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

Abstract

We present a self-contained review of the theory of dislocation-mediated quantum melting at zero temperature in two spatial dimensions. The theory describes the liquid-crystalline phases with spatial symmetries in between a quantum crystalline solid and an isotropic superfluid: quantum nematics and smectics. It is based on an Abelian-Higgs-type duality mapping of phonons onto gauge bosons (“stress photons”), which encode for the capacity of the crystal to propagate stresses. Dislocations and disclinations, the topological defects of the crystal, are sources for the gauge fields and the melting of the crystal can be understood as the proliferation (condensation) of these defects, giving rise to the Anderson–Higgs mechanism on the dual side. For the liquid crystal phases, the shear sector of the gauge bosons becomes massive signaling that shear rigidity is lost. After providing the necessary background knowledge, including the order parameter theory of two-dimensional quantum liquid crystals and the dual theory of stress gauge bosons in bosonic crystals, the theory of melting is developed step-by-step via the disorder theory of dislocation-mediated melting. Resting on symmetry principles, we derive the phenomenological imaginary time actions of quantum nematics and smectics and analyze the full spectrum of collective modes. The quantum nematic is a superfluidmore » having a true rotational Goldstone mode due to rotational symmetry breaking, and the origin of this ‘deconfined’ mode is traced back to the crystalline phase. The two-dimensional quantum smectic turns out to be a dizzyingly anisotropic phase with the collective modes interpolating between the solid and nematic in a non-trivial way. We also consider electrically charged bosonic crystals and liquid crystals, and carefully analyze the electromagnetic response of the quantum liquid crystal phases. In particular, the quantum nematic is a real superconductor and shows the Meissner effect. Furthermore, their special properties inherited from spatial symmetry breaking show up mostly at finite momentum, and should be accessible by momentum-sensitive spectroscopy.« less

Authors:
ORCiD logo [1];  [2];  [3];  [4];  [4];  [5];  [4];  [4]
  1. Keio Univ., Kanagawa (Japan); National Institute for Materials Science, Ibaraki (Japan); RIKEN Center for Emergent Matter (CEMS), Saitama (Japan)
  2. Leiden Univ., Leiden (The Netherlands); Aalto Univ., Aalto (Finland)
  3. SLAC National Accelerator Lab. and Stanford Univ., Menlo Park, CA (United States)
  4. Leiden Univ., Leiden (The Netherlands)
  5. Washington Univ., St. Louis, MO (United States)
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
OSTI Identifier:
1368572
Alternate Identifier(s):
OSTI ID: 1373121
Grant/Contract Number:  
AC02-76SF00515; S1511006; DMR 1411229
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physics Reports
Additional Journal Information:
Journal Volume: 683; Journal Issue: C; Journal ID: ISSN 0370-1573
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 36 MATERIALS SCIENCE; quantum liquid crystals; quantum phase transitions; Abelian-Higgs duality; superconductivity

Citation Formats

Beekman, Aron J., Nissinen, Jaakko, Wu, Kai, Liu, Ke, Slager, Robert -Jan, Nussinov, Zohar, Cvetkovic, Vladimir, and Zaanen, Jan. Dual gauge field theory of quantum liquid crystals in two dimensions. United States: N. p., 2017. Web. doi:10.1016/j.physrep.2017.03.004.
Beekman, Aron J., Nissinen, Jaakko, Wu, Kai, Liu, Ke, Slager, Robert -Jan, Nussinov, Zohar, Cvetkovic, Vladimir, & Zaanen, Jan. Dual gauge field theory of quantum liquid crystals in two dimensions. United States. doi:10.1016/j.physrep.2017.03.004.
Beekman, Aron J., Nissinen, Jaakko, Wu, Kai, Liu, Ke, Slager, Robert -Jan, Nussinov, Zohar, Cvetkovic, Vladimir, and Zaanen, Jan. Tue . "Dual gauge field theory of quantum liquid crystals in two dimensions". United States. doi:10.1016/j.physrep.2017.03.004. https://www.osti.gov/servlets/purl/1368572.
@article{osti_1368572,
title = {Dual gauge field theory of quantum liquid crystals in two dimensions},
author = {Beekman, Aron J. and Nissinen, Jaakko and Wu, Kai and Liu, Ke and Slager, Robert -Jan and Nussinov, Zohar and Cvetkovic, Vladimir and Zaanen, Jan},
abstractNote = {We present a self-contained review of the theory of dislocation-mediated quantum melting at zero temperature in two spatial dimensions. The theory describes the liquid-crystalline phases with spatial symmetries in between a quantum crystalline solid and an isotropic superfluid: quantum nematics and smectics. It is based on an Abelian-Higgs-type duality mapping of phonons onto gauge bosons (“stress photons”), which encode for the capacity of the crystal to propagate stresses. Dislocations and disclinations, the topological defects of the crystal, are sources for the gauge fields and the melting of the crystal can be understood as the proliferation (condensation) of these defects, giving rise to the Anderson–Higgs mechanism on the dual side. For the liquid crystal phases, the shear sector of the gauge bosons becomes massive signaling that shear rigidity is lost. After providing the necessary background knowledge, including the order parameter theory of two-dimensional quantum liquid crystals and the dual theory of stress gauge bosons in bosonic crystals, the theory of melting is developed step-by-step via the disorder theory of dislocation-mediated melting. Resting on symmetry principles, we derive the phenomenological imaginary time actions of quantum nematics and smectics and analyze the full spectrum of collective modes. The quantum nematic is a superfluid having a true rotational Goldstone mode due to rotational symmetry breaking, and the origin of this ‘deconfined’ mode is traced back to the crystalline phase. The two-dimensional quantum smectic turns out to be a dizzyingly anisotropic phase with the collective modes interpolating between the solid and nematic in a non-trivial way. We also consider electrically charged bosonic crystals and liquid crystals, and carefully analyze the electromagnetic response of the quantum liquid crystal phases. In particular, the quantum nematic is a real superconductor and shows the Meissner effect. Furthermore, their special properties inherited from spatial symmetry breaking show up mostly at finite momentum, and should be accessible by momentum-sensitive spectroscopy.},
doi = {10.1016/j.physrep.2017.03.004},
journal = {Physics Reports},
number = C,
volume = 683,
place = {United States},
year = {Tue Apr 18 00:00:00 EDT 2017},
month = {Tue Apr 18 00:00:00 EDT 2017}
}

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