Symmetry Breaking Order Research Articles

Category of SET orders

We propose the representation principle to study physical systems with a given symmetry. In the context of symmetry enriched topological orders, we give the appropriate representation category, the category of SET orders, which include SPT orders and symmetry breaking orders as special cases. For fusion n-category symmetries, we show that the category of SET orders encodes almost all information about the interplay between symmetry and topological orders, in a natural and canonical way. These information include defects and boundaries of SET orders, symmetry charges, explicit and spontaneous symmetry breaking, stacking of SET orders, gauging of generalized symmetry, as well as quantum currents (SymTFT or symmetry TO). We also provide a detailed categorical algorithm to compute the generalized gauging. In particular, we proved that gauging is always reversible, as a special type of Morita-equivalence. The explicit data for ungauging, the inverse to gauging, is given.

Linear magnetoresistance from glassy orders

Several strongly correlated metals display B-linear magnetoresistance (LMR) with a universal slope, in sharp contrast to the [Formula: see text] scaling predicted by Fermi liquid theory. We provide a unifying explanation of the origin of LMR by focusing on a common feature in their phase diagrams-proximity to symmetry-breaking orders. Specifically, we demonstrate via two microscopic models that LMR with a universal slope arises ubiquitously near ordered phases, provided the order parameter either i) has a finite wave-vector, or ii) has nodes on the Fermi surface. We elucidate the distinct physical mechanisms at play in these two scenarios and derive upper and lower bounds on the field range for which LMR is observed. Finally, we discuss possible extensions of our picture to strange metal physics at higher temperatures and argue that our theory provides an understanding of recent experimental results on thin film cuprates and moiré materials.

From Fractional Quantum Anomalous Hall Smectics to Polar Smectic Metals: Nontrivial Interplay Between Electronic Liquid Crystal Order and Topological Order in Correlated Topological Flat Bands.

Symmetry-breaking orders can not only compete with each other, but also be interwined, and the interwined topological and symmetry-breaking orders make the situation more intriguing. This work examines the archetypal correlated flat band model on a checkerboard lattice at filling ν = 2/3 and we find the unique interplay between smectic charge order and topological order gives rise to two novel quantum states. As the interaction strength increases, the system first transitions from a Fermi liquid into FQAH smectic (FQAHS) state, where FQAH topological order coexists cooperatively with smectic charge order with enlarged ground-state degeneracy and interestingly, the Hall conductivity is σxy = ν = 2/3, different from the band-folding or doping scenarios. Further increasing the interaction strength, the system undergoes another quantum phase transition and evolves into a polar smectic metal (PSM) state. This emergent PSM is an anisotropic non-Fermi liquid, whose interstripe tunneling is irrelevant while it is metallic inside each stripe. Different from the FQAHS and conventional smectic orders, this PSM spontaneously breaks the two-fold rotational symmetry, resulting in a nonzero electric dipole moment and ferroelectric order. In addition to the exotic ground states, large-scale numerical simulations are also used to study low-energy excitations and thermodynamic characteristics. We find the onset temperature of the incompressible FQAHS state, which also coincides with the onset of non-polar smectic order, is dictated by the magneto-roton modes. Above this onset temperature, the PSM state exists at intermediate-temperature regime. Although the T = 0 quantum phase transition between PSM and FQAHS is first order, the thermal FQAHS-PSM transition could be continuous. We expect the features of the exotic states and thermal phase transitions could be accessed in future experiments.

Spontaneous symmetry breaking in polar fluids

Spontaneous symmetry breaking and emergent polar order are each of fundamental importance to a range of scientific disciplines, as well as generating rich phase behaviour in liquid crystals (LCs). Here, we show the union of these phenomena to lead to two previously undiscovered polar liquid states of matter. Both phases have a lamellar structure with an inherent polar ordering of their constituent molecules. The first of these phases is characterised by polar order and a local tilted structure; the tilt direction processes about a helix orthogonal to the layer normal, the period of which is such that we observe selective reflection of light. The second new phase type is anti-ferroelectric, with the constituent molecules aligning orthogonally to the layer normal. This has led us to term the phases the SmCPH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{{{\\rm{Sm}}}}}}{{{{{{\\rm{C}}}}}}}_{{{{{{\\rm{P}}}}}}}^{{{{{{\\rm{H}}}}}}}$$\\end{document} and SmAAF phases, respectively. Further to this, we obtain room temperature ferroelectric nematic (NF) and SmCPH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{{{\\rm{Sm}}}}}}{{{{{{\\rm{C}}}}}}}_{{{{{{\\rm{P}}}}}}}^{{{{{{\\rm{H}}}}}}}$$\\end{document} phases via binary mixture formulation of the novel materials described here with a standard NF compound (DIO), with the resultant materials having melting points (and/or glass transitions) which are significantly below ambient temperature. The new soft matter phase types discovered herein can be considered as electrical analogues of topological structures of magnetic spins in hard matter.

Superconducting diode effect and interference patterns in kagome CsV3Sb5.

The interplay among frustrated lattice geometry, non-trivial band topology and correlation yields rich quantum states of matter in kagome systems1,2. A series of recent members in this family, AV3Sb5 (A = K, Rb or Cs), exhibit a cascade of symmetry-breaking transitions3, involving the 3Q chiral charge ordering4-8, electronic nematicity9,10, roton pair density wave11 and superconductivity12. The nature of the superconducting order is yet to be resolved. Here we report an indication of dynamic superconducting domains with boundary supercurrents in intrinsic CsV3Sb5 flakes. The magnetic field-free superconducting diode effect is observed with polarity modulated by thermal histories, suggesting that there are dynamic superconducting order domains in a spontaneous time-reversal symmetry-breaking background. Strikingly, the critical current exhibits double-slit superconductivity interference patterns when subjected to an external magnetic field. The characteristics of the patterns are modulated by thermal cycling. These phenomena are proposed as a consequence of periodically modulated supercurrents flowing along certain domain boundaries constrained by fluxoid quantization. Our results imply a time-reversal symmetry-breaking superconducting order, opening a potential for exploring exotic physics, for example, Majorana zero modes, in this intriguing topological kagome system.

Formation and Manipulation of Diatomic Rotors at the Symmetry-Breaking Surfaces of a Kagome Superconductor.

Construction of diatomic rotors, which is crucial for artificial nanomachines, remains challenging due to surface constraints and limited chemical design. Here we report the construction of diatomic Cr-Cs and Fe-Cs rotors where a Cr or Fe atom switches around a Cs atom at the Sb surface of the newly discovered kagome superconductor CsV3Sb5. The switching rate is controlled by the bias voltage between the rotor and scanning tunneling microscope (STM) tip. The spatial distribution of rates exhibits C2 symmetry, possibly linked to the symmetry-breaking charge orders of CsV3Sb5. We have expanded the rotor construction to include different transition metals (Cr, Fe, V) and alkali metals (Cs, K). Remarkably, designed configurations of rotors are achieved through STM manipulation. Rotor orbits and quantum states are precisely controlled by tuning the inter-rotor distance. Our findings establish a novel platform for the controlled fabrication of atomic motors on symmetry-breaking quantum materials, paving the way for advanced nanoscale devices.

Entanglement-enabled symmetry-breaking orders

A spontaneous symmetry-breaking order is conventionally described by a tensor-product wavefunction of some few-body clusters; some standard examples include the simplest ferromagnets and valence bond solids. We discuss a type of symmetry-breaking orders, dubbed entanglement-enabled symmetry-breaking orders, which cannot be realized by any such tensor-product state. Given a symmetry breaking pattern, we propose a criterion to diagnose if the symmetry-breaking order is entanglement-enabled, by examining the compatibility between the symmetries and the tensor-product description. For concreteness, we present an infinite family of exactly solvable gapped models on one-dimensional lattices with nearest-neighbor interactions, whose ground states exhibit entanglement-enabled symmetry-breaking orders from a discrete symmetry breaking. In addition, these ground states have gapless edge modes protected by the unbroken symmetries. We also propose a construction to realize entanglement-enabled symmetry-breaking orders with spontaneously broken continuous symmetries. Under the unbroken symmetries, some of our examples can be viewed as symmetry-protected topological states that are beyond the conventional classifications.

Temperature and Thickness Dependence of the Thermal Conductivity in 2D Ferromagnet Fe3GeTe2.

The emergence of symmetry-breaking orders such as ferromagnetism and the weak interlayer bonding in van der Waals materials offers a unique platform to engineer novel heterostructures and tune transport properties like thermal conductivity. Here, we report the experimental and theoretical study of the cross-plane thermal conductivity, κ⊥, of the van der Waals two-dimensional (2D) ferromagnet Fe3GeTe2. We observe an increase in κ⊥ with thickness, indicating a diffusive transport regime with ballistic contributions. These results are supported by the theoretical analyses of the accumulated thermal conductivity, which show an important contribution of phonons with mean free paths between 10 and 200 nm. Moreover, our experiments show a reduction of κ⊥ in the low-temperature ferromagnetic phase occurring at the magnetic transition. The calculations show that this reduction in κ⊥ is associated with a decrease in the group velocities of the acoustic phonons and an increase in the phonon-phonon scattering of the Raman modes that couple to the magnetic phase. These results demonstrate the potential of van der Waals ferromagnets for thermal transport engineering.

Visualizing symmetry-breaking electronic orders in epitaxial Kagome magnet FeSn films

Kagome lattice hosts a plethora of quantum states arising from the interplay of topology, spin-orbit coupling, and electron correlations. Here, we report symmetry-breaking electronic orders tunable by an applied magnetic field in a model Kagome magnet FeSn consisting of alternating stacks of two-dimensional Fe3Sn Kagome and Sn2 honeycomb layers. On the Fe3Sn layer terminated FeSn thin films epitaxially grown on SrTiO3(111) substrates, we observe trimerization of the Kagome lattice using scanning tunneling microscopy/spectroscopy, breaking its six-fold rotational symmetry while preserving the translational symmetry. Such a trimerized Kagome lattice shows an energy-dependent contrast reversal in dI/dV maps, which is significantly enhanced by bound states induced by Sn vacancy defects. This trimerized Kagome lattice also exhibits stripe modulations that are energy-dependent and tunable by an applied in-plane magnetic field, indicating symmetry-breaking nematicity from the entangled magnetic and charge degrees of freedom in antiferromagnet FeSn.

Signature of spin-phonon coupling driven charge density wave in a kagome magnet

The intertwining between spin, charge, and lattice degrees of freedom can give rise to unusual macroscopic quantum states, including high-temperature superconductivity and quantum anomalous Hall effects. Recently, a charge density wave (CDW) has been observed in the kagome antiferromagnet FeGe, indicative of possible intertwining physics. An outstanding question is that whether magnetic correlation is fundamental for the spontaneous spatial symmetry breaking orders. Here, utilizing elastic and high-resolution inelastic x-ray scattering, we observe a c-axis superlattice vector that coexists with the 2times2times1 CDW vectors in the kagome plane. Most interestingly, between the magnetic and CDW transition temperatures, the phonon dynamical structure factor shows a giant phonon-energy hardening and a substantial phonon linewidth broadening near the c-axis wavevectors, both signaling the spin-phonon coupling. By first principles and model calculations, we show that both the static spin polarization and dynamic spin excitations intertwine with the phonon to drive the spatial symmetry breaking in FeGe.

Evidence of pseudogravitational distortions of the Fermi surface geometry in the antiferromagnetic metal FeRh

The confluence between high-energy physics and condensed matter has produced groundbreaking results via unexpected connections between the two traditionally disparate areas. In this work, we elucidate additional connectivity between high-energy and condensed matter physics by examining the interplay between spin-orbit interactions and local symmetry-breaking magnetic order in the magnetotransport of thin-film magnetic semimetal FeRh. We show that the change in sign of the normalized longitudinal magnetoresistance observed as a function of increasing in-plane magnetic field results from changes in the Fermi surface morphology. We demonstrate that the geometric distortions in the Fermi surface morphology are more clearly understood via the presence of pseudogravitational fields in the low-energy theory. The pseudogravitational connection provides additional insights into the origins of a ubiquitous phenomenon observed in many common magnetic materials and points to an alternative methodology for understanding phenomena in locally-ordered materials with strong spin-orbit interactions.

Heavy quasiparticles and cascades without symmetry breaking in twisted bilayer graphene

Among the variety of correlated states exhibited by twisted bilayer graphene, cascades in the spectroscopic properties and in the electronic compressibility occur over larger ranges of energy, twist angle and temperature compared to other effects. This suggests a hierarchy of phenomena. Using a combined dynamical mean-field theory and Hartree calculation, we show that the spectral weight reorganisation associated with the formation of local moments and heavy quasiparticles can explain the cascade of electronic resets without invoking symmetry breaking orders. The phenomena reproduced here include the cascade flow of spectral weight, the oscillations of remote band energies, and the asymmetric jumps of the inverse compressibility. We also predict a strong momentum differentiation in the incoherent spectral weight associated with the fragile topology of twisted bilayer graphene.

Mixed orbital states and modulated crystal structures in La1−xCaxMnO3 deduced from synchrotron X-ray diffraction

In the model manganese perovskites La1−xCaxMnO3, several important phenomena have been observed, including ferromagnetic metallic/insulating states, colossal magnetoresistance effects, and charge- and orbital-ordered states. In the past, only compounds with x = 1/2, 2/3 and 3/4 and an insulating ground/antiferromagnetic state have been studied. To fully understand the crystal and electronic structures of these materials, it is important to study compounds with doping levels in the range of 0.5 < x < 2/3. Here we study the crystal structure in a series of compounds with 0.5 < x ≤ 0.6 using ultrahigh-resolution synchrotron X-ray diffraction. The experimental results reveal that all compounds undergo a structural transition at T < TCO(x) ≈ 200 − 220 K with the concomitant emergence of superlattice Bragg peaks, which can be indexed assuming a superstructure with a modulation propagation vector, τ. At the base temperature of 5 K, the modulation vector of the superstructure τ = [τa, 0, 0] is parallel to the a-axis, with τa varying linearly with x, as τa ≈ 1 − x. Our results may aid attempts to understand more deeply phenomena related to spin, charge, and orbital ordering, as well as colossal magnetoresistance and symmetry breaking and emergent order in quantum states.

Pressure Control of Nonferroelastic Ferroelectric Domains in ErMnO3.

Mechanical pressure controls the structural, electric, and magnetic order in solid-state systems, allowing tailoring of their physical properties. A well-established example is ferroelastic ferroelectrics, where the coupling between pressure and the primary symmetry-breaking order parameter enables hysteretic switching of the strain state and ferroelectric domain engineering. Here, we study the pressure-driven response in a nonferroelastic ferroelectric, ErMnO3, where the classical stress-strain coupling is absent and the domain formation is governed by creation-annihilation processes of topological defects. By annealing ErMnO3 polycrystals under variable pressures in the MPa regime, we transform nonferroelastic vortex-like domains into stripe-like domains. The width of the stripe-like domains is determined by the applied pressure as we confirm by three-dimensional phase field simulations, showing that pressure leads to oriented layer-like periodic domains. Our work demonstrates the possibility to utilize mechanical pressure for domain engineering in nonferroelastic ferroelectrics, providing a lever to control their dielectric and piezoelectric responses.

Weak-coupling to strong-coupling quantum criticality crossover in a Kitaev quantum spin liquid α-RuCl3

We report a quantum criticality crossover representing two different universal scaling behaviors in a Kitaev quantum magnetic material α-RuCl3. α-RuCl3 presents both a symmetry-breaking antiferromagnetic order and a long-range entangled topological order of a quantum spin liquid, and thus could be a candidate system for a unique universality class involving deconfined fractionalized excitations of the local Z2 fluxes and itinerant Majorana fermions. Theoretical analyses on the inelastic neutron scattering, ac-magnetic susceptibility, and specific heat results demonstrate that Wilson–Fisher-Yukawa-type ‘conventional’ weak-coupling quantum criticality in high-energy scales crosses over to heavy-fermion-type ‘local’ strong-coupling one in low-energy scales. Our findings provide deep insight on how quantum criticality evolves in fermion-boson coupled topological systems with different types of deconfined fermions.

Model-Independent Learning of Quantum Phases of Matter with Quantum Convolutional Neural Networks.

Quantum convolutional neural networks (QCNNs) have been introduced as classifiers for gapped quantum phases of matter. Here, we propose a model-independent protocol for training QCNNs to discover order parameters that are unchanged under phase-preserving perturbations. We initiate the training sequence with the fixed-point wave functions of the quantum phase and add translation-invariant noise that respects the symmetries of the system to mask the fixed-point structure on short length scales. We illustrate this approach by training the QCNN on phases protected by time-reversal symmetry in one dimension, and test it on several time-reversal symmetric models exhibiting trivial, symmetry-breaking, and symmetry-protected topological order. The QCNN discovers a set of order parameters that identifies all three phases and accurately predicts the location of the phase boundary. The proposed protocol paves the way toward hardware-efficient training of quantum phase classifiers on a programmable quantum processor.

Majorana lattice gauge theory: Symmetry breaking, topological order and intertwined orders all in one

The Majorana lattice gauge theory purely composed of Majorana fermions on square lattice is studied throughly. The ground state is obtained exactly and exhibits the coexistence of symmetry breaking and topological order. The Z_2Z2 symmetry breaking of matter fields leads to the intertwined antiferromagnetic spin order and \etaη-pairing order. The topological order is reflected in the Z_2Z2 quantum spin liquid ground state of gauge fields. The Majorana lattice gauge theory, alternatively can be viewed as interacting Majorana fermion model, is possibly realized on a Majorana-zero-mode lattice.

Ising superconductivity induced from spin-selective valley symmetry breaking in twisted trilayer graphene

We show that the e-e interaction induces a strong breakdown of valley symmetry for each spin channel in twisted trilayer graphene, leading to a ground state where the two spin projections have opposite sign of the valley symmetry breaking order parameter. This leads to a spin-valley locking in which the electrons of a Cooper pair are forced to live on different Fermi lines attached to opposite valleys. Furthermore, we find an effective intrinsic spin-orbit coupling explaining the protection of the superconductivity against in-plane magnetic fields. The effect of spin-selective valley symmetry breaking is validated as it reproduces the experimental observation of the reset of the Hall density at 2-hole doping. It also implies a breakdown of the symmetry of the bands from C6 to C3, with an enhancement of the anisotropy of the Fermi lines which is at the origin of a Kohn-Luttinger (pairing) instability. The isotropy of the bands is gradually recovered, however, when the Fermi level approaches the bottom of the second valence band, explaining why the superconductivity fades away in the doping range beyond 3 holes per moiré unit cell in twisted trilayer graphene.

Switchable moiré potentials in ferroelectric WTe2/WSe2 superlattices.

Moiré materials with superlattice periodicity many times the atomic length scale have shown strong electronic correlations and band topology with unprecedented tunability. Non-volatile control of the moiré potentials could allow on-demand switching of superlattice effects but has remained challenging to achieve. Here we demonstrate the switching of the correlated and moiré band insulating states, and the associated nonlinear anomalous Hall effect, by the ferroelectric effect. This is achieved in a ferroelectric WTe2 bilayer of the Td structure with a centred-rectangular moiré superlattice induced by interfacing with a WSe2 monolayer of the H structure. The results can be understood in terms of polarization-dependent charge transfer between two WTe2 monolayers, in which the interfacial layer has a much stronger moiré potential depth; ferroelectric switching thus turns on and off the moiré insulating states. Our study demonstrates the potential for creating new functional moiré materials by incorporating intrinsic symmetry-breaking orders.

Possible new phase transition in the 3D Ising model associated with boundary percolation

In the ordered phase of the 3D Ising model, minority spin clusters are surrounded by a boundary of dual plaquettes. As the temperature is raised, these spin clusters become more numerous, and it is found that eventually their boundaries undergo a percolation transition when about 13% of spins are minority. Boundary percolation differs from the more commonly studied site and link percolation, although it is related to an unusual type of site percolation that includes next to nearest neighbor relationships. Because the Ising model can be reformulated in terms of the domain boundaries alone, there is reason to believe boundary percolation should be relevant here. A symmetry-breaking order parameter is found in the dual theory, the 3D gauge Ising model. It is seen to undergo a phase transition at a coupling close to that predicted by duality from the boundary percolation. This transition lies in the disordered phase of the gauge theory and has the nature of a spin-glass transition. Its critical exponent is seen to match the finite-size shift exponent of the percolation transition further cementing their connection. This predicts a very weak specific heat singularity with exponent . The third energy cumulant fits well to the expected non-infinite critical behavior in a manner consistent with both the predicted exponent and critical point, indicating a true thermal phase transition. Unlike random boundary percolation, the Ising boundary percolation has two different ν exponents, one associated with largest-cluster scaling and the other with finite-size transition-point shift. This suggests there may be two different correlation lengths present.