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; Cvetković, Vladimir; Zaanen, Jan

doi:10.1016/j.physrep.2017.03.004

Cited by 147 publications

(218 citation statements)

References 196 publications

(468 reference statements)

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“…[52][53][54][55][56][57][58][59][60]. Some of these works generalize the well established theory of classical, thermal melting transitions [61,62], leading to electronic liquid crystal phases [63].…”

mentioning

confidence: 81%

“…The equilibrium physics of different patterns of symmetry breaking is described by the theory of elasticity, see e.g. [63], and dissipative hydrodynamics is built on top of that. The smectic case is anisotropic, so a bidirectional charge density wave will be necessary to have bad metallic behavior in all directions.…”

Section: A Hydrodynamic Derivationsmentioning

confidence: 99%

“…3, 025 (2017) established theory of classical, thermal melting transitions [61,62], leading to electronic liquid crystal phases [63].…”

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confidence: 99%

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Bad Metals from Fluctuating Density Waves

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Bad metals have a large resistivity without being strongly disordered. In many bad metals the Drude peak moves away from zero frequency as the resistivity becomes large at increasing temperatures. We catalogue the position and width of the 'displaced Drude peak' in the observed optical conductivity of several families of bad metals, showing that ω peak ∼ ∆ω ∼ k B T /ħ h. This is the same quantum critical timescale that underpins the T -linear dc resistivity of many of these materials. We provide a unified theoretical description of the optical and dc transport properties of bad metals in terms of the hydrodynamics of short range quantum critical fluctuations of incommensurate density wave order. Within hydrodynamics, pinned translational order is essential to obtain the nonzero frequency peak. Check for updates doi:10.21468/SciPostPhys.3.3.025 Bad metals are defined by the fact that if their electrical resistivity is interpreted within a conventional Drude formalism, the corresponding mean free path of the quasiparticles is so short that the Boltzmann equation underlying Drude theory is not consistent [1][2][3]. As such, bad metals pose a long-standing challenge to theory. In this work we show that the hydrodynamics of phase-fluctuating charge density waves can lead to bad metallic behavior. Hydrodynamics is a tightly constrained formalism for the low energy and long wavelength dynamics of media [4,5]. Non-quasiparticle media, in particular, exhibit fast local thermalization leading to extended hydrodynamics regimes. Phase fluctuations in the density wave can be robustly incorporated into this description and will be essential in order for the states to be metallic, rather than insulating. We will use the hydrodynamic framework to explain observed dc and optical transport behavior that is common to several families of bad metal materials.Recent work has emphasized that the absence of quasiparticles is not sufficient to obtain a bad metal [6]. If the total momentum of the charge carriers is long-lived, then the resistivity will be small even if all single-particle excitations decay rapidly. The importance of the fate of momentum for transport has long been appreciated [7,8], but has acquired renewed relevance 1 SciPost Phys. 3, 025 (2017) in the context of modern unconventional metals, e.g. [9,10]. Two previously considered scenarios for removing the long-lived momentum (sound) mode from the collective description of charge transport are as follows. Firstly, that the low energy, non-quasiparticle, description of bad metals is strongly non-translationally invariant and hence momentum is absent from the hydrodynamic description [6]. Secondly, that an emergent particle-hole symmetry at low energies decouples charge transport from momentum [11]. These mechanisms do not seem to be at work in bad metals. The resistivity of bad metals is not typically strongly dependent on the strength of disorder and some bad metals appear to be relatively clean. Emergent particle-hole symmetry does not decouple momentum ...

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confidence: 81%

Section: A Hydrodynamic Derivationsmentioning

confidence: 99%

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Bad Metals from Fluctuating Density Waves

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“…Recently, we have written an extensive review that comprehensively details the dual gauge field theory of these quantum liquid crystals in two dimensions [42], to which we shall hereafter refer as QLC2D. The present work is the extension of this theory to three spatial dimensions and we recommend the novice to the subject to have a close look at QLC2D first.…”

Section: A Quantum Liquid Crystals: the Contextmentioning

confidence: 99%

Dual gauge field theory of quantum liquid crystals in three dimensions

Beekman

Nissinen

et al. 2017

Phys. Rev. B

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The dislocation-mediated quantum melting of solids into quantum liquid crystals is extended from two to three spatial dimensions, using a generalization of boson-vortex or Abelian-Higgs duality. Dislocations are now Burgers-vector-valued strings that trace out worldsheets in space-time while the phonons of the solid dualize into two-form (Kalb-Ramond) gauge fields. We propose an effective dual Higgs potential that allows for restoring translational symmetry in either one, two, or three directions, leading to the quantum analogues of columnar, smectic, or nematic liquid crystals. In these phases, transverse phonons turn into gapped, propagating modes, while compressional stress remains massless. Rotational Goldstone modes emerge whenever translational symmetry is restored. We also consider the effective electromagnetic response of electrically charged quantum liquid crystals, and find among other things that as a hard principle only two out of the possible three rotational Goldstone modes are observable using propagating electromagnetic fields.

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“…A very general framework of a gauge field theory of quantum liquid crystals at T = 0 in continuum space has also been proposed and recently reviewed in [22].…”

Section: Introductionmentioning

confidence: 99%

Quantum and thermal melting of stripe forming systems with competing long-range interactions

2017

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We study the quantum melting of stripe phases in models with competing short range and long range interactions decaying with distance as 1/r σ in two space dimensions. At zero temperature we find a two step disordering of the stripe phases with the growth of quantum fluctuations. A quantum critical point separating a phase with long range positional order from a phase with long range orientational order is found when σ ≤ 4/3, which includes the Coulomb interaction case σ = 1. For σ > 4/3 the transition is first order, which includes the dipolar case σ = 3. Another quantum critical point separates the orientationally ordered (nematic) phase from a quantum disordered phase for any value of σ. Critical exponents as a function of σ are computed at one loop order in an expansion and, whenever available, compared with known results. For finite temperatures it is found that for σ ≥ 2 orientational order decays algebraically with distance until a critical Kosterlitz-Thouless line. Nevertheless, for σ < 2 it is found that long range orientational order can exist at finite temperatures until a critical line which terminates at the quantum critical point at T = 0. The temperature dependence of the critical line near the quantum critical point is determined as a function of σ.

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Dual gauge field theory of quantum liquid crystals in two dimensions

Cited by 147 publications

References 196 publications

Bad Metals from Fluctuating Density Waves

Bad Metals from Fluctuating Density Waves

Dual gauge field theory of quantum liquid crystals in three dimensions

Quantum and thermal melting of stripe forming systems with competing long-range interactions

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