Dual gauge field theory of quantum liquid crystals in three dimensions

Aron J. Beekman*, Jaakko Nissinen, Kai Wu, Jan Zaanen

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

37 Citations (Scopus)
131 Downloads (Pure)

Abstract

The dislocation-mediated quantum melting of solids into quantum liquid crystals is extended from two to three spatial dimensions, using a generalization of boson-vortex or Abelian-Higgs duality. Dislocations are now Burgers-vector-valued strings that trace out worldsheets in space-time while the phonons of the solid dualize into two-form (Kalb-Ramond) gauge fields. We propose an effective dual Higgs potential that allows for restoring translational symmetry in either one, two, or three directions, leading to the quantum analogues of columnar, smectic, or nematic liquid crystals. In these phases, transverse phonons turn into gapped, propagating modes, while compressional stress remains massless. Rotational Goldstone modes emerge whenever translational symmetry is restored. We also consider the effective electromagnetic response of electrically charged quantum liquid crystals, and find among other things that as a hard principle only two out of the possible three rotational Goldstone modes are observable using propagating electromagnetic fields.

Original languageEnglish
Article number165115
Pages (from-to)1-50
JournalPhysical Review B
Volume96
Issue number16
DOIs
Publication statusPublished - 9 Oct 2017
MoE publication typeA1 Journal article-refereed

Keywords

  • HIGH-TEMPERATURE SUPERCONDUCTORS
  • PAIR-DENSITY-WAVE
  • ROTATIONAL ELASTICITY
  • CRITICAL FLUCTUATIONS
  • II SUPERCONDUCTORS
  • PHASE-TRANSITION
  • MAGNETIC-FIELD
  • NEMATIC PHASES
  • SYSTEMS
  • ORDER

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