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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Elastocaloric signatures of symmetric and antisymmetric strain-tuning of quadrupolar and magnetic phases in DyB 2 C 2

The adiabatic elastocaloric effect measures the temperature change of a given system with strain and provides a thermodynamic probe of the entropic landscape in the temperature-strain space. Here, we demonstrate that the DC bias strain-dependence of AC elastocaloric effect allows decomposition of the latter into symmetric (rotation-symmetry-preserving) and antisymmetric (rotation-symmetry-breaking) strain channels, using a tetragonal f -electron intermetallic DyB 2 C 2 —whose antiferroquadrupolar order breaks local fourfold rotational symmetries while globally remaining tetragonal—as a showcase example. We capture the strain evolution of its quadrupolar and magnetic phase transitions using both singularities in the elastocaloric coefficient and its jumps at the transitions, and the latter we show follows a modified Ehrenfest relation. We find that antisymmetric strain couples to the underlying order parameter in a biquadratic (linear-quadratic) manner in the antiferroquadrupolar (canted antiferromagnetic) phase, which are attributed to a preserved (broken) global tetragonal symmetry, respectively. The broken tetragonal symmetry in the magnetic phase is further evidenced by elastocaloric strain-hysteresis and optical birefringence. Additionally, within the staggered quadrupolar order, the observed elastocaloric response reflects a quadratic increase of entropy with antisymmetric strain, analogous to the role magnetic field plays for Ising antiferromagnetic orders by promoting pseudospin flips. Our results demonstrate AC elastocaloric effect as a compact and incisive thermodynamic probe into the coupling between electronic degrees of freedom and strain in free energy, which holds the potential for investigating and understanding the symmetry of a wide variety of ordered phases in broader classes of quantum materials.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Nematic superconductivity in twisted bilayer graphene

Twisted bilayer graphene displays insulating and superconducting phases caused by exceptional flattening of its lowest energy bands. Superconductivity with highest T c appears near half filling of the valence band (n ≈ –2). The data show that in the large part of the superconducting dome near n = –2, threefold lattice rotation symmetry is broken in the superconducting phase, i.e., a superconductor is also a nematic. We perform a comprehensive analysis of superconductivity in twisted-bilayer graphene within an itinerant approach and present a mechanism for nematic superconductivity. We take as an input the fact that at dopings, where superconductivity has been observed, the Fermi energy lies in the vicinity of twist-induced Van Hove singularities in the density of states. We argue that the low-energy physics can be properly described by patch models with either six or twelve Van Hove points. We obtain pairing interactions for the patch models in terms of parameters of the microscopic model for the flat bands, which contains both local and twist-induced nonlocal interactions. Here, we show that the latter give rise to attraction in different superconducting channels. For six Van Hove points, there is just one attractive d-wave channel, and we find chiral d ± id superconducting order, which breaks time-reversal symmetry but leaves the lattice rotation symmetry intact. For twelve Van Hove points, we find two attractive channels, g and i waves, with almost equal coupling constants. We show that both order parameters are nonzero in the ground state and explicitly demonstrate that in this co-existence state the threefold lattice rotation symmetry is broken, i.e., the superconducting state is also a nematic. We find two possible nematic states, one is time-reversal symmetric, the other additionally breaks time-reversal symmetry. We apply our scenario to twisted bilayer graphene near n = –2 and argue that it is applicable also to other systems with two (or more) attractive channels with similar couplings as our reasoning for a nematic superconductivity is based on generic symmetry considerations.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Orbital selective spin waves in detwinned NaFeAs

The existence of orbital-dependent electronic correlations has been recognized as an essential ingredient to describe the physics of iron-based superconductors. NaFeAs, a parent compound of iron-based superconductors, exhibits a tetragonal-to-orthorhombic lattice distortion below T s ≈ 60 K, forming an electronic nematic phase with two 90° rotated (twinned) domains, and orders antiferromagnetically below T N ≈ 42 K. We use inelastic neutron scattering to study spin waves in uniaxial pressure-detwinned NaFeAs. By comparing the data with combined density functional theory and dynamical mean-field theory calculations, we conclude that spin waves up to an energy scale of E crossover ≈ 100 meV are dominated by d yz -d yz intraorbital scattering processes, which have the twofold (C 2 ) rotational symmetry of the underlying lattice. On the other hand, the spin wave excitations above E crossover , which have approximately fourfold (C 4 ) rotational symmetry, arise from the d xy -d xy intraorbital scattering that controls the overall magnetic bandwidth in this material. In addition, we find that the low-energy (E ≈ 6 meV) spin excitations change from approximate C 4 to C 2 rotational symmetry below a temperature T* (>T s ), while spin excitations at energies above E crossover have approximate C 4 rotational symmetry and are weakly temperature dependent. Here, these results are consistent with angle-resolved photoemission spectroscopy measurements, where the presence of a uniaxial strain necessary to detwin NaFeAs also raises the onset temperature T* of observable orbital-dependent band splitting to above T s , thus supporting the notion of orbital selective spin waves in the nematic phase of iron-based superconductors.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Strain-Induced Spin-Nematic State and Nematic Susceptibility Arising from 2 × 2 Fe Clusters in KFe 0.8 Ag 1.2 Te 2

Spin nematics break spin-rotational symmetry while maintaining time-reversal symmetry, analogous to liquid crystal nematics that break spatial rotational symmetry while maintaining translational symmetry. Although several candidate spin nematics have been proposed, the identification and characterization of such a state remain challenging because the spin-nematic order parameter does not couple directly to experimental probes. $\mathrm{KFe_{0.8}Ag_{1.2}Te_{2} (K_{5}Fe_{4}Ag_{6}Te_{10}}$, KFAT) is a local-moment magnet consisting of well-separated 2×2 Fe clusters, and in its ground state the clusters order magnetically, breaking both spin-rotational and time-reversal symmetries. Using uniform magnetic susceptibility and neutron scattering measurements, we find a small strain induces sizable spin anisotropy in the paramagnetic state of KFAT, manifestly breaking spin-rotational symmetry while retaining time-reversal symmetry, resulting in a strain-induced spin-nematic state in which the 2×2 clusters act as the spin analog of molecules in a liquid crystal nematic. Finally, the strain-induced spin anisotropy in KFAT allows us to probe its nematic susceptibility, revealing a divergentlike increase upon cooling, indicating the ordered ground state is driven by a spin-orbital entangled nematic order parameter.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Signature of magnetoelectric coupling driven finite momentum pairing in 3D ising superconductor

The finite momentum superconducting paring states (FMPs) represent a forefront of condensed matter physics. Here we report experimental evidence of FMP in a locally noncentrosymmetric bulk superconductor 4H b -TaS 2 . Using hard X-ray diffraction and angle-resolved photoemission spectroscopy, we reveal unusual 2D ferro-rotational charge density wave (CDW) and weak interlayer hopping in 4H b -TaS 2 . The superconducting upper critical field, H c2 , linearly increases via decreasing temperature, and well exceeds the Pauli limit, suggesting the dominant orbital pair-breaking mechanism. Remarkably, we observed evidence of field-induced superconductivity-to-superconductivity transition that breaks continuous rotational symmetry of the s-wave uniform pairing in the Bardeen-Cooper-Schrieffer theory down to the six-fold rotation symmetry. Ginzburg-Landau free energy analysis shows that magnetoelectric coupling, induced by 2D ferro-rotational CDW, stabilizes FMP that provides an explanation of the lowering rotation symmetry. Our results provide a new understanding of unconventional superconducting behaviors of the bulk quantum heterostructure 4H b -TaS 2 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Effective Model for Fractional Topological Corner Modes in Quasicrystals

High-order topological insulators (HOTIs), as generalized from topological crystalline insulators, are characterized with lower-dimensional metallic boundary states protected by spatial symmetries of a crystal, whose theoretical framework based on band inversion at special k points cannot be readily extended to quasicrystals because quasicrystals contain rotational symmetries that are not compatible with crystals, and momentum is no longer a good quantum number. In this work, we develop a low-energy effective model underlying HOTI states in 2D quasicrystals for all possible rotational symmetries. By implementing a novel Fourier transform developed recently for quasicrystals and approximating the long-wavelength behavior by their large-scale average, we construct an effective k · p Hamiltonian to capture the band inversion at the center of a pseudo-Brillouin zone. We show that an in-plane Zeeman field can induce mass kinks at the intersection of adjacent edges of a 2D quasicrystal topological insulators and generate corner modes (CMs) with fractional charge, protected by rotational symmetries. Our model predictions are confirmed by numerical tight-binding calculations. Furthermore, when the quasicrystal is proximitized by an s-wave superconductor, Majorana CMs can also be created by tuning the field strength and chemical potential. Our work affords a generic approach to studying the low-energy physics of quasicrystals, in association with topological excitations and fractional statistics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Charge-4e Superconductivity from Multicomponent Nematic Pairing: Application to Twisted Bilayer Graphene

We show that unconventional nematic superconductors with multicomponent order parameter in lattices with three- and sixfold rotational symmetries support a charge-4e vestigial superconducting phase above T c . The charge-4e state, which is a condensate of four-electron bound states that preserve the rotational symmetry of the lattice, is nearly degenerate with a competing vestigial nematic state, which is nonsuperconducting and breaks the rotational symmetry. This robust result is the consequence of a hidden discrete symmetry in the Ginzburg-Landau theory, which permutes quantities in the gauge sector and in the crystalline sector of the symmetry group. We argue that random strain generally favors the charge-4e state over the nematic phase, as it acts as a random mass to the former but as a random field to the latter. Furthermore, we propose that two-dimensional inhomogeneous systems displaying nematic superconductivity, such as twisted bilayer graphene, provide a promising platform to realize the elusive charge-4e superconducting phase.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Strain tuning of vestigial three-state Potts nematicity in a correlated antiferromagnet

Electronic nematicity is a state of matter in which rotational symmetry is spontaneously broken and translational symmetry is preserved. In strongly correlated materials, nematicity often emerges from fluctuations of a multicomponent primary order, such as spin or charge density waves, and is termed vestigial nematicity. One widely studied example is Ising nematicity, which arises as a vestigial order of collinear antiferromagnetism in the tetragonal iron pnictide superconductors. Because nematic directors in crystals are restricted by the underlying crystal symmetry, recently identified quantum materials with three-fold rotational symmetry offer a new platform to investigate nematic order with three-state Potts character. Here, in this study, we demonstrate strain control of three-state Potts nematicity as a vestigial order of zigzag antiferromagnetism in FePSe 3 . Optical linear dichroism measurements reveal the nematic state and demonstrate the rotation of the nematic director by uniaxial strain. We show that the nature of the nematic phase transition can also be controlled by strain, inducing a smooth crossover transition between a Potts nematic transition and an Ising nematic flop transition. Elastocaloric measurements demonstrate the signatures of two coupled phase transitions, indicating that the vestigial nematic transition is separated from the antiferromagnetic transition. This establishes FePSe 3 as a system to explore three-state Potts vestigial nematicity.

Hwangbo, Kyle↗
DOE OSTI2025

Prototypes of Nonrelativistic Spin Splitting and Polarization in Symmetry Broken Antiferromagnets

Antiferromagnets that break both space-time reversal and translation-spin-rotation symmetries were recently predicted [L.-D. Yuan, Z. Wang, J.-W. Luo, E. I. Rashba, and A. Zunger, Phys. Rev. B 102, 014422 (2020)] to possess splitting between the otherwise spin-degenerate energy bands even without the relativistic spin-orbit coupling (SOC). Here, we point out that such nonrelativistic spin splitting (NRSS)—in particular, “spin splitting type 4” (SST-4) symmetry-broken antiferromagnets—can be divided into subgroups having distinct patterns of spin splitting and spin textures, depending on additional auxiliary symmetries of spin interconversion and polarity. These SST-4 subgroups include the 𝛼-type (no spin-interconverting symmetry) having spin splitting at the Brillouin zone center, as well as the 𝛽 subgroup in which a rotation symmetry is applied and determines the alternating spin texture and the 𝛾 subgroup having exclusively reflection spin-interconverting symmetry. Unlike ferrimagnets, the 𝛼-type compounds are shown to have tiny net magnetization at finite temperature and thus avoid the adverse effect of the stray field. The 𝛼 and 𝛽 subgroups can be either polar or nonpolar, whereas the 𝛾 subgroup is polar only, providing a basis for possible switching by external fields. The combination of NRSS-enabling and auxiliary symmetries is used here as a filter for identifying previously synthesized compounds as specific prototypes. Their characteristic splitting and spin polarization are calculated by density functional theory to the benefit of potential future experimental testing. Interesting results are as follows: (i) SOC-independent NRSS can exceed the magnitude of the SOC-induced Rashba and Dresselhaus spin splitting in semiconductors. (ii) Examples of predicted 𝛼-type insulating compounds include BiCrO 3 (nonpolar) and Mn 2 ⁢ScSbO 6 (polar), the latter having spin splitting of 158 meV and 160 meV in the valence and conduction bands, respectively. (iii) The 𝛽-type (Cu 2 ⁢Y 2 ⁢O 5 and FeF 2 ) and 𝛾-type compounds (Mn 4 ⁢Nb 2 ⁢O 9 and FeScO 3 ) are distinguished both by their auxiliary symmetries and polarity. The spin textures of 𝛾-type compounds are mirror reflected with spin degeneracy of the wave vectors on that mirror. These observations will likely broaden the experimental playing field of NRSS physics significantly.

antiferromagnets↗
NASA NTRS2009

Lattice-Matched Semiconductor Layers on Single Crystalline Sapphire Substrate

SiGe is an important semiconductor alloy for high-speed field effect transistors (FETs), high-temperature thermoelectric devices, photovoltaic solar cells, and photon detectors. The growth of SiGe layer is difficult because SiGe alloys have different lattice constants from those of the common Si wafers, which leads to a high density of defects, including dislocations, micro-twins, cracks, and delaminations. This innovation utilizes newly developed rhombohedral epitaxy of cubic semiconductors on trigonal substrates in order to solve the lattice mismatch problem of SiGe by using trigonal single crystals like sapphire (Al2O3) as substrate to give a unique growth-orientation to the SiGe layer, which is automatically controlled at the interface upon sapphire (0001). This technology is different from previous silicon on insulator (SOI) or SGOI (SiGe on insulator) technologies that use amorphous SiO2 as the growth plane. A cubic semiconductor crystal is a special case of a rhombohedron with the inter-planar angle, alpha = 90 deg. With a mathematical transformation, all rhombohedrons can be described by trigonal crystal lattice structures. Therefore, all cubic lattice constants and crystal planes (hkl) s can be transformed into those of trigonal crystal parameters. These unique alignments enable a new opportunity of perfect lattice matching conditions, which can eliminate misfit dislocations. Previously, these atomic alignments were thought to be impossible or very difficult. With the invention of a new x-ray diffraction measurement method here, growth of cubic semiconductors on trigonal crystals became possible. This epitaxy and lattice-matching condition can be applied not only to SiGe (111)/sapphire (0001) substrate relations, but also to other crystal structures and other materials, including similar crystal structures which have pointgroup rotational symmetries by 120 because the cubic (111) direction has 120 rotational symmetry. The use of slightly miscut (less than plus or minus 10 deg.) sapphire (0001) substrate can be used to improve epitaxial relationships better by providing attractive atomic steps in the epitaxial process.

Choi, Sang↗
DOE OSTI2024

Controlling topology through targeted composite symmetry manipulation in magnetic systems

The possibility of selecting magnetic space groups by orienting the magnetization direction or tuning magnetic orders offers a vast playground for engineering symmetry-protected topological phases in magnetic materials. In this work, we study how selective tuning of symmetry and magnetism can influence and control the resulting topology in a two-dimensional magnetic system, and we illustrate such a procedure in the ferromagnetic monolayer MnPSe 3 . Density functional theory calculations reveal a symmetry-protected accidental semimetallic (SM) phase for out-of-plane magnetization, which becomes an insulator when the magnetization is tilted in-plane, reaching band-gap values close to 100 meV. We identify an order-2 composite antiunitary symmetry and threefold rotational symmetry that induce the band crossing, and we classify the possible topological phases using symmetry analysis, which we support with tight-binding and k · p models. Breaking of inversion symmetry opens a gap in the SM phase, giving rise to a Chern insulator. We demonstrate this explicitly in the isostructural Janus compound Mn 2 ⁢P 2 ⁢S 3 ⁢Se 3 , which naturally exhibits Rashba spin-orbit coupling that breaks inversion symmetry. Our results map out the phase space of topological properties of ferromagnetic transition-metal phosphorus trichalcogenides, and they demonstrate the potential of the magnetization-dependent metal-to-insulator transition as a spin switch in integrated two-dimensional electronics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Evidence of Ba-substitution induced spin-canting in the magnetic Weyl semimetal EuCd 2 As 2

Recently EuCd 2 As 2 was predicted to be a magnetic Weyl semimetal with a lone pair of Weyl nodes generated by A-type antiferromagnetism and protected by a rotational symmetry. However, it was soon discovered that the actual magnetic structure broke the rotational symmetry and internal pressure was later suggested as a route to stabilize the desired magnetic state. In this work we test this prediction by synthesizing a series of Eu 1-x BaxCd 2 As 2 single crystals and studying their structural, magnetic, and transport properties via both experimental techniques and first-principles calculations. We find that small concentrations of Ba (~3%–10%) lead to a small out-of-plane canting of the Eu moment. However, for higher concentrations this effect is suppressed and a nearly in-plane model is recovered. Studying the transport properties we find that all compositions show evidence of an anomalous Hall effect dominated by the intrinsic mechanism as well as large negative magnetoresistances in the longitudinal channel. A nonmonotonic evolution of the transport properties is seen across the series which correlates to the proposed canting suggesting canting may enhance the topological effects. Careful density functional theory calculations using an all-electron approach revise prior predictions finding a purely ferromagnetic ground state with in-plane moments for both the EuCd 2 As 2 and Eu 0.5 Ba 0.5 Cd 2 As 2 compounds, corroborating our experimental findings. This work suggests that Ba substitution can tune the magnetic properties in unexpected ways which correlate to changes in measures of topological properties, encouraging future work to locate the ideal Ba concentration for Eu moment canting.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Exploring the energy landscape of RBMs: reciprocal space insights into bosons, hierarchical learning and symmetry breaking

Deep generative models have become ubiquitous due to their ability to learn and sample from complex distributions. Despite the proliferation of various frameworks, the relationships among these models remain largely unexplored, a gap that hinders the development of a unified theory of AI learning. In this work, we address two central challenges: clarifying the connections between different deep generative models and deepening our understanding of their learning mechanisms. We focus on Restricted Boltzmann Machines (RBMs), a class of generative models known for their universal approximation capabilities for discrete distributions. By introducing a reciprocal space formulation for RBMs, we reveal a connection between these models, diffusion processes, and systems of coupled bosons. Our analysis shows that at initialization, the RBM operates at a saddle point, where the local curvature is determined by the singular values of the weight matrix, whose distribution follows the Marc̆enko-Pastur law and exhibits rotational symmetry. During training, this rotational symmetry is broken due to hierarchical learning, where different degrees of freedom progressively capture features at multiple levels of abstraction. This leads to a symmetry breaking in the energy landscape, reminiscent of Landau’s theory. This symmetry breaking in the energy landscape is characterized by the singular values and the weight matrix eigenvector matrix. We derive the corresponding free energy in a mean-field approximation. We show that in the limit of infinite size RBM, the reciprocal variables are Gaussian distributed. Our findings indicate that in this regime, there will be some modes for which the diffusion process will not converge to the Boltzmann distribution. To illustrate our results, we trained replicas of RBMs with different hidden layer sizes using the MNIST dataset. Our findings not only bridge the gap between disparate generative frameworks but also shed light on the fundamental processes underpinning learning in deep generative models.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2009

Diamond Machining of an Off-Axis Biconic Aspherical Mirror

Two diamond-machining methods have been developed as part of an effort to design and fabricate an off-axis, biconic ellipsoidal, concave aluminum mirror for an infrared spectrometer at the Kitt Peak National Observatory. Beyond this initial application, the methods can be expected to enable satisfaction of requirements for future instrument mirrors having increasingly complex (including asymmetrical), precise shapes that, heretofore, could not readily be fabricated by diamond machining or, in some cases, could not be fabricated at all. In the initial application, the mirror is prescribed, in terms of Cartesian coordinates x and y, by aperture dimensions of 94 by 76 mm, placements of -2 mm off axis in x and 227 mm off axis in y, an x radius of curvature of 377 mm, a y radius of curvature of 407 mm, an x conic constant of 0.078, and a y conic constant of 0.127. The aspect ratio of the mirror blank is about 6. One common, "diamond machining" process uses single-point diamond turning (SPDT). However, it is impossible to generate the required off-axis, biconic ellipsoidal shape by conventional SPDT because (1) rotational symmetry is an essential element of conventional SPDT and (2) the present off-axis biconic mirror shape lacks rotational symmetry. Following conventional practice, it would be necessary to make this mirror from a glass blank by computer-controlled polishing, which costs more than diamond machining and yields a mirror that is more difficult to mount to a metal bench. One of the two present diamond machining methods involves the use of an SPDT machine equipped with a fast tool servo (FTS). The SPDT machine is programmed to follow the rotationally symmetric asphere that best fits the desired off-axis, biconic ellipsoidal surface. The FTS is actuated in synchronism with the rotation of the SPDT machine to generate the difference between the desired surface and the best-fit rotationally symmetric asphere. In order to minimize the required stroke of the FTS, the blanks were positioned at a large off-axis distance and angle, and the axis of the FTS was not parallel to the axis of the spindle of the SPDT machine. The spindle was rotated at a speed of 120 rpm, and the maximum FTS speed was 8.2 mm/s.

Ohl, Raymond G.↗
DOE OSTI2020

Three-state nematicity in the triangular lattice antiferromagnet Fe 1/3 NbS 2

Nematic order is the breaking of rotational symmetry in the presence of translational invariance. While originally defined in the context of liquid crystals, the concept of nematic order has arisen in crystalline matter with discrete rotational symmetry, most prominently in the tetragonal Fe-based superconductors where the parent state is four-fold symmetric. In this case the nematic director takes on only two directions, and the order parameter in such 'Ising-nematic' systems is a simple scalar. In this study, using a spatially resolved optical polarimetry technique, we show that a qualitatively distinct nematic state arises in the triangular lattice antiferromagnet Fe 1/3 NbS 2 . The crucial difference is that the nematic order on the triangular lattice is a Z 3 or three-state Potts-nematic order parameter. As a consequence, the anisotropy axes of response functions such as the resistivity tensor can be continuously reoriented by external perturbations. This discovery lays the groundwork for devices that exploit analogies with nematic liquid crystals.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Phonon-induced rotation of the electronic nematic director in superconducting Bi 2 Se 3

The doped topological insulator A x Bi 2 Se 3 , with A = {Cu,Sr,Nb}, becomes a nematic superconductor below T c ≈ 3–4 K. The associated electronic nematic director is described by an angle α 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, α 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 c14 due to the fact that the in-plane shear strain doublet (ε xx – ε yy , – 2ε xy ) and the out-of-plane shear strain doublet (2ε yz , – 2ε 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 Bi 2 Se 3 , the nematic director α 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. Furthermore, 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 Bi 2 Se 3 , and for the presence of nodes inside the superconducting state.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Moiré nematic phase in twisted double bilayer graphene

Graphene moiré superlattices display electronic flat bands. At integer fillings of these flat bands, energy gaps due to strong electron-electron interactions are generally observed. However, the presence of other correlation-driven phases in twisted graphitic systems at non-integer fillings is unclear. Here, we report the existence of threefold rotational symmetry breaking in twisted double bilayer graphene. Using spectroscopic imaging over large and uniform areas to characterize the direction and degree of C 3 symmetry breaking, we find it to be prominent only at energies corresponding to the flat bands and nearly absent in the remote bands. We demonstrate that the magnitude of the rotational symmetry breaking does not depend on the degree of the heterostrain or the displacement field, being instead a manifestation of an interaction-driven electronic nematic phase. We show that the nematic phase is a primary order that arises from the normal metal state over a wide range of doping away from charge. Furthermore, our modelling suggests that the nematic instability is not associated with the local scale of the graphene lattice, but is an emergent phenomenon at the scale of the moiré lattice.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗