Time Inversion Symmetry Research Articles

3D 3,44T19 Type Carbon Allotrope (3,44T19‐CA): An Ideal Candidate with Phononic Stiefel–Whitney Topology and Multi–Dimensional Boundary Vibrational Modes

The Stiefel–Whitney (SW) insulator, which lacks spin‐orbit coupling and has space–time inversion () symmetry, has attracted significant interest due to its fragile topological state and unconventional bulk‐boundary correspondence. Previously, the identification of SW insulators has been widely proposed for 2D phononic systems, but it has received little attention for 3D phononic systems. Herein, it is recognized that the 3D 3,44T19 type carbon allotrope (3,44T19‐CA) possesses the possibility to attain the nontrivial phononic SW topology characterized by a nontrivial second SW number, specifically w2 = 1. In addition, the 3D 3,44T19‐CA has 2D surface vibrational modes and 1D hinge vibrational modes, providing an excellent platform for multi–dimensional topological phononic boundaries research.

Appearance of topological phase in YAs semimetal under hydrostatic pressure and epitaxial strain

By means of hybrid density functional theory, we present the evolution of the topological phase in rare earth monopnictide YAs with hydrostatic pressure and epitaxial strain. This material exists in NaCl-type structure at ambient conditions and shows structural phase transition into CsCl-type structure at 56.54 GPa hydrostatic pressure. The epitaxial strain reduces the structure into a compressed tetragonal-type. The thermodynamical and dynamical stability of the material is established with the calculation of enthalpy and phonon band structure within structural phase transition, respectively. The topologically trivial phase of the material is observed at ambient pressure in agreement with previous reports. This material shows topological phase transition at 24.8 GPa applied hydrostatic pressure and 10% epitaxial strain. The band inversion at the X-point between d-Y and p-As orbitals is verified with the help of the product of parity analysis of all the filled bands. The presence of the Dirac cone in the (001) plane and the existence of topologically non-trivial states at M‾-point in the Fermi arc contour also established our claim. The Z2 indices are calculated with the help of the product of parities and a change in Z2 indices from (0; 000) to (1; 000) is also verified with the evolution of Wannier change centers under the conditions of applied hydrostatic pressure and epitaxial strain. The time reversal and inversion symmetries are preserved throughout the study and the topological phase transition at 24.8 GPa is much lower than the structural phase transition pressure i.e., 56.54 GPa.

Inverse design of topological photonic time crystals via deep learning

Photonic time crystals are a new kind of photonic system in modern optical physics, leading to devices with new properties in time. However, so far, it is still a challenge to design photonic time crystals with specific topological states due to the complex relations between time crystal structures and topological properties. Here, we propose a deep-learning-based approach to address this challenge. In a photonic time crystal with time inversion symmetry, each band separated by momentum gaps can have a non-zero quantized Berry phase. We show that the neural network can learn the relationship between time crystal structures and Berry phases, and then determine the crystal structures of photonic time crystals based on given Berry phase properties. Our work shows a new way of applying machine learning to the inverse design of time-varying optical systems and has potential extensions to other fields, such as time-varying phononic devices.

2D MnTiX2 (X = F/Cl/Br) monolayers: Robust valley-polarized quantum anomalous Hall insulators with high transition temperatures and wide bandgaps

The valley-polarized quantum anomalous Hall (VP-QAH) materials, which combine valley polarization and the quantum anomalous Hall (QAH) effect, are of both fundamental and technological importance due to their potential applications for nanoscale devices. Here, we explored the stability, magnetic, and topological properties of two-dimensional MnTiX2 (X = F/Cl/Br) monolayers based on first-principles calculations. Our results show that all the structures have robust antiferromagnetic orders with large magnetic anisotropic energies and high transition temperatures (480–670 K). In the absence of spin–orbital coupling (SOC), the MnTiX2 monolayers represent antiferromagnetic quadratic crossing semimetals. In the presence of SOC, the quadratic crossing points of the systems are opened with sizable bandgaps (> 0.5 eV), and they are transformed to be QAH insulators with |C| = 1. Moreover, the MnTiF2 monolayer is found to be a spontaneous VP-QAH semiconductor due to the time reversal symmetry and inversion symmetry being broken. These insights provide an ideal platform for achieving VP-QAH materials for dissipationless transport and quantum computing.

Josephson diode effect in junctions of superconductors with band asymmetric metals

At interfaces connecting two superconductors (SCs) separated by a metallic layer, an electric current is induced when there is a disparity in the phases of the two superconductors. We elucidate this phenomenon based on the weights of the Andreev bound states associated with the states carrying currents in forward and reverse directions. Typically, current phase relation (CPR) in Josephson junctions is an odd function. When time reversal and inversion symmetries are broken at the junction, CPR ceases to be an odd function and the system may exhibit Josephson diode effect. This phenomenon has been studied in spin orbit coupled systems under an external Zeeman field wherein the magnetochiral anisotropy is responsible for the Josephson diode effect. Recently introduced the band asymmetric metal (BAM) model presents a novel avenue, featuring an asymmetric band structure. We investigate DC Josephson effect in SC-BAM-SC junctions and find that band asymmetry can lead to Josephson diode effect and anomalous Josephson effect. We explain the mechanism behind these effects based on interference of plane wave modes within the Bogoliubov de-Genne formalism. We calculate diode effect coefficient for different values of the parameters.

The type-I, III nodal ring, type-I, III quadratic nodal point, and Dirac valley phonons in 2D kagome lattices M2C3 (M = As, Bi, Cd, Hg, P, Sb, Zn)

Topological phases in kagome systems have garnered considerable interest since the introduction of the colloidal kagome lattice. Our study employs first-principle calculations and symmetry analysis to predict the existence of ideal type-I, III nodal rings (NRs), type-I, III quadratic nodal points (QNPs), and Dirac valley phonons (DVPs) in a collection of two-dimensional (2D) kagome lattices M2C3 (M = As, Bi, Cd, Hg, P, Sb, Zn). Specifically, the Dirac valley points (DVPs) can be observed at two inequivalent valleys with Berry phases of +π and −π , connected by edge arcs along the zigzag and armchair directions. Additionally, the QNP is pinned at the Γ point, and two edge states emerge from its projections. Notably, these kagome lattices also exhibit ideal type-I and III nodal rings protected by time inversion and spatial inversion symmetries. Our work examines the various categories of nodal points and nodal ring phonons within the 2D kagome systems and presents a selection of ideal candidates for investigating topological phonons in bosonic systems.

Semimetallic state transition in Two-Dimensional carbon nitride covalent networks and enhanced electrocatalytic activity for nitrate to ammonia conversion

Single-atom catalysts (SACs), due to their maximum atomic utilization rate, show tremendous potential for application in the electrocatalytic synthesis of ammonia from nitrate. Yet, the development of superior supports that preserve the high selectivity, activity, and stability of SACs remains an imperative challenge. In this work, based on first-principles calculations and tight-binding (TB) model analysis, a new two-dimensional (2D) carbon nitride monolayer, C7N6, is proposed. The C7N6 structure exhibits a strong covalent network, with dynamical, thermal, and mechanical stability. Surprisingly, the structural transition from C9N4 to C7N6 corresponds to a semimetallic state transition. Further symmetry analysis unveils that the Dirac states in C7N6 are protected by space–time inversion symmetry, and the physical origin of the Dirac cone was confirmed using the TB model. Additionally, a non-zero Z2 invariant and significant topological edge states demonstrate its topologically nontrivial nature. Considering the excellent structural and topological properties of C7N6, a three-step screening strategy is designed to identify eligible SACs for electrochemical nitrate reduction reaction (NO3RR), and Ti@C7N6 is identified as possessing the best activity, with the last proton-electron coupling step *NH2→*NH3 being the potential-determining step (PDS), for which the limiting potential is 0.48 V. Moreover, a free energy diagram shows that the *NOH reaction pathway is energetically preferred on Ti@C7N6, and ab initio molecular dynamics (AIMD) calculations at 500 K confirm its good thermal stability. Our study not only provides excellent CN-based support material but also offers theoretical guidance for constructing highly active and selective SACs for nitrate reduction.

Toroidic phase transitions in a direct-kagome artificial spin ice.

Ferrotoroidicity-the fourth form of primary ferroic order-breaks both space and time-inversion symmetry. So far, direct observation of ferrotoroidicity in natural materials remains elusive, which impedes the exploration of ferrotoroidic phase transitions. Here we overcome the limitations of natural materials using an artificial nanomagnet system that can be characterized at the constituent level and at different effective temperatures. We design a nanomagnet array as to realize a direct-kagome spin ice. This artificial spin ice exhibits robust toroidal moments and a quasi-degenerate ground state with two distinct low-temperature toroidal phases: ferrotoroidicity and paratoroidicity. Using magnetic force microscopy and Monte Carlo simulation, we demonstrate a phase transition between ferrotoroidicity and paratoroidicity, along with a cross-over to a non-toroidal paramagnetic phase. Our quasi-degenerate artificial spin ice in a direct-kagome structure provides a model system for the investigation of magnetic states and phase transitions that are inaccessible in natural materials.

Thin film Weyl semimetals with turning number of Fermi surface greater than unity

The development of Weyl semimetals (WSMs) as a new type of quantum material for a variety of novel phenomena is underway. In this context WSM with broken time reversal symmetry and inversion symmetry confined to a thin film which exhibits topologically distinct Fermi surface in the low energy regime is presented. The equi-energy contours possess a topological invariant called turning number ν. We extend the numerical investigation of the magnetotransport in the WSM to include systems with the turning number of Fermi surface greater than unity, ν=2, which is due to the self intersection of equi-energy contours. This results in exotic Weyl orbits which are a hybrid of bulk and surface states and are crucial for magnetotransport. This is in contrast to the conventional electron gas in which orbits are closed curves without self intersection. The contour of Weyl orbits in real space is connected to the shape of Fermi surface. In the presence of a perpendicular magnetic field on a slab geometry, the probability density of edge states are wide and narrow on each edge rather than symmetric on both edges (the hall mark of conventional quantum Hall effect). We explore the effect of disorder on these asymmetric edge states and find that the conductance remains quantized at 2e2/h up to a critical disorder strength. Our findings show that the transport characteristics of WSM are more robust to disorder in a particular direction for these systems with higher turning number. These systems also show unusual conductance by a slanted magnetic field as the slant can modify the Landau levels at the Fermi level.

Rol' vakansiy v spin-zhidkostnoy modeli Yao–Li

We consider the effect of vacancies on the low-energy excitation spectrum of a quantum spin liquid realized in the exactly solvable Yao–Lee model [H. Yao and D.-H. Lee, Phys. Rev. Lett. 107, 087205 (2011)]. Physically, vacancies can appear for different reasons (e.g., because of zero magnetic moments on the lattice, or the presence of nonmagnetic impurities, or a random reduction of local bonds of magnetic moments with the remaining lattice). It is shown numerically that the finite density of random vacancies in this model leads to the accumulation of states near zero energy, which can be detected from the change of the behavior of heat capacity at low temperatures. Moreover, it is shown that the low-energy modes are localized more strongly than remaining eigenmodes. This effect is illustrated using the inverse participation ratio (IPR). In the case of time reversal symmetry breaking (e.g., due to the presence of a magnetic field), a gap is opened in the fermion spectrum of the model, and vacancy-induced localized states appear. The energies of these states depend on the structure of the interactions responsible for the time inversion symmetry breaking.

Synthetic complex Weyl superconductors, chiral Josephson effect and synthetic half-vortices

We show that the most generic form of spin-singlet superconducting order parameter for chiral fermions in systems with broken time reversal symmetry and inversion symmetry is of the Delta _s+igamma ^5Delta _5 where Delta _s is the usual order parameter and Delta _5 is the pseudo-scalar order parameter. After factoring out the U(1) phase e^{iphi }, this form of superconductivity admits yet additional complex structure in the plane of (Delta _s,Delta _5). The polar angle chi in this plane, which we call the chiral angle, can be controlled by the external flux bias. We present a synthetic setup based on stacking of topological insulators (TIs) and superconductors (SCs). Alternatively flux biasing the superconductors with a fluxes pm Phi leads to Delta _5=Delta _0 sin (chi ), where Delta _0 is the superconducting order parameter of the SC layers, and the chiral angle chi ={2pi }Phi /Phi _0 is directly given by the flux Phi in units of the flux quantum Phi _0=h/(2e). This can be used as a building block to construct a two-dimensional Josephson array. In this setup chi will be a background field defining a pseudoscalar Delta _5 that can be tuned to desired configuration. While in a uniform background field Delta _5 the dynamics of phi is given by standard XY model and its associated vortices, a staggered background pm Delta _5 (or equivalently chi and chi +pi in alternating lattice sites) creates a new set of minima for the phi field that will support half-vortex excitations. An isolated single engineered “half-vortex” in the chi field in an otherwise uniform background will bind a phi -half-vortex. This is similar to the way a p-wave superconducting vortex core binds a Majorana fermion.

Spontaneous superconducting diode effect in non-magnetic Nb/Ru/Sr2RuO4 topological junctions

Non-reciprocal electronic transport in a material occurs if both time reversal and inversion symmetries are broken. The superconducting diode effect (SDE) is an exotic manifestation of this type of behavior where the critical current for positive and negative currents are mismatched, as recently observed in some non-centrosymmetric superconductors with a magnetic field. Here, we demonstrate a SDE in non-magnetic Nb/Ru/Sr2RuO4 Josephson junctions without applying an external magnetic field. The cooling history dependence of the SDE suggests that time-reversal symmetry is intrinsically broken by the superconducting phase of Sr2RuO4. Applied magnetic fields modify the SDE dynamically by randomly changing the sign of the non-reciprocity. We propose a model for such a topological junction with a conventional superconductor surrounded by a chiral superconductor with broken time reversal symmetry.

Sign reversal of the Josephson inductance magnetochiral anisotropy and 0-π-like transitions in supercurrent diodes.

The recent discovery of the intrinsic supercurrent diode effect, and its prompt observation in a rich variety of systems, has shown that non-reciprocal supercurrents naturally emerge when both space-inversion and time-inversion symmetries are broken. In Josephson junctions, non-reciprocal supercurrent can be conveniently described in terms of spin-split Andreev states. Here we demonstrate a sign reversal of the Josephson inductance magnetochiral anisotropy, a manifestation of the supercurrent diode effect. The asymmetry of the Josephson inductance as a function of the supercurrent allows us to probe the current-phase relation near equilibrium, and to probe jumps in the junction ground state. Using a minimal theoretical model, we can then link the sign reversal of the inductance magnetochiral anisotropy to the so-called 0-π-like transition, a predicted but still elusive feature of multichannel junctions. Our results demonstrate the potential of inductance measurements as sensitive probes of the fundamental properties of unconventional Josephson junctions.

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.

Nonequilibrium Josephson diode effect in periodically driven SNS junctions

In typical Josephson junctions, the Josephson current is an odd function of the superconducting phase difference. Recently, diode effect in Josephson junctions is observed in experiments wherein the maximum and the minimum values of the Josephson current in the current-phase relation do not have the same magnitude. We propose a superconductor-normal metal-superconductor (SNS) junction where Josephson diode effect manifests when the normal metal region is driven. Time reversal symmetry and inversion symmetry need to be broken in the SNS junction for the diode effect to show up. We calculate long time averaged current and show that the system exhibits diode effect for two configurations of the driven SNS junction - one in which inversion symmetry is broken in the undriven part of the Hamiltonian and the other wherein both the symmetries are broken by the driving potential. In the latter configuration, a nonzero current known as anomalous current appears at the junction in absence of phase bias. In the proposed setup, the diode effect vanishes in the adiabatic limit.

Anomalous Josephson effect between d-wave superconductors through a two-dimensional electron gas with both Rashba spin–orbit coupling and Zeeman splitting

Based on the Bogoliubov–de Gennes equation and the extended McMillan’s Green’s function formalism, we study theoretically the Josephson effect between two d-wave superconductors bridged by a ballistic two-dimensional electron gas with both Rashba spin–orbit coupling and Zeeman splitting. We show that due to the interplay of Rashba spin–orbit coupling and Zeeman splitting and d-wave pairing, the current–phase relation in such a heterostructure may exhibit a series of novel features and can change significantly as some relevant parameters are tuned. In particular, anomalous Josephson current may occur at zero phase bias under various different situations if both time reversal symmetry and inversion symmetry of the system are simultaneously broken, which can be realized by tuning some relevant parameters of the system, including the relative orientations and the strengths of the Zeeman field and the spin–orbit field in the bridge region, the relative orientations of the a axes in two superconductor leads, or the relative orientations between the Zeeman field in the bridge region and the a axes in the superconductor leads. We show that both the magnitude and the direction of the anomalous Josephson current may depend sensitively on these relevant parameters.

Non-Magnetic Circulator Based on a Time-Varying Phase Modulator

Non-reciprocal devices are key elements in modern wireless communication systems. The circulator devices can simultaneously save spectrum resources and antennas. A traditional circulator is made of ferrite materials with an external magnetic bias field, and its bulk and incompatibility with CMOS technology can hardly satisfy the miniaturization and integration of modern high-speed communication systems. In recent years, there have been many outstanding achievements in the study of non-magnetic circulators, among which, the method of producing non-reciprocity by temporal modulation is considered the most likely to have a transformative influence on the industry. By varying one of the parameters of the system with time, the time inversion symmetry of the system can be broken so that the non-reciprocal devices can be formed by applying appropriate topological structures without the use of magnetic materials. In the paper, a new concept of a time-varying phase modulator (TVPM) is proposed to achieve a relatively simple method to break the symmetry of time inversion. Two different time-varying phase modulators and buffering units can be integrated to form a gyrator, with which a circulator can be formed. This paper provides a relatively simple design idea and shows the circuit design and implementation method as well as the numerical analysis and simulation results. The simulation results show that the insertion loss of the circulator at the center frequency is −1.7 dB and the isolation is −18 dB. The proposed non-magnetic circulator shows potential applicability in related 5G and pre-6G systems.

Magnetoelectric‐Field Electrodynamics: Search for Magnetoelectric Point Scatterers

AbstractResonant scattering of electromagnetic (EM) waves by small particles is considered as one of the basic problems in metamaterial science. At present, special subwavelength resonators are considered as structural elements in chiral and bianisotropic metamaterials. There is a general consensus that these small scatterers behave like “artificial atoms” with strong electrical and magnetic responses and an interconnection between these responses. However, the observed effect of magnetoelectric (ME) coupling in these meta‐atoms is not associated with the near‐field manipulation properties caused by intrinsic magnetoelectricity. This arises the question whether ME point scatterers of EM radiation really exist. In this paper, we show that there are mesoscopic structures with electric and magnetic dipole‐carrying excitations that behave like point scatterers with their inherent magnetoelectricity. In such subwavelength resonators, coherent oscillations of the electric polarization and magnetization can be considered as quasistatic oscillations described by electrostatic (ES) and magnetostatic (MS) scalar wave functions. The ME resonance effect arises from the coupling of two, ES and MS, oscillations. The near fields of these resonators, called the ME near fields, are characterized by simultaneous violation of time reversal and inversion symmetry. In study of ME fields and EM problems associated with these fields, we put forward the concept of ME‐field electrodynamics.

Lifshitz transitions and hybrid Weyl points in RbAg5Se3

We explore the topological phase transitions of RbAg5Se3 using first-principles calculations in combination with the maximally localized Wannier function method. Our computations reveal that the type-II Dirac cone in RbAg5Se3 protected by the inversion and time-inversion (PT) symmetry in addition to the C4z rotation symmetry can be regulated to type-III and type-I Dirac points by applying strain along the [001] direction. More interestingly, when the inversion symmetry is lifted by intercalating a Pt atom into the unit cell, sixteen hybrid Weyl points emerge accompanied by the Fermi arcs connecting the adjacent Brillouin zones and surface states on the (010) surface. The type-II Weyl point has the chirality of 1, while the type-I Weyl point has the chirality of −1. Our work suggests that RbAg5Se3 serves as a promising platform for study of topological phases transitions with curious transport phenomena.

Ferromagnetism and valley polarization in Janus single-layer VSCl

Two-dimensional ferromagnetic semiconductors have received extensive attention due to their promising application for valleytronics along with the opportunity to realize spontaneous valley polarization. Herein, by means of the first-principles calculations, we design a two-dimensional ferromagnetic semiconductor single-layer VSCl with the direct band gap is 0.88 eV, and magnetic moment is 2 μB per unit. The Curie temperature of single-layer VSCl is estimated to be 125 K based on the mean field approximation. In addition, the ferromagnetism can be further improved by adopting moderate tensile strain. Importantly, the intrinsic breaking of time and spatial inversion symmetry leads to the spontaneous valley polarization in single-layer VSCl. The corresponding valley polarization energy is about 57.8 meV, which is sizeable enough for practical operations. Our findings provide a candidate material for realizing the potential application of two-dimensional valleytronic devices.