Dual gauge field theory of quantum liquid crystals in two dimensions
By A. Beekman, J. Nissinen, Kai-Hsin Wu, Ke Liu, Robert-Jan Slager, Zohar Nussinov, V. Cvetkovic, J. Zaanen. 2016
171 citations recorded by the source corpus.
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.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics
View Paper: https://www.semanticscholar.org/paper/94a9729ab6d415b76578e5531481d2b4b806546b
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In Atomic and Molecular Physics, and Optics
In Condensed Matter Physics
Citations in the corpus
- Fracton hydrodynamics (2020, background): “[60] Aron J.”
- Planckian dissipation, minimal viscosity and the transport in cuprate strange metals (2018, background): “Dealing with finite density stuff in the Galilean continuum, regardless whether it is a crystal [25], the strongly coupled quantum fluids of holography or a simple quantum gas, it will always exhibit an optical conductivity of the Drude form for the special value τK “ 8.”
- Towards Classification of Fracton Phases: The Multipole Algebra (2018, background): “Furthermore, theories with anisotropic scaling appear in the theories of liquid crystals [72,73] and nematic-smectic transitions [74].”