Dual gauge field theory of quantum liquid crystals in two dimensions
We present a selfcontained review of the theory of dislocationmediated quantum melting at zero temperature in two spatial dimensions. The theory describes the liquidcrystalline phases with spatial symmetries in between a quantum crystalline solid and an isotropic superfluid: quantum nematics and smectics. It is based on an AbelianHiggstype 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 twodimensional quantum liquid crystals and the dual theory of stress gauge bosons in bosonic crystals, the theory of melting is developed stepbystep via the disorder theory of dislocationmediated 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 »
 Authors:

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^{[4]};
^{[4]};
^{[5]};
^{[4]};
^{[4]}
 Keio Univ., Kanagawa (Japan); National Institute for Materials Science, Ibaraki (Japan); RIKEN Center for Emergent Matter (CEMS), Saitama (Japan)
 Leiden Univ., Leiden (The Netherlands); Aalto Univ., Aalto (Finland)
 SLAC National Accelerator Lab. and Stanford Univ., Menlo Park, CA (United States)
 Leiden Univ., Leiden (The Netherlands)
 Washington Univ., St. Louis, MO (United States)
 Publication Date:
 Grant/Contract Number:
 AC0276SF00515; S1511006; DMR 1411229
 Type:
 Accepted Manuscript
 Journal Name:
 Physics Reports
 Additional Journal Information:
 Journal Volume: 683; Journal Issue: C; Journal ID: ISSN 03701573
 Publisher:
 Elsevier
 Research Org:
 SLAC National Accelerator Lab., Menlo Park, CA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), High Energy Physics (HEP) (SC25)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 36 MATERIALS SCIENCE; quantum liquid crystals; quantum phase transitions; AbelianHiggs duality; superconductivity
 OSTI Identifier:
 1368572
 Alternate Identifier(s):
 OSTI ID: 1373121
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.,
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. 2017.
"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 selfcontained review of the theory of dislocationmediated quantum melting at zero temperature in two spatial dimensions. The theory describes the liquidcrystalline phases with spatial symmetries in between a quantum crystalline solid and an isotropic superfluid: quantum nematics and smectics. It is based on an AbelianHiggstype 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 twodimensional quantum liquid crystals and the dual theory of stress gauge bosons in bosonic crystals, the theory of melting is developed stepbystep via the disorder theory of dislocationmediated 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 twodimensional quantum smectic turns out to be a dizzyingly anisotropic phase with the collective modes interpolating between the solid and nematic in a nontrivial 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 momentumsensitive spectroscopy.},
doi = {10.1016/j.physrep.2017.03.004},
journal = {Physics Reports},
number = C,
volume = 683,
place = {United States},
year = {2017},
month = {4}
}