2017
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 Tijdschriftartikel
In: PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS, vol. 683, pp. 1-110, 2017, ISSN: 0370-1573.
Abstract | Links | BibTeX | Tags: Quantum liquid crystals; Quantum phase transitions; Abelian-Higgs duality; Superconductivity
@article{WOS:000401977000001,
title = {Dual gauge field theory of quantum liquid crystals in two dimensions},
author = {Aron J. Beekman and Jaakko Nissinen and Kai Wu and Ke Liu and Robert-Jan Slager and Zohar Nussinov and Vladimir Cvetkovic and Jan Zaanen},
doi = {10.1016/j.physrep.2017.03.004},
issn = {0370-1573},
year = {2017},
date = {2017-04-01},
journal = {PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS},
volume = {683},
pages = {1-110},
publisher = {ELSEVIER},
address = {RADARWEG 29, 1043 NX AMSTERDAM, NETHERLANDS},
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 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. (C) 2017 Elsevier B.V.
All rights reserved.},
keywords = {Quantum liquid crystals; Quantum phase transitions; Abelian-Higgs duality; Superconductivity},
pubstate = {published},
tppubtype = {article}
}
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. Their special properties inherited from
spatial symmetry breaking show up mostly at finite momentum, and should
be accessible by momentum-sensitive spectroscopy. (C) 2017 Elsevier B.V.
All rights reserved.
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. Their special properties inherited from
spatial symmetry breaking show up mostly at finite momentum, and should
be accessible by momentum-sensitive spectroscopy. (C) 2017 Elsevier B.V.
All rights reserved.