Parity Breaking Research Articles

Electric field–induced magnetochiral dichroism in a ferroaxial crystal

In a chiral medium, any mirror symmetries are broken, which induces unique physical properties represented by natural optical rotation. When electromagnetic waves propagate through a chiral medium placed in a magnetic field, the refractive index, or equivalently, the absorption encountered by the electromagnetic waves differs depending on whether it travels parallel or antiparallel to the magnetic field. Such a phenomenon is known as magnetochiral dichroism (MChD), which is the characteristic interplay between chirality and magnetism. Similar to chirality, the so-called ferroaxial order, an emergent ferroic state of crystalline materials, is also characterized by mirror symmetry breaking. In contrast to chiral materials, however, the mirror symmetry perpendicular to the crystalline principal axis is allowed in ferroaxial materials. In other words, chirality and thus phenomena unique to chirality can be induced by breaking the remaining mirror symmetry by applying an electric field. Here, we show electric control of chirality and resulting electric field-induced MChD (E-MChD) of the short-wavelength infrared region in a ferroaxial crystal, NiTiO3. We performed spectroscopy measurements of E-MChD by taking a difference of absorption coefficients obtained with and without electric and magnetic fields. As a result, E-MChD was observed around the excitation energy corresponding to Ni2+ d-d magnetic-dipole transitions. The result is nicely explained by adopting the theory of MChD concerning the pseudo-Stark splitting of the energy state. Ferroaxial materials therefore provide platforms to achieve electric control of chirality-related phenomena.

Linear stability analysis of chemical mechanism, Listanalchem: A tool for the search of spontaneous mirror symmetry breaking

Homochirality, the phenomenon by which one of two virtually identical (non-superimposable mirror images) compounds is favored over the other in the chemistry of life, has been regarded as a requisite for the emergence of all living things on earth. Spontaneous mirror symmetry breaking has been proposed to produce the imbalance. Under this framework, Frank presented, in his foundational article “On spontaneous asymmetric synthesis”, a simple chemical reaction network that displays spontaneous symmetry breaking for a specific set of reaction rates. Research has since focused on finding more complex and plausible models, each one with its advantages and disadvantages. Nevertheless, finding reaction rate values that make a model exhibit spontaneous symmetry breaking is a complex task, even for specially crafted models. LInear STability ANALysis of CHEmical Mechanism, Listanalchem, is a method and software for the search for appropriate reaction rates. It includes four different algorithms inspired by the analysis of Frank's network. Two classical algorithms are also included in Listanalchem: the Trace-Determinant plane and the Stoichiometric Network Analysis by Bruce Clarke. Listanalchem reads a chemical reaction network from plain text and runs one or more of the available algorithms according to the user selection. Listanalchem is tested and verified by studying classical, modified, and recent models proposed to explain the origin of biological homochirality.•Listanalchem allows a fast and reliable search for instability behavior in chemical mechanisms that pretend to explain spontaneous mirror symmetry breaking.•Listanalchem contains several model examples, including the most cited in the related literature.•Listanalchem is a tool that tests models that pretend to explain the origin of biological homochirality, helps find errors, and aids in designing new models.

Formation of 2D GaXY (X = S, Se; Y = F, Cl, Br, I) with enhanced piezoelectricity via decomposition of Ga-monochalcogenide by halogenation

Motivated by the excellent electronic and optoelectronic properties of two-dimensional (2D) Ga-monochalcogenides, we systematically investigated the effect of halogenation on physical properties of monolayer GaX (X = S, Se) by the first-principles calculations. Crystal lattices of GaX were decomposed with the halogen atom being absorbed on top of the Ga atom. Unexpectedly, a series of monolayer GaXY (X = S, Se; Y = F, Cl, Br, I) was formed. Except for GaXF, other monolayer GaXY has good structural stability at room temperature. With the broken mirror symmetry, monolayer GaXY has superior flexibility, a direct bandgap in the range of 0.78–4.43 eV, the intrinsic vertical polarization, and larger in-plane as well as out-of-plane piezoelectric coefficients than Ga-monochalcogenides. Moreover, by comparing the structural stability and side-dependent electronic band alignment, we concluded that monolayer GaXY (X = S, Se; Y = Cl, Br) is suitable for photocatalytic water-splitting applications.

Lift force in odd compressible fluids.

When a body moves through a fluid, it can experience a force orthogonal to its movement called lift force. Odd viscous fluids break parity and time-reversal symmetry, suggesting the existence of an odd lift force on tracer particles, even at vanishing Reynolds numbers and for symmetric geometries. It was previously found that an incompressible odd fluid cannot induce lift force on a tracer particle with no-slip boundary conditions, making signatures of odd viscosity in the two-dimensional bulk elusive. By computing the response matrix for a tracer particle, we show that an odd compressible fluid can produce an odd lift force. Using shell localization, we provide analytic expressions for the drag and odd lift forces acting on the tracer particle in a steady state and also at finite frequency. Importantly, we find that the existence of an odd lift force in a steady state requires taking into account the nonconservation of the fluid mass density due to the coupling between the two-dimensional surface and the three-dimensional bulk fluid.

A Complex Reaction Network Model for Spontaneous Mirror Symmetry Breaking in Viedma Deracemizations.

Attrition-enhanced chiral symmetry breaking in crystals, known as Viedma deracemization, is a promising method for converting racemic solid phases into enantiomerically pure ones under non equilibrium conditions. However, many aspects of this process remain unclear. In this study, we present a new investigation into Viedma deracemization using a comprehensive kinetic rate equation continuous model based on classical primary nucleation theory, crystal growth, and Ostwald ripening. Our approach employs a fully micro-reversible kinetic scheme with a size-dependent solubility following the Gibbs-Thomson rule. To validate our model, we use data from a real NaClO3deracemization experiment. After parametrization, the model shows spontaneous mirror symmetry breaking (SMSB) under grinding. Additionally, we identify a bifurcation scenario with a lower and upper limit of the grinding intensity that leads to deracemization, including a minimum deracemization time within this window. Furthermore, this model uncovers that SMSB is caused by multiple instances of concealed high-order autocatalysis. Our findings provide new insights into attrition-enhanced deracemization and its potential applications in chiral molecule synthesis and understanding biological homochirality.

Many-Body Superradiance and Dynamical Mirror Symmetry Breaking in Waveguide QED.

The many-body decay of extended collections of two-level systems remains an open problem. Here, we investigate whether an array of emitters coupled to a one-dimensional bath undergoes Dicke superradiance. This is a process whereby a completely inverted system becomes correlated via dissipation, leading to the release of all the energy in the form of a rapid photon burst. We derive the minimal conditions for the burst to happen as a function of the number of emitters, the chirality of the waveguide, and the single-emitter optical depth, both for ordered and disordered ensembles. Many-body superradiance occurs because the initial fluctuation that triggers the emission is amplified throughout the decay process. In one-dimensional baths, this avalanchelike behavior leads to a spontaneous mirror symmetry breaking, with large shot-to-shot fluctuations in the number of photons emitted to the left and right. Superradiant bursts may thus be a smoking gun for the generation of correlated photon states of exotic quantum statistics.

Strain Anisotropy Driven Spontaneous Formation of Nanoscrolls from 2D Janus Layers

Abstract2D Janus transition metal dichalcogenides (TMDs) have attracted attention due to their emergent properties arising from broken mirror symmetry and self‐driven polarization fields. While it has been proposed that their vdW superlattices hold the key to achieving superior properties in piezoelectricity and photovoltaic, available synthesis has ultimately limited their realization. Here, the first packed vdW nanoscrolls made from Janus TMDs through a simple one‐drop solution technique are reported. The results, including ab initio simulations, show that the Bohr radius difference between the top sulfur and the bottom selenium atoms within Janus (M = Mo, W) results in a permanent compressive surface strain that acts as a nanoscroll formation catalyst after small liquid interaction. Unlike classical 2D layers, the surface strain in Janus TMDs can be engineered from compressive to tensile by placing larger Bohr radius atoms on top (to yield inverted C scrolls. Detailed microscopy studies offer the first insights into their morphology and readily formed Moiré lattices. In contrast, spectroscopy and FETs studies establish their excitonic and device properties and highlight significant differences compared to 2D flat Janus TMDs. These results introduce the first polar Janus TMD nanoscrolls and introduce inherent strain‐driven scrolling dynamics as a catalyst to create superlattices.

Conditions for the origin of homochirality in primordial catalytic reaction networks

We study the generation of homochirality in a general chemical model (based on the homogeneous, fully connected Smoluchowski aggregation-fragmentation model) that obeys thermodynamics and can be easily mapped onto known origin of life models (e.g. autocatalytic sets, hypercycles, etc.), with essential aspects of origin of life modeling taken into consideration. Using a combination of theoretical modeling and numerical simulations, we look for minimal conditions for which our general chemical model exhibits spontaneous mirror symmetry breaking. We show that our model spontaneously breaks mirror symmetry in various catalytic configurations that only involve a small number of catalyzed reactions and nothing else. Of particular importance is that mirror symmetry breaking occurs in our model without the need for single-step autocatalytis or mutual inhibition, which may be of relevance for prebiotic chemistry.

High Orbital‐Moment Cooper Pairs by Crystalline Symmetry Breaking

AbstractThe pairing structure of superconducting materials is regulated by the point group symmetries of the crystal. The spin‐singlet multiorbital superconductivity of materials with unusually low crystalline symmetry content can host even‐parity (s‐wave) Cooper pairs with high orbital moment. The lack of mirror and rotation symmetries makes pairing states with quintet orbital angular momentum symmetry‐allowed. A remarkable fingerprint of this type of pairing state is provided by a nontrivial superconducting phase texture in momentum space with π‐shifted domains and walls with anomalous phase winding. The pattern of the quintet pairing texture is shown to depend on the orientation of the orbital polarization and the strength of the mirror and/or rotation symmetry breaking terms. Such a momentum dependent phase makes Cooper pairs with net orbital component suited to design orbitronic Josephson effects. This study discusses how an intrinsic orbital dependent phase can set out anomalous Josephson couplings by employing superconducting leads with nonequivalent breaking of crystalline symmetry.

Electronic structure and topological phase transition in multi-orbital triangular lattice with rotation and mirror symmetry breaking

Triangular lattice is one of the most generic structures in the two-dimensional (2D) limit with numerous exotic properties, such as magnetic frustration and quantum spin liquid. Here, we investigate the electronic properties of a multi-orbital (p x , p y , p z ) triangular lattice while focusing on the role of rotation and mirror symmetry breaking in regulating the topological phase diagram. The tight-binding modeling reveals that rotation symmetry () breaking splits the Dirac point and preserves the nodal loop. A further inclusion of broken horizontal mirror symmetry () destroys the nodal loop. Consequently, with spin–orbit coupling (SOC), the (p x , p y , p z )-orbital triangular lattice is topologically non-trivial with only or symmetry breaking. With both symmetries breaking, it becomes trivial, except when the SOC is large enough to initiate band inversion. For real materials, we propose that the recently grown AgSe/AgTe monolayer in a binary honeycomb structure is an ideal system to realize the multi-orbital triangular lattice. The first-principles calculations demonstrate that free-standing AgSe and AgTe are Z 2 non-trivial. On the Ag(111) substrate, AgSe becomes trivial because of the breaking of both and symmetries, whereas AgTe remains non-trivial because of the strong SOC of Te. Our work not only provides physical insights into the experimentally synthesized 2D binary honeycomb structures but also highlights the manipulation of electronic and topological properties through symmetry/orbital physics, which are valuable for designing new quantum materials and devices.

Anomalous valley Hall effect induced by mirror symmetry breaking in transition metal dichalcogenides

The control of the valley degree of freedom in Bloch electrons has opened up new avenues for information processing. The synthesis of ferrovalley materials, however, has been limited due to the stringent requirements for breaking both time and space inversion symmetries. To address this challenge, we propose a Janus method for inducing valley polarization in nonmagnetic transition metal dichalcogenides. Our study shows that the magnetic moment in monolayer TiTeI arises from the breaking of mirror symmetry and the presence of unpaired electrons. The Stoner criterion ${I}_{ex}N({E}_{F})>1$ confirms that the band splitting originates from the $d$ orbital of titanium. Moreover, the exchange interaction combined with spin-orbit coupling opens up the valley splitting. The anomalous valley Hall effect (AVHE) can be realized by applying an in-plane electric field, as a result of the valley-contrasting Berry curvature. The modulation of valley-selective circular dichroism and AVHE by optical, electronic, and magnetic fields make TiTeI a promising material for future studies and applications in valleytronics.

Topological nodal lines in bulk and monolayer W2O3I4

By means of first-principles calculations, we study the topological nontrivial electronic structures and lattice dynamics of bulk and monolayer ${\mathrm{W}}_{2}{\mathrm{O}}_{3}{\mathrm{I}}_{4}$. We find that both of them are nodal-line semimetals in the absence of spin-orbit coupling (SOC), in which the nodal lines are induced by the band inversion between conduction and valence bands contributed by W $d$ and I p orbitals. Moreover, ${\mathrm{W}}_{2}{\mathrm{O}}_{3}{\mathrm{I}}_{4}$ bulk and monolayer exhibit excellent mechanical and thermal stability. By studying the external field modulation of topological nodal lines without SOC effect in monolayer ${\mathrm{W}}_{2}{\mathrm{O}}_{3}{\mathrm{I}}_{4}$, we find that the nodal lines are extremely robust against the biaxial strain but destroyed under vertical electric field due to the breaking of horizonal mirror symmetry. It is studied that the SOC effect here is large and non-negligible, and after considering the SOC effect, ${\mathrm{W}}_{2}{\mathrm{O}}_{3}{\mathrm{I}}_{4}$ bulk and monolayer undergo change of topological state from a topological nodal-line semimetal to a topological insulator. Our work not only extends the member of inorganic three-dimensional and two-dimensional topological semimetals library but also provides a prototype material candidate to investigate the double nodal-line surface states.

Hydrodynamics, spin currents and torsion

We construct the canonical constitutive relations for a fluid description of a system with a spin current, valid in an arbitrary number of dimensions in the absence of parity breaking or time reversal breaking terms. Our study encompasses the hydrostatic partition function, the entropy current, Kubo formula, conformal invariance, and the effect of charge. At some stages of the computation we turn on a background torsion tensor which naturally couples to the spin current.

Chiral gravitational waves in Palatini-Chern-Simons gravity

We study the parity-breaking higher-curvature gravity theory of Chern-Simons (CS), using the Palatini formulation in which the metric and connection are taken to be independent fields. We first show that Palatini-CS gravity leads to first-order derivative equations of motion and thus avoid the typical instabilities of CS gravity in the metric formalism. As an initial application, we analyze the cosmological propagation of gravitational waves (GWs) in Palatini-CS gravity. We show that, due to parity breaking, the polarizations of GWs suffer two effects during propagation: amplitude birefringence (which changes the polarization ellipticity) and velocity birefringence (which rotates the polarization plane). While amplitude birefringence is known to be present in CS gravity in the metric formalism, velocity birefringence is not present in metric CS gravity for high frequency waves, but now appears in Palatini-CS due to the fact that left-handed and right-handed GW polarizations have a different dispersion relation. In the approximation of small deviations from general relativity (GR), we do find however that velocity birefringence appears at least quadratically in the CS coupling parameter $\ensuremath{\alpha}$, while amplitude birefringence appears linearly in $\ensuremath{\alpha}$. This means that amplitude birefringence will be the most relevant effect in Palatini-CS and hence this model will behave similarly to metric CS. We confirm this by applying current constraints on amplitude and velocity birefringence to Palatini-CS, and showing that those from amplitude birefringence give the tightest bounds.

Hamiltonian structure of 2D fluid dynamics with broken parity

Isotropic fluids in two spatial dimensions can break parity symmetry and sustain transverse stresses which do not lead to dissipation. Corresponding transport coefficients include odd viscosity, odd torque, and odd pressure. We consider an isotropic Galilean invariant fluid dynamics in the adiabatic regime with momentum and particle density conservation. We find conditions on transport coefficients that correspond to dissipationless and separately to Hamiltonian fluid dynamics. The restriction on the transport coefficients will help identify what kind of hydrodynamics can be obtained by coarse-graining a microscopic Hamiltonian system. Interestingly, not all parity-breaking transport coefficients lead to energy conservation and, generally, the fluid dynamics is energy conserving but not Hamiltonian. We show how this dynamics can be realized by imposing a nonholonomic constraint on the Hamiltonian system.

Restoring the reciprocity invariance in nonlinear systems with broken mirror symmetry

Circumventing the reciprocity invariance has posed an interesting challenge in the design of modern devices for wave engineering. In passive devices, operating the device in the nonlinear response regime is a common means for realizing nonreciprocity. Because mirror-symmetric systems are trivially reciprocal, breaking the mirror symmetry is a necessary requirement for nonreciprocal dynamics to exist in nonlinear systems. However, the response of an asymmetric nonlinear system is not necessarily nonreciprocal. In this work, we report on the existence of stable, steady-state nonlinear reciprocal dynamics in coupled asymmetric systems subject to external harmonic excitation. We restore reciprocity in the asymmetric system by tuning two symmetry-breaking parameters simultaneously under certain operating conditions. Specifically, we identify response regimes in the vicinity of the primary resonances of the system where the steady-state left-to-right transmission characteristics are identical to the right-to-left characteristics in terms of frequency, amplitude and phase. We interpret these regimes of reciprocal dynamics in the context of phase nonreciprocity, wherein incident waves undergo a nonreciprocal phase shift depending on their direction of travel. We hope these findings help design devices with new functionalities for controlling and steering of elastic waves.

Plasmon–Exciton Strong Coupling Effects of the Chiral Hybrid Nanostructures Based on the Plexcitonic Born–Kuhn Model

A deep understanding of the optical properties of the chiral plexcitonic systems not only adds a new dimension to the exploration of the strong plasmon–exciton interaction but also provides a new method to design chiroptical devices. We develop a plexcitonic Born–Kuhn model to explore the strong coupling dynamics of the chiral hybrid nanostructures made of corner-stacked nanorod dimers and molecules from the chiroptical perspective. As a consequence of strong interaction between plasmons and excitons, double normal mode splittings/Rabi splittings and an anti-crossing phenomenon appear in circular dichroism (CD) spectroscopy. The character of dual plexciton (symmetric and anti-symmetric plexciton) and associated chiroptical properties have been demonstrated. The interplay between mirror symmetry breaking and plasmon–plasmon/plasmon–exciton interaction leads to an optimal configuration with the maximal chiroptical response. Moreover, chirality (of incident light) selective excitation of plexcitonic modes has been achieved by structural design. Finally, we verify our theory experimentally by synthesizing chiral plasmonic nanodimers and coating these structures with J-aggregate dye molecules.

Suppressing the sample-to-sample variation of photonic crystal nanocavity Q-factors by air-hole patterns with broken mirror symmetry.

It is known that the quality factors (Q) of photonic crystal nanocavities vary from sample to sample due to air-hole fabrication fluctuations. In other words, for the mass production of a cavity with a given design, we need to consider that the Q can vary significantly. So far, we have studied the sample-to-sample variation in Q for symmetric nanocavity designs, that is, nanocavity designs where the positions of the holes maintain mirror symmetry with respect to both symmetry axes of the nanocavity. Here we investigate the variation of Q for a nanocavity design in which the air-hole pattern has no mirror symmetry (a so-called asymmetric cavity design). First, an asymmetric cavity design with a Q of about 250,000 was developed by machine learning using neural networks, and then we fabricated fifty cavities with the same design. We also fabricated fifty symmetric cavities with a design Q of about 250,000 for comparison. The variation of the measured Q values of the asymmetric cavities was 39% smaller than that of the symmetric cavities. This result is consistent with simulations in which the air-hole positions and radii are randomly varied. Asymmetric nanocavity designs may be useful for mass production since the variation in Q is suppressed.

Odd Mobility of a Passive Tracer in a Chiral Active Fluid.

Chiral active fluids break both time-reversal and parity symmetry, leading to exotic transport phenomena unobservable in ordinary passive fluids. We develop a generalized Green-Kubo relation for the anomalous lift experienced by a passive tracer suspended in a two-dimensional chiral active fluid subjected to an applied force. This anomalous lift is characterized by a transport coefficient termed the odd mobility. We validate our generalized response theory using molecular dynamics simulations, and we show that the asymmetric tracer mobility may be understood mechanically in terms of asymmetric deformations of the tracer-fluid density distribution function. We show that the even and odd components of the mobility decay at different rates with tracer size, suggesting the possibility of size-based particle separation using a chiral active working fluid.

Intrinsic nonreciprocal bulk plasmons in noncentrosymmetric magnetic systems

Nonreciprocal plasmonics plays a crucial role in enabling one-way light propagation at the nanoscale and is a fundamental building block for photonic applications. Here, we investigate intrinsic nonreciprocity in bulk plasmon dispersion in systems that break both parity and time-reversal symmetry. We demonstrate that both interband and intraband bulk plasmon modes exhibit intrinsically asymmetric dispersion depending on the sign of the wave vector. Our study reveals that the intrinsic nonreciprocity in interband plasmon dispersion is governed by quantum metric connection. The nonreciprocity in the intraband plasmon dispersion is dictated by the quantum metric dipole and a higher-order ``Drude''-weight-like term. We corroborate our findings via explicit numerical calculations for the two-dimensional Qi-Wu-Zhang model, and we demonstrate the existence of intrinsic nonreciprocal intraband and interband plasmon modes in moir\'e systems such as twisted bilayer graphene. Our findings offer insights into the underlying physics of nonreciprocal plasmonics and pave the way for designing novel photonic devices.