Symmetry-breaking Perturbations Research Articles

FLARE: field line analysis and reconstruction for 3D boundary plasma modeling

Abstract The FLARE code is a magnetic mesh generator that is integrated within a suite of tools for the analysis of the magnetic geometry in toroidal fusion devices. A magnetic mesh is constructed from field line segments and permits fast reconstruction of field lines in 3D boundary plasma codes such as EMC3-EIRENE. Both intrinsically non-axisymmetric configurations (stellarators) and those with symmetry breaking perturbations of an axisymmetric equilibrium (tokamaks) are supported. The code itself is written in Modern Fortran with MPI support for parallel computing, and it incorporates object-oriented programming for the definition of the magnetic field and the material surface geometry. Extended derived types for a number of different magnetohydrodynamic equilibrium and plasma response models are implemented. The core element of FLARE is a field line tracer with adaptive step-size control, and this is integrated into tools for the construction of Poincaré maps and invariant manifolds of X-points. A collection of high-level procedures that generate output files for visualization is build on top of that. The analysis modules are build with Python frontends that facilitate customization of tasks and/or scripting of parameter scans.

Active tuning of angular asymmetric thermal emission via carrier injection in metal-insulator-metal resonance gratings

We present a method to break the angular symmetry of infrared thermal emission using dynamic electrical control. An electrically tunable GaAs grating is designed to exhibit narrowband angular emission in the longwave infrared. The grating has GaAs stripes sandwiched between the top metallic contacts and the bottom reflector layer. The application of voltage across the GaAs allows for the change of the refractive index. Tuning one of the dielectric stripes within each unit cell enables symmetry-breaking index perturbation. The perturbed structure exhibits angular asymmetric thermal emission. We analyze our findings based on coupling coefficients and variational principle. Due to the reversible nature of the perturbation, this concept presents a route toward tunable asymmetric emission and directional ‘steering’ of thermal emission.

Realization of exciton-polariton optical chirality based on strong coupling between intrinsic chiral quasibound states in the continuum and monolayer WS2.

Hybrid quasiparticles produced by the strong interaction between nanostructures and excitons will exhibit optical chirality when one of the coupled components is chiral. Due to the tunability of hybrid states, the coupled system has potential applications in chiral devices and chiral sensing. However, reported chiral materials including chiral molecules and three-dimensional chiral structures in the coupled system limit the application due to the weak chiroptical responses and difficult fabrication, respectively. In this paper, we design chiral quasibound states in the continuum (q-BIC) metasurface by introducing planar symmetry-breaking and z-axis perturbation into an array structure whose unit cell is a C4 rotational symmetric disk. By tuning the polarization state of the eigenmode, a significant chiroptical response is obtained in our q-BIC metasurface. Furthermore, mode splitting is observed not only in the reflection spectrum but also in the circular dichroism (CD) spectrum in the chiral q-BIC and monolayer WS2 strong coupling system, which indicates the realization of the exciton-polariton optical chirality. More importantly, one order of magnitude difference in the reflection to left and right circularly polarized light is achieved resulting in significant CD signals. Our work provides a new strategy to realize the exciton polaritons with significant chiroptical responses, which exhibits promising applications in on-chip chiral devices.

Charge Correlations in Cuprate Superconductors

High-temperature superconductivity, with transition temperatures up to ≈134 K at ambient pressure, occurs in layered cuprate compounds. The conducting CuO2 planes, which are universally present, are responsible for the superconductivity but also show a disposition to other competing states including spin and charge order. Charge-density-wave (CDW) order appears to be a universal property of cuprate superconductors. It has been studied via a multitude of probes including X-ray and neutron scattering, nuclear magnetic resonance, scanning probe techniques, electronic transport, and quantum oscillations. Here, we review the microscopic properties of the CDW order. We discuss the nature of the ordered state, that is, its symmetry and microscopic structure. Furthermore, we show how the CDW order is related to quenched disorder, host structure, symmetry breaking perturbations, and magnetic fields. We also describe measurements of dynamic collective charge excitations that are closely related to the quasi-static CDW order. Finally, we highlight some of the debated issues in the field, including the origin of the CDW order, the relationship to spin order, and the nature of the spatial CDW correlations.

Magnetic Second-Order Topological Insulators in 2H-Transition Metal Dichalcogenides.

The transition metal dichalcogenides, 2H-VX2 (X = S, Se, Te), are identified astwo-dimensional second-order topological insulator (SOTI) with a ferromagnetic ground state by first-principles calculations. The 2H-VX2 (X = S, Se, Te) materials have a nontrivial band gap in two spin channels is found and exhibit topologically protected corner states with spin-polarization. These corner states only accommodate the quantized fractional charge (e/3). And the charge is bound at the corners of the nanodisk geometry 2H-VX2 (X = S, Se, Te) in real space. The corner states are robust against symmetry-breaking perturbations, which makes them more easily detectable in experiments. Further, it is demonstrated that the SOTI properties of 2H-VX2 (X = S, Se, Te) materials can be maintained in the presence of spin-orbit coupling and are stable against magnetization. Overall, the results reveal 2H-VX2 (X = S, Se, Te) as an ideal platform for the exploration of magnetic SOTI and suggest its great potential in experimental detection.

Topological pump of SU(Q) quantum chain and Diophantine equation

A topological pump of the $SU(Q)$ quantum chain is proposed associated with a current due to a local $[U(1)]^{\otimes Q}$ gauge invariance of colored fermions. The $SU(Q)$ invariant dimer phases are characterized by the $Z_Q$ Berry phases as a topological order parameter with a $d$-dimensional twist space ($d=Q-1$) as a synthetic Brillouin zone. By inclusion of the symmetry breaking perturbation specified by a rational parameter $\Phi=P/Q$, the pump, that encloses around the phase boundary, is characterized by the $Q$ Chern numbers associated with the currents due to uniform infinitesimal twists. The analysis of the systems under the open/periodic/twisted boundary conditions clarifies the bulk-edge correspondence of the pump where the large gauge transformation generated by the center of mass (CoM) plays a central role. An explicit formula for the Chern number is given by using the Diophanine equation. Numerical demonstration by the exact diagonalization and the DMRG for finite systems ($Q=3,4$ and $5$) have been presented to confirm the general discussions for low energy spectra, edge states, CoM's, Chern numbers and the bulk-edge correspondence. A modified Lieb-Schultz-Mattis type argument for the general $SU(Q)$ quantum chain is also mentioned.

Multipartite nonlocality and symmetry breaking in one-dimensional quantum chains

Multipartite nonlocality is a measure of multipartite quantum correlations. In this paper we investigate the influence of symmetry-breaking perturbations upon ground-state nonlocality by considering several typical finite-size quantum models, including the transverse-field Ising chains, the $XY$($XX$) chains, and the $XXZ$ chains. We find that even a slight perturbation can reshape the nonlocality curve dramatically. For instance, in the $XY$ chains, a perturbation can induce an oscillation behavior in the nonlocality curve. A clear microscopic mechanism for the results is proposed. Furthermore, we also connect the behaviors to the macroscopic symmetry properties of the chains and make some predictions on general models.

Out-of-equilibrium finite-size scaling in generalized Kibble-Zurek protocols crossing quantum phase transitions in the presence of symmetry-breaking perturbations

We study the effects of symmetry-breaking perturbations in the out-of-equilibrium quantum dynamics of many-body systems slowly driven by a time-dependent symmetry-preserving parameter, across the quantum critical regime associated with a continuous quantum transition (CQT). For this purpose, we analyze the out-of-equilibrium dynamics arising from generalized Kibble-Zurek (KZ) protocols, within a dynamic renormalization-group framework allowing for finite-size systems. We show that the time dependence of generic observables develops an out-of-equilibrium finite-size scaling (FSS) behavior, arising from the interplay between the timescale ${t}_{s}$ of the parameter variations in the KZ protocol, the size $L$ of the system, and the strength $h$ of the symmetry-breaking perturbation, in the limit of large ${t}_{s}$ and $L$. Moreover, scaling arguments based on the first-order adiabatic approximation of slow variations in quantum systems allow us to characterize the approach to the adiabatic regimes for some limits of the model parameters (for example, when we take ${t}_{s}\ensuremath{\rightarrow}\ensuremath{\infty}$ before $L\ensuremath{\rightarrow}\ensuremath{\infty}$), predicting asymptotic power-law suppressions of the nonadiabatic behaviors in the adiabatic limits. This out-of-equilibrium FSS is supported by numerical analyses for the paradigmatic quantum Ising chain along generalized KZ protocols, with a time-dependent transverse field crossing its CQT, in the presence of a static longitudinal field breaking the ${\mathbb{Z}}_{2}$ symmetry.

Boundary discrete time crystals induced by topological superconductors in solvable spin chains

The Floquet time crystal, which breaks discrete time-translation symmetry, is an intriguing phenomenon in nonequilibrium systems. It is crucial to understand the rigidity and robustness of discrete time crystal (DTC) phases in a many-body system, and finding a precisely solvable model can pave a way for understanding of the DTC phase. Here, we propose and study a solvable spin chain model by mapping it to a Floquet superconductor through the Jordan-Wigner transformation. The phase diagrams of Floquet topological systems are characterized by topological invariants and tell the existence of anomalous edge states. The subharmonic oscillation, which is the typical signal of the DTC, can be generated from such edge states and protected by topology and solvability. We also examine the robustness of the DTC by adding symmetry-preserving and symmetry-breaking perturbations. Our results on the topologically protected DTC can provide a deep understanding of the DTC when generalized to other interacting or dissipative systems.

Pair breaking in superconductors with strong spin-orbit coupling

We study the influence of symmetry-breaking perturbations on superconductivity in multiorbital materials, with a particular focus on an external magnetic field. We introduce the field-fitness function which characterizes the pair-breaking effects of the perturbation on a given superconducting state. For even-parity superconductors we find that this field-fitness function for an external magnetic field is one, implying that the paramagnetic response is controlled only by a generalized effective $g$ factor. For odd-parity superconductors, the interplay of the effective $g$ factor and the field-fitness function can lead to counterintuitive results. We demonstrate this for $p$-wave pairing in the effective $j=\frac{3}{2}$ electronic states of the Luttinger-Kohn model.

Enhanced symmetry-breaking tendencies in the S=1 pyrochlore antiferromagnet

We investigate the ground-state properties of the nearest-neighbor $S=1$ pyrochlore Heisenberg antiferromagnet using two complementary numerical methods, the density-matrix renormalization group (DMRG) and pseudofermion functional renormalization group (PFFRG). Within DMRG, we are able to reliably study clusters with up to 48 spins by keeping 20 000 SU(2) states. The investigated 32-site and 48-site clusters both show indications of a robust ${C}_{3}$ rotation symmetry breaking of the ground-state spin correlations and the 48-site cluster additionally features inversion symmetry breaking. Our PFFRG analysis of various symmetry-breaking perturbations corroborates the findings of either ${C}_{3}$ or a combined ${C}_{3}$/inversion symmetry breaking. Moreover, in both methods the symmetry-breaking tendencies appear to be more pronounced than in the $S=1/2$ system.

Complementary roles for auxin and auxin signalling revealed by reverse engineering lateral root stable prebranch site formation.

Priming is the process through which periodic elevations in auxin signalling prepattern future sites for lateral root formation, called prebranch sites. Thus far, the extent to which elevations in auxin concentration and/or auxin signalling are required for priming and prebranch site formation has remained a matter of debate. Recently, we discovered a reflux-and-growth mechanism for priming generating periodic elevations in auxin concentration that subsequently dissipate. Here, we reverse engineer a mechanism for prebranch site formation that translates these transient elevations into a persistent increase in auxin signalling, resolving the prior debate into a two-step process of auxin concentration-mediated initial signal and auxin signalling capacity-mediated memorization. A crucial aspect of the prebranch site formation mechanism is its activation in response to time-integrated rather than instantaneous auxin signalling. The proposed mechanism is demonstrated to be consistent with prebranch site auxin signalling dynamics, lateral inhibition, and symmetry-breaking mechanisms and perturbations in auxin homeostasis.

Modelling the nonlinear plasma response to externally applied three-dimensional fields with the Stepped Pressure Equilibrium Code

Small-amplitude, symmetry-breaking magnetic field perturbations, including resonant magnetic perturbations (RMPs) and error fields, can profoundly impact plasma properties in both tokamaks and stellarators. In this work, we perform the first comparison between the Stepped Pressure Equilibrium Code (SPEC) (a comparatively fast and efficient equilibrium code based on energy-minimisation principles) and M3D-C $^{1}$ (a high-fidelity albeit computationally expensive initial-value extended-magnetohydro- dynamic (MHD) code) to assess the conditions under which SPEC can be used to model the nonlinear, non-ideal plasma response to an externally applied $(m=2,n=1)$ RMP field in an experimentally relevant geometry. We find that SPEC is able to capture the plasma response in the weakly nonlinear regime – meaning perturbation amplitudes below the threshold for break up of the separatrix and onset of secondary magnetic island formation – when around half of the total toroidal flux is enclosed in the volume containing the $q=2$ resonant surface. The observed dependence of SPEC solutions on input parameters, including toroidal flux and the number of volumes into which the plasma is partitioned, indicates that additional exploration of the underlying Multi-Region Relaxed MHD physics model is needed to constrain the choice of parameters. Nonetheless, this work suggests promising applications of SPEC to optimisation and fusion plasma design.

Phase transitions as a manifestation of spontaneous unitarity violation

Spontaneous symmetry breaking is well understood under equilibrium conditions as a consequence of the singularity of the thermodynamic limit. How a single global orientation of the order parameter dynamically emerges from an initially symmetric state during a phase transition, however, is not captured by this paradigm. Here, we present a series of symmetry arguments suggesting that singling out a global choice for the ordered state is in fact forbidden under unitary time evolution, even in the presence of an environment and infinitesimal symmetry breaking perturbations. We thus argue that the observation of phase transitions in our everyday world presents a manifestation of the unitarity of quantum dynamics itself being spontaneously broken. We argue that this agrees with the observation that Schrödinger’s time dependent equation is rendered unstable for macroscopic objects owing to the same singular thermodynamic limit that affects equilibrium configurations.

Josephson junctions of topological nodal superconductors

Transition metal dichalcogenides (TMDs) offer a unique platform to study unconventional superconductivity, owing to the presence of strong spin-orbit coupling and a remarkable stability to an in-plane magnetic field. A recent study found that when an in-plane field applied to a superconducting monolayer TMD is increased beyond the Pauli critical limit, a quantum phase transition occurs into a topological nodal superconducting phase which hosts Majorana flat bands. We study the current-phase relation of this nodal superconductor in a Josephson junction geometry. We find that the nodal superconductivity is associated with an energy-phase relation that depends on the momentum transverse to the current direction, with a 4\pi4π periodicity in between pairs of nodal points. We interpret this response as a result of a series of quantum phase transitions, driven by the transverse momentum, which separate a trivial phase and two distinct topologically non-trivial phases characterized by different winding invariants. This analysis sheds light on the stability of the Majorana flat bands to symmetry-breaking perturbations.

Critical structure and emergent symmetry of Dirac fermion systems

Emergent symmetry in Dirac system means that the system acquires an enlargement of two basic symmetries at some special critical point. The continuous quantum criticality between the two symmetry broken phases can be described within the framework of Gross–Neveu–Yukawa (GNY) model. Using the first-order ε expansion in dimensions, we study the critical structure and emergent symmetry of the O(N)-GNY model with N f flavors of four-component Dirac fermions coupled strongly to an O(N) scalar field under a small O(N)-symmetry breaking perturbation. After determining the stable fixed point, we calculate the inverse correlation length exponent and the anomalous dimensions (bosonic and fermionic) for general N and N f . Further, we discuss the emergent-symmetry and the emergent supersymmetric critical point for on the basis of O(N)-GNY model. It turns out that the O(N)-GNY universality class is physically meaningful if and only if . On this premise, the small O(N)-symmetry breaking perturbation is always irrelevant in the O(N)-GNY universality class. Our studies show that the emergent symmetry in Dirac systems has an upper limit , depending on the flavor numbers N f . As a result, the emergent-O(4) and O(5) symmetries are possible to be found in Dirac systems with fermion flavor , and the emergent-O(4), O(5), O(6) and O(7) symmetries are expected to be found in the systems with fermion flavor . Our result suggests some richer transitions with emergent- symmetry, and so on. Interestingly, in the O(4)-GNY universality class, we find that there is a new supersymmetric critical point which is expected to be found in Dirac systems with fermion flavor .

Bose-Hubbard realization of fracton defects

Bose-Hubbard models are simple paradigmatic lattice models used to study dynamics and phases of quantum bosonic matter. We combine the extended Bose-Hubbard model in the hard-core regime with ring-exchange hoppings. By investigating the symmetries and low-energy properties of the Hamiltonian we argue that the model hosts fractonic defect excitations. We back up our claims with exact numerical simulations of defect dynamics exhibiting mobility constraints. Moreover, we confirm the robustness of our results against fracton symmetry breaking perturbations. Finally we argue that this model can be experimentally realized in recently proposed quantum simulator platforms with big time crystals, thus paving a way for the controlled study of many-body dynamics with mobility constraints.

Edge spin transport in the disordered two-dimensional topological insulator WTe2

The spin conductance of two-dimensional topological insulators (2D TIs) is not expected to be quantized in the presence of perturbations that break the spin-rotational symmetry. However, the deviation from the pristine-limit quantization has yet to be studied in detail. In this paper, we define the spin current operator for the helical edge modes of a 2D TI and introduce a four-terminal setup to measure spin conductances. Using the developed formalism, we consider the effects of disorder terms that break spin-rotational symmetry or give rise to edge-to-edge coupling. We identify a key role played by spin torque in an out-of-equilibrium edge. We then utilize a tight-binding model of topological monolayer ${\mathrm{WTe}}_{2}$ and scattering matrix formalism to numerically study spin transport in a four-terminal 2D TI device. In particular, we calculate the spin conductances and characteristic spin decay length in the presence of magnetic disorder. In addition, we study the effects of interedge scattering in a quantum point contact geometry. We find that the spin Hall conductance is surprisingly robust to spin symmetry-breaking perturbations, as long as time-reversal symmetry is preserved and interedge scattering is weak.

Topological transitions in arrays of dipoles coupled to a cavity waveguide

Topological valley-Hall edge states have been realized in a variety of photonic structures across the electromagnetic spectrum because they can be easily engineered by breaking certain lattice symmetries. However, the valley-Chern numbers that characterize the topological phase are usually fixed by the symmetry-breaking perturbation and therefore the valley-Hall edge states are forced to propagate in a fixed direction. Here we consider a kagome metasurface comprised of a subwavelength array of dipole emitters/antennas, and we unveil that one can modify the geometrical and topological properties of the polaritons by structuring the local photonic environment. As a proof of concept, we show that one can induce topological transitions via accidental Dirac points by embedding the metasurface inside a cavity waveguide. Varying the cavity width modifies the nature of the dipole-dipole interactions which enables one to manipulate the Berry curvature and invert the valley-Chern numbers without inverting the symmetry-breaking perturbation. Consequently, we demonstrate that one can switch the chirality of the polariton valley-Hall edge states by varying only the cavity width. This alternative approach to engineering topological transitions via structuring the photonic environment could also have implications for other topological phases such as photonic higher-order topological insulators.Received 26 October 2020Accepted 9 November 2021DOI:https://doi.org/10.1103/PhysRevResearch.4.013078Published 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 AreasAtom opticsAtoms, ions, & molecules in cavitiesCavity quantum electrodynamicsLight-matter interactionMetamaterialsPolaritonsTopological effects in photonic systemsTopological phase transitionTopological phases of matterCondensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Adaptive rewiring in nonuniform coupled oscillators.

Structural plasticity of the brain can be represented in a highly simplified form as adaptive rewiring, the relay of connections according to the spontaneous dynamic synchronization in network activity. Adaptive rewiring, over time, leads from initial random networks to brain-like complex networks, that is, networks with modular small-world structures and a rich-club effect. Adaptive rewiring has only been studied, however, in networks of identical oscillators with uniform or random coupling strengths. To implement information-processing functions (e.g., stimulus selection or memory storage), it is necessary to consider symmetry-breaking perturbations of oscillator amplitudes and coupling strengths. We studied whether nonuniformities in amplitude or connection strength could operate in tandem with adaptive rewiring. Throughout network evolution, either amplitude or connection strength of a subset of oscillators was kept different from the rest. In these extreme conditions, subsets might become isolated from the rest of the network or otherwise interfere with the development of network complexity. However, whereas these subsets form distinctive structural and functional communities, they generally maintain connectivity with the rest of the network and allow the development of network complexity. Pathological development was observed only in a small proportion of the models. These results suggest that adaptive rewiring can robustly operate alongside information processing in biological and artificial neural networks.