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DOE OSTI2024

Evidence for an odd-parity nematic phase above the charge-density-wave transition in a kagome metal

The search for quantum states arising from the interplay between correlation, frustration and topology is a central topic for condensed-matter physics. Recently discovered non-magnetic kagome metals AV 3 Sb 5 (A = K, Cs or Rb) with charge-density-wave and superconducting instabilities may host such exotic states. Here we report evidence that an odd-parity electronic nematic state emerges at a higher temperature than the charge density wave in CsV 3 Sb 5 . Our torque measurements reveal a two-fold in-plane magnetic anisotropy that breaks the crystal rotational symmetry. Moreover, in the temperature range between the formation of the charge density wave and a nematic state, rotating an external magnetic field in a conical fashion yields a distinct first-order phase transition, indicating time-reversal symmetry breaking. These results provide thermodynamic evidence for the emergence of an odd-parity nematic order. In addition, elastoresistance shows no discernible anomalies near the onset of nematicity, consistent with the odd-parity order. In conclusion, these findings suggest that an exotic loop current state precedes the charge-density-wave transition in CsV 3 Sb 5 .

36 MATERIALS SCIENCE↗

DOE OSTI2024

Photosynthetically-powered phototactic active nematic liquid crystal fluids and gels

Abstract One of the most ancient forms of life dating to ~3.5 billion years ago, cyanobacteria are highly abundant organisms that convert light into energy and motion, often within conjoined filaments and larger colonies that attract a great deal of interest but their active nematic behavior remained unexplored. Here we demonstrate how light causes a spontaneous self-assembly of two- and three-dimensional active nematic states of cyanobacterial filaments, with a plethora of topological defects. We quantify light-controlled evolutions of orientational and velocity order parameters during the transition between disordered and orientationally ordered states of photosynthetic active matter, as well as the subsequent active nematic’s fluid-gel transformation. Patterned illumination and foreign inclusions with different shapes interact with cyanobacterial active nematics in nontrivial ways while inducing interfacial boundary conditions and fractional boojum defects. Our phototactic model system promises opportunities to systematically explore fundamental properties and technological utility of the liquid crystalline active matter.

Repula, Andrii↗

DOE OSTI2021

Elastomeric nematic colloids, colloidal crystals and microstructures with complex topology

Control of physical behaviors of nematic colloids and colloidal crystals has been demonstrated by tuning particle shape, topology, chirality and surface charging. However, the capability of altering physical behaviors of such soft matter systems by changing particle shape and the ensuing responses to external stimuli has remained elusive. We fabricated genus-one nematic elastomeric colloidal ring-shaped particles and various microstructures using two-photon photopolymerization. Nematic ordering within both the nano-printed particle and the surrounding medium leads to anisotropic responses and actuation when heated. With the thermal control, elastomeric microstructures are capable of changing from genus-one to genus-zero surface topology. Using these particles as building blocks, we investigated elastomeric colloidal crystals immersed within a liquid crystal fluid, which exhibit crystallographic symmetry transformations. Furthermore, our findings may lead to colloidal crystals responsive to a large variety of external stimuli, including electric fields and light. Pre-designed response of elastomeric nematic colloids, including changes of colloidal surface topology and lattice symmetry, are of interest for both fundamental research and applications.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Orbital-selective time-domain signature of nematicity dynamics in the charge-density-wave phase of La 1.65 Eu 0.2 Sr 0.15 CuO 4

Understanding the interplay between charge, nematic, and structural ordering tendencies in cuprate superconductors is critical to unraveling their complex phase diagram. Using pump–probe time-resolved resonant X-ray scattering on the (0 0 1) Bragg peak at the Cu L 3 and O K resonances, we investigate nonequilibrium dynamics of Q a = Q b = 0 nematic order and its association with both charge density wave (CDW) order and lattice dynamics in La 1.65 Eu 0.2 Sr 0.15 CuO 4 . The orbital selectivity of the resonant X-ray scattering cross-section allows nematicity dynamics associated with the planar O 2 p and Cu 3 d states to be distinguished from the response of anisotropic lattice distortions. A direct time-domain comparison of CDW translational-symmetry breaking and nematic rotational-symmetry breaking reveals that these broken symmetries remain closely linked in the photoexcited state, consistent with the stability of CDW topological defects in the investigated pump fluence regime.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Colossal transverse magnetoresistance due to nematic superconducting phase fluctuations in a copper oxide

Electronic anisotropy (“nematicity”) has been detected in cuprate superconductors by various experimental techniques. Using angle-resolved transverse resistance (ARTR) measurements, a very sensitive and background-free technique that can detect 0.5% anisotropy in transport, we have observed it also in La 2-x Sr x CuO 4 (LSCO) for 0.02 ≤ x ≤ 0.25. A central enigma in LSCO is the rotation of the nematic director (orientation of the largest longitudinal resistance) with temperature; this has not been seen before in any material. Here, we address this puzzle by measuring the angle-resolved transverse magnetoresistance (ARTMR) in LSCO. We report the discovery of colossal transverse magnetoresistance (CTMR)—an order-of-magnitude drop in the transverse resistivity in the magnetic field of 6 T. We show that the apparent rotation of the nematic director is caused by anisotropic superconducting fluctuations, which are not aligned with the normal electron fluid, consistent with coexisting bond-aligned and diagonal nematic orders. We quantify this by modeling the (magneto-)conductivity as a sum of normal (Drude) and paraconducting (Aslamazov–Larkin) channels but extended to contain anisotropic Drude and Cooper-pair effective mass tensors. Strikingly, the anisotropy of Cooper-pair stiffness is much larger than that of the normal electrons. It grows dramatically on the underdoped side, where the fluctuations become quasi-one-dimensional. Our analysis is general rather than model dependent. Still, we discuss some candidate microscopic models, including coupled strongly-correlated ladders where the transverse (interladder) phase stiffness is low compared with the longitudinal intraladder stiffness, as well as the anisotropic superconducting fluctuations expected close to the transition to a pair-density wave state.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Role of Nematic Fluctuations on Superconductivity in FeSe 0.47 ⁢Te 0.53 Revealed by Nuclear Magnetic Resonance under Pressure

The relationship between antiferromagnetic (AFM) spin fluctuations (SF), nematic fluctuations, and superconductivity (SC) has been central to understanding the pairing mechanism in iron-based superconductors (IBSCs). Iron chalcogenides, which hold the simplest crystal structure in IBSCs, provide a good platform to investigate the relationship. Here, we report 77 Se and 125 Te nuclear magnetic resonance studies of FeSe 0.47⁢ Te 0.53 , which is located close to a nematic quantum critical point (QCP), under pressures up to 1.35 GPa. Further, both the superconducting critical temperature and AFMSF were found to be enhanced under pressure, which suggests a correlation between SC and AFMSF in FeSe 0.47 ⁢Te 0.53 . However, the contribution of AFMSF to SC in FeSe 0.47 ⁢Te 0.53 was found to be much less compared to that in FeSe 1−𝑥 ⁢S 𝑥 , suggesting that nematic fluctuations play a dominant role in the SC in FeSe 1−𝑥⁢ Te 𝑥 around the nematic QCP.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Nematic superconductivity in LiFeAs

The role of nematic order for the mechanism of high-temperature superconductivity is highly debated. In most iron-based superconductors (IBSs) the tetragonal symmetry is broken already in the normal state, resulting in orthorhombic lattice distortions, static stripe magnetic order, or both. Superconductivity then emerges, at least at weak doping, already from the state with broken C 4 rotational symmetry. One of the few stoichiometric IBSs, lithium iron arsenide superconducts below 18 K and does not display either structural or magnetic transition in the normal state. Here we demonstrate, using angle-resolved photoemission spectroscopy, that even the superconducting state in LiFeAs is also a nematic one. We observe spontaneous breaking of the rotational symmetry in the gap amplitude on all Fermi surfaces, as well as unidirectional distortion of the Fermi pockets. Remarkably, these deformations are hardly visible above superconducting T c . Our results demonstrate the realization of the phenomenon of superconductivity-induced nematicity in IBSs, emphasizing the intimate relation between them. Furthermore, we suggest a theoretical explanation based on the emergence of a secondary instability inside the superconducting state, which leads to the nematic order and s–d mixing in the gap function.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Fragility of the nematic spin liquid induced by diagonal couplings in the square-lattice SU(3) model

Here, we present a large-scale density matrix renormalization group (DMRG) study of the spin-1 SU(3) bilinear-biquadratic model on the square lattice, which was suggested to host a nematic spin liquid state in recent DMRG calculations. We report that this spin liquid appears to strongly compete with a three-sublattice magnetic order. To further study the competition between the two states, and the reason of the emergent nematic spin liquid, we included an additional next-nearest-neighbor SU(3) symmetric interactions along one of the two plaquette diagonal directions. This allows to tune the square-lattice model to the triangular-lattice model. By computing spin correlation functions and various order parameters, we find that the three-sublattice order may develop at infinitesimal additional new coupling, at least within the precision of our study. Compared with the previous findings that the nematic spin liquid is stable in extended parameter regions with additional couplings that respect the lattice symmetries of the square lattice, we argue that here the diagonal couplings, which frustrate the bipartite-lattice structure, rapidly suppress the two-sublattice fluctuations and the three-sublattice order thus wins. This numerical result is consistent with the conjecture that the nematic spin liquid emerges from the competition between two- and three-sublattice fluctuations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

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 paper, we review the thermodynamic description of nematicity in Ba(Fe 1- x Cox) 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. We report this result shows that the nematic transition is exceedingly well described by a mean-field model in the underdoped regime of the phase diagram.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Raman Response in the Nematic Phase of FeSe

Raman experiments on bulk FeSe revealed that the low-frequency part of the B 1g Raman response R B1 g (Ω), which probes nematic fluctuations, rapidly decreases below the nematic transition at T n ~ 85 K. Such behavior is expected when a gap opens up and at a first glance is inconsistent with the fact that FeSe remains a metal below Tn. We argue that the drop of R B1 g (Ω) can be ascribed to the fact that the nematic order drastically changes the orbital content of low-energy excitations near hole and electron pockets, making them nearly mono-orbital. In this situation, the B 1g Raman response gets reduced by the same vertex corrections that enforce charge conservation in the symmetric Raman channel. The reduction holds at low frequencies and gives rise to gaplike behavior of R B1 g (Ω). Here, we also show that the enhancement of the B 1g Raman response near T n is consistent with the sign change of the nematic order parameter between hole and electron pockets.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Potential Lifshitz transition at optimal substitution in nematic pnictide Ba 1 x Sr x Ni 2 As 2

BaNi 2 As 2 is a structural analog of the pnictide superconductor BaFe 2 As 2 , which, like the iron-based superconductors, hosts a variety of ordered phases including charge density waves (CDWs), electronic nematicity, and superconductivity. Upon isovalent Sr substitution on the Ba site, the charge and nematic orders are suppressed, followed by a sixfold enhancement of the superconducting transition temperature (T c ). To understand the mechanisms responsible for enhancement of T c , we present high-resolution angle-resolved photoemission spectroscopy (ARPES) measurements of the Ba 1-x Sr x Ni 2 As 2 series, which agree well with our density functional theory (DFT) calculations throughout the substitution range. Analysis of our ARPES-validated DFT results indicates a Lifshitz transition and reasonably nested electron and hole Fermi pockets near optimal substitution where T c is maximum. These nested pockets host Ni d xz /d yz orbital compositions, which we associate with the enhancement of nematic fluctuations, revealing unexpected connections to the iron-pnictide superconductors. This gives credence to a scenario in which nematic fluctuations drive an enhanced T c .

36 MATERIALS SCIENCE↗

DOE OSTI2021

Anomalous nematic state to stripe phase transition driven by in-plane magnetic fields

Anomalous nematic states, recently discovered in ultraclean two-dimensional electron gas, emerge from quantum Hall stripe phases upon further cooling. These states are hallmarked by a local minimum (maximum) in the hard (easy) longitudinal resistance and by an incipient plateau in the Hall resistance in nearly half-filled Landau levels. In this work, we demonstrate that a modest in-plane magnetic field, applied either along $\langle$110$\rangle$ or $\langle1\bar{1}0\rangle$ crystal axis of GaAs, destroys anomalous nematic states and restores quantum Hall stripe phases aligned along their native $\langle$110$\rangle$ direction. These findings confirm that anomalous nematic states are distinct from other ground states and will assist future theories to identify their origin.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Mechanochemical topological defects in an active nematic

We propose a reaction-diffusion system that converts topological information of an active nematic into chemical signals. We show that a curvature-activated reaction dipole is sufficient for creating a system that dynamically senses topology by producing a concentration field possessing local extrema coinciding with ±$\frac{1}{2}$ defects. The enabling term is analogous to polarization charge density seen in dielectric materials. We demonstrate the ability of this system to identify defects in both passive and active nematics. Our results illustrate that a relatively simple feedback scheme, expressed as a system of partial differential equations, is capable of producing chemical signals in response to inherently nonlocal structures in anisotropic media. Here, we posit that such coarse-grained systems can help generate testable hypotheses for regulated processes in biological systems, such as morphogenesis, and motivate the creation of bio-inspired materials that utilize dynamic coupling between nematic structure and biochemistry.

42 ENGINEERING↗

DOE OSTI2020

Electronic nematicity in Sr 2 RuO 4

We have measured the angle-resolved transverse resistivity (ARTR), a sensitive indicator of electronic anisotropy, in high-quality thin films of the unconventional superconductor Sr 2 RuO 4 grown on various substrates. The ARTR signal, heralding the electronic nematicity or a large nematic susceptibility, is present and substantial already at room temperature and grows by an order of magnitude upon cooling down to 4 K. In Sr 2 RuO 4 films deposited on tetragonal substrates the highest-conductivity direction does not coincide with any crystallographic axis. In films deposited on orthorhombic substrates it tends to align with the shorter axis; however, the magnitude of the anisotropy stays the same despite the large lattice distortion. These are strong indications of actual or incipient electronic nematicity in Sr 2 RuO 4 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Anisotropic quasiparticle coherence in nematic BaFe 2 As 2 studied with strain-dependent ARPES

The hallmark of nematic order in iron-based superconductors is a resistivity anisotropy but it is unclear to which extent quasiparticle dispersions, lifetimes, and coherence contribute. While the lifted degeneracy of the Fe d xz and d yz dispersions has been studied extensively, only little is known about the two other factors. In this work, we combine in situ strain tuning with ARPES and study the nematic response of the spectral weight in BaFe 2 As 2 . The symmetry analysis of the ARPES spectra demonstrates that the d xz band gains quasiparticle spectral weight compared to the d yz band for negative antisymmetric strain Δε yy suggesting the same response inside the nematic phase. Our results are compatible with a different coherence of the d xz and d yz orbital within a Hund's metal picture. We also discuss the influence of orbital mixing.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Cascade of vestigial orders in two-component superconductors: Nematic, ferromagnetic, s -wave charge- 4 e , and d -wave charge- 4 e states

Electronically ordered states that break multiple symmetries can melt in multiple stages, similarly to liquid crystals. In a partially melted phase, known as vestigial phase, a bilinear made out of combinations of the multiple components of the primary order parameter condenses. Multicomponent superconductors are thus natural candidates for vestigial order since they break both the U⁡(1)-gauge and also time-reversal or lattice symmetries. Here, we use group theory to classify all possible real-valued and complex-valued bilinears of a generic two-component superconductor on a tetragonal or hexagonal lattice. While the more widely investigated real-valued bilinears correspond to vestigial nematic or ferromagnetic order, the little explored complex-valued bilinears correspond to a vestigial charge-4e condensate, which itself can have an underlying s-wave, d x 2 –y 2 -wave, or d xy -wave symmetry. To properly describe the fluctuating regime of the superconducting Ginzburg-Landau action and thus access these competing vestigial phases, we employ both a large-N and a variational method. We show that while vestigial order can be understood as a weak-coupling effect in the large-N approach, it is akin to a moderate-coupling effect in the variational method. Despite these distinctions, both methods yield similar results in wide regions of the parameter space spanned by the quartic Landau coefficients. Specifically, we find that the nematic and ferromagnetic phases are the leading vestigial instabilities, whereas the various types of charge-4⁢e order are attractive albeit subleading vestigial channels. The only exception is for the hexagonal case, in which the nematic and s-wave charge-4e vestigial states are degenerate. Finally, we discuss the limitations of our approach, as well as the implications of our results for the realization of exotic charge-4⁢e states in material candidates.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Electronic nematic order in the normal state of strontium ruthenate

Despite significant achievements in characterizing the properties of Sr 2 ⁢RuO 4 over the last three decades, the precise nature of its electronic ground state is still unresolved. In this work, we provide a missing piece of the puzzle by uncovering evidence of electronic nematic order in the normal state of Sr 2 ⁢RuO 4 , revealed by ultrafast time-resolved optical dichroism measurements of uniaxially strained thin films. This nematic order, whose domains are aligned by the strain, spontaneously breaks the fourfold rotational symmetry of the crystal. The temperature dependence of the dichroism resembles an Ising-like order parameter, and optical pumping induces a coherent oscillation of its amplitude mode. The existence of electronic nematic order in the normal state of Sr2⁢RuO4 may have consequences for the form and mechanism of superconductivity in this material.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Exact Coherent Structures and Phase Space Geometry of Preturbulent 2D Active Nematic Channel Flow

Confined active nematics exhibit rich dynamical behavior, including spontaneous flows, periodic defect dynamics, and chaotic “active turbulence.” Here, we study these phenomena using the framework of exact coherent structures, which has been successful in characterizing the routes to high Reynolds number turbulence of passive fluids. Exact coherent structures are stationary, periodic, quasiperiodic, or traveling wave solutions of the hydrodynamic equations that, together with their invariant manifolds, serve as an organizing template of the dynamics. We compute the dominant exact coherent structures and connecting orbits in a preturbulent active nematic channel flow, which enables a fully nonlinear but highly reduced-order description in terms of a directed graph. Using this reduced representation, we compute instantaneous perturbations that switch the system between disparate spatiotemporal states occupying distant regions of the infinite-dimensional phase space. Overall, our results lay the groundwork for a systematic means of understanding and controlling active nematic flows in the moderate- to high-activity regime.

36 MATERIALS SCIENCE↗