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Title: Dual gauge field theory of quantum liquid crystals in three dimensions

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. Lastly, 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.
Authors:
 [1] ;  [2] ;  [3] ;  [4]
  1. Keio Univ., Kanagawa (Japan)
  2. Leiden Univ., Leiden (The Netherlands); Aalto Univ., Aalto (Finland)
  3. SLAC National Accelerator Lab., Stanford Univ., Menlo Park, CA (United States)
  4. Leiden Univ., Leiden (The Netherlands)
Publication Date:
Grant/Contract Number:
AC02-76SF00515; S1511006; 694248
Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 96; Journal Issue: 16; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Research Org:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 36 MATERIALS SCIENCE
OSTI Identifier:
1408231

Beekman, Aron J., Nissinen, Jaakko, Wu, Kai, and Zaanen, Jan. Dual gauge field theory of quantum liquid crystals in three dimensions. United States: N. p., Web. doi:10.1103/physrevb.96.165115.
Beekman, Aron J., Nissinen, Jaakko, Wu, Kai, & Zaanen, Jan. Dual gauge field theory of quantum liquid crystals in three dimensions. United States. doi:10.1103/physrevb.96.165115.
Beekman, Aron J., Nissinen, Jaakko, Wu, Kai, and Zaanen, Jan. 2017. "Dual gauge field theory of quantum liquid crystals in three dimensions". United States. doi:10.1103/physrevb.96.165115. https://www.osti.gov/servlets/purl/1408231.
@article{osti_1408231,
title = {Dual gauge field theory of quantum liquid crystals in three dimensions},
author = {Beekman, Aron J. and Nissinen, Jaakko and Wu, Kai and Zaanen, Jan},
abstractNote = {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. Lastly, 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.},
doi = {10.1103/physrevb.96.165115},
journal = {Physical Review B},
number = 16,
volume = 96,
place = {United States},
year = {2017},
month = {10}
}

Works referenced in this record:

Ordering, metastability and phase transitions in two-dimensional systems
journal, April 1973
  • Kosterlitz, J M; Thouless, D J
  • Journal of Physics C: Solid State Physics, Vol. 6, Issue 7, p. 1181-1203
  • DOI: 10.1088/0022-3719/6/7/010