Dual gauge field theory of quantum liquid crystals in two dimensions

Beekman, Aron J.; Nissinen, Jaakko; Wu, Kai; Liu, Ke; Slager, Robert -Jan; Nussinov, Zohar; Cvetkovic, Vladimir; Zaanen, Jan

doi:10.1016/j.physrep.2017.03.004

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

Journal Article · Tue Apr 18 00:00:00 EDT 2017 · Physics Reports

DOI:https://doi.org/10.1016/j.physrep.2017.03.004· OSTI ID:1368572

^[1]; Nissinen, Jaakko ^[2]; Wu, Kai ^[3]; Liu, Ke ^[4]; Slager, Robert -Jan ^[4]; Nussinov, Zohar ^[5]; Cvetkovic, Vladimir ^[4]; Zaanen, Jan ^[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)

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. 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. Their special properties inherited from spatial symmetry breaking show up mostly at finite momentum, and should be accessible by momentum-sensitive spectroscopy.

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Research Organization:: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: AC02-76SF00515; S1511006; DMR 1411229

OSTI ID:: 1368572

Alternate ID(s):: OSTI ID: 1373121

Journal Information:: Physics Reports, Vol. 683, Issue C; ISSN 0370-1573

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 81 works

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