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This paper presents two methods for topological analysis of the complex Hermitian Su–Schrieffer–Heeger (SSH) model using the quantum geometric tensor: Berry phase and topological data analysis. We demonstrate how both methods can effectively generate topological phase diagrams for the model, revealing two distinct regions based on the relative magnitudes of the parameters | v | and | w | . Specifically, when | v | > | w | , the system is found to be topologically trivial, whereas for | v | < | w | , it exhibits topologically non-trivial behavior. Our results contribute to building the groundwork for topological analysis of more complicated SSH-type models. [ABSTRACT FROM AUTHOR]

In chemistry and biochemistry, chirality represents the structural asymmetry characterized by nonsuperimposable mirror images for a material such as DNA. In physics, however, chirality commonly refers to the spin–momentum locking of a particle or quasiparticle in the momentum space. While seemingly disconnected, structural chirality in molecules and crystals can drive electronic chirality through orbital–momentum locking; that is, chirality can be transferred from the atomic geometry to electronic orbitals. Electronic chirality provides an insightful understanding of chirality-induced spin selectivity, in which electrons exhibit salient spin polarization after going through a chiral material, and electrical magnetochiral anisotropy, which is characterized by diode-like transport. It further gives rise to new phenomena, such as anomalous circularly polarized light emission, in which the light handedness relies on the emission direction. These chirality-driven effects will generate broad impacts for fundamental science and technology applications in spintronics, optoelectronics, and biochemistry. [ABSTRACT FROM AUTHOR]

In this work, we introduce a Berry phase model which is very important in physics relative to the frontals in de-Sitter 2-space. With this approach, we examine the relationship between a singular curve and Fermi–Walker's law and Berry's phase law in de-Sitter 2-space. We give the Rytov curves by using an orthonormal frame of spacelike frontals and timelike frontals with Fermi–Walker parallelism. We express parametric representations of Rytov curves associated with a singular optical fiber. We examine electromagnetic curves associated with orthonormal vectors of spacelike frontals and timelike frontals in de-Sitter 2-space. Hence, we express the magnetic field equations, Lorentz force equations and magnetic trajectory equations along a singular optical fiber. Finally, we give examples that support the theories both physically and geometrically. [ABSTRACT FROM AUTHOR]

Van Hove singularities in proximity to the Fermi level promote electronic interactions and generate diverse competing instabilities. It is also known that a nontrivial Berry phase derived from spin–orbit coupling can introduce an intriguing decoration into the interactions and thus alter correlated phenomena. However, it is unclear how and what type of new physics can emerge in a system featured by the interplay between van Hove singularities (VHSs) and the Berry phase. Here, based on a general Rashba model on the square lattice, we comprehensively explore such an interplay and its significant influence on the competing electronic instabilities by performing a parquet renormalization group analysis. Despite the existence of a variety of comparable fluctuations in the particle–particle and particle-hole channels associated with higher-order VHSs, we find that the chiral p ± i p pairings emerge as two stable fixed trajectories within the generic interaction parameter space, namely the system becomes a robust topological superconductor. The chiral pairings stem from the hopping interaction induced by the nontrivial Berry phase. The possible experimental realization and implications are discussed. Our work sheds new light on the correlated states in quantum materials with strong spin–orbit coupling (SOC) and offers fresh insights into the exploration of topological superconductivity. [ABSTRACT FROM AUTHOR]

We study the spreading of an initially localized wave packet of a particle hopping on a one-dimensional superlattice during a cycle of a topological Thouless pump. Two contributions to the dispersion of the adiabatic pumping process are identified: a dynamical part and a geometrical part. The magnitude of the dynamical contribution to the spreading depends on the dispersion of the adiabatic transfer state and the cycle time. Unlike the dynamical one, the geometrical contribution does not depend on the duration of the adiabatic process and can be made much smaller than the lattice spacing. We show that as the adiabaticity is enhanced by prolonging the period of the pumping process, the uncertainty in coordinate space is increased linearly with the adiabaticity parameter. We propose a mechanism to smoothen the energy surface of the adiabatic transfer state to reduce the spreading of the spatial distribution of the transported particle. This diminishes or even eliminates (up to the geometric contribution) the dispersion of the coordinate during the transport process. [ABSTRACT FROM AUTHOR]

Superconductivity is reformulated as a phenomenon in which a stable velocity field is created by a U (1) phase neglected by Dirac in the Schrödinger representation of quantum mechanics. The neglected phase gives rise to a U (1) gauge field expressed as the Berry connection from many-body wave functions. The inclusion of this gauge field transforms the standard particle-number non-conserving formalism of superconductivity to a particle-number conserving one with many results of the former unaltered. In other words, the new formalism indicates that the current standard one is an approximation that effectively takes into account this neglected U (1) gauge field by employing the particle-number non-conserving formalism. Since the standard and new formalisms are physically different, conflicting results are predicted in some cases. We reexamine the Josephson relation and show that a capacitance contribution of the Josephson junction to the U (1) phase is missing in the standard formalism, and inclusion of it indicates that the standard theory actually does not agree with the experiment while the new one does. It is also shown that the dissipative quantum phase transition in Josephson junctions predicted in the standard theory does not exist in the new one in accordance with a recent experiment (Murani et al 2020 Phys. Rev. X 10 021003). [ABSTRACT FROM AUTHOR]

We have studied quantum systems on finite-dimensional Hilbert spaces and found that all these systems are connected through local transformations. Actually, we have shown that these transformations give rise to a gauge group that connects the Hamiltonian operators associated with each quantum system. This bridge allows us to connect different quantum systems, in such a way that studying one of them allows to understand the other through a gauge transformation. Furthermore, we included the case where the Hamiltonian operator can be time-dependent. An application for this construction will be achieved in the theory of control quantum systems. [ABSTRACT FROM AUTHOR]

We obtained the geometric phase for states of a particle in a spherical infinite potential well with moving walls in two different cases: First, when the radius of the well increases (or decreases) monotonically. Secondly, when the radius changes are oscillatory. In the latter case, we have solved the Schrödinger equation and found its solutions approximately. We obtained the transition rate for the possible real situation in an acousto-optic case which can reveal the effect of the geometric phase. We show that the absorption or radiation peaks will appear if the energy gap between the incident photon and the modified energy difference of two levels by the geometric phase is equal to the integer multiple of oscillation frequency. [ABSTRACT FROM AUTHOR]

The Berry phase, which reveals the intimate geometrical structure underlying quantum mechanics, plays a central role in the anomalous Hall effect. In this work, we observed a sign change of Berry curvatures at the interface between the ferromagnet SrRuO3 (SRO) layer and the SrIrO3 (SIO) layer with strong spin-orbit coupling. The negative Berry curvature at the interface, induced by the strongly spin-orbit-coupled Ir 5d bands near the Fermi level, makes the SRO/SIO interface different from the SRO layer that has a positive Berry curvature. These opposite Berry curvatures led to two anomalous Hall effect (AHE) channels with opposite signs at the SRO/SIO interface and in the SRO layer, respectively, resulting in a hump-like feature in the Hall resistivity loop. This observation offers a straightforward explanation of the hump-like feature that is usually associated with the chiral magnetic structure or magnetic skyrmions. Hence, this study provides evidence to oppose the widely accepted claim that magnetic skyrmions induce the hump-like feature.

Circuits provide ideal platforms of topological phases and matter, yet the study of topological circuits in the strongly nonlinear regime, has been lacking. We propose and experimentally demonstrate strongly nonlinear topological phases and transitions in one-dimensional electrical circuits composed of nonlinear capacitors. Nonlinear topological interface modes arise on domain walls of the circuit lattices, whose topological phases are controlled by the amplitudes of nonlinear voltage waves. Experimentally measured topological transition amplitudes are in good agreement with those derived from nonlinear topological band theory. Our prototype paves the way towards flexible metamaterials with amplitude-controlled rich topological phases and is readily extendable to two and three-dimensional systems that allow novel applications. [ABSTRACT FROM AUTHOR]

We report the topological properties, in terms of the Berry phase, of the 2D noninteracting system with electron–hole band inversion, described by the two-band generalized analogue of the low-energy Bernevig–Hughes–Zhang Hamiltonian, yielding the W-shaped energy bands in the form of two intersecting cones with the gap along the closed continuous loop. We identify the range of parameters where the Berry phase attains qualitatively different values: (a) the integer multiplier of 2π, (b) the integer multiplier of π, and (c) the nontrivial value between the latter two, which depends on the system parameters. The system thus exhibits the anomalous quantum Hall effect associated with the nontrivial geometric phase, which is presumably tunable through the choice of parameters at hand.

Abstract Metasurface can use artificial microstructures to manipulate electromagnetic waves more accurately and flexibly. All-dielectric metalens have a wide range of materials and low cost so it has a wide application prospect. Herein, we propose a all-dielectric achromatic metalens built with Si as the structural unit that can operate over a broadband of wavelengths in the visible region. It controls the wavefront of light through the Pancharatnam–Berry phase and propagation phase to eliminate the chromatic aberration. Meanwhile, we also use Gerchberg–Saxton algorithm and its improved algorithm to iterate over multiple design wavelengths and obtain holographic phases suitable for broadband. Thus, both the metalenses and holographic metasurfaces can achieve achromatic broadband in the visible light range, which provides a new method for the development of meta-optical imaging devices.

A new electrically controlled photonic liquid crystal device in the form of a twist-q-plate for the generation of a given number of polarization and phase optical singularities on the wavefront of a light beam in a wide spectral range is proposed. The ability of the element to function in two modes was demonstrated experimentally: generation of a given number of singularities or generation of a Gaussian beam and application of this element in a scheme of optical tweezers. A theoretical model was developed to determine the range of controlling voltages for achromatic functioning of the proposed element. [ABSTRACT FROM AUTHOR]

In their last article [Phys. Lett. A 2021, 389, 127091], the authors have extended the k⋅p approach by considering crossings with the spin–orbit interaction (SOI) up to the second order and studied the spin texture and Berry phase of the heavy‐mass holes (HHs) confined in the SiGe 2D quantum well system. HHs cause quasi‐degeneracy via the intersub‐band interaction (ISI) working as Dirac‐like singularity, leading to the energy‐dependent Berry phase "quantized" by π. This π quantization is understandable by counting the number of quasi‐degenerate points in the Brillouin zone alongside recognizing the sign of the Berry curvature there. Herein, the remaining holes of the light‐mass holes (LHs) and separate holes (SHs) are studied. The spin textures and the Berry curvatures and phases are explored comprehensively, focusing on the competition between the Rashba and Dresselhaus SOIs via ISI. Comparisons with HHs elucidate that LHs and SHs cause similar quasi‐degeneracy through ISI, functioning as the Dirac‐like singularity. As such, the Berry phase is quantized by π, confirming the validity of the counting model irrespective of hole type. In some peculiar cases, HHs and LHs cause a possible sign inversion in the Berry phase, leading to zero Berry phase against temperature. [ABSTRACT FROM AUTHOR]

Although the photonic spin-Hall effect (PSHE) at optical interfaces has been widely studied in past years, its physical origin remains obscure. Here, through studying the scatterings of circularly polarized beams obliquely incident on a series of junctions linking two homogenous optical media, how the physical origin of the PSHE evolves as the interface changes from a slowly varying junction to a step-like sharp one is explored. Beams transmitted through a generic interface consist of two modes, a spin-maintained normal mode carrying a spin-redirection Berry (SRB) phase and a spin-flipped abnormal mode exhibiting a Pancharatnam-Berry (PB) phase. Under linear-polarization incidence, a spin-polarized beam transmitted through each junction is generally an interference of normal and abnormal modes corresponding to two different incident circular polarizations, and thus the resulting PSHE is dictated by the interplay and competition between two effects dictated by SRB and PB phases, respectively. Shrinking the interfacial region can increase the strength of the abnormal mode, making the measured PSHE change from the SRB-dominated one to the PB-dominated one. The results establish a unified framework to understand the PSHE at generic interfaces, offering practical ways to control the PSHE by "designing" the abnormal scatterings on optical interfaces. [ABSTRACT FROM AUTHOR]

The study of topological semimetals has been extended to more general topological nodal systems such as metamaterials and artificial periodic structures. Among various nodal structures, triply degenerate nodal line (TDNL) is rare and, hence, has received little attention. In this work, we have proposed a simple tight-binding (TB) model, which hosts a topological non-trivial TDNL. This TDNL not only has the drumhead surface states (DSSs) as usual nodal line systems but also has surface states that form a contracted-drumhead shape. The shape and area of this contracted drumhead can be tuned by the hopping parameters of the model. This provides an effective way to modulate surface states and their density of states, which can be important in future applications of topological nodal systems.

Computational modules were developed to numerically determine electronic band structures, berry curvatures, Chern numbers, localization lengths, and critical exponents for tight- binding and related models. These modules were applied to a variety tight-binding and related models including the Hofstadter Model, Anderson Model, and the Chalker- Coddington model. When analytic solutions were available, numeric energy bands agreed with analytic solutions to within machine precision. In addition Chern numbers for well known models were reproduced, and localization lengths and critical exponents agreed with values in the literature.

The historic de Haas-van Alphen effect observed in the late 1950s in CSIR-NPL by J.S. Dhillon and D. Shoenberg in pure bismuth and zinc metal is revisited in this article through a single-crystalline phase of bismuth crystal, which is observed in terms of resistivity as predicted by Shubnikov-de Haas (SdH) oscillations. The single crystal of bismuth is grown through solid-state reaction under an optimized heat treatment whose purity and structural phase are confirmed through XRD, SEM, and EDAX. The transport properties of single crystal show the presence of SdH oscillations from a temperature range of 2 to 10 K. The occurrence of oscillations in the transverse magnetic field confirms the presence of the Fermi surface. Landau level (LL) fan diagram reveals the presence of topological surface states and the Berry's phase confirmation from temperature-dependent SdH oscillations, concluding the presence of a noble topological phase of bismuth exhibiting SdH oscillations. [ABSTRACT FROM AUTHOR]

The first part of this article attempts to highlight in chronological order some prominent papers that have direct connexion with the Born‐Oppenheimer approximation. This timeline successively points to the role of level crossing, the notions of gauge field and geometrical or Berry phase, early experiments that were accounted for with that concept, and its major role in understanding anomalous transport in solids. The second part analyzes the time evolution of states under the adiabatic approximation when the states are spin degenerate. The geometrical phase thus found entails an electron spin evolution. Then, we examine the case of moleclar dynamics. Starting from the Born‐Oppenheimer approximation, we obtain a spin evolution by replacing the classical nuclear positions by their quantum mechanical counterparts in the terms that describe electrostatic interactions between nuclei and electrons. [ABSTRACT FROM AUTHOR]

Topology is now securely established as a means to explore and classify electronic states in crystalline solids. This review provides a gentle but firm introduction to topological electronic band structure suitable for new researchers in the field. I begin by outlining the relevant concepts from topology, then give a summary of the theory of non-interacting electrons in periodic potentials. Next, I explain the concepts of the Berry phase and Berry curvature, and derive key formulae. The remainder of the article deals with how these ideas are applied to classify crystalline solids according to the topology of the electronic states, and the implications for observable properties. Among the topics covered are the role of symmetry in determining band degeneracies in momentum space, the Chern number and Z 2 topological invariants, surface electronic states, two- and three-dimensional topological insulators, and Weyl and Dirac semimetals [ABSTRACT FROM AUTHOR]

Self-intersecting energy band structures in momentum space can be induced by nonlinearity at the mean-field level, with the so-called nonlinear Dirac cones as one intriguing consequence. Using the Qi-Wu-Zhang model plus power law nonlinearity, we systematically study in this paper the Aharonov–Bohm (AB) phase associated with an adiabatic process in the momentum space, with two adiabatic paths circling around one nonlinear Dirac cone. Interestingly, for and only for Kerr nonlinearity, the AB phase experiences a jump of π at the critical nonlinearity at which the Dirac cone appears and disappears (thus yielding π -quantization of the AB phase so long as the nonlinear Dirac cone exists), whereas for all other powers of nonlinearity, the AB phase always changes continuously with the nonlinear strength. Our results may be useful for experimental measurement of power-law nonlinearity and shall motivate further fundamental interest in aspects of geometric phase and adiabatic following in nonlinear systems. [ABSTRACT FROM AUTHOR]

We report the topological properties, in terms of the Berry phase, of the 2D noninteracting system with electron–hole band inversion, described by the two-band generalized analogue of the low-energy Bernevig–Hughes–Zhang Hamiltonian, yielding the W-shaped energy bands in the form of two intersecting cones with the gap along the closed continuous loop. We identify the range of parameters where the Berry phase attains qualitatively different values: (a) the integer multiplier of 2 π , (b) the integer multiplier of π , and (c) the nontrivial value between the latter two, which depends on the system parameters. The system thus exhibits the anomalous quantum Hall effect associated with the nontrivial geometric phase, which is presumably tunable through the choice of parameters at hand. [ABSTRACT FROM AUTHOR]

We have studied the intrinsic contribution to anomalous Hall conductivity in presence of the normal magnetic field. A semiclassical approach for calculating the Hall conductivity in presence of the nontrivial Berry phase is used. This method is based on the semiclassical equations of motion with anomalous velocity correction and the Boltzmann transport equation. We present the formulation of anomalous Hall conductivity in this approach. We perform explicit calculations for a two-dimensional system which is described by Dirac Hamiltonian. At zero magnetic field, our results coincide with previous results which are obtained both using the semiclassical method and Kubo formalism. For the strong magnetic field, Hall conductivity decreases as a power-law. The exponent of the power-law behavior for the infinite energy band is 1/3 and for the finite energy band, there is a crossover from 1/3 to1.

Topological insulators have drawn tremendous interest in current research for their exotic quantum phenomena and new-generation technological applications. In this literature, we have explored the topological properties of a 100 nm Bi 2 Te 3 thin film, prepared by co-deposition technique through a custom-built electron-beam-evaporator. The detailed structural, compositional, and morphological analysis indicates the formation of a good-quality, well-stoichiometric, smooth film on Si (100) substrate. Our electrical-transport measurement exhibits three different types of temperature (T) dependency of resistance, where substrate Si-carrier dominates the transport at much higher-T (>250K), whereas a constant and logarithmic variation of filmʼs resistance are seen for below 250K and 25K, respectively. The logarithmic dependency is originated due to 2D electron-electron interaction, while the constant nature is arising from electron-phonon interaction. Finally, systematic temperature and angle-dependent magneto-conductance studies are performed. From which, we have found the existence of topological-surface-state in our Bi 2 Te 3 film through the evidence of non-zero Berry phase (β = 0.66π), high phase-coherence-length (l ϕ = 101.8 nm), and 2D coherency factor (α = −0.33). • 100 nm Bi 2 Te 3 thin films are prepared by EBE-setup through co-deposition process. • GI-XRD, Raman spectroscopy, XPS, EDX, SEM, AFM indicate good-quality film formation. • Electrical-transport exhibits TSS and Si-carrier dominated transport at low and high temperature, respectively. • Existence of TSS is verified through exploring topological parameters (α, β, l ϕ). [ABSTRACT FROM AUTHOR]

Quantum oscillation is an important phenomenon in low temperature transport studies of topological materials. In three-dimensional topological insulators, Dirac semimetals, Weyl semimetals, and other topological nontrivial materials, the topologically nontrivial band structure will add a phase correction to the quantum oscillation patterns, which is known as the nontrivial Berry phase. Berry phase analysis via quantum oscillation is a powerful method to investigate the nontrivial band topology of topological materials. In this review, we introduce the concepts of the Berry phase and quantum oscillations, and provide some classification of topological materials. We then employ some important studies on each type of topological material to discuss the nontrivial Berry phase. We conclude by pointing out the importance of quantum transport studies on topological materials, as well as drawing attention to the exploration of the nontrivial Berry phase in a new material system that could shed more light on the topology-based electronics.

In this article, the theory, design, and experimental validation of wideband generalized sequential rotation arrays (GSRAs) are reported. In particular, the GSRA has the ability to provide dual-circularly polarized (dual-CP) beams with different handedness using a single feeding network, whose aperture amplitude and phase distributions can both be independently controlled. Such functionality is achieved by jointly utilizing the dynamic phase and Berry phase, as well as exploiting elliptically polarized (EP) array elements with different axial ratio (AR) values. The proposed technique and the design methodology are verified by two proof-of-concept microstrip GSRAs consisting of an $8\times8$ array of EP stacked-patch elements operating in the K-band. The first prototype exhibits a 3 dB gain difference between the two CP beams, while the other offers a 6 dB gain difference and different sidelobe levels (SLLs) for the generated dual-CP beams. Both arrays are fabricated and measured, experimentally achieving a joint $S_{11} < -10$ dB, AR < 3 dB, and 3 dB gain bandwidth of more than 28.4% and 20.1% with a beam squinting of less than 3°. In addition, the two GSRAs enable a bandwidth of about 19% and 3% within which the gain difference between the two CP beams of different handedness deviates from the targeted value by less than 1 dB. With the large degree of freedom in aperture field control, the proposed GSRAs could be potential candidates for use in satellite communications, point-to-multipoint communications, and so on. [ABSTRACT FROM AUTHOR]

Metasurface can use artificial microstructures to manipulate electromagnetic waves more accurately and flexibly. All-dielectric metalens have a wide range of materials and low cost so it has a wide application prospect. Herein, we propose a all-dielectric achromatic metalens built with Si as the structural unit that can operate over a broadband of wavelengths in the visible region. It controls the wavefront of light through the Pancharatnam–Berry phase and propagation phase to eliminate the chromatic aberration. Meanwhile, we also use Gerchberg–Saxton algorithm and its improved algorithm to iterate over multiple design wavelengths and obtain holographic phases suitable for broadband. Thus, both the metalenses and holographic metasurfaces can achieve achromatic broadband in the visible light range, which provides a new method for the development of meta-optical imaging devices. [ABSTRACT FROM AUTHOR]

The Berry phase of wave functions is a key quantity to understand various low-energy properties of matter, among which electric polarisation, orbital magnetism, as well as topological and ultra-relativistic phenomena. Standard approaches to probe the Berry phase in solids rely on the electron dynamics in response to electromagnetic forces. In graphene, probing the Berry phase $\pi $ of the massless relativistic electrons requires an external magnetic field. Here, we show that the Berry phase also affects the static response of the electrons to a single atomic scatterer, through wavefront dislocations in the surrounding standing-wave interference. This provides a new experimental method to measure the graphene Berry phase in the absence of any magnetic field and demonstrates that local disorder can be exploited as probe of topological quantum matter in scanning tunnelling microscopy experiments.

Orbital anisotropy at interfaces in magnetic heterostructures has been key to pioneering spin–orbit‐related phenomena. However, modulating the interface's electronic structure to make it abnormally asymmetric has been challenging because of lack of appropriate methods. Here, the authors report that low‐energy proton irradiation achieves a strong level of inversion asymmetry and unusual strain at interfaces in [Co/Pd] superlattices through nondestructive, selective removal of oxygen from Co3O4/Pd superlattices during irradiation. Structural investigations corroborate that progressive reduction of Co3O4 into Co establishes pseudomorphic growth with sharp interfaces and atypically large tensile stress. The normal component of orbital to spin magnetic moment at the interface is the largest among those observed in layered Co systems, which is associated with giant orbital anisotropy theoretically confirmed, and resulting very large interfacial magnetic anisotropy is observed. All results attribute not only to giant orbital anisotropy but to enhanced interfacial spin–orbit coupling owing to the pseudomorphic nature at the interface. They are strongly supported by the observation of reversal of polarity of temperature‐dependent Anomalous Hall signal, a signature of Berry phase. This work suggests that establishing both giant orbital anisotropy and strong spin–orbit coupling at the interface is key to exploring spintronic devices with new functionalities. [ABSTRACT FROM AUTHOR]

Deformed Jaynes–Cummings model (JCM) has a physical importance in quantum optics. Hence, we investigated the nonlinear JCM including the intensity-dependent coupling constant and the additional Kerr term. The cavity was assumed to be in thermal equilibrium with a heat reservoir at temperature T. Using the generators of a closed algebra which reduces to the su(1, 1) and Heisenberg–Weyl algebras at limiting cases, and considering the total excitation number as a constant of motion, the total Hilbert space decomposes into two subspaces. So the eigenvalues and the corresponding eigenvectors were obtained. We derived the thermal density matrix and analysed the fidelity and thermal entanglement using negativity measure. Furthermore, we studied the Berry phase of the nonlinear atom–field system and explored the influence of nonlinearity on the quantum phase transition (QPT) point and entanglement. It is found that the deformation parameter can strongly affect the fidelity, negativity and QPT point. [ABSTRACT FROM AUTHOR]

This paper demonstrates that the parity‐time (PT$PT$)‐symmetric non‐Hermitian Hamiltonian for a periodically driven system can be generated from a kernel Hamiltonian by a generalized gauge transformation. The kernel Hamiltonian is Hermitian and static, while the time‐dependent transformation operator has to be PT$PT$ symmetric and non‐unitary in general. Biorthogonal sets of eigenstates appear necessarily as a consequence of the non‐Hermitian Hamiltonian. The wave functions and associated non‐adiabatic Berry phase γn$\gamma _{n}$ for the nth eigenstate are obtained analytically. The classical version of the non‐Hermitian Hamiltonian becomes a complex function of canonical variables and time. The corresponding kernel Hamiltonian is derived with PT$PT$ symmetric canonical‐variable transfer in the classical gauge transformation. Moreover, with the change of position‐momentum to angle‐action variables it is revealed that the non‐adiabatic Hannay's angle ΔθH$\Delta \theta _{\text{H}}$ and Berry phase satisfy precisely the quantum‐classical correspondence, γn=(n+1/2)ΔθH$\gamma _{n}= (n+1/2)\Delta \theta _{\text{H}}$. [ABSTRACT FROM AUTHOR]

We deploy an asymptotic model for the interaction between nearby dispersion surfaces and respective eigenstates towards explicit evaluation of the Berry phase governed by the scalar wave equation in two-dimensional periodic media. The model, featuring a pair of coupled Dirac equations, entails a four-dimensional parametric space and endows the interacting Bloch eigenstates with an explicit gauge that caters for analytical integration in the wavenumber domain. Among the featured parameters, the one (s∈[0,12]) that synthesizes the phase information on the coupling term is shown to decide whether the Berry connection round the loop is singular (s=0) or analytic (s>0). The analysis demonstrates that the Berry phase for two-dimensional lattices is π -quantal and topological when s=0 , equalling π when the contour encloses a Dirac point and zero in all other situations (avoided crossings or line crossings). The analogous result is obtained, up to an O(s) residual, when s≃0 and similarly for s≃12. In the interior of the s -domain, we find that the Berry phase either approximately equals π or is not quantal. Beyond shedding light on the anatomy of the Berry phase in periodic continua, the analysis carries a practical benefit as it permits a single-wavenumber evaluation of this geometrical phase quantity. The asymptotic estimates of the Berry phase are found to be in agreement with their numerical counterparts. For generality, we also include an application to a Dirac-like, three-energy-level system. [ABSTRACT FROM AUTHOR]

Abstract Orbital anisotropy at interfaces in magnetic heterostructures has been key to pioneering spin–orbit‐related phenomena. However, modulating the interface's electronic structure to make it abnormally asymmetric has been challenging because of lack of appropriate methods. Here, the authors report that low‐energy proton irradiation achieves a strong level of inversion asymmetry and unusual strain at interfaces in [Co/Pd] superlattices through nondestructive, selective removal of oxygen from Co3O4/Pd superlattices during irradiation. Structural investigations corroborate that progressive reduction of Co3O4 into Co establishes pseudomorphic growth with sharp interfaces and atypically large tensile stress. The normal component of orbital to spin magnetic moment at the interface is the largest among those observed in layered Co systems, which is associated with giant orbital anisotropy theoretically confirmed, and resulting very large interfacial magnetic anisotropy is observed. All results attribute not only to giant orbital anisotropy but to enhanced interfacial spin–orbit coupling owing to the pseudomorphic nature at the interface. They are strongly supported by the observation of reversal of polarity of temperature‐dependent Anomalous Hall signal, a signature of Berry phase. This work suggests that establishing both giant orbital anisotropy and strong spin–orbit coupling at the interface is key to exploring spintronic devices with new functionalities.

Abstract Quantum interference between multiple pathways in molecular photodissociation often results in angular momentum polarization of atomic products and this can give deep insight into fundamental physical processes. For dissociation of diatomic molecules, the resulting orbital polarization is fully understood and consistent with quantum mechanical theory. For polyatomic molecules, however, coherent photofragment orbital polarization is frequently observed but so far has eluded theoretical explanation, and physical insight is lacking. Here, we present a model of these effects for ozone photodissociation that reveals the importance of a novel manifestation of the geometric phase. We show this geometric phase effect permits the existence of coherent polarization in cases where it would otherwise vanish, and cancels it in some cases where it might otherwise exist. The model accounts for measurements in ozone that have hitherto defied explanation, and represents a step toward a deeper understanding of coherent electronic excitation in polyatomic molecules and a new role of the geometric phase. Key Points Coherent photofragment atomic orbital polarization reveals matter wave interference in dissociation along multiple paths. In diatomic molecules, this is well‐understood, but in polyatomic molecules, large effects are seen but these have defied a rigorous explanation. A model is developed describing these phenomena in the UV dissociation of ozone that accounts for a number of conflicting observations and reveals a new manifestation of the geometric phase in molecular physics.

We study in this paper the time evolution of PT-symmetric non-Hermitian Hamiltonian consisting of periodically driven SU(1,1)generators. A non-Hermitian invariant operator is adopted to solve the Schrödinger equation, since the time-dependent Hamiltonian is no longer a conserved quantity. We propose a PT-symmetric but non-unitary transformation operator in the construction of the non-Hermitian invariant. The eigenstates of invariant and its complex conjugate form a bi-orthogonal basis to formulate the exact solution. We obtain the non-adiabatic Berry phase, which reduces to the adiabatic one in the slow time-variation limit. A non-unitary time- evolution operator is found analytically. As a consequence of the non-unitarity the ket (|ψ(t)〉) and bra (〈ψ(t)|) states are not normalized each other. While the inner product of two states can be evaluated with the help of a metric operator. It is shown explicitly that the model can be realized by a periodically driven oscillator.

Transition metal oxides have been the materials of interest in modern‐day science and technology. Among these materials, double perovskites have been studied very often. To explore such types of oxides and to provide a better understanding especially about lanthanum manganates, herein, the system of La2NiMnO6 is investigated, which exists in two phases, viz., monoclinic and rhombohedral via density functional theory. So far, the monoclinic phase which usually exists at low temperatures has been probed a lot; however, very little information is available about the rhombohedral phase and thus needs to be investigated. Herein, the rhombohedral phase of the material is simulated and various properties like band structure, electronic distribution of states, and absorption within the material are investigated. The study of the complex dielectric nature of the material and its refractive index with frequency variations of the incident field is also presented. The self‐interactions have been taken care‐off taking the Hubbard parameter into account. The spontaneous polarization for the first time as a berry phase using a quantum mechanical approach has also been calculated. The high dielectric constant at visible frequencies ensures the potential use of this material in the case of storage devices. [ABSTRACT FROM AUTHOR]

A Sagnac interferometer’s ring structure causes electromagnetic waves traversing it to periodically encounter the same optical elements. Due to this discrete translational symmetry, the frequency spectrum of the clockwise and counter-clockwise modes acquire a band structure with a characteristic band gap. When the interferometer is rotated, an additional non-reciprocal phase shift between the counter propagating modes arises and it results in the loss of time reversal symmetry. While prior understanding of the impact of Sagnac rotation on the band structure exists, the prevalence of topological geometric phase in Sagnac interferometer under rotation has not been prominently discussed. We propose a coupled mode theory with the required time reversal symmetry properties which influences the Berry curvature and we show that it leads to the accumulation of Berry phase with tunable topological charge. [ABSTRACT FROM AUTHOR]

Optical and microwave communication classically focus more on the magnitude manipulation of electromagnetic carriers. Recently, a multiplexing method utilizing orbital angular momentum (OAM) is developed, which has been an important study of communication art. Based on OAM multiplexing, a communication method that introduces Berry‐phase carriers is presented in this research, which can naturally eliminate the channel disturbance. To verify the proposed method, two information systems are presented, including a multiplexing communication system in a large‐scale scenario and a double‐helical information system in a microscale scenario. All the results are verified by the corresponding experiments. This method achieves some advanced performances, for instance, directional communication and self‐anti‐interference, which shows potential applications in areas such as information, materials, and bionics. [ABSTRACT FROM AUTHOR]

We give a pedagogical overview of exciting quantum phenomena that are unique to two-dimensional electron solids. The uniqueness arises from the role of the quantum phase that influences various remarkable attributes such as the relativistic Rashba interaction, the Berry curvature, quantum Hall effect, magnetic oscillation, etc., which are intimately connected to Landau diamagnetism and the concomitant Aharonov–Bohm phase. These attributes are characteristics of two-dimensional quantum solids such as graphene, interfaces of oxides and some topological insulators. Because these material properties hinge on the interplay of the intrinsic spin of the electron with its motion, the resultant field is known as Spintronics. [ABSTRACT FROM AUTHOR]

We derive the semiclassical Bloch dynamics with second-order Berry phase correction in the presence of the slow-varying scalar potential as perturbation. Our mathematical derivation is based on a two-scale WKB asymptotic analysis. For a uniform external electric field, the bi-characteristics system after a positional shift introduced by Berry connections agrees with the recent result in previous works. Moreover, for the case with a linear external electric field, we show that the extra terms arising in the bi-characteristics system after the positional shift are also gauge independent. [ABSTRACT FROM AUTHOR]

Programmable quantum processors are suitable platforms for simulating quantum systems, of which topological phases are of particular interest. We simulate the quench dynamics of a one-dimensional system on IBM Q devices. The topological properties of the dynamics are described by the dynamical topological invariants, the dynamical winding number, and the time-dependent Berry phase, which are simulated with the quantum circuit model. The results show that despite the noise present in the current quantum computers, the dynamical topological invariants are robust. Moreover, to investigate the influence of open quantum system, we analytically solve the master equation in Lindblad form and show that the dynamical winding number and the change in Berry phase are not affected by the dissipation. This study sheds light on the robustness of topological phases on the noisy intermediate-scale quantum computers. [ABSTRACT FROM AUTHOR]