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Register a new userClassification of nematic order in 2+1D: Dislocation melting and $O(2)/Z_N$ lattice gauge theory
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Nematic phases, breaking spontaneously rotational symmetry, provide for ubiquitously observed states of matter in both classical and quantum systems. These nematic states may be further classified by their $N$--fold rotational invariance described by cyclic groups $C_N$ in 2+1D. Starting from the space groups of underlying $2d$ crystals, we present a general classification scheme incorporating $C_N$ nematic phases that arise from dislocation-mediated melting and discuss the conventional tensor order parameters. By coupling the $O(2)$ matter fields to the $Z_N$ lattice gauge theory, an unified $O(2)/Z_N$ lattice gauge theory is constructed in order to describe all these nematic phases. This lattice gauge theory is shown to reproduce the $C_N$ nematic-isotropic liquid phase transitions and contains an additional deconfined phase. Finally, using our $O(2)/Z_N$ gauge theory framework, we discuss phase transitions between different $C_N$ nematics.
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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 crystal re-emerges in the direction orthogonal to the director. Novel insights follow from the duality on the fundamental nature of superfluidity and superconductivity. The superfluid can be viewed as an elastic medium having lost its rigidity against shear stresses. Upon dualizing the electrically charged crystal the electromagnetic Meissner phase is recovered, showing peculiar screening current oscillations when the shear penetration depth becomes larger than the London penetration depth.
We demonstrate the existence of the spin nematic interactions in an easy-plane type antiferromagnet Ba$_{2}$CoGe$_{2}$O$_{7}$ by exploring the magnetic anisotropy and spin dynamics. Combination of neutron scattering and magnetic susceptibility measurements reveals that the origin of the in-plane anisotropy is an antiferro-type interaction of the spin nematic operator. The relation between the nematic operator and the electric polarization in the ligand symmetry of this compound is presented. The introduction of the spin nematic interaction is useful to understand the physics of spin and electric dipole in multiferroic compounds.
The tetragonal compound YbRu$_{2}$Ge$_{2}$ exhibits a non-magnetic transition at $T_0$=10.2K and a magnetic transition at $T_1$=6.5K in zero magnetic field. We present a model for this material based on a quasi-quartet of Yb$^{3+}$ crystalline electric field (CEF) states and discuss its mean field solution. Taking into account the broadening of the specific heat jump at $T_0$ for magnetic field perpendicular to [001] and the decrease of $T_0$ with magnetic field parallel to [001], it is shown that ferro-quadrupole order of either O$_{2}^{2}$ or O$_{rm xy}$ - type are prime candidates for the non-magnetic transition. Considering the matrix element of these quadrupole moments, we show that the lower CEF states of the level scheme consist of a $Gamma_{6}$ and a $Gamma_{7}$ doublet. This leads to induced type of O$_{2}^{2}$ and O$_{rm xy}$ quadrupolar order parameters. The quadrupolar order introduces exchange anisotropy for planar magnetic moments. This causes a spin flop transition at low fields perpendicular [001] which explains the observed metamagnetism. We also obtain a good explanation for the temperature dependence of magnetic susceptibility and specific heat for fields both parallel and perpendicular to the [001] direction.
Fascinating new phases of matter can emerge from strong electron interactions in solids. In recent years, a new exotic class of many-body phases, described by generalized electromagnetism of symmetric rank-2 electric and magnetic fields and immobile charge excitations dubbed fractons, has attracted wide attention. Beside interesting properties in their own right, they are also closely related to gapped fracton quantum orders, new phases of dipole-coversing systems, quantum information, and quantum gravity. However, experimental realization of the rank-2 U(1) gauge theory is still absent, and even known practical experimental routes are scarce. In this work we propose a scheme of coupled optical phonons and nematics as well as several of its concrete experimental constructions. They can realize the electrostatics sector of the rank-2 U(1) gauge theory. A great advantage of our scheme is that it requires only basic ingredients of phonon and nematic physics, hence can be applied to a wide range of nematic matters from liquid crystals to electron orbitals. We expect this work will provide crucial guidance for the realization of rank-2 U(1) and fracton states of matter on a variety of platforms.
Magnetic fluctuations induced by geometric frustration of local Ir-spins disturb the formation of long range magnetic order in the family of pyrochlore iridates, R$_{2}$Ir$_{2}$O$_{7}$ (R = lanthanide)$^{1}$. As a consequence, Pr$_{2}$Ir$_{2}$O$_{7}$ lies at a tuning-free antiferromagnetic-to-paramagnetic quantum critical point and exhibits a diverse array of complex phenomena including Kondo effect, biquadratic band structure, metallic spin-liquid (MSL), and anomalous Hall effect$^{2-5}$. Using spectroscopic imaging with the scanning tunneling microscope, complemented with machine learning K-means clustering analysis, density functional theory, and theoretical modeling, we probe the local electronic states in single crystal of Pr$_{2}$Ir$_{2}$O$_{7}$ and discover an electronic phase separation. Nanoscale regions with a well-defined Kondo resonance are interweaved with a non-magnetic metallic phase with Kondo-destruction. Remarkably, the spatial nanoscale patterns display a correlation-driven fractal geometry with power-law behavior extended over two and a half decades, consistent with being in proximity to a critical point. Our discovery reveals a new nanoscale tuning route, viz. using a spatial variation of the electronic potential as a means of adjusting the balance between Kondo entanglement and geometric frustration.
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