Symmetry Breaking Phase Research Articles

DFT insights into the origin of d0 ferromagnetism, mechanical stability, elastic, and acoustic anisotropy in AZrO3 (A= K, rb, Cs) cubic perovskites

The d0 ferromagnetism through hole induction can be realized in oxide perovskites. The electronic and magnetic properties of AZrO3 (A = K, Rb, and Cs) cubic perovskites have been computationally analyzed using generalized gradient approximation (GGA) and modified Becke-Johnson (mBJ) potentials. From the evaluation of tolerance factor, volume optimization, formation energy, and phonon dispersion, their structural, magnetic, and dynamical stabilities in the ferromagnetic cubic phase have been verified. Additionally, Blackman's and Every's diagrams ensure their elastic stability without any symmetry-breaking phase transitions. The three-dimensional surfaces of elastic moduli and acoustic wave velocities indicate the degree of anisotropy in these perovskites. The compounds become more ductile for larger alkali cations. The band structures from both functionals confirm that the localized magnetic moments around oxygen atoms arise only from the exchange spin splitting of O-2p orbitals. The integer magnetic moment of 1 μB and complete spin polarization implies the presence of half-metallic ferromagnetism. Among the proposed compounds, the predicted mean-field curie temperature of CsZrO3 is above room temperature and may serve as optimal magnetic layers in spin-valve sensors and magnetic tunnel junctions.

Kibble-Zurek Mechanism for Dynamical Ordering in a Driven Vortex System.

The Kibble-Zurek mechanism describes the formation of topological defects in systems crossing a continuous symmetry-breaking phase transition at a finite quench rate. While this mechanism has been extensively studied for equilibrium transitions, its applicability to nonequilibrium transitions has not yet been fully examined. Recent simulation has shown the applicability of the Kibble-Zurek mechanism to dynamical ordering transitions in particlelike assemblies, including superconducting vortices, driven over random disorder. Here, we experimentally study the configurational order of vortices in the course of dynamical ordering with various quench rates. We verify a power-law scaling of the defect density with the quench rate and an impulse-adiabatic crossover on the ordered side of the transition, which are key predictions of the Kibble-Zurek mechanism. Our results suggest the applicability of the Kibble-Zurek mechanism to other nonequilibrium phase transitions.

PT symmetric single-mode line-defect photonic crystal lasers with asymmetric loss design.

The exploration of parity-time (PT) symmetry in micro-/nano-cavity lasers has recently gained immense research interest. The PT symmetric phase transition to single-mode lasing has been achieved by arranging the spatial distribution of optical gain and loss in single or coupled cavity systems. In terms of photonic crystal (PhC) lasers, a non-uniform pumping scheme is usually employed to enter the PT symmetry-breaking phase in a longitudinal PT symmetric system. Instead, we use a uniform pumping scheme to enable the PT symmetric transition to the desired single lasing mode in line-defect PhC cavities based on a simple design with asymmetric optical loss. The flexible control of gain-loss contrast is realized by removing a few rows of air holes in PhCs. We obtain single-mode lasing with a side mode suppression ratio (SMSR) of around 30 dB without affecting the threshold pump power and linewidth. The output power of the desired mode is six times higher than that in multimode lasing. This simple approach enables single-mode PhC lasers without sacrificing the output power, threshold pump power, and linewidth of a multimode cavity design.

Experimental X-ray Charge-Density Studies─A Suitable Probe for Superconductivity? A Case Study on MgB2.

Case studies of 1T-TiSe2 and YBa2Cu3O7-δ have demonstrated that X-ray diffraction (XRD) studies can be used to trace even subtle structural phase transitions which are inherently connected with the onset of superconductivity in these benchmark systems. However, the utility of XRD in the investigation of superconductors like MgB2 lacking an additional symmetry-breaking structural phase transition is not immediately evident. Nevertheless, high-resolution powder XRD experiments on MgB2 in combination with maximum entropy method analyses hinted at differences between the electron density distributions at room temperature and 15 K, that is, below the Tc of approx. 39 K. The high-resolution single-crystal XRD experiments in combination with multipolar refinements presented here can reproduce these results but show that the observed temperature-dependent density changes are almost entirely due to a decrease of atomic displacement parameters as a natural consequence of a reduced thermal vibration amplitude with decreasing temperature. Our investigations also shed new light on the presence or absence of magnesium vacancies in MgB2 samples─a defect type claimed to control the superconducting properties of the compound. We propose that previous reports on the tendency of MgB2 to form non-stoichiometric Mg1-xB2 phases (1 - x ∼ 0.95) during high-temperature (HT) synthesis might result from the interpretation of XRD data of insufficient resolution and/or usage of inflexible refinement models. Indeed, advanced refinements based on an Extended Hansen-Coppens multipolar model and high-resolution X-ray data, which consider explicitly the contraction of core and valence shells of the magnesium cations, do not provide any significant evidence for the formation of non-stoichiometric Mg1-xB2 phases during HT synthesis.

Possible transition between charge density wave and Weyl semimetal phase in Y2Ir2O7

The subtle interplay of band topology and symmetry broken phase, induced by electron correlations, has immense contemporary relevance and potentially offers novel physical insights. Here, we demonstrate charge density wave (CDW) in bulk Y$_2$Ir$_2$O$_7$ for T < 10 K, and its transition to the Weyl semimetal (WSM) phase at higher temperatures. The CDW phase is evidenced by a) current induced nonlinear conductivity with negative differential resistance at low temperature, b) low frequency Debye like dielectric relaxation at low temperature with a large dielectric constant, and c) an anomaly in the temperature dependence of the thermal expansion coefficient. The WSM phase at higher temperature is confirmed by the DC and AC transport measurements which show an inductive response at low frequencies. More interestingly, we show that by reducing the crystallite size, the low temperature CDW phase can be eliminated leading to the restoration of the WSM phase.

Discovery of conjoined charge density waves in the kagome superconductor CsV3Sb5

The electronic instabilities in CsV3Sb5 are believed to originate from the V 3d-electrons on the kagome plane, however the role of Sb 5p-electrons for 3-dimensional orders is largely unexplored. Here, using resonant tender X-ray scattering and high-pressure X-ray scattering, we report a rare realization of conjoined charge density waves (CDWs) in CsV3Sb5, where a 2 × 2 × 1 CDW in the kagome sublattice and a Sb 5p-electron assisted 2 × 2 × 2 CDW coexist. At ambient pressure, we discover a resonant enhancement on Sb L1-edge (2s→5p) at the 2 × 2 × 2 CDW wavevectors. The resonance, however, is absent at the 2 × 2 × 1 CDW wavevectors. Applying hydrostatic pressure, CDW transition temperatures are separated, where the 2 × 2 × 2 CDW emerges 4 K above the 2 × 2 × 1 CDW at 1 GPa. These observations demonstrate that symmetry-breaking phases in CsV3Sb5 go beyond the minimal framework of kagome electronic bands near van Hove filling.

Belief propagation on the random k-SAT model

Corroborating a prediction from statistical physics, we prove that the belief propagation message passing algorithm approximates the partition function of the random k-SAT model well for all clause/variable densities and all inverse temperatures for which a modest absence of long-range correlations condition is satisfied. This condition is known as “replica symmetry” in physics language. From this result we deduce that a replica symmetry breaking phase transition occurs in the random k-SAT model at low temperature for clause/variable densities below but close to the satisfiability threshold.

Interaction between games give rise to the evolution of moral norms of cooperation.

In many biological populations, such as human groups, individuals face a complex strategic setting, where they need to make strategic decisions over a diverse set of issues and their behavior in one strategic context can affect their decisions in another. This raises the question of how the interaction between different strategic contexts affects individuals' strategic choices and social norms? To address this question, I introduce a framework where individuals play two games with different structures and decide upon their strategy in a second game based on their knowledge of their opponent's strategy in the first game. I consider both multistage games, where the same opponents play the two games consecutively, and reputation-based model, where individuals play their two games with different opponents but receive information about their opponent's strategy. By considering a case where the first game is a social dilemma, I show that when the second game is a coordination or anti-coordination game, the Nash equilibrium of the coupled game can be decomposed into two classes, a defective equilibrium which is composed of two simple equilibrium of the two games, and a cooperative equilibrium, in which coupling between the two games emerge and sustain cooperation in the social dilemma. For the existence of the cooperative equilibrium, the cost of cooperation should be smaller than a value determined by the structure of the second game. Investigation of the evolutionary dynamics shows that a cooperative fixed point exists when the second game belongs to coordination or anti-coordination class in a mixed population. However, the basin of attraction of the cooperative fixed point is much smaller for the coordination class, and this fixed point disappears in a structured population. When the second game belongs to the anti-coordination class, the system possesses a spontaneous symmetry-breaking phase transition above which the symmetry between cooperation and defection breaks. A set of cooperation supporting moral norms emerges according to which cooperation stands out as a valuable trait. Notably, the moral system also brings a more efficient allocation of resources in the second game. This observation suggests a moral system has two different roles: Promotion of cooperation, which is against individuals' self-interest but beneficial for the population, and promotion of organization and order, which is at both the population's and the individual's self-interest. Interestingly, the latter acts like a Trojan horse: Once established out of individuals' self-interest, it brings the former with itself. Importantly, the fact that the evolution of moral norms depends only on the cost of cooperation and is independent of the benefit of cooperation implies that moral norms can be harmful and incur a pure collective cost, yet they are just as effective in promoting order and organization. Finally, the model predicts that recognition noise can have a surprisingly positive effect on the evolution of moral norms and facilitates cooperation in the Snow Drift game in structured populations.

Unusual thermodynamic signature of topological quantum criticality in two coupled Su-Schrieffer-Heeger chains

Symmetry breaking and topological quantum phase transitions (QPTs) are usually accompanied by a gap opening or closing. For the continuous QPT, it is marked by a quantum critical point. Herein, we study the topological feature of quantum phase boundary-quantum criticality of two coupled Su-Schrieffer-Heeger chains. Two topological nontrivial insulating phases and a trivial one are recapped with two different topological phase boundaries, which are termed as Dirac semimetals (DSMs) with one or two Dirac nodal points within considering spin degeneracy. Specially, a tricritical point holds the character of quadratic contact point semimetal (QCPSM) that is regarded as a parent phase of DSMs. Meanwhile, the QCPSM and DSMs are featured by the quantum critical scaling of thermal Drude weight and specific heat. Furthermore, the Grüneisen ratio serves as a superb tool for the diagnosis of topological semimetals, which is demonstrated with or without self-duality of quantum criticality explicitly.

Capturing the ground state of uranium dioxide from first principles: Crystal distortion, magnetic structure, and phonons

Uranium dioxide (UO$_2$) remains a formidable challenge for first-principles approaches, due to the complex interplay among spin-orbit coupling, Mott physics, magnetic ordering, and crystal distortions. Here we use DFT+$U$ to explore UO$_2$ at zero temperature, incorporating all the aforementioned phenomena. The technical challenge is to navigate the many metastable electronic states produced by DFT+$U$, which is acomplished using $f$-orbital occupation matrix control to search for the ground state. We restrict our search to the high-symmetry ferromagnetic phase, including spin-orbit coupling, which produces a previously unreported occupation matrix. This newfound occupation matrix is then used as an initialization to explore the broken symmetry phases. We find the oxygen cage distortion of the 3k antiferromagnetic state to be in excellent agreement with experiments, and both the spin-orbit coupling and the Hubbard $U$ are critical ingredients. We demonstrate that only select phonon modes have a strong dependence on the Hubbard $U$, whereas magnetic ordering has only a small influence overall. We perform measurements of the phonon dispersion curves using inelastic neutron scattering, and our calculations show good agreement when using reasonable values of $U$. The quantitative success of DFT+$U$ warrants exploration of thermal transport and other observables within this level of theory.

Spin liquid state in a rare-earth hyperkagome lattice

Quantum fluctuations enhanced by frustration and subtle interplay between competing degrees of freedom offer an ideal ground to realize novel states with fractional quantum numbers in quantum materials that defy standard theoretical paradigms. Quantum spin liquid (QSL) is a highly entangled state wherein frustration induced strong quantum fluctuations preclude symmetry breaking phase transitions down to zero temperature without any order parameter. Experimental realizations of QSL in quantum materials with spin dimensionality greater than one is very rare. Here, we present our thermodynamic, nuclear magnetic resonance, muon spin relaxation and inelastic neutron scattering studies of a new rare-earth hyperkagome compound Li3Yb3Te2O12 in which Yb3+ ions constitute a three dimensional spin-lattice without any detectable disorder. Our comprehensive experiments evince neither signature of magnetic ordering nor spin freezing down to 38 mK that suggest the realization of dynamic liquid-like ground state in this antiferromagnet. The ground state of this material is interpreted by a low energy Jeff = 1/2 degrees of freedom with short range spin correlations. The present results demonstrate a viable basis to explore spin-orbit driven enigmatic correlated quantum states in a new class of rare-earth based three dimensional frustrated magnets that may open new avenues in theoretical and experimental search for spin liquids.

Charge carrier coupling to the soft phonon mode in a ferroelectric semiconductor

Many crystalline solids possess strongly anharmonic ``soft'' phonon modes characterized by diminishing frequency as temperature approaches a critical point associated with a symmetry breaking phase transition. While electron--soft phonon coupling can introduce unique scattering channels for charge carriers in ferroelectrics, recent studies on the nonferroelectric lead halide perovskites have also suggested the central role of anharmonic phonons bearing resemblance to soft modes in charge carrier screening. Here we apply coherent phonon spectroscopy to directly study electron coupling to the soft transverse optical phonon mode in a ferroelectric semiconductor SbSI. Photogenerated charge carriers in SbSI are found to be exceptionally long lived and are associated with a transient electro-optical effect that can be explained by interactions between charge carriers and thermally stimulated soft phonon excitations. These results provide strong evidence for the role of electron--soft phonon coupling in the efficient screening of charge carriers and in reducing charge recombination rates, both desirable properties for optoelectronics.

Structural transformations of nematic disclinations.

Topological defects (TDs) are a consequence of symmetry breaking phase transitions and are ubiquitous in nature. An ideal testbed for their study are liquid crystals (LCs) owing to their large response to external stimuli and their large electrical and optical anisotropies. In this paper, we perform numerical simulations of topological defects of [Formula: see text] or [Formula: see text] enforced by the confining boundary. We use the Landau-de Gennes phenomenological model in terms of the tensor nematic order parameter and the Jones beam propagation model to simulate polarized optical microscopy images. We demonstrate the structure of closed disclination loops near the boundary known as boojums that can be topologically charged or chargeless. We show that pairs of chargeless disclination loops can interact repulsively or attractively depending on if they are arranged parallel or antiparallel, respectively. Sufficiently closely spaced antiparallel pairs can rewire while parallel pairs simply exhibit stronger bending due to the repulsion.

Fluid-fluid phase transitions in a chiral molecular model.

Molecular chirality is a fundamental phenomenon, underlying both life as we know it and industrial pharmaceutical syntheses. Understanding the symmetry breaking phase transitions exhibited by many chiral molecular substances provides basic insights for topics ranging from the origin of life to the rational design of drug manufacturing processes. In this work, we have performed molecular dynamics simulations to investigate the fluid-fluid phase transitions of a flexible three-dimensional four-site chiral molecular model developed by Latinwo et al. [J. Chem. Phys. 145, 154503 (2016)] and Petsev et al. [J. Chem. Phys. 155, 084105 (2021)]. By introducing a bias favoring local homochiral vs heterochiral interactions, the system exhibits a phase transition from a single achiral phase to a single chiral phase that undergoes infrequent interconversion between the two thermodynamically identical chiral states: the L-rich and D-rich phases. According to the phase rule, this reactive binary system has two independent degrees of freedom and exhibits a density-dependent critical locus. Below the liquid-liquid critical locus, there exists a first-order vapor-liquid coexistence region with a single independent degree of freedom. Our results provide basic thermodynamic and kinetic insights for understanding many-body chiral symmetry breaking phenomena.

Linear level repulsions near exceptional points of non-Hermitian systems

The nearest-neighbor level-spacing distributions are a fundamental quantity of disordered systems and are classified into different universality classes. They are the Wigner-Dyson and the Poisson functions for extended and localized states in Hermitian systems, respectively. The distributions follow the Ginibre functions for the non-Hermitian systems whose eigenvalues are complex and away from exceptional points (EPs). However, the level-spacing distributions of disordered non-Hermitian systems near EPs are still unknown, and a corresponding random matrix theory is absent. Here, we show another class of universal level-spacing distributions in the vicinity of EPs of non-Hermitian Hamiltonians. Two distribution functions, ${P}_{\text{SP}}(s)$ for the symmetry-preserved phase and ${P}_{\text{SB}}(s)$ for the symmetry-broken phase, are needed to describe the nearest-neighbor level-spacing distributions near EPs. Surprisingly, both ${P}_{\text{SP}}(s)$ and ${P}_{\text{SB}}(s)$ are proportional to $s$ for small $s$, or linear level repulsions, in contrast to cubic level repulsions of the Ginibre ensembles. For disordered non-Hermitian tight-binding Hamiltonians, ${P}_{\text{SP}}(s)$ and ${P}_{\text{SB}}(s)$ can be well described by a surmise ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{P}}_{\text{ep}}(s)={\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{c}}_{1}sexp[\ensuremath{-}{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{c}}_{2}{s}^{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\alpha}}}]$ in the thermodynamic limit (infinite systems) with a constant $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\alpha}}$ that depends on the localization nature of states at EPs rather than the dimensionality of non-Hermitian systems and the order of EPs.

Partially coherent spiral phase contrast imaging with a 3D-like effect

Spiral phase contrast (SPC) imaging provides an effective way to isotropic edge detection for biomedical applications. Here, we present a computational SPC imaging method which combines the partially coherent illumination with the symmetry-breaking spiral phase filtering. Such an operation enables the SPC imaging to generate sharp, high-contrast and pseudo three-dimensional edge images that are almost free of speckle. The superior performance is demonstrated by imaging both amplitude and phase objects, and the speckle suppression is validated by comparing the coherent and partially coherent imaging results. This computational SPC method is expected to bring potential advantages to phase contrast imaging modality.

Anomalous Hall effect at half filling in twisted bilayer graphene

Magic-angle twisted bilayer graphene (tBLG) has been studied extensively owing to its wealth of symmetry-broken phases, correlated Chern insulators, orbital magnetism, and superconductivity. In particular, the anomalous Hall effect (AHE) has been observed at odd integer filling factors ($\nu=1$ and $3$) in a small number of tBLG devices, indicating the emergence of a zero-field orbital magnetic state with spontaneously broken time-reversal symmetry. However, the AHE is typically not anticipated at half filling ($\nu=2$) owing to competing intervalley coherent states, as well as spin-polarized and valley Hall states that are favored by an intervalley Hund's coupling. Here, we present measurements of two tBLG devices with twist angles slightly away from the magic angle (0.96$^{\circ}$ and 1.20$^{\circ}$), in which we report the surprising observation of the AHE at $\nu=+2$ and $-2$, respectively. These findings imply that a valley-polarized phase can become the ground state at half filling in tBLG rotated slightly away from the magic angle. Our results reveal the emergence of an unexpected ground state in the intermediately-coupled regime ($U/W \sim 1$, where $U$ is the strength of Coulomb repulsion and $W$ is the bandwidth), in between the strongly-correlated insulator and weakly-correlated metal, highlighting the need to develop a more complete understanding of tBLG away from the strongly-coupled limit.

Mechanisms for Spontaneous Symmetry Breaking in Developing Visual Cortex

For the brain to recognize local orientations within images, neurons must spontaneously break the translation and rotation symmetry of their response functions—an archetypal example of unsupervised learning. The dominant framework for unsupervised learning in biology is Hebb’s principle, but how Hebbian learning could break such symmetries is a longstanding biophysical riddle. Theoretical studies argue that this requires inputs to the visual cortex to invert the relative magnitude of their correlations at long distances. Empirical measurements have searched in vain for such an inversion and report the opposite to be true. We formally approach the question through the Hermitianization of a multilayer model, which maps it into a problem of zero-temperature phase transitions. In the emerging phase diagram, both symmetries break spontaneously as long as (i) recurrent interactions are sufficiently long range and (ii) Hebbian competition is duly accounted for. A key ingredient for symmetry breaking is competition among connections sprouting from the same afferent cell. Such a competition, along with simple monotonic falloff of input correlations with distance, is capable of triggering the broken-symmetry phase required by image processing. We provide analytic predictions on the relative magnitudes of the relevant length scales needed for this novel mechanism to occur. These results reconcile experimental observations to the Hebbian paradigm, shed light on a new mechanism for visual cortex development, and contribute to our growing understanding of the relationship between learning and symmetry breaking.4 MoreReceived 8 October 2021Revised 3 May 2022Accepted 28 June 2022DOI:https://doi.org/10.1103/PhysRevX.12.031024Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasLearningNeuronal networksNeuroplasticityNeuroscienceSynapsesBiological Physics

On the Inherent Instability of Biocognition: Toward New Probability Models and Statistical Tools.

A central conundrum enshrouds biocognition: almost all such phenomena are inherently unstable and must be constantly controlled by external regulatory machinery to ensure proper function, in much the same sense that blood pressure and the ‘stream of consciousness’ require persistent delicate regulation for the survival of higher organisms. Here, we derive the Data Rate Theorem of control theory that characterizes such instability via the Rate Distortion Theorem of information theory for adiabatically stationary nonergodic systems. We then outline a novel approach to building new statistical tools for data analysis based on those theorems, focusing on groupoid symmetry-breaking phase transitions characterized by Fisher Zero analogs.

Lee-Yang theory of the two-dimensional quantum Ising model

Determining the phase diagram of interacting quantum many-body systems is an important task for a wide range of problems such as the understanding and design of quantum materials. For classical equilibrium systems, the Lee-Yang formalism provides a rigorous foundation of phase transitions, and these ideas have also been extended to the quantum realm. Here, we develop a Lee-Yang theory of quantum phase transitions that can include thermal fluctuations caused by a finite temperature, and it thereby provides a link between the classical Lee-Yang formalism and recent theories of phase transitions at zero temperature. Our methodology exploits analytic properties of the moment generating function of the order parameter in systems of finite size, and it can be implemented in combination with tensor-network calculations. Specifically, the onset of a symmetry-broken phase is signaled by the zeros of the moment generating function approaching the origin in the complex plane of a counting field that couples to the order parameter. Moreover, the zeros can be obtained by measuring or calculating the high cumulants of the order parameter. We determine the phase diagram of the two-dimensional quantum Ising model and thereby demonstrate the potential of our method to predict the critical behavior of two-dimensional quantum systems at finite temperatures.