic order.

Nematic phase interpreted as a topologically ordered quantum phase.

Superfluidity viewed as elastic medium losing shear rigidity.

Abstract

The generalization of the Nelson-Halperin-Young theory of 2D melting to the dynamical 2+1D quantum case is presented. The bosonic quantum crystal dualizes in superfluids or superconductors exhibiting nematic liquid crystalline orders, corresponding with bose condensates of dislocations exhibiting a dual shear Meissner-Higgs mechanism. The topologically ordered nematic phase suggested by Lammert, Toner and Rokshar finds a simple interpretation in this framework. The ordered nematic is a true quantum phase: the dynamical glide principle interferes with the effect that the phonon spectrum of the crystal re-emerges in the direction orthogonal to the director. Novel insights follow from the duality on the fundamental nature of superfluidity and superconductivity. The superfluid can be viewed as an elastic medium having lost its rigidity against shear stresses. Upon dualizing the electrically charged crystal the electromagnetic Meissner phase is recovered, showing peculiar screening current oscillations when the shear penetration depth becomes larger than the London penetration depth.