2016/03/31 by Aron Beekman, Aron J. Beekman, Jaakko Nissinen +7 · 159 citations
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Condensed matter physics #Gauge theory #Liquid crystal #Microscopic theory #Phase (matter) #Phase diagram #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum mechanics #Quantum phase transition #Quantum phases #Quantum, superfluid, helium dynamics #Superfluidity #Supersolid #Theoretical physics #Translational symmetry #cond-mat.str-el #cond-mat.supr-con
paper · pdf · doi:10.1016/j.physrep.2017.03.004
published in Physics Reports 683, 1-110 (Elsevier BV) · Review article, 137 pages, 32 figures. Accepted version
openalex publication_date 2017/04/01 · arxiv created 2017/06/06 · arxiv updated 2017/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.