Nematic Transition Research Articles

Finger front propagation in smectic-A Fréedericksz transition.

Systems with multistability are characterized by exhibiting complex nonlinear waves between equilibria. Experimentally, near the smectic-A to chiral nematic transition in a liquid crystal mixture cell with planar anchoring, we observe finger fronts emerge in the smectic-A phase when applying an electric field, a reorientation transition. Finger fronts propagate in the direction orthogonal to the anchoring. Colorimetry characterization allows us to describe the molecular reorientation transition and front dynamics. We reveal that the reorientation transition is of the first-order type and determine their critical points. The front speed is determined as a function of the applied voltage. Theoretically, based on a prototype model of liquid crystal transitions, we qualitatively describe the experimental observations. We have analytically determined the bifurcation diagram and the propagation speeds of finger fronts, finding a fair agreement with the experimental observations.

Phonon-induced rotation of the electronic nematic director in superconducting Bi2Se3

The doped topological insulator ${A}_{x}{\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$, with $A={\mathrm{Cu},\mathrm{Sr},\mathrm{Nb}}$, becomes a nematic superconductor below ${T}_{c}\ensuremath{\approx}3$--4 K. The associated electronic nematic director is described by an angle $\ensuremath{\alpha}$ and is experimentally manifested in the elliptical shape of the in-plane critical magnetic field ${H}_{c2}$. Because of the threefold rotational symmetry of the lattice, $\ensuremath{\alpha}$ is expected to align with one of three high-symmetry directions corresponding to the in-plane nearest-neighbor bonds, consistent with a ${Z}_{3}$-Potts nematic transition. Here, we show that the nematic coupling to the acoustic phonons, which makes the nematic correlation length tend to diverge along certain directions only, can fundamentally alter this phenomenology in trigonal lattices. Compared to hexagonal lattices, the former possesses a sixth independent elastic constant ${c}_{14}$ due to the fact that the in-plane shear strain doublet $({\ensuremath{\epsilon}}_{xx}\ensuremath{-}{\ensuremath{\epsilon}}_{yy},\ensuremath{-}2{\ensuremath{\epsilon}}_{xy})$ and the out-of-plane shear strain doublet $(2{\ensuremath{\epsilon}}_{yz},\ensuremath{-}2{\ensuremath{\epsilon}}_{zx})$ transform as the same irreducible representation. We find that, when ${c}_{14}$ overcomes a threshold value, which is expected to be the case in doped ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$, the nematic director $\ensuremath{\alpha}$ unlocks from the high-symmetry directions due to the competition between the quadratic phonon-mediated interaction and the cubic nematic anharmonicity. This implies the breaking of the residual in-plane twofold rotational symmetry (${C}_{2x}$), resulting in a triclinic phase. We discuss the implications of these findings for the structure of nematic domains, for the shape of the in-plane ${H}_{c2}$ in ${A}_{x}{\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$, and for the presence of nodes inside the superconducting state.

Unusual Band Splitting and Superconducting Gap Evolution with Sulfur Substitution in FeSe

High-resolution angle-resolved photoemission measurements were taken on FeSe1–x S x (x = 0, 0.04, and 0.08) superconductors. With an ultrahigh energy resolution of 0.4 meV, unusual two hole bands near the Brillouin-zone center, which was possibly a result of additional symmetry breaking, were identified in all the sulfur-substituted samples. In addition, in both of the hole bands highly anisotropic superconducting gaps with resolution limited nodes were evidenced. We find that the larger superconducting gap on the outer hole band is reduced linearly to the nematic transition temperature while the gap on the inner hole is nearly S-substitution independent. Our observations strongly suggest that the superconducting gap increases with enhanced nematicity although the superconducting transition temperature is not only governed by the pairing strength, demonstrating strong constraints on theories in the FeSe family.

Nematic Quantum Criticality in Dirac Systems.

We investigate nematic quantum phase transitions in two different Dirac fermion models. The models feature twofold and fourfold, respectively, lattice rotational symmetries that are spontaneously broken in the ordered phase. Using negative-sign-free quantum MonteCarlo simulations and an ε-expansion renormalization group analysis, we show that both models exhibit continuous phase transitions. In contrast to generic Gross-Neveu dynamical mass generation, the quantum critical regime is characterized by large velocity anisotropies, with fixed-point values being approached very slowly. Both experimental and numerical investigations will not be representative of the infrared fixed point, but of a quasiuniversal regime where the drift of the exponents tracks the velocity anisotropy.

Structure of the twist-bend nematic phase with respect to the orientational molecular order of the thioether-linked dimers.

An analysis of the IR absorbance for the segmented functional groups of liquid crystal dimers mesogen and linker enabled the orientation order to be determined and information about the dipole interactions in the nematic and twist-bend nematic phases to be obtained. The long axis orientational order increases as the temperature decreases in the nematic phase, although much more slowly than for the classical nematics, and then reverses this trend in the twist-bend nematic phase due to the tilt of the molecules. In the nematic phase, the short axis of the molecule performs an isotropic uniform rotation and has a uniaxial alignment. In the twist-bend nematic phase, however, biaxial ordering occurs and grows significantly in accordance with the helical deformation of the director. Changes in the mean absorbance in the twist-bend nematic phase were observed: a decrease for the longitudinal dipole at the nematic-twist-bend nematic phase transition, thus emphasizing the antiparallel axial interaction of the dipoles, while the absorbance of the transverse dipoles remains unchanged up to 340 K, and then the latter become parallelly correlated.

Optical Fingerprints of Nematicity in Iron-Based Superconductors

Nematicity, which refers to a phase of broken rotational but preserved translational symmetry, is underlined by the appearance of anisotropic properties and leaves remarkable fingerprints in all measurable physical quantities upon crossing the structural tetragonal-orthorhombic transition at Ts in several iron-based materials. Here, we review part of our own broadband optical investigations, addressing the impact of nematicity on the charge dynamics, as a function of temperature and of tunable applied stress, the latter acting as an external symmetry breaking field. We shall first focus our attention on FeSe, which undergoes a nematic (structural) transition without any subsequent onset of magnetic ordering below Ts. FeSe thus provides an opportunity to study nematicity without the limitations due to the reconstruction of the Fermi surface because of the spin-density-wave collective state in the orthorhombic phase, typical for several other iron-based superconductors. Our data reveal an astonishing anisotropy of the optical response in the mid-infrared-to-visible spectral range, which bears testimony of an important polarization of the underlying electronic structure in agreement with angle-resolved-photoemission-spectroscopy results. Our findings at high energy scales support models for the nematic phase resting on an orbital-ordering mechanism, supplemented by orbital selective band renormalization. The optical results at energies close to the Fermi level furthermore emphasize scenarios relying on scattering by anisotropic spin-fluctuations and shed new light on the origin of nematicity in FeSe. Moreover, the composition at which the associated Weiss temperature of the nematic susceptibility extrapolates to zero is found to be close to optimal doping (i.e., in coincidence with the largest superconducting transition temperature), boosting the debate to what extent nematic fluctuations contribute to the pairing-mechanism and generally affect the electronic structure of iron-based superconductors. The present review then offers a discussion of our optical data on the optimally hole-doped Ba0.6K0.4Fe2As2. We show that the stress-induced optical anisotropy in the infrared spectral range is reversible upon sweeping the applied stress and occurs only below the superconducting transition temperature. These findings demonstrate that there is a large electronic nematicity at optimal doping which extends right under the superconducting dome.

DFT+U study on the multipolar nematic state of nonmagnetic FeSe

In this study, we investigate the electronic structure of FeSe in the normal and nematic states based on the DFT+U method in combination with the multipole analyses, and discuss their microscopic properties and origin. In the normal state, the topological change of the Fermi surface occurs before the nematic transition with increasing the on-site Coulomb interaction U. The resulting nematic ground state is a multipolar state having both hexadecapoles in the E-representation and multipoles in the B 2-representation on each Fe site, where the appearance of the E-type multipoles induces non-trivial spontaneous orbital hybridizations between dxy, dx2-y2 and dxz /dyz orbitals. Such the spontaneous orbital mixings due to E-type multipoles is inherent in the FeSe and related systems, and is expected to play an important role in the formation of the nematic states in other iron-based superconductors.

Quantitative relationship between structural orthorhombicity, shear modulus, and heat capacity anomaly of the nematic transition in iron-based superconductors

Electronic nematicity in iron pnictide materials has been extensively studied by various experimental techniques, yet its heat capacity anomaly at the phase transition has not been examined quantitatively. In this work we review the thermodynamic description of nematicity in $Ba(Fe_{1-x}Co_{x})_{2}As_{2}$ using the Landau free energy, which defines the behavior of three thermodynamic quantities: the structural orthorhombicity that develops below the nematic transition, the softening shear modulus above the transition, and the discontinuous heat capacity at the transition. We derive a quantitative relationship between these three quantities, which is found to hold for a range of dopings. This result shows that the nematic transition is exceedingly well described by a mean-field model in the underdoped regime of the phase diagram.

Anatomy of a Discovery: The Twist–Bend Nematic Phase

New fluid states of matter, now known as liquid crystals, were discovered at the end of the 19th century and still provide strong themes in scientific research. The applications of liquid crystals continue to attract attention, and the most successful so far has been to the technology of flat panel displays; this has diversified in recent years and LCDs no longer dominate the industry. Despite this, there is plenty more to be uncovered in the science of liquid crystals, and as well as new applications, novel types of liquid crystal phases continue to be discovered. The simplest liquid crystal phase is the nematic together with its handed or chiral equivalent, named the cholesteric phase. In the latter, the aligned molecules of the nematic twist about an axis perpendicular to their alignment axis, but in the 1970s a heliconical phase with a tilt angle of less than 90° was predicted. The discovery of this phase nearly 40 years later is described in this paper. Robert Meyer proposed that coupling between a vector order parameter in a nematic and a splay or bend elastic distortion could result in spontaneously splayed or bent structures. Later, Ivan Dozov suggested that new nematic phases with splay–bend or twist–bend structures could be stabilised if the appropriate elastic constants became negative. Theoretical speculation on new nematic phases and the experimental identification of nematic–nematic phase transitions are reviewed in the paper, and the serendipitous discovery in 2010 of the nematic twist–bend phase in 1″,7″-bis(4-cyanobiphenyl-4′-yl)heptane (CB7CB) is described.

Controlled morphing of architected liquid crystal elastomer elements: modeling and simulations

Liquid crystal elastomers (LCE) are elastomeric materials possessing a network microstructure made of chains with a preferential orientation, induced by mesogen units embedded in the material prior to polymerization. This peculiarity can be harnessed to induce deformation of a LCE element by making its network to switch from the preferentially oriented nematic state to the isotropic one, as occurs for instance by rising the temperature above the transition value characteristic of the material. This mechanism can be combined with an architected arrangement of LCE blocks whose nematic orientation and transition temperature are properly differentiated among the different zones constituting the element. In this way, a controlled morphing can be obtained out of an architected elastomer made of LCE portions (ALCE), leading to a morphing structure whose deformation can be activated and precisely tuned by heating up or cooling down the material. In this research, we investigate architected LCE elements showing the capability of producing a variety of deformed shapes. A micromechanical theoretical model for LCE is firstly illustrated and several examples of morphing of architected LCE elements, whose mechanical response is obtained through finite element (FE) numerical analyses based on the proposed micromechanical model, are illustrated and critically discussed.

Charge-density-wave-driven electronic nematicity in a kagome superconductor

Electronic nematicity, in which rotational symmetry is spontaneously broken by electronic degrees of freedom, has been demonstrated as a ubiquitous phenomenon in correlated quantum fluids including high-temperature superconductors and quantum Hall systems1,2. Notably, the electronic nematicity in high-temperature superconductors exhibits an intriguing entanglement with superconductivity, generating complicated superconducting pairing and intertwined electronic orders. Recently, an unusual competition between superconductivity and a charge-density-wave (CDW) order has been found in the AV3Sb5 (A = K, Rb, Cs) family with two-dimensional vanadium kagome nets3-8. Whether these phenomena involve electronic nematicity is still unknown. Here we report evidence for the existence of electronic nematicity in CsV3Sb5, using a combination of elastoresistance measurements, nuclear magnetic resonance (NMR) and scanning tunnelling microscopy/spectroscopy (STM/S). The temperature-dependent elastoresistance coefficient (m11 minus m12) and NMR spectra demonstrate that, besides a C2 structural distortion of the 2a0 × 2a0 supercell owing to out-of-plane modulation, considerable nematic fluctuations emerge immediately below the CDW transition (approximately 94 kelvin) and finally a nematic transition occurs below about 35 kelvin. The STM experiment directly visualizes the C2-structure-pinned long-range nematic order below the nematic transition temperature, suggesting a novel nematicity described by a three-state Potts model. Our findings indicate an intrinsic electronic nematicity in the normal state of CsV3Sb5, which sets a new paradigm for revealing the role of electronic nematicity on pairing mechanism in unconventional superconductors.

Nematic state of the FeSe superconductor

We study the crystal structure of the tetragonal iron selenide FeSe and its nematic phase transition to the low-temperature orthorhombic structure using synchrotron x-ray and neutron scattering analyzed in both real and reciprocal space. We show that in the local structure the orthorhombic distortion associated with the electronically driven nematic order is more pronounced at short length scales. It also survives up to temperatures above 90 K where reciprocal-space analysis suggests tetragonal symmetry. Additionally, the real-space pair distribution function analysis of the synchrotron x-ray diffraction data reveals a tiny broadening of the peaks corresponding to the nearest Fe-Fe, nearest Fe-Se, and the next-nearest Fe-Se bond distances as well as the tetrahedral torsion angles at a short length scale of 20 angstr\"om. This broadening appears below 20 K and is attributed to a pseudogap. However, we did not observe any further reduction in local symmetry below orthorhombic down to 3 K. Our results suggest that the superconducting gap anisotropy in FeSe is not associated with any symmetry-lowering short-range structural correlations.

Three-dimensional Atomic Image of FeSe High-temperature Superconductor by X-ray Fluorescence Holography

Fe Kα X-ray fluorescence holography measurements were carried out at room temperature on an FeSe high-temperature superconductor to clarify the relationship between the local structures around the Fe atoms and the superconducting nature. The obtained three-dimensional atomic arrangements strongly reveal a formation of strong FeSe4 clusters. On the other hand, the Se—Fe—Se bond angle largely spreads, causing a large ambiguity in the chalcogen height and large displacements of the Fe sublattice. Thus, it is reasonable that the tetragonal-to-orthorhombic structural (nematic) transition does not affect the magnetic ordering in the Fe layer.

Elasto-Raman scattering: Arsenic optical phonon as a probe of nematicity in BaFe2As2

We report a Raman scattering study of nematic degrees of freedom in the iron-based superconductor parent compound BaFe$_2$As$_2$ under tunable uniaxial strain. We demonstrate that the polarization resolved arsenic (As) phonon intensity can be used to monitor the nematic order parameter as a function of both temperature and strain. At low temperature in the nematic ordered phase we use it to track the continuous and reversible orientation of nematic domains under variable strain. At higher temperature, the evolution of the As phonon intensity under strain reflects an enhanced nematic susceptibility close to the nematic transition $T_S$. Its temperature dependence under strong strain follows qualitatively the expected behavior of an Ising order parameter under a symmetry breaking field. Our elasto-Raman study illustrates the interest of combining selective anisotropic strain with a symmetry resolved probe like Raman scattering. Elasto-Raman scattering can be applied to a wide variety of quantum materials where uniaxial strain tunes electronic orders.

Probing three-state Potts nematic fluctuations by ultrasound attenuation

Motivated by recent studies of three-state Potts nematic states in magic-angle twisted bilayer graphene and doped-${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$, we analyze the impact of critical nematic fluctuations on the low-energy properties of phonons. In this study, we propose how to identify the three-state Potts nematic fluctuations by ultrasound attenuation. The Gaussian fluctuation analysis shows that the Landau damping term becomes isotropic due to fluctuations of the ${C}_{3}$-breaking bond-order, and the nematoelastic coupling is also shown to be isotropic. These two features lead to an isotropic divergence of the transverse sound attenuation coefficient and an isotropic lattice softening, in contrast to the case of the ${C}_{4}$-breaking bond-order, which shows strong anisotropy. Moreover, we use a mean-field approximation and discuss the impurity effects. The transition temperature takes its maximum near the filling of the van Hove singularity, and the large density of states favors the nematic phase transition. It turns out that the phase transition is of weak first-order in the wide range of filling and, upon increasing the impurity scattering, the first-order transition line at low temperatures gradually shifts towards the second-order line, rendering the transition a weak first-order in a wider range of parameters. Furthermore, it is confirmed that the enhancement of the ultrasound attenuation coefficient will be clearly observed in experiments in the case of a weak first-order phase transition.

Anomalous quantum oscillations of CeCoIn5 in high magnetic fields

We report on magnetic-torque and resistivity measurements of the heavy-fermion compound ${\mathrm{CeCoIn}}_{5}$ in static magnetic fields up to 36 T and temperatures down to 50 mK. While quantum oscillations of the de Haas--van Alphen (dHvA) as well as the Shubnikov--de Haas (SdH) effect confirm the previously reported Fermi surfaces, an analysis of the field dependence reveals two anomalous features. The first is seen at about 22 T as a sharp anomaly in the resistivity for current applied along the $a$ direction. The second appears as nonmonotonic field-dependent oscillation frequencies and amplitudes in both dHvA and SdH signals. This second feature emerges at about 28 T. This field is close to that of the nematic transition reported for ${\mathrm{CeRhIn}}_{5}$ and the proposed Lifshitz transition in ${\mathrm{CeIrIn}}_{5}$. We discuss possible common grounds of these latter features that might originate from the very similar band structures of these materials.

Signatures of a Quantum Griffiths Phase Close to an Electronic Nematic Quantum Phase Transition.

In the vicinity of a quantum critical point, quenched disorder can lead to a quantum Griffiths phase, accompanied by an exotic power-law scaling with a continuously varying dynamical exponent that diverges in the zero-temperature limit. Here, we investigate a nematic quantum critical point in the iron-based superconductor FeSe_{0.89}S_{0.11} using applied hydrostatic pressure. We report an unusual crossing of the magnetoresistivity isotherms in the nonsuperconducting normal state that features a continuously varying dynamical exponent over a large temperature range. We interpret our results in terms of a quantum Griffiths phase caused by nematic islands that result from the local distribution of Se and S atoms. At low temperatures, the Griffiths phase is masked by the emergence of a Fermi liquid phase due to a strong nematoelastic coupling and a Lifshitz transition that changes the topology of the Fermi surface.

Precision adiabatic scanning calorimetry of a nematic – ferroelectric nematic phase transition

ABSTRACT In high-resolution adiabatic scanning calorimetry (ASC) experiments, data for the temperature dependence of the specific enthalpy, h(T), and of the specific heat capacity, cp (T), are simultaneously obtained, from which the order of the phase transition and critical behaviour can be evaluated. ASC was applied to study the nematic to ferroelectric nematic phase transition (N–NF) in the liquid crystal molecule 4-[(4-nitrophenoxy)carbonyl]phenyl 2,4-dimethoxybenzoate (RM734). The N–NF was found to be very weakly first order with a latent heat Δh = 0.115 ± 0.005 J/g. The pretransitional specific heat capacity behaviour is substantially larger in the high-temperature N phase than in the low-temperature NF phase. In both phases the power-law analysis of cp (T) resulted in a critical exponent α = 0.50 ± 0.05 and amplitude ratio A NF/A N = 0.42 ± 0.03. The very small latent heat and the value of α indicate that the N–NF transition is close to a tricritical point. This is confirmed by a value of the order parameter exponent β ≈ 0.25, recently obtained from electric polarisation measurements. Invoking two-scale-factor universality, it follows from the low value of A NF/A N ratio that the size of the critical fluctuations is much larger in the NF phase than in the N phase.

Entropy-driven phases at high coverage adsorption of straight rigid rods on two-dimensional square lattices.

Polymers are frequently deposited on different surfaces, which has attracted the attention of scientists from different viewpoints. In the present approach polymers are represented by rigid rods of length k (k-mers), and the substrate takes the form of an L×L square lattice whose lattice constant matches exactly the interspacing between consecutive elements of the k-mer chain. We briefly review the classical description of the nematic transition presented by this system for k≥7 observing that the high-coverage (θ) transition deserves a more careful analysis from the entropy point of view. We present a possible viewpoint for this analysis that justifies the phase transitions. Moreover, we perform Monte Carlo (MC) simulations in the grand canonical ensemble, supplemented by thermodynamic integration, to first calculate the configurational entropy of the adsorbed phase as a function of the coverage, and then to explore the different phases (and orientational transitions) that appear on the surface with increasing the density of adsorbed k-mers. In the limit of θ→1 (full coverage) the configurational entropy is obtained for values of k ranging between 2 and 10. MC data are discussed in comparison with recent analytical results [D. Dhar and R. Rajesh, Phys. Rev. E 103, 042130 (2021)2470-004510.1103/PhysRevE.103.042130]. The comparative study allows us to establish the applicability range of the theoretical predictions. Finally, the structure of the high-coverage phase is characterized in terms of the statistics of k×l domains (domains of l parallel k-mers adsorbed on the surface). A distribution of finite values of l (l≪L) is found with a predominance of k×1 (single k-mers) and k×k domains. The distribution is the same in each lattice direction, confirming that at high density the adsorbed phase goes to a state with mixed orientations and no orientational preference. An order parameter measuring the number of k×k domains in the adsorbed layer is introduced.

Rotational symmetry breaking at the incommensurate charge-density-wave transition in Ba(Ni,Co)2(As,P)2 : Possible nematic phase induced by charge/orbital fluctuations

Nematic phase transitions in high-temperature superconductors have a strong impact on the electronic properties of these systems. BaFe$_2$As$_2$,\@ with an established nematic transition around 137 K induced by magnetic fluctuations, and BaNi$_2$As$_2$,\@ a non-magnetic analog of BaFe$_2$As$_2$ with a structural transition in the same temperature range,\@ share a common tetragonal aristotype crystal structure with space-group type $I4/mmm$.\@ In contrast to BaFe$_2$As$_2$ where collinear stripe magnetic order is found for the orthorhombic low-$T$ phase, a unidirectional charge density wave together with (distorted) zig-zag chains are observed for the triclinic low-$T$ phase of BaNi$_2$As$_2$.\@ Here we show that between the high- and low-$T$ phases of Ba(Ni,Co)$_2$(As,P)$_2$ an additional phase with broken fourfold symmetry and $d_{xz}$ orbital order exists which is a promising candidate for charge/orbital-fluctuation-induced nematicity. Moreover, our data suggest that the enhanced $T_{\rm c}$ found for Ba(Ni,Co)$_2$(As,P)$_2$ for higher Co or P substitution levels might result from suppression of the (distorted) zig-zag chains by reducing the contribution of the $d_{xy}$ orbitals.