Determining the nature of electronic states in doped Mott insulators remains a challenging task. In the case of tetragonal La$_{2-x}$Sr$_{x}$NiO$_{4}$, the occurrence of diagonal charge and spin stripe order in the ground state is now well established. In contrast, the nature of the high-temperature "disordered" state from which the stripe order develops has long been a subject of controversy, with considerable speculation regarding a polaronic liquid. Following on the recent detection of dynamic charge stripes, we use neutron scattering measurements on an $x=0.25$ crystal to demonstrate that the dispersion of the charge stripe excitations is anisotropic. This observation provides compelling evidence for the presence of electronic nematic order.
We have successfully grown epitaxial La$_{1.67}$Sr$_{0.33}$NiO$_4$ films with a small crystalline mosaic using pulsed laser deposition. With synchrotron radiation, the x-ray diffraction peaks associated with charge stripes have been successfully observed for relatively thick films. Anomalies due to the charge-ordering transition have been examined using four-point probe resistivity measurements. X-ray scattering provides direct evidence for suppression of the stripe phase in thin samples; the phase disappears for film thicknesses $\leqslant$ 2600 ~Å. The suppression appears to be a result of s…
The electronic nematic phase occurs when the point-group symmetry of the lattice structure is broken, due to electron-electron interactions. We study a model for the nematic phase on a square lattice with emphasis on the phase transition between isotropic and nematic phases within mean field theory. We find the transition to be first order, with dramatic changes in the Fermi surface topology accompanying the transition. Furthermore, we study the conductivity tensor and Hall constant as probes of the nematic phase and its transition. The relevance of our findings to Hall resistivity experiments…
This letter extends my recent paper on antiferromagnetic NiO [Structural Distortion Stabilizing the Antiferromagnetic and Insulating Ground State of NiO, Symmetry 2020, 12(1), 56] by including also the paramagnetic phase of this compound. I report evidence that paramagnetic NiO possesses a narrow, roughly half-filled energy band that produces a nonadiabatic atomic-like motion providing the basis for a Mott insulator in the paramagnetic phase. While the atomic-like motion operating in the antiferromagnetic phase is adapted to the symmetry of the antiferromagnetic state, in the paramagnetic phas…
An electronic nematic phase can be classified by a spontaneously broken discrete rotational symmetry of a host lattice. In a square lattice, there are two distinct nematic phases. The parallel nematic phase breaks $x$ and $y$ symmetry, while the diagonal nematic phase breaks the diagonal $(x+y)$ and anti-diagonal $(x-y)$ symmetry. We investigate the interplay between the parallel and diagonal nematic orders using mean field theory. We found that the nematic phases compete with each other, while they coexist in a finite window of parameter space. The quantum critical point between the diagonal …
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…
We study frustrated spin-1/2 dimer systems in two dimensions with a bilayer structure, where spins are ferromagnetically coupled in dimers. Our model includes frustrated two-spin exchange interactions as well as four-spin interaction. We pay particular attention to the spin nematic phase, which does not exhibit any magnetic (spin-dipole) order but has a spin-quadrupolar long-range order. Employing a perturbation calculation, a mean-field approximation, and a numerical many-variable variational Monte Carlo method, we determine ground-state phase diagrams on various two-dimensional lattices. It …
We investigate the stability of a quadratic band-crossing point (QBCP) in 2D fermionic systems. At the non-interacting level, we show that a QBCP exists and is topologically stable for a Berry flux $\pm 2π$, if the point symmetry group has either fourfold or sixfold rotational symmetries. This putative topologically stable free-fermion QBCP is marginally unstable to {\em arbitrarily weak} short-range repulsive interactions. We consider both spinless and spin-1/2 fermions. Four possible ordered states result: a quantum anomalous Hall phase, a quantum spin Hall phase, a nematic phase, and a nema…
In this paper, we study theoretically the behaviors of the magnetic excitations(MEs) in the normal and nematic phases of iron pnictides. The normal state MEs exhibit commensurability to diamond and to square-like structure transition with the increase of energy. This structure transition persists in the spin and orbital scenarios of nematic phases, although the MEs show anisotropic behaviors due to the C4 symmetry breaking induced by the nematic orders. The MEs exhibit distinct energy evolution behaviors between the spin and orbital scenarios of nematicity. For the spinnematic scenario, the an…
For La_(1 2/3)Sr_(1/3)NiO_4 -- a commensurately doped Mott-Hubbard system -- charge- and spin-ordering in a stripe phase has been investigated by phononic and magnetic Raman scattering. Formation of a superlattice and an opening of a pseudo-gap in the electron-hole excitation spectra as well as two types of double-spin excitations -- within the antiferromagnetic domain and across the domain wall -- are observed below the charge-ordering transition. The temperature dependence suggests that the spin ordering is driven by charge ordering and that fluctuating stripes persist above the ordering tra…
We study the formation of an electronic nematic phase characterized by a broken point-group symmetry in interacting fermion systems within the weak coupling theory. As a function of interaction strength and chemical potential, the phase transition between the isotropic Fermi liquid and nematic phase is first order at zero temperature and becomes second order at a finite temperature. The transition is present for all typical, including quasi-2D, electronic dispersions on the square lattice and takes place for arbitrarily small interaction when at van Hove filling, thus suppressing the Lifshitz …
We discuss the magnetization process slightly below the saturation field in frustrated magnets. A condensation of bound magnons on the spin-polarized state induces either a spin nematic phase or a state with phase separation. The (effective) interaction between the bound magnon pairs not only is crucial to the stability of the nematic phase, but also determines the slope of the magnetization curve near saturation. We generally derive the expression of this interaction by using the perturbative scattering theory. By applying the method to coupled zigzag chains LiCuVO4, we find the positive pair…
Nematicity is a well known property of liquid crystals and has been recently discussed in the context of strongly interacting electrons. An electronic nematic phase has been seen by many experiments in certain strongly correlated materials, in particular, in the pseudogap phase generic to many hole-doped cuprate superconductors. Recent measurements in high $T_c$ superconductors has shown even if the lattice is perfectly rotationally symmetric, the ground state can still have strongly nematic local properties. Our study of the two-dimensional Hubbard model provides strong support of the recent …
Motivated by the recent discovery of broken four-fold symmetry in the hidden order phase of URu$_2$Si$_2$[R. Okazaki et al., Science {\bf 331}, 439 (2011)], we examine a scenario of a spin nematic state as a possible candidate of the hidden order phase. We demonstrate that the scenario naturally explains most of experimental observations, and furthermore, reproduces successfully the temperature dependence of the spin anisotropy detected by the above-mentioned experiment in a semi-quantitative way. This result provides strong evidence for the realization of the spin nematic order.
The magnetization process of the $S=1$ antiferromagnetic chain with the single-ion anisotropy $D$ and the biquadratic interaction is investigated using the numerical diagonalization. Both interactions stabilize the 2-magnon Tomonaga-Luttinger liquid (TLL) phase in the magnetization process. Based on several excitation gaps calculated by the numerical diagonalization, some phase diagrams of the magnetization process are presented. These phase diagrams reveal that the spin nematic dominant TLL phase appears at higher magnetizations for sufficiently large negative $D$.
Strongly interacting systems are known to often spontaneously develop exotic ground states under certain conditions. For instance, spin nematic phases have been discovered in various magnetic models. Such phases, which break spin symmetry but have no net local magnetization, have also been proposed by Nersesyan et al. (J. Phys.: Cond. Matt. 3, 3353 (1991)) in the context of electronic models. We introduce a N-flavor microscopic model that interpolates from the large-N limit, where mean-field is valid and such a nematic phase occurs, to the more realistic N=1 case. By using a sign-free quantum …
Electronic-liquid-crystal phases, in which part of the spatial symmetries are broken spontaneously, are considered to play a vital role in interpreting the structure-property relation in strongly-correlated materials. Although electronic-liquid-crystal phases have been inferred in studies of a wide range of materials, the nature of the transition between such phases has received little experimental attention. Here we report the direct observation of an electronic smectic-nematic phase transition in a doped manganite utilizing transmission electron microscopic techniques. We show that, in this …
Measurements of the differential elastoresistance of URu$_2$Si$_2$ reveal that the fluctuations associated with the 17 K Hidden Order phase transition have a nematic component. Approaching the "Hidden Order" phase transition from above, the nematic susceptibility abruptly changes sign, indicating that while the Hidden Order phase has a nematic component, it breaks additional symmetries.
It is shown that the quantum phase transition in metallic non-s-wave ferromagnets, or spin nematics, is generically of first order. This is due to a coupling of the order parameter to soft electronic modes that play a role analogous to that of the electromagnetic vector potential in a superconductor, which leads to a fluctuation-induced first-order transition. A generalized mean-field theory for the p-wave case is constructed that explicitly shows this effect. Tricritical wings are predicted to appear in the phase diagram in a spatially varying magnetic field, but not in a homogeneous one.
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…
It is shown that metamagnetic transition in metals can occur via the formation of electronic nematic order. We consider a simple model where the spin-dependent Fermi surface instability gives rise to the formation of an electronic nematic phase upon increasing the applied Zeeman magnetic field. This leads to two consecutive metamagnetic transitions that separate the nematic phase from the low-field and high-field 'isotropic' metallic phases. Possible connection to the physics of the bilayer Ruthenate, Sr$_3$Ru$_2$O$_7$, is also discussed.
We show that in order to describe the isotropic-nematic transition in stripe forming systems with isotropic competing interactions of the Brazovskii class it is necessary to consider the next to leading order in a 1/N approximation for the effective Hamiltonian. This can be conveniently accomplished within the self-consistent screening approximation. We solve the relevant equations and show that the self-energy in this approximation is able to generate the essential wave vector dependence to account for the anisotropic character of two-point correlation function characteristic of a nematic pha…
The insulator to metal phase transition in NiO is studied within the framework of reduced density matrix functional theory and density functional theory. We find that the spectral density obtained using reduced density matrix functional theory is in good agreement with experiments both undoped as well as doped NiO. We find that the physical description of the hole-doping induced phase transition \emph{qualitatively differs} depending on whether NiO is calculated within density functional theory or reduced density matrix functional. In the former case the underlying mechanism of the phase trans…
We study the interaction effect in a three dimensional Dirac semimetal and find that two competing orders, charge-density-wave orders and nematic orders, can be induced to gap the Dirac points. Applying a magnetic field can further induce an instability towards forming these ordered phases. The charge density wave phase is similar as that of a Weyl semimetal while the nematic phase is unique for Dirac semimetals. Gapless zero modes are found in the vortex core formed by nematic order parameters, indicating the topological nature of nematic phases. The nematic phase can be observed experimental…
Half-filled Landau levels form a zoo of strongly correlated phases. These include non-Fermi liquids (NFL), fractional quantum Hall (FQH) states, nematic phases, and FQH nematic phases. This diversity poses the question: what keeps the balance between the seemingly unrelated phases? The answer is elusive because the Halperin-Lee-Read (HLR) description that offers a natural departure point is inherent strongly coupled. But the observed nematic phases suggest nematic fluctuations play an important role. To study this possibility, we apply a recently formulated controlled double expansion approach…
Charge-$4e$ superconductivity as a novel phase of matter remains elusive so far. Here we show that charge-$4e$ phase can arise as a vestigial order above the nematic superconducting transition temperature in time-reversal-invariant nematic superconductors. On the one hand, the nontrivial topological defect -- nematic vortex -- is energetically favored over the superconducting phase vortex when the nematic stiffness is less than the superfluid stiffness; consequently the charge-$4e$ phase emerges by proliferation of nematic vortices upon increasing temperatures. On the other hand, the Ginzburg-…
The intra-unit-cell nematic phase is studied within the three-band Emery model of the cuprates with the use of the approach based on the diagrammatic expansion of the Gutzwiller wave function (DE-GWF). According to our analysis the spontaneous $C_4$ symmetry breaking of the electronic wave function, leading to the nematic behavior, can appear due to electron correlations induced mainly by the onsite Coulomb repulsion, even in the absence of the corresponding intersite oxygen-oxygen repulsion term. The latter has been considered as the triggering factor of the nematic state formation in a numbe…
At small momenta, the Girvin-MacDonald-Platzman (GMP) mode in the fractional quantum Hall (FQH) effect can be identified with gapped nematic fluctuations in the isotropic FQH liquid. This correspondence would be exact as the GMP mode softens upon approach to the putative point of a quantum phase transition to a FQH nematic. Motivated by these considerations as well as by suggestive evidence of an FQH nematic in tilted field experiments, we have sought evidence of such a nematic FQHE in a microscopic model of interacting electrons in the lowest Landau level at filling factor 1/3. Using a family…
Ultrafast techniques have emerged as promising methods to study and control quantum materials. To maintain the quantum nature of the systems under study, excess heating must be avoided. In this work, we demonstrate a method that employs the nonequilibrium laser excitation of planar stretching optical phonons in tetragonal systems to quench an electronic nematic state across a quantum phase transition. Appropriately tuned off-resonant pulses can perform a quantum quench of the system either into the nematic phase (red detuning) or out of it (blue detuning). The nonlinear coupling of this phonon…
We show that topological states are often developed in two dimensional semimetals with quadratic band crossing points (BCPs) by electron-electron interactions. To illustrate this, we construct a concrete model with the BCP on an extended Lieb lattice and investigate the interaction-driven topological instabilities. We find that the BCP is marginally unstable against infinitesimal repulsions. Depending on the interaction strengths, topological quantum anomalous/spin Hall, charge nematic, and nematic-spin-nematic phases, develop separately. Possible physical realizations of quadratic BCPs are pr…
The exotic normal state of iron chalcogenide superconductor FeSe, which exhibits vanishing magnetic order and possesses an electronic nematic order, triggered extensive explorations of its magnetic ground state. To understand its novel properties, we study the ground state of a highly frustrated spin-$1$ system with bilinear-biquadratic interactions using unbiased large-scale density matrix renormalization group. Remarkably, with increasing biquadratic interactions, we find a paramagnetic phase between Néel and stripe magnetic ordered phases. We identify this phase as a candidate of nematic qu…
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 …
We investigate quantum phase transitions and quantum coherence in infinite biquadratic spin-1 and -2 XY chains with rhombic single-ion anisotropy. All considered coherence measures such as the $l_1$ norm of coherence, the relative entropy of coherence, and the quantum Jensen-Shannon divergence, and the quantum mutual information show consistently that singular behaviors occur for the spin-1 system, which enables to identity quantum phase transitions. For the spin-2 system, the relative entropy of coherence and the quantum mutual information properly detect no singular behavior in the whole sys…
The concept of a vestigial nematic order emerging from a "mother" spin or charge density-wave state has been applied to describe the phase diagrams of several systems, including unconventional superconductors. In a perfectly clean system, the two orders appear simultaneously via a first-order quantum phase transition, implying the absence of quantum criticality. Here, we investigate how this behavior is affected by impurity-free droplets that are naturally present in inhomogeneous systems. Due to their quantum dynamics, finite-size droplets sustain long-range nematic order but not long-range d…
Strongly interacting electrons can exhibit novel collective phases, among which the electronic nematic phases are perhaps the most surprising as they spontaneously break rotational symmetry of the underlying crystal lattice. The electron nematicity has been recently observed in the iron-pnictide and cuprate high-temperature superconductors. Whether such a tendency of electrons to self-organise unidirectionally has a common feature in these superconductors is, however, a highly controversial issue. In the cuprates, the nematicity has been suggested as a possible source of the pseudogap phase, w…
We study an interacting electronic system exhibiting a spin nematic instability. Using a phenomenological form for the spin fluctuation spectrum near the spin-density-wave (SDW) phase, we compute the spin nematic susceptibility in energy and momentum space as a function of temperature and the magnetic correlation length xi. The spin nematic instability occurs when xi reaches a critical value xi_{cr}, i.e., its transition temperature T_{SN} is always higher than the SDW critical temperature T_{SDW}. In particular, xi_{cr} decreases monotonically with increasing T_{SN}. Concomitantly, low-energy…
Within the Landau paradigm of continuous phase transitions, ordered states of matter are characterized by a broken symmetry. Although the broken symmetry is usually evident, determining the driving force behind the phase transition is often a more subtle matter due to coupling between otherwise distinct order parameters. In this paper we show how measurement of the divergent nematic susceptibility of an iron pnictide superconductor unambiguously distinguishes an electronic nematic phase transition from a simple ferroelastic distortion. These measurements also reveal an electronic nematic quant…
We present a theory of the isotropic-nematic quantum phase transition in the composite Fermi liquid arising in half-filled Landau levels. We show that the quantum phase transition between the isotropic and the nematic phase is triggered by an attractive quadrupolar interaction between electrons, as in the case of conventional Fermi liquids. We derive the theory of the nematic state and of the phase transition. This theory is based on the flux attachment procedure which maps an electron liquid in half-filled Landau levels into the composite Fermi liquid close to a nematic transition. We show th…
During the last decade, translational and rotational symmetry-breaking phases -- density wave order and electronic nematicity -- have been established as generic and distinct features of many correlated electron systems, including pnictide and cuprate superconductors. However, in cuprates, the relationship between these electronic symmetry-breaking phases and the enigmatic pseudogap phase remains unclear. Here, we employ resonant x-ray scattering in a cuprate high-temperature superconductor La$_{1.6-x}$Nd$_{0.4}$Sr$_{x}$CuO$_{4}$ (Nd-LSCO) to navigate the cuprate phase diagram, probing the rel…
Clean two-dimensional electron systems in GaAs/AlGaAs heterostructures exhibit anisotropic collective phases, the quantum Hall nematics, at high Landau level occupancy and low temperatures. An as yet unknown native symmetry-breaking potential consistently orients these phases relative to the crystalline axes of the host material. Here we report an extensive set of measurements examining the role of the structural symmetries of the heterostructure in determining the orientation of the nematics. In single quantum well samples we find that neither the local symmetry of the confinement potential n…
It was suggested that the two consecutive metamagnetic transitions and the large residual resistivity discovered in Sr$_3$Ru$_2$O$_7$ can be understood via the nematic order and its domains in a single layer system. However, a recently reported anisotropy between two longitudinal resistivities induced by tilting the magnetic field away from the c-axis cannot be explained within the single layer nematic picture. To fill the gap in our understanding within the nematic order scenario, we investigate the effects of bilayer coupling and in-plane magnetic field on the electronic nematic phases in a …
It is shown that zero point quantum fluctuations (ZPQFs) completely lift the accidental continuous degeneracy that is found in mean field analysis of quantum spin nematic phases of hyperfine spin 2 cold atoms. The result is two distinct ground states which have higher symmetries: a uniaxial spin nematic and a biaxial spin nematic with dihedral symmetry ${Dih}_4$. There is a novel first order quantum phase transition between the two phases as atomic scattering lengths are varied. We find that the ground state of $^{87}Rb$ atoms should be a uniaxial spin nematic. We note that the energy barrier …
We consider insulating phases of cold spin-1 bosonic particles with antiferromagnetic interactions, such as Na-23, in optical lattices. We show that spin-exchange interactions give rise to several distinct phases, which differ in their spin correlations. In two- and three- dimensional lattices insulating phases with odd number of particles per site are always nematic. For insulating states with even number of particles per site there is always a spin-singlet phase and there may also be a first-order transition into the nematic phase. The nematic phase breaks spin rotational symmetry, but prese…
We derive an effective field theory for the isotropic-nematic quantum phase transition of fractional quantum Hall (FQH) states. We demonstrate that for a system with an isotropic background the low-energy effective theory of the nematic order parameter has $z=2$ dynamical scaling exponent, due to a Berry phase term of the order parameter, which is related to the non-dissipative Hall viscosity. Employing the composite fermion theory with a quadrupolar interaction between electrons, we show that a sufficiently attractive quadrupolar interaction triggers a phase transition from the isotropic FQH …
We provide a quantitative characterization of generic weakly first-order thermal phase transitions out of planar spin-nematic states in three-dimensional spin-one quantum magnets, based on calculations using Poisson-Dirichlet distributions (PD) within a universal loop model formulation, combined with large-scale quantum Monte Carlo calculations. In contrast to earlier claims, the thermal melting of the nematic state is not continuous, instead a weakly first-order transition is identified from both thermal properties and the distribution of the nematic order parameter. Furthermore, based on PD …
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…
We investigate the phase diagram of S=1 quantum spin systems with SU(2)-invariant interactions, at low temperatures and in three spatial dimensions. Symmetry breaking and the nature of pure states can be studied using random loop representations. The latter confirm the occurrence of ferro- and antiferromagnetic transitions and the breaking of SU(3) invariance. And they reveal the peculiar nature of the nematic pure states which MINIMIZE \sum_x (S_x^i)^2.
