Nematic Instability Research Articles

Spinodal instabilities in polydisperse lyotropic nematics.

Many lyotropic liquid crystals are composed of mesogens that display a considerable spread in size or shape affecting their material properties and thermodynamics via various demixing and multi-phase coexistence scenarios. Starting from a generalized Onsager theory, we formulate a generic framework that enables locating spinodal polydispersities as well as identifying the nature of incipient size fractionation for arbitrary model potentials and size distributions. We apply our theory to nematic phases of both hard rods and disks whose main particle dimension is described by a unimodal log-normal distribution. We find that both rod-based and discotic nematics become unstable at a critical polydispersity of about 20%. We also investigate the effect of doping nematic assemblies with a small fraction of large species and highlight their effect on the stability of the uniform nematic fluid. Our main finding is that while rod-based are only weakly affected by the presence of large species, doping discotic nematics with very large platelets leads to a remarkable suppression of the spinodal instabilities. This could open up routes towards controlling the mechanical properties of nematic materials by manipulating the local stability of nematic fluid and its tendency to undergo fractionation-driven microphase separation.

Spin-driven nematic instability of the multiorbital Hubbard model: Application to iron-based superconductors

Nematic order resulting from the partial melting of density-waves has been proposed as the mechanism to explain nematicity in iron-based superconductors. An outstanding question, however, is whether the microscopic electronic model for these systems -- the multi-orbital Hubbard model -- displays such an ordered state as its leading instability. In contrast to usual electronic instabilities, such as magnetic and charge order, this fluctuation-driven phenomenon cannot be captured by the standard RPA method. Here, by including fluctuations beyond RPA in the multi-orbital Hubbard model, we derive its nematic susceptibility and contrast it with its ferro-orbital order susceptibility, showing that its leading instability is the spin-driven nematic phase. Our results also demonstrate the primary role played by the $d_{xy}$ orbital in driving the nematic transition, and reveal that high-energy magnetic fluctuations are essential to stabilize nematic order in the absence of magnetic order.

Excitonic and nematic instabilities on the surface of topological Kondo insulators

We study the effects of strong electron-electron interactions on the surface of cubic topological Kondo insulators (such as samarium hexaboride, SmB$_6$). Cubic topological Kondo insulators generally support three copies of massless Dirac nodes on the surface, but only two of them are energetically degenerate and exhibit an energy offset relative to the third one. With a tunable chemical potential, when the surface states host electron and hole pockets of comparable size, strong interactions may drive this system into rotational symmetry breaking nematic and translational symmetric breaking excitonic spin- or charge-density-wave phases, depending on the relative chirality of the Dirac cones. Taking a realistic surface band structure into account we analyze the associated Ginzburg-Landau theory and compute the mean field phase diagram for interacting surface states. Beyond mean field theory, this system can be described by a two-component isotropic Ashkin-Teller model at finite temperature, and we outline the phase diagram of this model. Our theory provides a possible explanation of recent measurements which detect a two-fold symmetric magnetoresistance and an upturn in surface resistivity with tunable gate voltage in SmB$_6$. Our discussion can also be germane to other cubic topological insulators, such as ytterbium hexaboride (YbB$_6$), plutonium hexaboride (PuB$_6$).

Spin nematic fluctuations near a spin-density-wave phase

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 ξ. The spin nematic instability occurs when ξ reaches a critical value , i.e., its transition temperature is always higher than the SDW critical temperature . In particular, decreases monotonically with increasing . Concomitantly, low-energy nematic fluctuations are present in a wider temperature region as becomes higher. Approaching the spin nematic instability, the nematic spectral function at zero momentum exhibits a central peak as a function of energy for a finite temperature and a soft mode at zero temperature. These properties originate from the general feature that the imaginary part of the spin-fluctuation bubble has a term linear in energy and its coefficient is proportional to the square of temperature. Furthermore we find that the nematic spectral function exhibits a diffusive peak around zero momentum and zero energy without clear dispersive features. A possible phase diagram for the spin nematic and SDW transitions is also discussed.

Electronic nematic phase transition in the presence of anisotropy

We study the phase diagram of electronic nematic instability in the presence of xy anisotropy. While a second order transition cannot occur in this case, mean-field theory predicts that a first order transition occurs near van Hove filling and its phase boundary forms a wing structure, which we term a Griffiths wing, referring to his original work of He3-He4 mixtures. When crossing the wing, the anisotropy of the electronic system exhibits a discontinuous change, leading to a meta-nematic transition, i.e., the analog to a meta-magnetic transition in a magnetic system. The upper edge of the wing corresponds to a critical end line, which shows a non-monotonic temperature dependence as a function of the external anisotropy and vanishes at a quantum critical end point for a strong anisotropy. The mean-field phase diagram is, however, very sensitive to fluctuations of the nematic order parameter, yielding a topologically different phase diagram. The Griffiths wing is broken into two pieces. A tiny wing appears close to zero anisotropy and the other is realized for a strong anisotropy. Consequently three quantum critical end points are realized. We discuss that these results can be related to various materials including a cold atom system.

Quantum multicriticality in bilayer graphene with a tunable energy gap

We develop a theory for quantum phases and quantum multicriticality in bilayer graphene in the presence of an explicit energy gap in the noninteracting spectrum by extending previous renormalization group (RG) analyses of electron-electron interactions in gapless bilayer graphene at finite temperature to include the effect of an electric field applied perpendicular to the sample, which produces an energy gap in the single-particle electron-hole dispersion. We determine the possible outcomes of the resulting RG equations, represented by ``fixed rays'' along which ratios of the coupling constants remain constant and map out the leading instabilities of the system for an interaction of the form of a Coulomb interaction that is screened by two parallel conducting plates placed equidistant from the electron. We find that some of the fixed rays on the ``target plane'' found in the zero-field case are no longer valid fixed rays, but that all four of the isolated rays are still valid. We also find five additional fixed rays that are not present in the zero-field case. We then construct maps of the leading instability (or instabilities) of the system for the screened Coulomb-like interaction as a function of the overall interaction strength and interaction range for four values of the applied electric field. We find that the pattern of leading instabilities is the same as that found in the zero-field case, namely, that the system is unstable to a layer antiferromagnetic state for short-ranged interactions, to a nematic state for long-ranged interactions, and to both for intermediate-ranged interactions. However, if the interaction becomes too long ranged or too weak, then the system will exhibit no instabilities. The ranges at which the nematic instability first appears, the antiferromagnetic instability disappears, and the nematic instability disappears all decrease with increasing applied electric field. Our main qualitative finding, that the applied electric field opposes the emergence of symmetry-broken phases in general, suppressing, however, the antiferromagnetc phase more strongly compared with the nematic phase, is directly testable experimentally.

Approaching Pomeranchuk instabilities from ordered phase: A crossing-symmetric equation method

We explore features of a 3D Fermi liquid near generalized Pomeranchuk instabilities using a tractable crossing symmetric equation method. We approach the instabilities from the ordered ferromagnetic phase. We find quantum multi-criticality as approach to the ferromagnetic instability drives instability in other channel(s). It is found that a charge nematic instability precedes and is driven by Pomeranchuk instabilities in both the l = 0 spin and density channels.

28aCG-12 電子ネマチック不安定性に伴うグリフィスの翼(28aCG 低温理論1(超伝導(Ru酸化物・銅酸化物)),領域8(強相関系))

28aCG-12 電子ネマチック不安定性に伴うグリフィスの翼(28aCG 低温理論1(超伝導(Ru酸化物・銅酸化物)),領域8(強相関系))

Observation of Incipient Charge Nematicity inBa(Fe1−XCoX)2As2

Using electronic Raman spectroscopy, we report direct measurements of charge nematic fluctuations in the tetragonal phase of strain-free Ba(Fe(1-x)Co(x))2As2 single crystals. The strong enhancement of the Raman response at low temperatures unveils an underlying charge nematic state that extends to superconducting compositions and which has hitherto remained unnoticed. Comparison between the extracted charge nematic susceptibility and the elastic modulus allows us to disentangle the charge contribution to the nematic instability, and to show that charge nematic fluctuations are weakly coupled to the lattice.

Spatially modulated electronic nematicity in the three-band model of cuprate superconductors

Charge order in cuprate superconductors is a possible source of anomalous electronic properties in the underdoped regime. Intra-unit cell charge ordering tendencies point to electronic nematic order involving oxygen orbitals. In this context we investigate charge instabilities in the Emery model and calculate the charge susceptibility within diagrammatic perturbation theory. In this approach, the onset of charge order is signalled by a divergence of the susceptibility. Our calculations reveal three different kinds of order: a commensurate ($q=0$) nematic order, and two incommensurate nematic phases with modulation wavevectors that are either axial or oriented along the Brillouin zone diagonal. We examine the nematic phase diagram as a function of the filling, the interaction parameters, and the band structure. We also present results for the excitation spectrum near the nematic instability, and show that a soft nematic mode emerges from the particle-hole continuum at the transition. The Fermi surface reconstructions that accompany the modulated nematic phases are discussed with respect to their relevance for magneto-oscillation and photoemission measurements. The modulated nematic phases that emerge from the three-band Emery model are compared to those found previously in one-band models.

Transport signatures of electronic-nematic stripe phases

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, this finite-q nematic (nematic stripe) phase has also been identified as an additional leading instability that is as strong as the superconducting instability near the onset of spin density wave order. Here, we study the electrical conductivity tensor in the modulated nematic phase for a general modulation vector. Our results can be used to identify nematic stripe phases in correlated materials.

Possible charge instabilities in two-dimensional doped Mott insulators

Motivated by the growing evidence of the importance of charge fluctuations in the pseudogap phase in high-temperature cuprate superconductors, we apply a large-N expansion formulated in a path integral representation of the two-dimensional t-J model on a square lattice. We study all possible charge instabilities of the paramagnetic state in leading order of the 1/N expansion. While the d-wave charge density wave (flux phase) becomes the leading instability for various choices of model parameters, we find that a d-wave Pomeranchuk (electronic nematic phase) instability occurs as a next leading one. In particular, the nematic state has a strong tendency to become inhomogeneous. In the presence of a large second nearest-neighbor hopping integral, the flux phase is suppressed and the electronic nematic instability becomes leading in a high doping region. Besides these two major instabilities, bond-order phases occur as weaker instabilities close to half-filling. Phase separation is also detected in a finite temperature region near half-filling.

Incommensurate nematic fluctuations in two-dimensional metals

To assess the strength of nematic fluctuations with a finite wave vector in a two-dimensional metal, we compute the static d-wave polarization function for tight-binding electrons on a square lattice. At Van Hove filling and zero temperature the function diverges logarithmically at q=0. Away from Van Hove filling the ground state polarization function exhibits finite peaks at finite wave vectors. A nematic instability driven by a sufficiently strong attraction in the d-wave charge channel thus leads naturally to a spatially modulated nematic state, with a modulation vector that increases in length with the distance from Van Hove filling. Above Van Hove filling, for a Fermi surface crossing the magnetic Brillouin zone boundary, the modulation vector connects antiferromagnetic hot spots with collinear Fermi velocities.

Flexoelectricity and pattern formation in nematic liquid crystals

We present in this paper a detailed analysis of the flexoelectric instability of a planar nematic layer in the presence of an alternating electric field (frequency ω), which leads to stripe patterns (flexodomains) in the plane of the layer. This equilibrium transition is governed by the free energy of the nematic, which describes the elasticity with respect to the orientational degrees of freedom supplemented by an electric part. Surprisingly the limit ω→0 is highly singular. In distinct contrast to the dc case, where the patterns are stationary and time independent, they appear at finite, small ω periodically in time as sudden bursts. Flexodomains are in competition with the intensively studied electrohydrodynamic instability in nematics, which presents a nonequilibrium dissipative transition. It will be demonstrated that ω is a very convenient control parameter to tune between flexodomains and convection patterns, which are clearly distinguished by the orientation of their stripes.

Liquid crystal phases of ultracold dipolar fermions on a lattice

Motivated by the search for quantum liquid crystal phases in a gas of ultracold atoms and molecules, we study the density-wave and nematic instabilities of dipolar fermions on the two-dimensional square lattice (in the $x\text{\ensuremath{-}}y$ plane) with dipoles pointing to the $z$ direction. We determine the phase diagram using two complementary methods, the Hartree-Fock mean-field theory and the linear-response analysis of compressibility. Both give consistent results. In addition to the staggered $(\ensuremath{\pi},\ensuremath{\pi})$ density wave, over a finite range of densities and hopping parameters, the ground state of the system first becomes nematic and then smectic, when the dipolar interaction strength is increased. Both phases are characterized by the same broken fourfold $({C}_{4})$ rotational symmetry. The difference is that the nematic phase has a closed Fermi surface but the smectic does not. The transition from the nematic to the smectic phase is associated with a jump in the nematic order parameter. This jump is closely related to the Van Hove singularities. We derive the kinetic equation for collective excitations in the normal isotropic phase and find that the zero sound mode is strongly Landau damped and thus is not a well-defined excitation. Experimental implications of our results are discussed.

Momentum-sector-selective metal-insulator transition in the eight-site dynamical mean-field approximation to the Hubbard model in two dimensions

We explore the momentum-sector-selective metal-insulator transitions recently found in the eight-site dynamical cluster approximation to the two-dimensional Hubbard model. The phase diagram in the space of interaction and second-neighbor hopping is established. The initial transitions from Fermi-liquid-like to sector-selective phases are found to be of second order, caused by the continuous opening of an energy gap whereas the other transitions are found to be of first order. In the sector-selective phase the Fermi surface regions which are not gapped are found to have a non-Fermi-liquid self-energy. We demonstrate that the phenomenon is not caused by the Van Hove divergence in the density of states. The sector-selective and insulating phases are characterized by a cluster spin-correlation function that is strongly peaked at the commensurate antiferromagnetic wave vector $(\ensuremath{\pi},\ensuremath{\pi})$ but the model has no nematic instability. Comparison to dynamical mean-field studies on smaller clusters is made.

Dispersions of multiwalled carbon nanotubes in different nematic mesogens: The study of optical transmittance and electrical conductivity

Optical transmittance and electric conductivity were studied for dispersions of multiwall carbon nanotubes (MWCNTs) in nematic liquid crystals of four different chemical classes (cyanobiphenyls, Schiff bases, azoxy compounds, and cyclohexanecarboxylic acids). The optical transmittance data showed deep integration of MWCNTs into the orientationally ordered nematic structure. The effect observed was apparently related to interactions between the MWCNTs and mesogen matrix, which appeared to be weaker when the nematic host was formed by non-aromatic molecules. Dependences of the electrical conductivity versus applied DC voltage were noticeably different for different nematic matrices. Voltage amplification of electrical conductivity was observed at relatively higher voltages (above 10 V). The increased threshold voltages for electrohydrodynamical instability in nematics were observed in MWCNT-doped dispersions.

Theory of microphase separation on side-chain liquid-crystalline polymers with flexible spacers

We model a melt of monodisperse side-chain liquid-crystalline polymers as a melt of comb copolymers in which the side groups are rod-coil diblock copolymers. We consider both excluded-volume and Maier-Saupe interactions. The first acts among any pair of segments while the latter acts only between rods. Using a free-energy functional calculated from this microscopic model, we study the spinodal stability of the isotropic phase against density and orientational fluctuations. The phase diagram obtained in this way predicts nematic and smectic instabilities as well as the existence of microphases or phases with modulated wave vector but without nematic ordering. Such microphases are the result of the competition between the incompatibility among the blocks and the connectivity constraints imposed by the spacer and the backbone. Also the effects of the polymerization degree and structural conformation of the monomeric units on the phase behavior of the side-chain liquid-crystalline polymers are studied.

Heat bath approach to Landau damping and Pomeranchuk quantum critical points

We study the problem of the damping of collective modes close to a Pomeranchuk quantum critical point in a Fermi liquid. In analogy with problems in dissipative open quantum systems, we derive the Landau damping of a Fermi liquid by integrating out a macroscopic number of degrees of freedom from a generating functional. Being a reformulation of the linearized Boltzmann equation, this approach reproduces well-known results from the theory of Fermi liquids. We also study the Bethe-Salpeter equations within the Landau theory and discuss the implications of these results on quantum phase transitions of the Pomeranchuk type and its dynamical exponent, $z$. We apply our results to the electronic nematic instability and find $z=3$ in the collisionless limit.

Ideal glass transitions for hard ellipsoids

For hard ellipsoids of revolution we calculate the phase diagram for the idealized glass transition. Our equations cover the glass physics in the full phase space, for all packing fractions and all aspect ratios X0. With increasing aspect ratio we find the idealized glass transition to become primarily driven by orientational degrees of freedom. For needlelike or platelike systems the transition is strongly influenced by a precursor of a nematic instability. We obtain three types of glass transition line. The first one (straight phi((B))(c)) corresponds to the conventional glass transition for spherical particles which is driven by the cage effect. At the second one (straight phi((B'))(c)), which occurs for rather nonspherical particles, a glass phase is formed that consists of domains. Within each domain there is a nematic order where the center of mass motion is quasiergodic, whereas the interdomain orientations build an orientational glass. The third glass transition line (straight phi((A))(c)) occurs for nearly spherical ellipsoids where the orientational degrees of freedom with odd parity, e.g., 180 degrees flips, freeze independently from the positions.