Nematic Symmetry Research Articles

Layer topology of smectic grain boundaries

ABSTRACT Grain boundaries in extremely confined colloidal smectics possess a topological fine structure with coexisting nematic and tetratic symmetry of the director field. An alternative way to approach the problem of smectic topology is via the layer structure, which is typically more accessible in experiments on molecular liquid crystals. Here, we consider exemplary density functional theory results for two-dimensional hard rods to illustrate how the concept of endpoint defects, which appear as tetratic disclinations of quarter charge in director topology, translates to smectic layer topology built around the networks formed by density maxima and minima. By doing so, we elaborate on further advantages of a topological concept evolving around the layer structure rather than the director field, such as providing insight in the structure of edge dislocations or virtual defects at the confining walls.

Nanostructure Quantification of Hard Carbon Electrodes through Advanced HRTEM Image Analysis

The currently remaining uncertainties on nanostructure has severely hindered the optimal design of hard carbon electrodes. HRTEM characterizations allow us to carry out structural measurements at the atomic level, however, extracting physically meaningful and statistically robust data from HRTEM images is not an easy process. In this work, intelligent fringe analysis and Gabor filtering algorithm were combined to reduce subjective bias and improve statistical reliability. Fringe orientation was described by nematic symmetry of second-order statistics. As a representative, detailed structural analysis of sucrose-derived hard carbon prepared at different heat treatment temperatures (HTTs) was performed. Advanced HRTEM image analysis reveals that the nanostructural evolution of hard carbon is manifested in several aspects, involving the growth and flattening of fringes, enhancement of ordering alignment, increase of stacking, and development of symmetry. More importantly, these structural parameters were quantitatively analyzed in detail. The structural parameters obtained by HRTEM are consistent with similar parameters obtained by other techniques such as XRD. This work provides an unprecedented quantitative insight into the nanostructural trends of hard carbon, with potential to aid researchers in elucidating the structure-property relationships of carbon electrodes

Magnetism-driven unconventional effects in Ising superconductors: Role of proximity, tunneling, and nematicity

Hybrid Ising superconductor-ferromagnetic insulator heterostructures provide a unique opportunity to explore the interplay between proximity-induced magnetism, spin-orbit coupling and superconductivity. Here we use a combination of first-principles calculations of NbSe$_{2}$/CrBr$_{3}$ heterostructures and an analytical theory of Ising superconductivity to analyze the existing experiments and provide a complete explanation of highly nontrivial and largely counterintuitive effects: an increase in the magnitude of the superconducting gap accompanied by the broadening of the tunneling peaks; hysteretic behavior of the tunneling conductance that sets in $\approx 2$ K below $T_c$; and nematic symmetry breaking in the superconducting state. The microscopic reason in all three cases appears to be the interplay between the proximity-induced exchange splitting and intrinsic defects. Finally, we predict additional interesting effects that at the moment cannot be addressed experimentally: spin-filtering when tunneling across CrBr$_{3}$ and tunneling ``hot spots'' in momentum space that are anticorrelated with regions where the spin-orbit splitting is maximum.

Photoinduced long-lived state in FeSe0.4Te0.6

FeSexTe1−x compounds display a rich phase diagram, ranging from the nematicity of FeSe to the (π,π) magnetism of FeTe. We focus on FeSe0.4Te0.6, and exploit tr-ARPES to study its ultrafast electron dynamics following photoexcitation by near-infrared pump pulses. By exploiting probe-polarization-dependent matrix element effects, we reveal a photoinduced long-lived state, lasting for a few tens of picoseconds, showing features compatible with a nematic state. The possibility to induce a long-lived state in this compound by using ultra-short pulses might shed a new light on the driving force behind the nematic symmetry breaking in iron-based superconductors. With the aid of a phenomenological model, we illustrate how our results possibly question the common belief that a low-energy coupling with fluctuations is a necessary condition to stabilize the nematic order. On the contrary, the tendency towards orbital differentiation due to strong electronic correlations induced by the Hund’s coupling could be at the origin of the nematic order in iron-based superconductors.

Pattern formation and polarity sorting of driven actin filaments on lipid membranes

Collective motion of active matter is ubiquitously observed, ranging from propelled colloids to flocks of bird, and often features the formation of complex structures composed of agents moving coherently. However, it remains extremely challenging to predict emergent patterns from the binary interaction between agents, especially as only a limited number of interaction regimes have been experimentally observed so far. Here, we introduce an actin gliding assay coupled to a supported lipid bilayer, whose fluidity forces the interaction between self-propelled filaments to be dominated by steric repulsion. This results in filaments stopping upon binary collisions and eventually aligning nematically. Such a binary interaction rule results at high densities in the emergence of dynamic collectively moving structures including clusters, vortices, and streams of filaments. Despite the microscopic interaction having a nematic symmetry, the emergent structures are found to be polar, with filaments collectively moving in the same direction. This is due to polar biases introduced by the stopping upon collision, both on the individual filaments scale as well as on the scale of collective structures. In this context, positive half-charged topological defects turn out to be a most efficient trapping and polarity sorting conformation.

Spin density wave and electron nematicity in magic-angle twisted bilayer graphene

We study theoretically many-body properties of magic-angle twisted bilayer graphene for different doping levels. Our investigation is focused on the emergence, stability, and manifestations of nematicity of the ordered low-temperature electronic state. It is known that, at vanishing interactions, the low-energy spectrum of the system studied consists of four almost-flat almost-degenerate bands. Electron-electron repulsion lifts this degeneracy. To account for such an interaction effect, a numerical mean-field theory is used. Assuming that the ground state has spin-density-wave-like order, we introduce a multicomponent order parameter describing spin magnetization. Our simulations show that the order parameter structure depends on the doping level. In particular, doping away from the charge neutrality point reduces the rotational symmetry of the ordered state, indicating the appearance of an electron nematic state. Manifestations of the nematicity can be observed in the spatial distribution of the spin magnetization within a moir{\'e} cell, as well as in the single-electron band structure. The nematicity is strongest at half-filling (two extra electron or holes per supercell). We argue that nematic symmetry breaking is a robust feature of the system ground state, stable against model parameters variations. Specifically, it is shown that, away from the charge neutrality point, it persists for all three parametrizations of the interlayer hopping amplitudes discussed in the paper. Obtained theoretical results are consistent with the available experimental data.

Detecting nematic order in STM/STS data with artificial intelligence

Detecting the subtle yet phase defining features in Scanning Tunneling Microscopy and Spectroscopy data remains an important challenge in quantum materials. We meet the challenge of detecting nematic order from the local density of states data with supervised machine learning and artificial neural networks for the difficult scenario without sharp features such as visible lattice Bragg peaks or Friedel oscillation signatures in the Fourier transform spectrum. We train the artificial neural networks to classify simulated data of symmetric and nematic two-dimensional metals in the presence of disorder. The supervised machine learning succeeds only with at least one hidden layer in the ANN architecture, demonstrating it is a higher level of complexity than a nematic order detected from Bragg peaks, which requires just two neurons. We apply the finalized ANN to experimental STM data on CaFe_22As_22, and it predicts nematic symmetry breaking with dominating confidence, in agreement with previous analysis. Our results suggest ANNs could be a useful tool for the detection of nematic order in STM data and a variety of other forms of symmetry breaking.

Mechanisms to splay-bend nematic phases.

While twist-bend nematic phases have been extensively studied, the experimental observation of two dimensional, oscillating splay-bend phases is recent. We consider two theoretical models that have been used to explain the formation of twist-bend phases-flexoelectricity and bond orientational order-as mechanisms to induce splay-bend phases. Flexoelectricity is a viable mechanism, and splay and bend flexoelectric couplings can lead to splay-bend phases with different modulations. We show that while bond orientational order circumvents the need for higher order terms in the free energy, the important role of nematic symmetry and phase chirality rules it out as a basic mechanism.

Emergence of coexisting ordered states in active matter systems.

Active systems can produce a far greater variety of ordered patterns than conventional equilibrium systems. In particular, transitions between disorder and either polar- or nematically ordered phases have been predicted and observed in two-dimensional active systems. However, coexistence between phases of different types of order has not been reported. We demonstrate the emergence of dynamic coexistence of ordered states with fluctuating nematic and polar symmetry in an actomyosin motility assay. Combining experiments with agent-based simulations, we identify sufficiently weak interactions that lack a clear alignment symmetry as a prerequisite for coexistence. Thus, the symmetry of macroscopic order becomes an emergent and dynamic property of the active system. These results provide a pathway by which living systems can express different types of order by using identical building blocks.

Peculiarities of electron density distribution in bismuth chalcogenides, iron pnictides, cuprates and related unconventional superconductors

With the aim to reveal the origin of instabilities in the electron subsystem of unconventional superconductors, such as stripes or nematic symmetry breaking, electron band structure calculations were performed for a number of bismuth chalcogenides, bismuth oxide, iron pnictides, as well as for Bi2Sr2CaCu2O8, YBa2Cu3O7 and La2CuO4. It was found that bond critical points in the electron density distribution ρ(r) of all the studied compounds were characterized by positive sign of electron density Laplacian evidencing on depletion of electron charge from the area of bond critical points. A correlation was found between the Tc and the value of electron density Laplacian in the strongest bond critical points of superconductors and related substances.

Mean first-passage time of an anisotropic diffusive searcher

We consider an anisotropic needle-like Brownian particle with nematic symmetry confined in a 2D domain. For this system, the coupling of translational and rotational diffusion makes the process of the positions of the particle non Markovian. Using scaling arguments, a Gaussian approximation and numerical methods, we determine the mean first passage time of the particle to a target of radius a and show in particular that for , in contrast with the classical logarithmic divergence obtained in the case of an isotropic 2D Brownian particle.

Orbital-driven nematicity in FeSe.

A fundamental and unconventional characteristic of superconductivity in iron-based materials is that it occurs in the vicinity of two other instabilities. In addition to a tendency towards magnetic order, these Fe-based systems have a propensity for nematic ordering: a lowering of the rotational symmetry while time-reversal invariance is preserved. Setting the stage for superconductivity, it is heavily debated whether the nematic symmetry breaking is driven by lattice, orbital or spin degrees of freedom. Here, we report a very clear splitting of NMR resonance lines in FeSe at Tnem = 91 K, far above the superconducting Tc of 9.3 K. The splitting occurs for magnetic fields perpendicular to the Fe planes and has the temperature dependence of a Landau-type order parameter. Spin-lattice relaxation rates are not affected at Tnem, which unequivocally establishes orbital degrees of freedom as driving the nematic order. We demonstrate that superconductivity competes with the emergingnematicity.

Gapped broken symmetry states in ABC-stacked trilayer graphene

We use a self-consistent Hartree-Fock approximation with realistic Coulomb interactions for $\pi$-band electrons to explore the possibility of broken symmetry states in weakly disordered ABC stacked trilayer graphene. The competition between gapped and gapless broken symmetry states, and normal states is studied by comparing total energies. We find that gapped states are favored and that, unlike the bilayer case, gapless nematic broken symmetry states are not metastable. Among the gapped states the layer antiferromagnetic state is favored over anomalous and spin Hall states.

Self-regulation in self-propelled nematic fluids

We consider the hydrodynamic theory of an active fluid of self-propelled particles with nematic aligning interactions. This class of materials has polar symmetry at the microscopic level, but forms macrostates of nematic symmetry. We highlight three key features of the dynamics. First, as in polar active fluids, the control parameter for the order-disorder transition, namely the density, is dynamically convected by the order parameter via active currents. The resulting dynamical self-regulation of the order parameter is a generic property of active fluids and destabilizes the uniform nematic state near the mean-field transition. Secondly, curvature-driven currents render the system unstable deep in the nematic state, as found previously. Finally, and unique to self-propelled nematics, nematic order induces local polar order that in turn leads to the growth of density fluctuations. We propose this as a possible mechanism for the smectic order of polar clusters seen in numerical simulations.

Anisotropic Brownian motion in ordered phases of DNA fragments

Using Fluorescence Recovery After Photobleaching, we investigate the Brownian motion of DNA rod-like fragments in two distinct anisotropic phases with a local nematic symmetry. The height of the measurement volume ensures the averaging of the anisotropy of the in-plane diffusive motion parallel or perpendicular to the local nematic director in aligned domains. Still, as shown in using a model specifically designed to handle such a situation and predicting a non-Gaussian shape for the bleached spot as fluorescence recovery proceeds, the two distinct diffusion coefficients of the DNA particles can be retrieved from data analysis. In the first system investigated (a ternary DNA-lipid lamellar complex), the magnitude and anisotropy of the diffusion coefficient of the DNA fragments confined by the lipid bilayers are obtained for the first time. In the second, binary DNA-solvent system, the magnitude of the diffusion coefficient is found to decrease markedly as DNA concentration is increased from isotropic to cholesteric phase. In addition, the diffusion coefficient anisotropy measured within cholesteric domains in the phase coexistence region increases with concentration, and eventually reaches a high value in the cholesteric phase.

Electronic structure of the cuprate superconducting and pseudogap phases from spectroscopic imaging STM

We survey the use of spectroscopic imaging scanning tunneling microscopy (SI-STM) to probe the electronic structure of underdoped cuprates. Two distinct classes of electronic states are observed in both the d-wave superconducting (dSC) and the pseudogap (PG) phases. The first class consists of the dispersive Bogoliubov quasiparticle excitations of a homogeneous d-wave superconductor, existing below a lower energy scale E=Δ0. We find that the Bogoliubov quasiparticle interference (QPI) signatures of delocalized Cooper pairing are restricted to a k-space arc, which terminates near the lines connecting k=±(π/a0,0) to k=±(0,π/a0). This arc shrinks continuously with decreasing hole density such that Luttinger's theorem could be satisfied if it represents the front side of a hole-pocket that is bounded behind by the lines between k=±(π/a0,0) and k=±(0,π/a0). In both phases, the only broken symmetries detected for the |E|<Δ0 states are those of a d-wave superconductor. The second class of states occurs proximate to the PG energy scale E=Δ1. Here the non-dispersive electronic structure breaks the expected 90°-rotational symmetry of electronic structure within each unit cell, at least down to 180°-rotational symmetry. This electronic symmetry breaking was first detected as an electronic inequivalence at the two oxygen sites within each unit cell by using a measure of nematic (C2) symmetry. Incommensurate non-dispersive conductance modulations, locally breaking both rotational and translational symmetries, coexist with this intra-unit-cell electronic symmetry breaking at E=Δ1. Their characteristic wavevector Q is determined by the k-space points where Bogoliubov QPI terminates and therefore changes continuously with doping. The distinct broken electronic symmetry states (intra-unit-cell and finite Q) coexisting at E∼Δ1 are found to be indistinguishable in the dSC and PG phases. The next challenge for SI-STM studies is to determine the relationship of the E∼Δ1 broken symmetry electronic states with the PG phase, and with the E<Δ0 states associated with Cooper pairing.

Orientational order in two dimensions from competing interactions at different scales

We discuss orientational order in two dimensions in the context of systems with competing isotropic interactions at different scales. We consider an extension of the Brazovskii model for stripe phases including explicitly quartic terms with nematic symmetry in the energy. We show that leading fluctuations of the mean-field nematic solution drive the isotropic-nematic transition into the Kosterlitz-Thouless universality class; i.e., these systems have a thermodynamic phase with orientational quasi-long-range order.

Critical fluctuations and random-anisotropy glass transition in nematic elastomers

We carry out a detailed deuterium nuclear magnetic resonance (NMR) study of local nematic ordering in polydomain nematic elastomers. This system has a close analogy to the random-anisotropy spin glass. We find that, in spite of the quadrupolar nematic symmetry in three dimensions requiring a first-order transition, the order parameter in the quenched ``nematic glass'' emerges via a continuous phase transition. In addition to this remarkable effect, by a careful analysis of the NMR line shape, we deduce that the local director fluctuations grow in a critical manner around the transition point. This could become an essential experimental evidence for the quenched disorder changing the order of discontinuous transition.

Spin-exchange interactions of spin-one bosons in optical lattices: Singlet, nematic, and dimerized phases

We consider insulating phases of cold spin-1 bosonic particles with antiferromagnetic interactions, such as {sup 23}Na, 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 an odd number of particles per site are always nematic. For insulating states with an 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 preserves time reversal symmetry, and has gapless spin-wave excitations. The spin-singlet phase does not break spin symmetry and has a gap to all excitations. In one-dimensional lattices, insulating phases with an odd number of particles per site always have a regime where translational symmetry is broken and the ground state is dimerized. We discuss signatures of various phases in Bragg scattering and time-of-flight measurements.

A tensor model of liquid crystalline polymers: application to basic disclination processes

One of the features of liquid crystalline polymers (LCPs) is their strong elastic anisotropy, which means they have unequal elastic constants. Elastic anisotropy plays a crucial role in the microstructure and macroscopic properties of LCPs. In this paper, the effect of unequal elastic constants on microstructure is investigated without an external field by using a deterministic tensorial approach. In this model, the evolution of the director field can be viewed as a process driven towards the state of zero elastic torque. A tensor expression of the elastic torque is used so that the nematic symmetry is automatically conserved. In simulations of bulk samples, disclination lines of strength half and escaped integer disclinations are observed. The distortion fields around the disclinations are found to depend on elastic anisotropy. If the twist constant is the lowest, as is the case for main chain liquid crystalline polymers, the disclination lines are predominantly of the twist type.