Electronic Liquid Crystal Phases Research Articles

Charge-stripe crystal phase in an insulating cuprate.

High-temperature (high-Tc) superconductivity in cuprates arises from carrier doping of an antiferromagnetic Mott insulator. This carrier doping leads to the formation of electronic liquid-crystal phases1. The insulating charge-stripe crystal phase is predicted to form when a small density of holes is doped into the charge-transfer insulator state1-3, but this phase is yet to be observed experimentally. Here, we use surface annealing to extend the accessible doping range in Bi-based cuprates and realize the lightly doped charge-transfer insulating state of the cuprate Bi2Sr2CaCu2O8+x. In this insulating state with a charge transfer gap on the order of ~1 eV, our spectroscopic imaging scanning tunnelling microscopy measurements provide strong evidence for a unidirectional charge-stripe order with a commensurate 4a0 period along the Cu-O-Cu bond. Notably, this insulating charge-stripe crystal phase develops before the onset of the pseudogap and formation of the Fermi surface. Our work provides fresh insight into the microscopic origin of electronic inhomogeneity in high-Tc cuprates.

Possible nematic to smectic phase transition in a two-dimensional electron gas at half-filling

Liquid crystalline phases of matter permeate nature and technology, with examples ranging from cell membranes to liquid-crystal displays. Remarkably, electronic liquid-crystal phases can exist in two-dimensional electron systems (2DES) at half Landau-level filling in the quantum Hall regime. Theory has predicted the existence of a liquid-crystal smectic phase that breaks both rotational and translational symmetries. However, previous experiments in 2DES are most consistent with an anisotropic nematic phase breaking only rotational symmetry. Here we report three transport phenomena at half-filling in ultra-low disorder 2DES: a non-monotonic temperature dependence of the sample resistance, dramatic onset of large time-dependent resistance fluctuations, and a sharp feature in the differential resistance suggestive of depinning. These data suggest that a sequence of symmetry-breaking phase transitions occurs as temperature is lowered: first a transition from an isotropic liquid to a nematic phase and finally to a liquid-crystal smectic phase.

Effective field theory of an anomalous Hall metal from interband quantum fluctuations

We construct an effective field theory, a two-dimensional two-component metallic system described by a model with two Fermi surfaces ("pockets"). This model describes a translationally invariant metallic system with two types of fermions, each with its own Fermi surface, with forward scattering interactions. This model, in addition to the $O(2)$ rotational invariance, has a $U(1) \times U(1)$ symmetry of separate charge conservation for each Fermi surface. For sufficiently attractive interactions in the $d$-wave (quadrupolar) channel this model has an interesting phase diagram that includes a spontaneously generated anomalous Hall metal phase. We derive the Landau-Ginzburg effective action of quadrupolar order parameter fields which enjoys an $O(2)\times U(1)$ global symmetry associated to spatial isotropy and the internal $U(1)$ relative phase symmetries respectively. We show that the order parameter theory is dynamically local with a dynamical scaling of $z=2$ and perform a one-loop renormalization group analysis of the Landau-Ginzburg theory. The electronic liquid crystal phases that result from spontaneous symmetry breaking are studied and we show the presence of Landau damped Nambu-Goldstone modes at low momenta that is a signature of non-Fermi liquid behavior. Electromagnetic linear response is also analyzed in both the normal and symmetry broken phases from the point of view of the order parameter theory. The nature of the coupling of electromagnetism to the order parameter fields in the normal phase is non-minimal and decidedly contains a precursor to the anomalous Hall response in the form of a order-parameter-dependent Chern-Simons term in the effective action.

Multi-Qhexagonal spin density waves and dynamically generated spin-orbit coupling: Time-reversal invariant analog of the chiral spin density wave

We study hexagonal spin-channel ("triplet") density waves with commensurate $M$-point propagation vectors. We first show that the three $Q=M$ components of the singlet charge density and charge-current density waves can be mapped to multi-component $Q=0$ nonzero angular momentum order in three dimensions ($3D$) with cubic crystal symmetry. This one-to-one correspondence is exploited to define a symmetry classification for triplet $M$-point density waves using the standard classification of spin-orbit coupled electronic liquid crystal phases of a cubic crystal. Through this classification we naturally identify a set of non-coplanar spin density and spin-current density waves: the chiral spin density wave and its time-reversal invariant analog. These can be thought of as $3D$ $L=2$ and $L=4$ spin-orbit coupled isotropic $\beta$-phase orders. In contrast, uniaxial spin density waves are shown to correspond to $\alpha$-phases. The non-coplanar triple-$M$ spin-current density wave realizes a novel $2D$ semimetal state with three flavors of four-component spin-momentum locked Dirac cones, protected by a crystal symmetry akin to non-symmorphic symmetry, and sits at the boundary between a trivial and topological insulator. In addition, we point out that a special class of classical spin states, defined as classical spin states respecting all lattice symmetries up to global spin rotation, are naturally obtained from the symmetry classification of electronic triplet density waves. These symmetric classical spin states are the classical long-range ordered limits of chiral spin liquids.

Pair-density-wave superconducting states and electronic liquid-crystal phases

In conventional superconductors the Cooper pairs have a zero center of mass momentum. In this paper we present a theory of superconducting states where the Cooper pairs have a nonzero center of mass momentum, inhomogeneous superconducting states known as a pair-density-waves (PDW) states. We show that in a system of spin-1/2 fermions in 2 dimensions in an electronic nematic spin triplet phase where rotational symmetry is broken both in real and in spin space PDW phases arise naturally in a theory that can be analyzed using controlled approximations. We show that several superfluid phases that may arise in this phase can be treated within a controlled BCS mean field theory, with the strength of the spin-triplet nematic order parameter playing the role of the small parameter of this theory. We find that in a spin-triplet nematic phase, in addition of a triplet $p$-wave and spin-singlet $d$-wave (or $s$ depending on the nematic phase) uniform superconducting states, it is also possible to have a $d$-wave (or $s$) PDW superconductor. The PDW phases found here can be either unidirectional, bidirectional or tridirectional depending on the spin-triplet nematic phase and which superconducting channel is dominant. In addition, a triple-helix state is found in a particular channel. We show that these PDW phases are present in the weak coupling limit, in contrast to the usual Fulde-Ferrell-Larkin-Ovchinnikov phases which require strong coupling physics in addition to a large magnetic field (and often both).

Evidence for competing magnetic instabilities in underdoped YBa2Cu3O6+x

We report a polarized neutron-scattering study of the orbital-like magnetic order in strongly underdoped ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6.45}$ and ${\mathrm{YBa}}_{2}({\mathrm{Cu}}_{0.98}{\mathrm{Zn}}_{0.02}){}_{3}{\mathrm{O}}_{6.6}$. Their hole-doping levels are located on both sides of the critical doping ${p}_{\mathrm{MI}}$ of a metal-insulator transition inferred from transport measurements. Our study reveals a drop down of the orbital-like order slightly below ${p}_{\mathrm{MI}}$ with a steep decrease of both the ordering temperature ${T}_{\mathrm{mag}}$ and the ordered moment. Above ${p}_{\mathrm{MI}}$, substitution of quantum impurities does not change ${T}_{\mathrm{mag}}$, whereas it lowers significantly the bulk ordered moment. The modifications of the orbital-like magnetic order are interpreted in terms of a competition with electronic liquid crystal phases around ${p}_{\mathrm{MI}}$. This competition gives rise to a mixed magnetic state in ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6.45}$ and a phase separation in ${\mathrm{YBa}}_{2}({\mathrm{Cu}}_{0.98}{\mathrm{Zn}}_{0.02}){}_{3}{\mathrm{O}}_{6.6}$.