Electrical transport properties near an electronic Ising-nematic quantum critical point in two dimensions are of both theoretical and experimental interest. In this work, we derive a kinetic equation valid in a broad regime near the quantum critical point using the memory matrix approach. The formalism is applied to study the effect of the critical fluctuations on the dc resistivity through different scattering mechanisms, including umklapp, impurity scattering, and electron-hole scattering in a compensated metal. We show that electrical transport in the quantum critical regime exhibits a rich behavior that depends sensitively on the scattering mechanism and the band structure. In the case of a single large Fermi surface, the resistivity due to umklapp scattering crosses over from $ρ\sim T^2$ at low temperature to sublinear at high temperature. The crossover temperature scales as $q_0^3$, where $q_0$ is the minimal wavevector for umklapp scattering. Impurity scattering leads to $ρ-ρ_0\sim T^α$ ($ρ_0$ being the residual resistivity), where $α$ is either larger than 2 if there is only a single Fermi sheet present, or 4/3 in the case of multiple Fermi sheets. Finally, in a perfectly compensated metal with an equal density of electrons and holes, the low temperature behavior depends strongly on the structure of "cold spots" on the Fermi surface, where the coupling between the quasiparticles and order parameter fluctuations vanishes by symmetry. In particular, for a system where cold spots are present on some (but not all) Fermi sheets, $ρ\sim T^{5/3}$. At higher temperatures there is a broad crossover regime where $ρ$ either saturates or $ρ\sim T$, depending on microscopic details. We discuss these results in the context of recent quantum Monte Carlo simulations of a metallic Ising nematic critical point, and experiments in certain iron-based superconductors.
The NMR spectrum of FeSe shows a dramatic broadening on cooling towards the bulk nematic phase at $T_s=90$ K, due to the formation of a quasi-static, short-range-ordered nematic domain structure. However, a quantitative understanding of the NMR broadening and its relationship to the nematic susceptibility is still lacking. Here, we show that the temperature and pressure dependence of the broadening is in quantitative agreement with the mean-field Edwards-Anderson parameter of an Ising-nematic model in the presence of random-field disorder introduced by non-magnetic impurities. Furthermore, the…
The Ising nematic quantum critical point (QCP) associated with the zero temperature transition from a symmetric to a nematic {\it metal} is an exemplar of metallic quantum criticality. We have carried out a minus sign-free quantum Monte Carlo study of this QCP for a two dimensional lattice model with sizes up to $24\times 24$ sites. The system remains non-superconducting down to the lowest accessible temperatures. The results exhibit critical scaling behavior over the accessible ranges of temperature, (imaginary) time, and distance. This scaling behavior has remarkable similarities with recent…
Motivated by the properties of the iron chalcogenides, we study the phase diagram of a generalized Heisenberg model with frustrated bilinear-biquadratic interactions on a square lattice. We identify zero-temperature phases with antiferroquadrupolar and Ising-nematic orders. The effects of quantum fluctuations and interlayer couplings are analyzed. We propose the Ising-nematic order as underlying the structural phase transition observed in the normal state of FeSe, and discuss the role of the Goldstone modes of the antiferroquadrupolar order for the dipolar magnetic fluctuations in this system.…
The Schwinger-boson theory of the frustrated square lattice antiferromagnet yields a stable, gapped $\mathbb{Z}_2$ spin liquid ground state with time-reversal symmetry, incommensurate spin correlations and long-range Ising-nematic order. We obtain an equivalent description of this state using fermionic spinons (the fermionic spinons can be considered to be bound states of the bosonic spinons and the visons). Upon doping, the $\mathbb{Z}_2$ spin liquid can lead to a fractionalized Fermi liquid (FL*) with small Fermi pockets of electron-like quasiparticles, while preserving the $\mathbb{Z}_2$ to…
Recent Raman scattering experiments have revealed a "quasi-elastic peak" in $\mathrm{FeSe_{1-x}S_x}$ near an Ising-nematic quantum critical point (QCP) \cite{zhang17}. Notably, the peak occurs at sub-temperature frequencies, and softens as $T^α$ when temperature is decreased toward the QCP, with $α>1$. In this work, we present a theoretical analysis of the low-frequency Raman response using a memory matrix approach. We show that such a quasi-elastic peak is associated with the relaxation of an Ising-nematic deformation of the Fermi surface. Specifically, we find that the peak frequency is prop…
At low temperatures in ultraclean GaAs-AlGaAs heterojunctions, high fractional Landau levels break rotational symmetry, leading to increasingly anisotropic transport properties as temperature is lowered below $\sim$150mK. While the onset of transport anisotropy is well described by an XY model of an electron nematic in the presence of a weak uniform symmetry-breaking term, the low temperature behavior deviates significantly from this model. We find that inclusion of interactions between the electron nematic and the underlying crystalline lattice in the form of a 4-fold symmetry breaking term i…
We present a model of classical hard-core dimers on the square lattice that contains an Ising nematic phase in its phase diagram. We consider a model with an attractive interaction for parallel dimers on a given plaquette of the square lattice and an attractive interaction for neighboring parallel dimers on the same row ({\it viz} column) of the lattice. By extensive Monte carlo simulations we find that with a finite density of holes the phase diagram has, with rising temperatures, a columnar crystalline phase, an Ising nematic liquid phase and a disordered fluid phase, separated by Ising cont…
An electron nematic is a translationally invariant state which spontaneously breaks the discrete rotational symmetry of a host crystal. In a clean square lattice, the electron nematic has two preferred orientations, while dopant disorder favors one or the other orientations locally. In this way, the electron nematic in a host crystal maps to the random field Ising model (RFIM). Since the electron nematic has anisotropic conductivity, we associate each Ising configuration with a resistor network, and use what is known about the RFIM to predict new ways to test for electron nematicity using nois…
The instability of a Fermi surface against Ising nematic order destroys the quasiparticle character of the low-energy degrees of freedom. Therefore, observables exhibit deviations from Fermi liquid behavior which gives rise to the term Ising nematic quantum critical metal. To obtain a theoretical description we use a finite-temperature version of Eliashberg theory which allows to treat the strong coupling between quantum and thermal fluctuations in the absence of well-defined quasiparticles. Here, we use this self-consistent, diagrammatic approach to compute, in particular, the nematic suscept…
We study finite temperature properties of metals close to an Ising-nematic quantum critical point in two spatial dimensions. In particular we show that at any finite temperature there is a regime where order parameter fluctuations are characterized by a dynamical critical exponent $z=2$, in contrast to $z=3$ found at zero temperature. Our results are based on a simple Eliashberg-type approach, which gives rise to a boson self-energy proportional to $Ω/γ(T)$ at small momenta, where $γ(T)$ is the temperature dependent fermion scattering rate. These findings might shed some light on recent Monte-…
Electronic nematicity, a correlated state that spontaneously breaks rotational symmetry, is observed in several layered quantum materials. In contrast to their liquid-crystal counterparts, the nematic director cannot usually point in an arbitrary direction (XY nematics), but is locked by the crystal to discrete directions (Ising nematics),resulting in strongly anisotropic fluctuations above the transition. Here, we report on the observation of nearly isotropic XY-nematic fluctuations, via elastoresistance measurements, in hole-doped Ba$_{1-x}$Rb$_{x}$Fe$_{2}$As$_{2}$ iron-based superconductors…
The paradigmatic example of a continuous quantum phase transition is the transverse field Ising ferromagnet. In contrast to classical critical systems, whose properties depend only on symmetry and the dimension of space, the nature of a quantum phase transition also depends on the dynamics. In the transverse field Ising model, the order parameter is not conserved and increasing the transverse field enhances quantum fluctuations until they become strong enough to restore the symmetry of the ground state. Ising pseudo-spins can represent the order parameter of any system with a two-fold degenera…
We consider two-dimensional metals near a Pomeranchuk instability which breaks 90$^\circ$ lattice rotation symmetry. Such metals realize strongly-coupled non-Fermi liquids with critical fluctuations of an Ising-nematic order. At low temperatures, impurity scattering provides the dominant source of momentum relaxation, and hence a non-zero electrical resistivity. We use the memory matrix method to compute the resistivity of this non-Fermi liquid to second order in the impurity potential, without assuming the existence of quasiparticles. Impurity scattering in the $d$-wave channel acts as a rand…
Many-body systems subject to a high-frequency drive can show intriguing thermalization behavior. Prior to heating to a featureless infinite-temperature state, these systems can spend an exponentially long time in prethermal phases characterized by various kinds of order. Here, we uncover the rich non-equilibrium phase diagram of a driven frustrated two-dimensional Ising magnet with competing short-range ferromagnetic and long-range dipolar interactions. We show that the ordered stripe and nematic phases, which appear in equilibrium as a function of temperature, underpin subsequent prethermal p…
Motivated by the recent inelastic neutron scattering (INS) measurements in the iron pnictides which show a strong anisotropy of spin excitations in directions perpendicular and parallel to the ordering wave-vector even above the magnetic transition temperature $T_N$, we study the frustrated Heisenberg model with a biquadratic spin-spin exchange interaction. Using the Dyson-Maleev (DM) representation, which proves appropriate for all temperature regimes, we find that the spin-spin dynamical structure factors are in excellent agreement with experiment, exhibiting breaking of the $C_4$ symmetry e…
In an isotropic strongly interacting quantum liquid without quasiparticles, general scaling arguments imply that the dimensionless ratio $(k_B /\hbar)\, η/s$, where $η$ is the shear viscosity and $s$ is the entropy density, is a universal number. We compute the shear viscosity of the Ising-nematic critical point of metals in spatial dimension $d=2$ by an expansion below $d=5/2$. The anisotropy associated with directions parallel and normal to the Fermi surface leads to a violation of the scaling expectations: $η$ scales in the same manner as a chiral conductivity, and the ratio $η/s$ diverges …
Nematic Ising superconductivity with hidden magnetism in few-layer 6R-TaS2
Peking University（北京大学）；Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；Shanghai Jiao Tong University（上海交通大学）；Southern University of Science and Technology（南方科技大学）；ShanghaiTech University（上海科技大学）；Fudan University（复旦大学）；University of Chinese Academy of Sciences（中国科学院大学）；Hefei National Laboratory（合肥国家实验室）；Hong Kong University of Science and Technology（香港科技大学）
We use inelastic neutron scattering to study the temperature and energy dependence of the spin excitation anisotropy in uniaxial-strained electron-doped iron pnictide BaFe$_{1.9}$Ni$_{0.1}$As$_2$ near optimal superconductivity ($T_c=20$ K). Our work has been motivated by the observation of in-plane resistivity anisotropy in the paramagnetic tetragonal phase of electron-underdoped iron pnictides under uniaxial pressure, which has been attributed to a spin-driven Ising-nematic state or orbital ordering. Here we show that the spin excitation anisotropy, a signature of the spin-driven Ising-nemati…
We study the the interplay between spontaneously broken valley symmetry and spatial disorder in multivalley semiconductors in the quantum Hall regime. In cases where valleys have anisotropic electron dispersion a previous long-wavelength analysis [Phys. Rev. B 82, 035428 (2010)] identified two new phases exhibiting the QHE. The first is the quantum Hall Ising nematic (QHIN), a phase with long-range orientational order manifested in macroscopic transport anisotropies. The second is the quantum Hall random-field paramagnet (QHRFPM) that emerges when the Ising ordering is disrupted by quenched di…
Understanding optical conductivity data in the optimally doped cuprates in the framework of quantum criticality requires a strongly-coupled quantum critical metal which violates hyperscaling. In the simplest scaling framework, hyperscaling violation can be characterized by a single non-zero exponent $θ$, so that in a spatially isotropic state in $d$ spatial dimensions, the specific heat scales with temperature as $T^{(d-θ)/z}$, and the optical conductivity scales with frequency as $ω^{(d-θ-2)/z}$ for $ω\gg T$, where $z$ is the dynamic critical exponent. We study the Ising-nematic critical poin…
We present a renormalization group theory for the onset of Ising-nematic order in a Fermi liquid in two spatial dimensions. This is a quantum phase transition, driven by electron interactions, which spontaneously reduces the point-group symmetry from square to rectangular. The critical point is described by an infinite set of 2+1 dimensional local field theories, labeled by points on the Fermi surface. Each field theory contains a real scalar field representing the Ising order parameter, and fermionic fields representing a time-reversed pair of patches on the Fermi surface. We demonstrate that…
We examine the quantum theory of the spontaneous breaking of lattice rotation symmetry in d-wave superconductors on the square lattice. This is described by a field theory of an Ising nematic order parameter coupled to the gapless fermionic quasiparticles. We determine the structure of the renormalization group to all orders in a 1/N_f expansion, where N_f is the number of fermion spin components. Asymptotically exact results are obtained for the quantum critical theory in which, as in the large N_f theory, the nematic order has a large anomalous dimension, and the fermion spectral functions a…
Using functional renormalization group methods, we study an effective low-energy model describing the Ising-nematic quantum critical point in two-dimensional metals. We treat both gapless fermionic and bosonic degrees of freedom on equal footing and explicitly calculate the momentum and frequency dependent effective interaction between the fermions mediated by the bosonic fluctuations. Following earlier work by S.-S. Lee for a one-patch model, Metlitski and Sachdev [Phys. Rev. B {\bf{82}}, 075127] recently found within a field-theoretical approach that certain three-loop diagrams strongly modi…
We address the quantum-critical behavior of a two-dimensional itinerant ferromagnetic systems described by a spin-fermion model in which fermions interact with close to critical bosonic modes. We consider Heisenberg ferromagnets, Ising ferromagnets, and the Ising nematic transition. Mean-field theory close to the quantum critical point predicts a superconducting gap with spin-triplet symmetry for the ferromagnetic systems and a singlet gap for the nematic scenario. Studying fluctuations in this ordered phase using a nonlinear sigma model, we find that these fluctuations are not suppressed by a…
We show that the interference between scattering by impurities and by critical spin fluctuations gives rise to anisotropic transport in the Ising-nematic state of the iron pnictides. The effect is closely related to the non-Fermi liquid behavior of the resistivity near an antiferromagnetic quantum critical point. Our theory not only explains the observed sign of the resistivity anisotropy $Δρ$ in electron doped systems, but also predicts a sign change of $Δρ$ upon sufficient hole doping. Furthermore, our model naturally addresses the changes in $Δρ$ upon sample annealing and alkaline-earth sub…
The origin of the 90 K nematic transition in the chalcogenide FeSe, which displays no magnetic order down to T=0, remains a major puzzle for a unifying theory for the iron-based superconductors. We analyze this problem in light of recent experimental data which reveal very small Fermi pockets in this material. We show that the smallness of the Fermi energy leads to a near-degeneracy between magnetic fluctuations and fluctuations in the charge-current density-wave channel. While the two fluctuation modes cooperate to promote the same preemptive Ising-nematic order, they compete for primary orde…
We report a Raman scattering study of nematic degrees of freedom in the iron-based superconductor parent compound BaFe$_2$As$_2$ under tunable uniaxial strain. We demonstrate that the polarization resolved arsenic (As) phonon intensity can be used to monitor the nematic order parameter as a function of both temperature and strain. At low temperature in the nematic ordered phase we use it to track the continuous and reversible orientation of nematic domains under variable strain. At higher temperature, the evolution of the As phonon intensity under strain reflects an enhanced nematic susceptibi…
We report results of low-temperature heat capacity, magnetocaloric effect and neutron diffraction measurements of TmVO$_{4}$, an insulator that undergoes a continuous ferroquadrupolar phase transition associated with local partially-filled $4f$ orbitals of the thulium (Tm$^{3+}$) ions. The ferroquadrupolar transition, a realization of Ising nematicity, can be tuned to a quantum critical point using a magnetic field oriented along the $c$-axis of the tetragonal crystal lattice, which acts as an effective transverse field for the Ising-nematic order. In small magnetic fields, the thermal phase t…
Using a specially designed Monte Carlo algorithm with directed loops, we investigate the triangular lattice Ising antiferromagnet with coupling beyond nearest neighbour. We show that the first-order transition from the stripe state to the paramagnet can be split, giving rise to an intermediate nematic phase in which algebraic correlations coexist with a broken symmetry. Furthermore, we demonstrate the emergence of several properties of a more topological nature such as fractional edge excitations in the stripe state, the proliferation of double domain walls in the nematic phase, and the Kastel…
As in between liquid and crystal phases lies a nematic liquid crystal, which breaks rotation with preservation of translation symmetry, there is a nematic superfluid phase bridging a superfluid and a supersolid. The nematic order also emerges in interacting electrons and has been found to largely intertwine with multi-orbital correlation in high-temperature superconductivity, where Ising nematicity arises from a four-fold rotation symmetry $C_4$ broken down to $C_2$. Here we report an observation of a three-state ($\mathbb{Z}_3$) quantum nematic order, dubbed "Potts-nematicity", in a system of…
We study the character of an Ising nematic quantum phase transition (QPT) deep inside a d-wave superconducting state with nodal quasiparticles in a two-dimensional tetragonal crystal. We find that, within a 1/N expansion, the transition is continuous. To leading order in 1/N, quantum fluctuations enhance the dispersion anisotropy of the nodal excitations, and cause strong scattering which critically broadens the quasiparticle (qp) peaks in the spectral function, except in a narrow wedge in momentum space near the Fermi surface where the qp's remain sharp. We also consider the possible existenc…
In part (I) of this two paper series on stripe fractionalization, we argued that in principle the `domain wall-ness' of the stripe phase could persist in the spin and charge disordered superconductors, and we demonstrated how this physics is in one-to-one correspondence with Ising gauge theory. Here we focus on yet another type of order suggested by the gauge theory: the quantum spin nematic. Although it is not easy to measure this order directly, we argue that the superconducting vortices act as perturbations destroying the gauge symmetry locally. This turns out to give rise to a simple examp…
We study experimental signatures of the Ising nematic quantum phase transition in d-wave superconductors, associated with the change of lattice symmetry from tetragonal to orthorhombic in the superconducting state. The characteristic feature of this transition is that the ratio between the Fermi velocity $v_F$ and gap velocity $v_Δ$ flows to a maximally anisotropic fixed point, i.e. the renormalization group fixed point is situated at (v_Δ/v_F)^*=0$. Our main point is that the logarithmic approach to this fixed point has visible signatures in the thermal transport. The analysis of the quasipar…
We show that spin-spin correlations in a non-Abelian Kitaev spin liquid are associated with a characteristic inhomogeneous charge density distribution in the vicinity of $\mathbb{Z}_2$ vortices. This density profile and the corresponding local electric fields are observable, e.g., by means of surface probe techniques. Conversely, by applying bias voltages to several probe tips, one can stabilize Ising anyons ($\mathbb{Z}_2$ vortices harboring a Majorana zero mode) at designated positions, where we predict a clear Majorana signature in energy absorption spectroscopy.
Using determinantal quantum Monte Carlo, we compute the properties of a lattice model with spin $\frac 1 2$ itinerant electrons tuned through a quantum phase transition to an Ising nematic phase. The nematic fluctuations induce superconductivity with a broad dome in the superconducting $T_c$ enclosing the nematic quantum critical point. For temperatures above $T_c$, we see strikingly non-Fermi liquid behavior, including a "nodal - anti nodal dichotomy" reminiscent of that seen in several transition metal oxides. In addition, the critical fluctuations have a strong effect on the low frequency o…
We compare the position of an ordering transition in a metal to that in a superconductor. For the spin density wave (SDW) transition, we find that the quantum critical point shifts by order |Delta|, where Delta is pairing amplitude, so that the region of SDW order is smaller in the superconductor than in the metal. This shift is larger than the ~ |Delta|^2 shift predicted by theories of competing orders which ignore Fermi surface effects. For Ising-nematic order, the shift from Fermi surface effects remains of order |Delta|^2. We discuss implications of these results for the phase diagrams of …
The quantum phase transition in iron-based superconductors with 'half-Dirac' node at the electron Fermi surface as a $T=0$ structural phase transition described in terms of nematic order is discussed. An effective low energy theory that describes half-Dirac nodal Fermions and their coupling to Ising nematic order that describes the phase transition is derived and analyzed using renormalization group (RG) study of the large-$N_f$ version of the theory. The inherent absence of Lorentz invariance of the theory leads to RG flow structure where the velocities $v_F$ and $v_Δ$ at the paired half-Dira…
A magnetic order can be completely suppressed at zero temperature($T$), by doping carriers or applying pressure, at a quantum critical point(QCP), around which physical properties change drastically. However, the situation is unclear for an electronic nematic order that breaks rotation symmetry. Here we report nuclear magnetic resonance(NMR) studies on NaFe$_{1-x}$Co$_{x}$As where magnetic and nematic transitions are well separated. The NMR spectrum is sensitive to inhomogeneous magnetic fields in the vortex state, which is related to London penetration depth $λ_{\rm L}$ that measures the elec…
We explore the propagation of a single hole in the quantum compass model, whose nematic ground state is given by mutually decoupled antiferromagnetic chains. The compass model can be seen as the strong-coupling limit of a spinless two-band Hubbard model, which we study here using mean field theory and the variational cluster approach. Due to the symmetries of the compass model, the inherent disorder along one lattice direction turns out not to affect hole motion and doping a hole consequently does not lift the subextensive degeneracy of the nematic phase. In order to broaden and deepen underst…
We analyze the scaling theory of two-dimensional metallic electron systems in the presence of critical bosonic fluctuations with small wave vectors, which are either due to a U(1) gauge field, or generated by an Ising nematic quantum critical point. The one-loop dynamical exponent z=3 of these critical systems was shown previously to be robust up to three-loop order. We show that the cancellations preventing anomalous contributions to z at three-loop order have special reasons, such that anomalous dynamical scaling emerges at four-loop order.
Quantum spin ice materials, pyrochlore magnets with competing Ising and transverse exchange interactions, have been widely discussed as candidates for a quantum spin-liquid ground state. Here, motivated by quantum chemical calculations for Pr pyrochlores, we present the results of a study for frustrated transverse exchange. Using a combination of variational calculations, exact diagonalisation, numerical linked-cluster and series expansions, we find that the previously-studied U(1) quantum spin liquid, in its pi-flux phase, transforms into a nematic quantum spin liquid at a high-symmetry, SU(2…
We report high-resolution measurements of the in-plane thermal expansion anisotropy in the vicinity of the electronic nematic phase in Sr$_3$Ru$_2$O$_7$ down to very low temperatures and in varying magnetic field orientation. For fields applied along the c-direction, a clear second-order phase transition is found at the nematic phase, with critical behavior compatible with the two-dimensional Ising universality class (although this is not fully conclusive). Measurements in a slightly tilted magnetic field reveal a broken four-fold in-plane rotational symmetry, not only within the nematic phase…
Electronic nematic phases are broadly characterized by spontaneously broken rotational symmetry. Although they have been widely recognized in the context of high temperature cuprates, bilayer ruthenates, and iron-based superconductors, the focus so far has been exclusively on the uniform nematic phase. Recently, however, it was proposed that on a square lattice a nematic instability in the d-wave charge channel could lead to a spatially modulated nematic state, where the modulation vector q is determined by the relative location of the Fermi level to the van Hove singularity. Interestingly, th…
Recent neutron scattering observations by Plumb et al. [1] reveal that the ground state of $FeSc_2S_4$ is magnetic with two distinct Fe environments, instead of a quantum spin liquid as had been previously thought. Starting with the relevant O(N)-symmetric vector model of $FeSc_2S_4$, we study how the discrete ($Z_2$) and continuous rotational symmetries are successively broken, yielding nematic and ordered phases. At high temperatures, we find that the nematic order parameter falls as $T^{-γ}$ ($γ>0$), and therefore, $FeSc_2S_4$ lacks any distinct nematic ordering temperature. This feature in…
We use the symmetry constrained low energy effective Hamiltonian of iron based superconductors to study the Raman scattering in the normal state of underdoped iron-based superconductors. The incoming and scattered Raman photons couple directly to orbital fluctuations and indirectly to the spin fluctuations. We computed both couplings within the same low energy model. The symmetry constrained Hamiltonian yields the coupling between the orbital and spin fluctuations of only the same symmetry type. Attraction in B2g symmetry channel was assumed for the system to develop the subleading instability…
We study the pairing instability of a two-dimensional metallic system induced by Ising-nematic quantum fluctuations in the presence of an unavoidable relevant coupling of the nematic order parameter to the elastic modes (acoustic phonons) of the lattice. We find that this nematoelastic coupling $λ_\mathrm{latt}$ leads to a decrease of both the superconducting (SC) critical temperature $T_c$ and the gap function $Δ$, regardless of the gap symmetry. Interestingly, we show that $λ_\mathrm{latt}$ provides a knob that allows us to investigate the emergence of the SC phase at low temperatures, as an…
The generalization of the Nelson-Halperin-Young theory of 2D melting to the dynamical 2+1D quantum case is presented. The bosonic quantum crystal dualizes in superfluids or superconductors exhibiting nematic liquid crystalline orders, corresponding with bose condensates of dislocations exhibiting a dual shear Meissner-Higgs mechanism. The topologically ordered nematic phase suggested by Lammert, Toner and Rokshar finds a simple interpretation in this framework. The ordered nematic is a true quantum phase: the dynamical glide principle interferes with the effect that the phonon spectrum of the …
