Broken Translational Symmetry Research Articles

Discrete time crystal phase of higher dimensional integrable models

This paper investigates the possibility of generating Floquet-time crystals in higher dimensions (d≥2) through the time-periodic driving of integrable free-fermionic models. The realization leads to rigid time-crystal phases that are ideally resistant to thermalization and decoherence. By utilizing spin-orbit coupling, we are able to realize a robust time-crystal phase that can be detected using novel techniques. Moreover, we discuss the significance of studying the highly persistent subharmonic responses and their implementation in a Kitaev spin liquid, which contributes to our understanding of time translational symmetry breaking and its practical implications.

Nonequilibrium Criticality at the Onset of Time-Crystalline Order.

We explore the phase transitions at the onset of time-crystalline order in O(N) models driven out of equilibrium. The spontaneous breaking of time translation symmetry and its Goldstone mode are captured by an effective description with O(N)×SO(2) symmetry, where the emergent external SO(2) results from a transmutation of the internal symmetry of time translations. Using the renormalization group and the ε=4-d expansion in a leading two-loop analysis, we identify a new nonequilibrium universality class. Strikingly, it controls the long-distance physics no matter how small the microscopic breaking of equilibrium conditions is. The O(N=2)×SO(2) symmetry group is realized for magnon condensation in pumped yttrium iron garnet films and in exciton-polariton systems with a polarization degree of freedom.

A study on spontaneously translational symmetry breaking in the excited states of holographic superconductor

We revisit HHH model [1] and extend the ansatz of matter fields to being of depending on a spatial dimension except the holographic direction. Despite homogeneous solutions of ground and excited states, especially for the excited states, there also exists solutions where the translational invariance is broken. It is worth mentioning that no periodic sources are assigned to the matter fields, so the translational symmetry is broken spontaneously. We investigate how the new solutions and the condensates of excited states develop with the change of temperature. Moreover, since this kind of condensate will decrease at certain temperature and eventually vanish at sufficiently low temperature, we also study the relation between this interval and length of lattice. Besides, we compare the free energies of non-translational invariant solutions and those of translational invariance in the HHH model, and find that the free energies of the former situations are lower.

Frustrated Extended Bose-Hubbard Model and Deconfined Quantum Critical Points with Optical Lattices at the Antimagic Wavelength.

The study of geometrically frustrated many-body quantum systems is of central importance to uncover novel quantum mechanical effects. We design a scheme where ultracold bosons trapped in a one-dimensional state-dependent optical lattice are modeled by a frustrated Bose-Hubbard Hamiltonian. A derivation of the Hamiltonian parameters based on Cesium atoms, further show large tunability of contact and nearest-neighbor interactions. For pure contact repulsion, we discover the presence of two phases peculiar to frustrated quantum magnets: the bond-order-wave insulator with broken inversion symmetry and a chiral superfluid. When the nearest-neighbor repulsion becomes sizable, a further density-wave insulator with broken translational symmetry can appear. We show that the phase transition between the two spontaneously symmetry-broken phases is continuous, thus representing a one-dimensional deconfined quantum critical point not captured by the Landau-Ginzburg-Wilson symmetry-breaking paradigm. Our results provide a solid ground to unveil the novel quantum physics induced by the interplay of nonlocal interactions, geometrical frustration, and quantum fluctuations.

Imperfect phononic crystals work too: The effect of translational and mid-plane symmetry breaking on hypersound propagation

Translationally symmetric nanostructures, termed phononic crystals (PnCs), offer control over the propagation of acoustic phonons in the gigahertz (GHz) range for signal-processing applications and thermal management at sub-Kelvin temperatures. In this work, we utilize Brillouin light scattering to investigate the impact of symmetry breaking on GHz phonon propagation in PnCs made of holey silicon nanomembranes. We show that the lattice of thimble-like holes leads to broken mid-plane symmetry and, hence, to anticrossing acoustic band gaps. With the rising level of uncorrelated translational disorder, the phononic effects are gradually suppressed, starting at higher frequencies. Strikingly, the low-frequency partial Bragg bandgap remains robust up to the highest level of disorder.

Symmetry breaking induced asymmetric dislocation-planar fault interactions in ordered intermetallic alloys

In this study, we present the first comprehensive examination of symmetry breaking in the interactions between dislocation and superlattice planar faults, including anti-phase boundary (APB), complex stacking fault (CSF), superlattice intrinsic stacking fault (SISF), to reveal the underlying asymmetric dislocation reaction mechanisms depending on the sense of applied stress, employing both large-scale atomistic simulations and continuum dislocation theory. Four ordered intermetallic alloy systems including γ−Ni/γ′−Ni3Al and γ−Ni/γ′−Ni3Fe, γ−Al/γ−TiAl, and α−Ti/α2−Ti3Al were selected as the representative model systems, with two primary symmetry breaking effects, i.e., translational and three-fold rotational symmetry breaking considered. Detailed atomic steps of asymmetrical dislocation reactions and the corresponding asymmetrical dislocation bypassing mechanisms of precipitation have been elucidated, shown to be highly dependent on the geometrical configuration of the precipitate and the relative magnitudes of APB, CSF and SISF fault energies. A continuum model framework was then developed, which, for the first time, provides accurate and quantitative predictions of the threshold conditions triggering critical asymmetrical dislocation slips, verified to be in good agreement with the simulation results. Our study also successfully reproduced the experimentally observed dislocation-induced APB-SISF transformation, with a new dislocation reaction mechanism proposed to explain the transformation process. The findings are expected to be a key enabling stepstone for future innovation in intermetallic alloys strengthened through ordered phases for advanced applications in aeronautic and automotive industries.

Quantum spin liquids and the phases of the cuprates

Soon after the discovery of high temperature superconductivity in the cuprates, Anderson proposed a connection to quantum spin liquids. But observations since then have shown that the low temperature phase diagram is dominated by conventional states, with a competition between superconductivity and charge-ordered states which break translational symmetry. We employ the "pseudogap metal" phase, found at intermediate temperatures and low hole doping, as the parent to the phases found at lower temperatures. We argue that the pseudogap is associated with a spin liquid, and that a particular spin liquid has the needed confining instabilities to resolve a number of open puzzles on the cuprate phase diagram.

Anomalous Hall Crystals or Moiré Chern Insulators? Spontaneous versus explicit translational symmetry breaking in graphene pentalayers

Anomalous Hall Crystals or Moiré Chern Insulators? Spontaneous versus explicit translational symmetry breaking in graphene pentalayers

Tuning commensurability in twisted van der Waals bilayers.

Moiré superlattices based on van der Waals bilayers1-4 created at small twist angles lead to a long wavelength pattern with approximate translational symmetry. At large twist angles (θt), moiré patterns are, in general, incommensurate except for a few discrete angles. Here we show that large-angle twisted bilayers offer distinctly different platforms. More specifically, by using twisted tungsten diselenide bilayers, we create the incommensurate dodecagon quasicrystals at θt = 30° and the commensurate moiré crystals at θt = 21.8° and 38.2°. Valley-resolved scanning tunnelling spectroscopy shows disparate behaviours between moiré crystals (with translational symmetry) and quasicrystals (with broken translational symmetry). In particular, the Kvalley shows rich electronic structures exemplified by the formation of mini-gaps near the valence band maximum. These discoveries demonstrate that bilayers with large twist angles offer a design platform to explore moiré physics beyond those formed with small twist angles.

Topological circular dichroism for asymmetric converging light beams

Light beams possess three types of angular momentum. They are the spin angular momentum, the extrinsic orbital angular momentum, and the intrinsic orbital angular momentum. Interaction of these momenta due to translational or cylindrical symmetry breaking leads to effects of the spin-orbit interaction of light, including topological effects. Topological optical activity or topological circular phase anisotropy, known as Rytov-Vladimirsky-Berry-Chao-Tomita plane polarization rotation, is the result of the extrinsic orbital angular momentum influence on the spin angular momentum. The effect manifests under linear polarized light propagation along a curved trajectory when the translational symmetry is breaking. We predict a new topological effect under the cylindrical symmetry breaking. This effect is the result of the extrinsic orbital angular momentum influence on the spin angular momentum in the converging asymmetrical light beam. It manifests as the transformation of linear polarized light into elliptically polarized one when an asymmetrical in the vertical direction beam passes through the left or right half of the focal plane. We have estimated the value of the ellipticity and proposed an experimental setup. We successfully observed the ellipticity change of 10(−3) using our method of small ellipticity determination. We have considered this transformation as the topological circular dichroism (topological circular amplitude anisotropy). We have demonstrated the connection of the ellipticity change with the value of the topological circular amplitude anisotropy R. The measured value of the topological circular amplitude anisotropy R turned out to be R=±(0.60±0.08)×10−3. This new effect of the spin-orbit interaction of light contributes to our understanding of the nature of light. It can be used to develop new sensors in optics, including nano and quantum optics.

Realization of an inherent time crystal in a dissipative many-body system

Time crystals are many-body states that spontaneously break translation symmetry in time the way that ordinary crystals do in space. While experimental observations have confirmed the existence of discrete or continuous time crystals, these realizations have relied on the utilization of periodic forces or effective modulation through cavity feedback. The original proposal for time crystals is that they would represent self-sustained motions without any external periodicity, but realizing such purely self-generated behavior has not yet been achieved. Here, we provide theoretical and experimental evidence that many-body interactions can give rise to an inherent time crystalline phase. Following a calculation that shows an ensemble of pumped four-level atoms can spontaneously break continuous time translation symmetry, we observe periodic motions in an erbium-doped solid. The inherent time crystal produced by our experiment is self-protected by many-body interactions and has a measured coherence time beyond that of individual erbium ions.

Robust Estimation of Position-Dependent Anisotropic Diffusivity Tensors from Molecular Dynamics Trajectories.

Confinement breaks translational and rotational symmetry in materials and makes all physical properties functions of position. Such spatial variations are key to modulating material properties at the nanoscale, and characterizing them accurately is therefore an intense area of research in the molecular simulations community. This is relatively easy to accomplish for basic mechanical observables. Determining spatial profiles of transport properties, such as diffusivity, is, however, much more challenging, as it requires calculating position-dependent autocorrelations of mechanical observables. In our previous paper (Domingues, T.S.; Coifman, R.; Haji-Akbari, A. J. Phys. Chem. B 2023, 127, 5273 10.1021/acs.jpcb.3c00670), we analytically derive and numerically validate a set of filtered covariance estimators (FCEs) for quantifying spatial variations of the diffusivity tensor from stochastic trajectories. In this work, we adapt these estimators to extract diffusivity profiles from MD trajectories and validate them by applying them to a Lennard-Jones fluid within a slit pore. We find our MD-adapted estimator to exhibit the same qualitative features as its stochastic counterpart, as it accurately estimates the lateral diffusivity across the pore while systematically underestimating the normal diffusivity close to hard boundaries. We introduce a conceptually simple and numerically efficient correction scheme based on simulated annealing and diffusion maps to resolve the latter artifact and obtain normal diffusivity profiles that are consistent with the self-part of the van Hove correlation functions. Our findings demonstrate the potential of this MD-adapted estimator in accurately characterizing spatial variations of diffusivity in confined materials.

Weyl Fermions and broken symmetry phases of laterally confined 3He films

Broken symmetries in topological condensed matter systems have implications for the spectrum of Fermionic excitations confined on surfaces or topological defects. The Fermionic spectrum of confined (quasi-2D) 3He-A consists of branches of chiral edge states. The negative energy states are related to the ground-state angular momentum, , for Cooper pairs. The power law suppression of the angular momentum, for , in the fully gapped 2D chiral A-phase reflects the thermal excitation of the chiral edge Fermions. We discuss the effects of wave function overlap, and hybridization between edge states confined near opposing edge boundaries on the edge currents, ground-state angular momentum and ground-state order parameter of superfluid 3He thin films. Under strong lateral confinement, the chiral A phase undergoes a sequence of phase transitions, first to a pair density wave (PDW) phase with broken translational symmetry at . The PDW phase is described by a periodic array of chiral domains with alternating chirality, separated by domain walls. The period of PDW phase diverges as the confinement length . The PDW phase breaks time-reversal symmetry, translation invariance, but is invariant under the combination of time-reversal and translation by a one-half period of the PDW. The mass current distribution of the PDW phase reflects this combined symmetry, and originates from the spectra of edge Fermions and the chiral branches bound to the domain walls. Under sufficiently strong confinement a second-order transition occurs to the non-chiral ‘polar phase’ at , in which a single p-wave orbital state of Cooper pairs is aligned along the channel.

Exciton Superposition across Moiré States in a Semiconducting Moiré Superlattice

Moiré superlattices of semiconducting transition metal dichalcogenides enable unprecedented spatial control of electron wavefunctions, leading to emerging quantum states. The breaking of translational symmetry further introduces a new degree of freedom: high symmetry moiré sites of energy minima behaving as spatially separated quantum dots. We demonstrate the superposition between two moiré sites by constructing a trilayer WSe2/monolayer WS2 moiré heterojunction. The two moiré sites in the first layer WSe2 interfacing WS2 allow the formation of two different interlayer excitons, with the hole residing in either moiré site of the first layer WSe2 and the electron in the third layer WSe2. An electric field can drive the hybridization of either of the interlayer excitons with the intralayer excitons in the third WSe2 layer, realizing the continuous tuning of interlayer exciton hopping between two moiré sites and a superposition of the two interlayer excitons, distinctively different from the natural trilayer WSe2.

A Lie-algebra-based description of disclination densities and the quantification of partial disclinations in deformed polycrystalline metals

Crystalline defects (e.g., dislocations, disclinations and grain boundaries) play a critical role in determining the mechanical and functional properties of metallic materials. From a physical point of view, dislocations and disclinations are the two fundamental types of topological defects in crystals, which originate from the breaking of translational symmetry and rotational symmetry, respectively. In spite of extensive studies on dislocations in the literature, the effects of disclinations on mechanical properties of metals have not been well recognized, partially due to the lack of an appropriate description for the rotational nature of disclinations. Here we suggest a Lie-algebra-based method to quantify the rotational properties of disclinations, which leads to a convenient way to determine disclination density distribution directly from Electron Backscatter Diffraction data. Through quasi-in-situ Electron Backscatter Diffraction characterizations, three major formation mechanisms of disclinations have been identified in deformed polycrystalline Mg alloys, i.e., dislocation-grain boundary interaction, dislocation redistribution and twin-twin reaction, all of which can be treated as topological reactions among various types of defects under a general framework. Our work not only suggests a new mathematical tool to investigate the interactions and reactions among multiple types of crystalline defects, but also provides a new insight to understand the deformation behaviors of metals and alloys based on dislocation/disclination theory.

Time Translation Symmetry Breaking in an Isolated Spin-Orbit-Coupled Fluid of Light.

We study the interplay between intrinsic spin-orbit coupling and nonlinear photon-photon interactions in a nonparaxial, elliptically polarized fluid of light propagating in a bulk Kerr medium. We find that in situations where the nonlinear interactions induce birefringence, i.e., a polarization-dependent nonlinear refractive index, their interplay with spin-orbit coupling results in an interference between the two polarization components of the fluid traveling at different wave vectors, which entails the breaking of translation symmetry along the propagation direction. This phenomenon leads to a Floquet band structure in the Bogoliubov spectrum of the fluid, and to characteristic oscillations of its intensity correlations. We characterize these oscillations in detail and point out their exponential growth at large propagation distances, revealing the presence of parametric resonances.

Phases of the hard-plate lattice gas on a three-dimensional cubic lattice.

We study the phase diagram of a lattice gas of 2×2×1 hard plates on the three-dimensional cubic lattice. Each plate covers an elementary plaquette of the cubic lattice, with the constraint that a site can belong to utmost one plate. We focus on the isotropic system, with equal fugacities for the three orientations of plates. We show, using grand canonical Monte Carlo simulations, that the system undergoes two phase transitions when the density of plates is increased: the first from a disordered fluid phase to a layered phase, and the second from the layered phase to a sublattice-ordered phase. In the layered phase, the system breaks up into disjoint slabs of thickness two along one spontaneously chosen Cartesian direction, corresponding to a twofold (Z_{2}) symmetry breaking of translation symmetry along the layering direction. Plates with normals perpendicular to this layering direction are preferentially contained entirely within these slabs, while plates straddling two adjacent slabs have a lower density, thus breaking the symmetry between the three types of plates. We show that the slabs exhibit two-dimensional power-law columnar order even in the presence of a nonzero density of vacancies. In contrast, interslab correlations of the two-dimensional columnar order parameter decay exponentially with the separation between the slabs. In the sublattice-ordered phase, there is twofold symmetry breaking of lattice translation symmetry along all three Cartesian directions. We present numerical evidence that the disordered to layered transition is continuous and consistent with universality class of the three-dimensional O(3) model with cubic anisotropy, while the layered to sublattice transition is first-order in nature.

Spontaneous layering and power-law order in the three-dimensional fully packed hard-plate lattice gas.

We obtain the phase diagram of fully packed hard plates on the cubic lattice. Each plate covers an elementary plaquette of the cubic lattice and occupies its four vertices, with each vertex of the cubic lattice occupied by exactly one such plate. We consider the general case with fugacities s_{μ} for "μ plates," whose normal is the μ direction (μ=x,y,z). At and close to the isotropic point, we find, consistent with previous work, a phase with long-range sublattice order. When two of the fugacities s_{μ_{1}} and s_{μ_{2}} are comparable, and the third fugacity s_{μ_{3}} is much smaller, we find a spontaneously layered phase. In this phase, the system breaks up into disjoint slabs of width two stacked along the μ_{3} axis. μ_{1} and μ_{2} plates are preferentially contained entirely within these slabs, while plates straddling two successive slabs have a lower density. This corresponds to a twofold breaking of translation symmetry along the μ_{3} axis. In the opposite limit, with μ_{3}≫μ_{1}∼μ_{2}, we find a phase with long-range columnar order, corresponding to simultaneous twofold symmetry breaking of lattice translation symmetry in directions μ_{1} and μ_{2}. The spontaneously layered phases display critical behavior, with power-law decay of correlations in the μ_{1} and μ_{2} directions when the slabs are stacked in the μ_{3} direction, and represent examples of "floating phases" discussed earlier in the context of coupled Luttinger liquids and quasi-two-dimensional classical systems. We ascribe this remarkable behavior to the constrained motion of defects in this phase, and we sketch a coarse-grained effective field theoretical understanding of the stability of power-law order in this unusual three-dimensional floating phase.

Topological and quantum critical properties of the interacting Majorana chain model

We study Majorana chain with the shortest possible interaction term and in the presence of hopping alternation. When formulated in terms of spins the model corresponds to the transverse field Ising model with nearest-neighbor transverse and next-nearest-neighbor longitudinal repulsion. The phase diagram obtained with extensive DMRG simulations is very rich and contains six phases. Four gapped phases include paramagnetic, period-2 with broken translation symmetry, \mathbb{Z}_2ℤ2 with broken parity symmetry and the period-2-\mathbb{Z}_2ℤ2 phase with both symmetries broken. In addition there are two floating phases: gapless and critical Luttinger liquid with incommensurate correlations, and with an additional spontaneously broken \mathbb{Z}_2ℤ2 symmetry in one of them. By analyzing an extended phase diagram we demonstrate that, in contrast with a common belief, the Luttinger liquid phase along the self-dual critical line terminates at a weaker interaction strength than the end point of the Ising critical line that we find to be in the tri-critical Ising universality class. We also show that none of these two points is a Lifshitz point terminating the incommensurability. In addition, we analyzed topological properties through Majorana zero modes emergent in the two topological phases, with and without incommensurability. In the weak interaction regime, a self-consistent mean-field treatment provides a remarkable accuracy for the description of the spectral pairing and the parity switches induced by the interaction.

Discrete time translation symmetry breaking in a Josephson junction laser

A Josephson junction laser is realized when a microwave cavity is driven by a voltage-biased Josephson junction. Through the ac Josephson effect, a dc voltage generates a periodic drive that acts on the cavity and generates interactions between its modes. A sufficiently strong drive enables processes that downconvert a drive resonant with a high harmonic into photons at the cavity fundamental frequency, breaking the discrete time translation symmetry set by the Josephson frequency. Using a classical model, we determine when and how this transition occurs as a function of the bias voltage and the number of cavity modes. We find that certain combinations of mode number and voltage tend to facilitate the transition which emerges via an instability within a subset of the modes. Despite the complexity of the system, there are cases in which the critical drive strength can be obtained analytically.