Search

Three-dimensional Dirac semimetal Cd3As2 has been considered as an excellent candidate for applications of electronic devices owing to its ultrahigh mobility and air-stability. However, current researches are focused mainly on the use of gate-voltage to control its carrier transport tunability, while the manipulation of transport properties by element-doping is quite limited. Here we report the tunable magneto-transport properties by adjusting Mn-doping in the Cd3As2 compound. We find that Mn-element doping has a strong influence on the Fermi level positions, and the Fermi energy approaches to Dirac point with higher Mn-doping. More importantly, the introduction of Mn atoms transforms diamagnetic Cd3As2 to antiferromagnetic (Cd, Mn)3As2, which provides an approach to control topological protected Dirac materials by manipulating antiferromagnetic order parameters. The Shubnikov-de Hass oscillation originates from the surface states, and the Landau fan diagram yields a nontrivial Berry phase, indicating the existence of massless Dirac fermions in the (Cd1-xMnx)3As2 compounds. Our present results may pave a way for further investigating antiferromagnetic topological Dirac semimetal and expand the potential applications in optoelectronics and spintronics.

In this article, two transmissive metasurfaces with different phase control mechanisms and working polarization condition are proposed to efficiently generate zero order Bessel beams (BBs), respectively. For the linear polarization condition, a dual-mode meta-atom constructed by three layers of dielectric substrate and four layers of metal patch is designed. By changing the size of metal patches of meta-atom along $x$ -axis and $y$ -axis, respectively, the phase shift for $x$ - and $y$ -polarized incident wave can be tuned relative independently of 0–2 $\pi $ while the transmission coefficient keeps high value at 10 GHz. For the circular polarization condition, a sandwich type meta-atom applying geometric phase to realize full phase control while keep high efficiency near 10 GHz is designed. According to the designed phase profile of BBs, select meta-atoms with certain phase and efficiency, then arrange them to construct metasurfaces. Full wave simulation results indicate that the dual-mode metasurface working in linear polarization condition generates BBs with the maximum transmission efficiency 0.79 and 0.85 for $x$ and $y$ polarization wave, respectively, and the geometric phase metasurface working in circular polarization condition generates BBs with the maximum transmission efficiency 0.92. Besides, the propagation characteristics of the excited BBs are studied.

van der Waals crystals exhibit excellent material performance when exfoliated to few-atomic-layer thickness. In contrast, the van der Waals thin films more than 10 nm thick are believed to show bulk properties, in which outstanding material performance is rarely found. Here we report the largest anomalous Hall conductivity observed so far in a 170 nm van der Waals ferromagnetic 1T-CrTe2 flake, which reaches 67,000 Ω-1 cm-1. Such a colossal anomalous Hall conductivity in 1T-CrTe2 is dominated by the extrinsic skew scattering process rather than the intrinsic Berry phase effect, as evidenced by the linear relation between the anomalous Hall conductivity and the longitudinal conductivity. Defying the dilemma of mutually exclusive large anomalous Hall angle and high electric conductivity for most ferromagnets, 1T-CrTe2 achieves both in a thin film sample. Considering the shared physics of the anomalous Hall effect and the spin Hall effect, our finding offers a guideline for searching large spin Hall materials of high conductivity which may overcome the bottleneck of overheating in spintronics devices.

Quantum degenerate systems can be simulated by the classical resonant oscillators in the means of quantum-classical mapping theory. In this work, we show the classical version of shortcuts to adiabaticity-transitionless quantum driving (TQD) for the non-Abelian quantum systems by averaging the quantum version. The non-Abelian geometric angle corresponding to the quantum Wilczek-Zee phase is given and the non-Abelian angle gauge potential is just the opposite of the third term of TQD Hamiltonian or the averaging of Wilczek-Zee gauge potential. An example of Hamiltonian with two degenerate subspaces is employed to illustrate the classical non-Abelian dynamics, geometric angle and shortcuts to adiabaticity. This provides a promising platform to simulate the quantum shortcut or for quantum computation and quantum information processing.

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.

In this work, we study the adiabatic phases and shortcut for a pseudo-Hermitian interacting spin-1/2 composite system in which one system is driven by a non-Hermitian magnetic field. The biorthonormal eigenbasis and the condition for real eigenvalues have been derived and discussed. By studying the Berry phases and the transitionless quantum driving (TQD) Hamiltonian, the roles of correlation between the subsystems and the non-Hermicity are discussed. The non-Hermitian dynamics and the Berry phases of the subsystem, as well as their influences on the TQD Hamiltonian are studied in both no correlation and large correlation cases. These results mean that we can modify the correlation between the subsystems to control the adiabatic shortcuts of the subsystems. These schemes can provide a feasible way for studying the adiabatic shortcuts of the composite system and the non-Hermitian system.

The intriguing quasiparticles in solids, known as Dirac, Weyl, and Majorana fermions, etc. with properties akin to those theoretically predicted but never realized in high-energy physics, have excited intensive research activities in recent years. The transition metal dipnictides are attractive because of their extremely large magnetoresistance that is usually attributed to the carrier compensation effect. We briefly review herein the crystal growth, magneto-transport measurements, and theoretical studies of tantalum dipnictides TaAs2 and TaP2, with the emphasis being put on discussion of the nontrivial topological states in both materials. The analysis of quantum oscillations of the magnetoresistance unveils nonzero Berry phase. The chiral negative longitudinal magnetoresistance further points to possible Weyl state, which was recently theoretically suggested as the result of the magnetic field-induced Zeeman splitting effect no matter how large the field is. The analysis of these intriguing behaviors could brush up our understanding about the family of materials and would be valuable for future work on investigating the magnetic field-induced topological phase transition in such semimetals.

The evolutions of polarization and orbital angular momentum (OAM) states of light in helically twisted birefringent photonic crystal fibers (TB-PCFs) are analyzed. It is shown that a circular polarization (CP) component ( S 3 of a Stokes parameter) is periodically excited when usual linearly polarized (LP) modes of PCF are launched. The excitation originates from a geometric phase in TB-PCFs. The S 3 excitation is larger for larger linear birefringence for a fixed twisting rate. If the linear birefringence is large enough, a CP filtering behavior can be seen in addition to the S 3 excitation. From the analytical consideration of the sign of the geometric phase, the TB-PCF with periodical inversion of twisting is proposed to generate arbitrary polarization state on the Poincaré sphere. Next, an OAM state generation in multimode TB-PCFs is shown for higher-order LP mode input. By observing a far-field interference pattern from TB-PCF mixed with LP 01 mode, a vortex associated with the OAM state can be seen. Similar to the single-mode case, by using periodical twisting inversion, efficient OAM generation is possible. These results indicate that by simply launching fiber’s LP mode into TB-PCF, arbitrary polarization and OAM states can be generated, leading to a novel mechanism for the manipulation of the spatial state of light.

In this work, we introduce a model of a two-atom interacting with a multi-level atom governed by su(2) Lie algebra in the presence of external classical field. The influence of the classical field on the system is discussed in detail for certain values for the classical terms. The atomic density matrix of the proposed system is obtained. The dynamical behavior of the atomic Fisher information as an indicator of the nonlocal correlation between a two-atom and su(2) field is discussed. Moreover, we examine the effect of classical field on the evolution of entropy squeezing and the geometric phase induced between the initial and final state of the proposed system. The results outlined some important phenomena as sudden death and sudden birth of entanglement in presence of the classical terms is observed through the dynamics of atomic Fisher information in the presence of classical field for the large number of levels.

Two superconducting (SC) qubits interacting with a radiation field in the coherent state (CS) in the presence of Stark shift are investigated. The density matrix is expressed in terms of the wave function to describe the proposed system. Physical properties, such as the geometric phase, linear entropy, and negativity are used to describe the behavior of the system. The effects of the Stark shift and the initial state on the linear entropy, geometric phase, and nonclassical correlation are discussed. Thermal and magnetic field interactions are also examined during the time evolution of the two SC qubits. By raising the temperature and decreasing the qubit–qubit entanglement, the nonclassical connection between the CS field and the two SC qubits is strengthened. Moreover, the Stark shift considerably affects the dynamical and physical properties of both types of entanglement.

In this paper, we propose a scheme for realizing controlled phase gate of transmon qubits by combining the unconventional geometric phase and the inverse Hamiltonian engineering. The scheme possesses built-in fault tolerance and can be implemented in only one step without additional single qubit operations on each transmon qubit. In addition, the Rabi frequencies of the designed driving fields are smooth and vanish at boundary, so that the driving fields can be easily turned on and off . Numerical simulations show that the controlled phase gate is robust against several types of noise and the decoherence factors. Thus, the scheme may provide an alternative approach in constructing controlled phase gate with superconducting qubits.

The Dirac equation with a spatially dependent mass can be used as a simple, exactly soluble, continuum model of a three-dimensional Topological Insulator. For a bulk system, the sign of the mass de...

Two-dimensional (2D) Dirac-like electron gases have attracted tremendous research interest ever since the discovery of free-standing graphene. The linear energy dispersion and nontrivial Berry phase play a pivotal role in the electronic, optical, mechanical, and chemical properties of 2D Dirac materials. The known 2D Dirac materials are gapless only within certain approximations, for example, in the absence of spin-orbit coupling (SOC). Here, we report a route to establishing robust Dirac cones in 2D materials with nonsymmorphic crystal lattice. The nonsymmorphic symmetry enforces Dirac-like band dispersions around certain high-symmetry momenta in the presence of SOC. Through μ-ARPES measurements, we observe Dirac-like band dispersions in α-bismuthene. The nonsymmorphic lattice symmetry is confirmed by μ-low-energy electron diffraction and scanning tunneling microscopy. Our first-principles simulations and theoretical topological analysis demonstrate the correspondence between nonsymmorphic symmetry and Dirac states. This mechanism can be straightforwardly generalized to other nonsymmorphic materials. The results enlighten the search of symmetry-enforced Dirac fermions in the vast uncharted world of nonsymmorphic 2D materials.

In order to improve the transmitted efficiency of metasurfaces, the three-layer unit cell structure with coupling characteristics between layers was proposed. Using these Pancharatnam-Berry phase element particles with three-layer structure, we constructed encoded metasurfaces with different sequences to control the transmitted scattered waves. However, the manipulation of continuous transmission angle requires the continuous change of encoding metasurface period. Since the size of encoding particles in the coded metasurfaces cannot be designed to be infinitesimally small, it is impossible to obtain the continuously changing period of coded metasurfaces. In order to obtain the continuous manipulation of transmission scattering angles, we introduced the principle of Fourier convolution operation in digital signal processing on encoding metasurface sequences. By performing the addition and subtraction operation between two different encoding metasurface sequences, a new encoding metasurface sequence can be obtained with different scattering angle. The transmission scattering angles can be obtained continuously, and the terahertz wave can be manipulated freely. Moreover, by using the proposed three-layer highly efficient Pancharatnam-Berry phase encoding meta-atoms, these coded particles with different rotation angles can be precisely arranged to build the generators of the orbital angular momentum beam with different topological charges.

In this manuscript, we basically focus on the geometric dynamics of the charged particle propagation through the spherical frame. To be able to investigate this process, we suppose that the trajectory of the linearly polarizable light coincides with the path of the point-particle having charges, in which this action is exerted to take place along with the optical fiber designated by the spherical frame on the unit two-sphere. We prove in an elegant fashion that two famous parallel transportations i.e. Fermi-Walker parallel transportation and Rytov parallel transportation are applicable for our case so that we can obtain the geometric phase of the charged point-particle. Later, we present a description of spherical electromagnetic curves on the unit sphere by using the fundamental definition of the Lorentz force and electromagnetic force of the charged point-particle. We further apply our findings to compute the optical magnetic-torque, optical linear and angular momentum, energy-exchanges rate, Poynting vector, electromagnetic force, etc. to comprehend the physical dynamics of the moving charged particle.

Graphene quantum dots (GQDs) not only have potential applications on spin qubit,but also serve as essential platforms to study the fundamental properties of Dirac fermions, such as Klein tunneling and Berry phase. By now, the study of quantum confinement in GQDs still attract much attention in condensed matter physics. In this article, we review the experimental progresses on quantum confinement in GQDs mainly by using scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS). Here, the GQDs are divided into Klein GQDs, bound-state GQDs and edge-terminated GQDs according to their different confinement strength. Based on the realization of quasi-bound states in Klein GQDs, external perpendicular magnetic field is utilized as a manipulation approach to trigger and control the novel properties by tuning Berry phase and electron-electron (e-e) interaction. The tip induced edge-free GQDs can serve as an intuitive mean to explore the broken symmetry states at nanoscale and single-electron accuracy, which are expected to be used in studying physical properties of different two-dimentional materials. Moreover, high-spin magnetic ground states are successfully introduced in edge-terminated GQDs by designing and synthesizing triangulene zigzag nanographenes., Comment: https://rdcu.be/cBFYq

We demonstrate the generation of a stable topologically nontrivial biphoton state with a high degree of quantum entanglement by the bosonic Bogoliubov Hamiltonian in a quadratic nonlinear waveguide array (QNWA) under the Su-Schrieffer-Heeger model. Analysis of its energy spectrum and eigenmode spectra verifies that this biphoton state is a topological nontrivial edge state characterized by the nonzero Berry phase at 1/4 and 3/4 fillings. The changes of Berry phase at 1/4 and 3/4 fillings indicate the topological quantum transition. The topological robustness of the biphoton edge state can be demonstrated by the spatial correlation under random disorders in propagation constant of the QNWA. It is also shown that the R\'enyi entanglement entropy of this topologically nontrivial biphoton state can approach high values. The robustness of this topologically nontrivial property suggests the promising application of this highly entangled biphoton state in quantum computing and information.

In [5] (2018), Capolupo et al. calculate the noncyclic geometric phases associated with neutrino flavor transitions in the two-neutrino scenario, and claim that the results depend on the choice of representations of neutrino mixing matrix thus can be used to distinguish between Dirac and Majorana neutrinos. In this paper, we show that their calculation is flawed due to incorrect application of the definition of noncyclic geometric phase and the omission of one term in Wolfenstein effective Hamiltonian. Their results are neither gauge invariant nor lepton field rephasing invariant. We present an alternative calculation, which is solely in order to demonstrate that the Majorana CP-violating phase enters the geometric phase essentially by lepton field rephasing transformation. We point out that the seemingly nontrivial dependence of geometric phase on Majorana CP-violating phase presented in Capolupo et al. (2018) [5] is unphysical and thus unmeasurable.

The adiabatic shortcut, which can achieve the adiabatic effect by a non-adiabatic process, has drawn considerable attention in the context of quantum control recently. In this work, we study the adiabatic shortcut for an interacting spin-1/2 composite system and the quantum correlation between the subsystems. The results show that, the Berry phases and the transitionless quantum driving (TQD) Hamiltonian for the composite system and the subsystems are related to the correlation between the two subsystems. By study the cases of no correlation and large correlation, the quantum entanglement and the Berry phases of the subsystem, as well as their influences on the TQD Hamiltonian are discussed. This means that, we can modify the correlation between the subsystem to control the adiabatic shortcuts of the subsystems. This provides a feasible way to study the adiabatic shortcuts of the composite system and its subsystems.

The probability distribution of the magnitude C of the curvature 2-form, that underlies the quantum geometric phase and the reaction force of geometric magnetism, is calculated for an ensemble of three-parameter Hamiltonians represented by the gaussian unitary ensemble of N × N matrices. The distributions are determined analytically: exactly for N = 2 and approximately for N ≥ 3, and compared with simulations. The distributions decay asymptotically as 1/C5/2; this is a consequence of the codimension of energy-level degeneracies in the ensemble.

The Berry phase of Bloch states can have profound effects on electron dynamics1-3 and lead to novel transport phenomena, such as the anomalous Hall effect and the valley Hall effect4-6. Recently, it was predicted that the Berry phase effect can also modify the exciton states in transition metal dichalcogenide monolayers, and lift the energy degeneracy of exciton states with opposite angular momentum through an effective valley-orbital coupling1,7-11. Here, we report the observation and control of the Berry phase-induced splitting of the 2p exciton states in monolayer molybdenum diselenide (MoSe2) using the intraexciton optical Stark spectroscopy. We observe the time-reversal-symmetric analogue of the orbital Zeeman effect resulting from the valley-dependent Berry phase, which leads to energy difference of +14 (-14) meV between the 2p+ and 2p- exciton states in the K (K') valley, consistent with the ordering from our ab initio GW-Bethe-Salpeter equation results. In addition, we show that the light-matter coupling between intraexciton states is remarkably strong, leading to a prominent valley-dependent Autler-Townes doublet under resonant driving. Our study opens up pathways to coherently manipulate the quantum states and excitonic excitation with infrared radiation in two-dimensional semiconductors.

We examine the noncommutation of Pancharatnam–Berry phase elements in the generation of vector beams. Any desirable vector beams on the two high-order Poincare spheres can be generated by incorporating the noncommutation and certain input polarization states. We show that the vector polarization states can be switched between two different high-order Poincare spheres by simply exchanging the order of two Pancharatnam–Berry phase elements. More importantly, the point-to-point conversion of vector beams makes our scheme highly flexible and easy to operate.

Within the Born-Oppenheimer (BO) approximation, nuclear motions of a molecule are often envisioned to occur on an adiabatic potential energy surface (PES). However, this single PES picture should be reconsidered if a conical intersection (CI) is present, although the energy is well below the CI. The presence of the CI results in two additional terms in the nuclear Hamiltonian in the adiabatic presentation, i.e., the diagonal BO correction (DBOC) and the geometric phase (GP), which are divergent at the CI. At the same time, there are cusps in the adiabatic PESs. Thus usually it is regarded that there is numerical difficulty in a quantum dynamics calculation for treating CI in the adiabatic representation. A popular numerical method in nuclear quantum dynamics calculations is the Sinc discrete variable representation (DVR) method. We examine the numerical accuracy of the Sinc DVR method for solving the Schrodinger equation of a two dimensional model of two electronic states with a CI in both the adiabatic and diabatic representation. The results suggest that the Sinc DVR method is capable of giving reliable results in the adiabatic representation with usual density of the grid points, without special treatment of the divergence of the DBOC and the GP. The numerical uncertainty is not worse than that after the introduction of an arbitrary vector potential for accounting the GP, whose accurate form usually is not easy to obtain.

A simple combination of density functional theory/time-dependent density functional theory (DFT/TDDFT) and configuration interaction is presented to fix the incorrect topology of the S0- S1 conical intersection (CI) and allow a description of bond making and bond breaking in photoinduced dynamics. The proposed TDDFT-1D method includes one lone optimized doubly excited configuration in addition to the DFT/TDDFT singly excited states within the context of a large configuration interaction Hamiltonian. Results for ethylene and stilbene are provided to demonstrate that this ansatz can yield physically meaningful potential energy surfaces near S0- S1 avoided crossings without changing the vertical excitation energies far from the relevant crossings. We also investigate the famous linear water example to show that the algorithm calculates the correct topology of the S0- S1 CI and yields the correct geometric phase.

Three different methods of experimental mesoscopic physics, namely, weak antilocalization effects, universal conductance fluctuations, and Aharonov-Bohm oscillations, have been used to extract the electron phase-coherence scattering rate in two-dimensional gas of InGaAs/AlInAs heterostructures. The Aharonov-Bohm oscillations reveal strong beating effects, indicating the existence of two similar periodicities of the flux dependencies. As suggested by certain theoretical models, such a behavior might be expected from the so-called Berry phase acquired by electrons with different spin orientations in the presence of strong spin-orbit coupling and Zeeman splitting. In our paper we deduce the experimental values of the dephasing length and try to compare the observed beating pattern with possible scenarios for the appearance of the Berry phase.

As a footprint of primordial perturbations in cosmological observations, the Berry phase of cosmological perturbations can serve to probe the cosmological inflation. Considering linear perturbations in two-field slow-roll inflation, we derive the Hamiltonians of the scalar and tensor Fourier modes in the form of time-dependent harmonic oscillator Hamiltonians. We find the invariant operators of the resulting Hamiltonians and use these invariants to calculate the Berry phase for sub-horizon scalar and tensor modes in the adiabatic limit.

The motion of a handle spinning in space has an odd behavior. It seems to unexpectedly flip back and forth in a periodic manner as seen in a popular YouTube video. As an asymmetrical top, its motion is completely described by the Euler equations and the equations of motion have been known for more than a century. However, recent concepts of the geometric phase have allowed a new perspective on this classical problem. Here we explicitly use the equations of motion to find a closed form expression for total phase and hence the geometric phase of the force-free asymmetric top and explore some consequences of this formula with the particular example of the spinning handle for demonstration purposes. As one of the simplest dynamical systems, the asymmetric top should be a canonical example to explore the classical analog of Berry phase., Comment: 12 pages, 6 figures; Accepted by the American Journal of Physics

Electrons in solids constitute quantum many-body systems showing a variety of phenomena. It often happens that the eigen states of the Hamiltonian are classified into subgroups separated by energy gaps. Band structures in solids and spin polarization in Mott insulators are two representative examples. The subspace spanned by these wavefunctions belonging to each of this subgroup can be regarded as a manifold in Hilbert space, and concepts concerning differential geometry become relevant. Connection and curvature are two key quantities, which correspond to the vector potential and field strength of electromagnetism, respectively. Therefore, one can construct an effective electromagnetic field from the structure of the Hilbert space, which is called an "emergent electromagnetic field". In this article, we review the physics related to this emergent electromagnetic field in solids, including the gauge theory of strongly correlated electrons, various Hall effects, multiferroics, topological matter, magnetic texture such as skyrmions, and the shift current in noncentrosymmetric materials.

Exploration of the topological quantum materials with electron correlation is at the frontier of physics, as the strong interaction may give rise to new topological phases and transitions. Here we report that a family of kagome magnets RMn_{6}Sn_{6} manifest the quantum transport properties analogical to those in the quantum-limit Chern magnet TbMn_{6}Sn_{6}. The topological transport in the family, including quantum oscillations with nontrivial Berry phase and large anomalous Hall effect arising from Berry curvature field, points to the existence of Chern gapped Dirac fermions. Our observation demonstrates a close relationship between rare-earth magnetism and topological electron structure, indicating the rare-earth elements can effectively engineer the Chern quantum phase in kagome magnets.

We explore emergent geometry of the spacetime at the microscopic scale by adiabatic transport of a quasi-coherent state of a fermionic string, with quantum spacetime described by the matrix theory (BFSS matrix model). We show that the generator of the Berry phase is the shift vector of the spacetime foliation by spacelike surfaces associated with the quasi-coherent state. The operator-valued generator of the geometric phase of weak adiabatic transport is the Lorentz connection of the emergent geometry which is not torsion free at the microscopic scale. The effects of the torsion seem consistent with the usual interpretation of the Berry curvature as a pseudo magnetic field.

In general, a spin-polarized light beam cannot couple its spin angular momentum (SAM) with intrinsic orbital angular momentum (IOAM) without spin reversal. Here we find that nonlinear media can give the spin-polarized photon an IOAM, as they travel in the media due to the nonlinear susceptibility along the transmission direction, which does not require spin reversal. To characterize this SAM-to-IOAM conversion process, we establish an evolution ray equation for photons carrying IOAM by reference to the Schrödinger equation. We further reveal the inherent physics of such a phenomenon from a full-wave perspective and find that the vortex generation originates from the nonlinear-induced geometric phase.

We study quantum field theory of a U(1) gauge connection in an arbitrary space-time geometry. We choose the Fermi coordinates adapted to a general null geodesic, and derive the equation for interaction between the Riemann tensor and the photon. We solve the equation by mapping it to a time-dependent Schrodinger equation in 2+1 dimensions. The solution illustrates that as a Gaussian time-bin wave-packet with a narrow bandwidth travels over a null geodesic, it gains an extra geometric phase. We calculate the geometric phase for communication between satellites around the Earth.

We report the observation of the Barnett field, rotational Doppler effect, and Berry phase using the rotating nuclear quadrupole resonance (NQR) method. We have developed coil-spinning techniques that enable us to systematically study the effects of rotation in setups involving rotation of the signal detector, rotation of the sample, and simultaneous rotation of both the signal detector and sample. Applying these setups to NQR measurements, we observe NQR line splittings in which the spectral structures are clearly distinct among the setups. By analyzing these structures, we clarify the origin of the NQR line splittings and discuss the relationship between the rotational Doppler effect, Barnett field effect, and Berry phase in terms of the rotational degrees of freedom, such as the relative rotation and the sample rotation itself, and the observation frame of reference. We also provide clear evidence of the difference between the rotational Doppler effect and the Barnett field and the equivalence of the Barnett field and the Berry phase.

We report on the Shubnikov--de Haas (SdH) oscillations in the quasi-two-dimensional molecular conductor $\ensuremath{\alpha}\text{\ensuremath{-}}{(\mathrm{BETS})}_{2}{\mathrm{I}}_{3}$ [BETS: bis(ethylenedithio)tetraselenafulvalene] laminated on polyimide films at 1.7 K. From the SdH phase factor we verified experimentally that the material is in the Dirac fermion phase under pressure. $\ensuremath{\alpha}\text{\ensuremath{-}}{(\mathrm{BETS})}_{2}{\mathrm{I}}_{3}$ is in the vicinity of the phase transition between strongly correlated insulating and Dirac fermion phases, and is a possible candidate for an ambient-pressure molecular Dirac fermion system. However, the SdH oscillations indicate that the Berry phase is zero at ambient pressure. Under pressure, a $\ensuremath{\pi}$ Berry phase emerges when the metal-insulator crossover is almost suppressed at $\ensuremath{\sim}0.5$ GPa. The results contrast with those for the pioneering molecular Dirac fermion system $\ensuremath{\alpha}\text{\ensuremath{-}}{(\mathrm{BEDT}\text{\ensuremath{-}}\mathrm{TTF})}_{2}{\mathrm{I}}_{3}$ [BEDT-TTF: bis(ethylenedithio)tetrathiafulvalene] in which Dirac fermions and semiconducting behavior are simultaneously observed.

Topological semimetals have been a focal point of research in recent years. One of the salient characters of topological semimetals is the anomalous Hall effect arising from the nontrivial momentum-space Berry phase. In contrast, the anomalous transverse thermoelectric coefficient and thermal Hall effect have been much less explored to date. In this paper, we report thermoelectric and thermal transport properties of ${\mathrm{Fe}}_{3}{\mathrm{Sn}}_{2}$, a prototypical Dirac semimetal. We find that ${\mathrm{Fe}}_{3}{\mathrm{Sn}}_{2}$ exhibits a large topological Nernst effect which is associated with the nonzero spin chirality of the skyrmion bubble phase. Furthermore, ${\mathrm{Fe}}_{3}{\mathrm{Sn}}_{2}$ shows a prominent anomalous thermal Hall effect and the anomalous Nernst effect with features similar to the anomalous Hall effect. The anomalous Nernst signal is about $2.1\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{V}/\mathrm{K}$ at room temperature, which is comparable to the largest value reported thus far. These results highlight the synergic effects of the Berry phase in both real space and momentum space of ${\mathrm{Fe}}_{3}{\mathrm{Sn}}_{2}$, and this study demonstrates an effective strategy of investigating topological materials by measuring their transverse thermal and thermoelectric responses.

We apply geometric phase ideas to coherent states to shed light on interference phenomenon in the phase space description of continuous variable Cartesian quantum systems. The motivating idea is Pancharatnam's concept of two Hilbert space vectors being ’’in phase”. This leads to special sums and integrals of vectors which are locally in-phase superpositions. Geometric phase considerations naturally lead to the emergence of phase space areas. Applied to the overcomplete family of coherent states, we are led to preferred in-phase integral representations for various states of physical significance, such as the position, momentum and Fock states as well as the squeezed vacuum state. Interestingly, the Husimi-Kano Q function is maximized along the line of such superpositions. We also get a fresh perspective on the Bohr-Sommerfeld quantization condition. Finally, we use our exact integral representations to obtain asymptotic expansions for state overlaps and matrix elements, leading to phase space area considerations similar to the ones noted earlier in the seminal works of Schleich, Wheeler and collaborators, but now from a geometric phase perspective.

We generalize the concept of topological invariants for mixed states based on the ensemble geometric phase (EGP) introduced for one-dimensional lattice models to two dimensions. In contrast to the geometric phase for density matrices suggested by Uhlmann, the EGP leads a proper Chern number for Gaussian, finite-temperature or non-equilibrium steady states. The Chern number can be expressed as an integral of the Berry curvature of the so-called fictitious Hamiltonian, constructed from single-particle correlations, over the two-dimensional Brillouin zone. For the Chern number to be non-zero the fictitious Hamiltonian has to break time-reversal symmetry.

Controlling the anomalous Hall effect (AHE) in magnetic topological materials is an important property. Because of the close relationship between anomalous Hall conductance (AHC) and topological band (strong Berry curvature), AHC can be effectively tuned by magnetic field combined with strong spin-orbit interaction and special band structure. In this work, we observed a magnetic field driving the nonmonotonic magnetic field dependence of anomalous Hall resistivity and the sign change in magnetic-field-induced Weyl semimetal HoPtBi. The tunable ranges of the AHC and the anomalous Hall angle are $\ensuremath{-}75\ensuremath{\sim}73\phantom{\rule{0.16em}{0ex}}{\mathrm{\ensuremath{\Omega}}}^{--1}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{--1}$ and $\ensuremath{-}12.3\ensuremath{\sim}9.1%$, respectively. Anisotropic measurements identified the magnetic field is the key factor in controlling the additional Hall term sign. Further analysis indicated that it originated from the field-induced shift of the Weyl points via exchange splitting of bands near the Fermi level. The large tunable effect of the magnetic field on the electronic band structure provides a path to tune the topological properties in this system. These findings suggest that HoPtBi is a good platform for tuning the Berry phase and AHC with the magnetic field.

The topological nodal-line semimetals (NLSMs) possess a loop of Dirac nodes in the $k$ space with linear dispersion, different from the point nodes in Dirac/Weyl semimetals. While the quantum transport associated with the topologically nontrivial Dirac fermions has been investigated extensively, features uniquely associated with the extended nodal lines remain to be demonstrated. Here, we investigate the quantum oscillations (QOs) in the nodal-line semimetal ZrSiS, with the electron transport along the $c$ axis and magnetic field rotating in the $ab$ plane. The extremal orbits identified through the field orientation dependence of the QOs interlock with the nodal line, leading to a nonzero Berry phase. Most importantly, the Berry phase shows a significant dependence on the magnetic field orientation, which we argue to be due to the finite spin-orbit coupling gap. Our results demonstrate the importance of the spin-orbit coupling and the nodal-line dispersion in understanding the quantum transport of NLSMs.

A well-known and already having many material processing applications zero-order Bessel beam makes a great base for improvements to have even broader applicability. In our work, we analyze vector Bessel beams (VBB), which can be generated with high efficiency and quality via the use of Geometric Phase Optical Elements. The beam transverse polarization distribution enables to change intensity distribution easily, i.e. a polarizer in front of the beam will generate invariant over the propagation multi-peak ring- the shaped structure which could be very beneficial to modify material at multiple sights with a single laser shot. We analyze higher-order VBB generated modifications in thin glass and analyze the applicability for etching of large diameter holes.

We study the electronic resonant states of ${\mathrm{H}}_{3}$ with energies above the potential energy surface of the ${\mathrm{H}}_{3}^{\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}+}$ ground state. These resonant states are important for the dissociative recombination of ${\mathrm{H}}_{3}^{\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}+}$ at higher collision energies, and previous studies have indicated that these resonant states exhibit a triple intersection. We introduce a complex generalization of the pseudo--Jahn-Teller model to describe these resonant states. The potential energies and the autoionization widths of the resonant states are computed with electron scattering calculations using the complex Kohn variational method, and the complex model parameters are extracted by a least-square fit to the results. This treatment results in a non-Hermitian pseudo--Jahn-Teller Hamiltonian describing the system. The nonadiabatic coupling and geometric phase are further calculated and used to characterize the enriched topology of the complex adiabatic potential energy surfaces.

Controlling electronic band structure is an important step toward harnessing quantum materials for practical uses. This is exemplified in the spin-polarized bands near the Fermi level of a ferromagnet where small variation to the Berry curvature can be used to control the intrinsic anomalous Hall effect (AHE). Since these pathways are highly sensitive to crystal structure, iterative post-synthesis manipulation of the underlying lattice can act as a fundamental probe and provide new opportunities for functionalization. In this work, depth-dependent magnetic inhomogeneity in a $4d$ itinerant ferromagnet ${\mathrm{SrRuO}}_{3}$ film is controlled by applying low energy He ion irradiation. Combined magnetometry, polarized neutron reflectometry, and magnetotransport experiments demonstrate that the Berry phase and associated AHE can be continuously and iteratively modified post-synthesis. The findings of this work should be widely applicable to other quantum materials where crystal distortions and symmetry are tightly bound to band structure and resulting Berry phase effects.

A Bessel beam has the properties of propagation invariance and a self-healing effect, leading to a variety of interesting phenomena and applications. Recently, as a planar diffractive element with miniaturized size, metasurfaces are widely employed to manipulate light in the subwavelength region, including generating a Bessel beam. However, such a metasurface-generated Bessel beam allows output light with no tunable functions. Here, with the interplay of the geometric phase and the dynamic phase, we propose a method to generate and allow conversion from any orthogonal polarizations to independent Bessel beams with a single-layer dielectric metasurface. The simulation results indicate that the arbitrary conversion between different Bessel beams is related to the spin-dependent orbit motion caused by the tight-focusing effect, leading to the singularity of the spot. This physical mechanism is well studied and the theoretical model for revealing the dependence of different incident polarization on the conversion dynamics is presented. Our approach paves a way for efficient generation and multifunctional applications, ranging from high-numerical-aperture devices to compact nanophotonic platforms for spin-dependent structured beams.

Real-time time-dependent density functional theory (RT-TDDFT) and ab initio molecular dynamics (AIMD) are combined to calculate non-resonant and resonant Raman scattering cross sections of periodic systems, allowing for an explicit quantum mechanical description of condensed phase systems and environmental effects. It is shown that this approach to Raman spectroscopy corresponds to a short time approximation of Heller's time-dependent formalism for the description of Raman scattering. Two ways to calculate the frequency-dependent polarizability in a periodic system are presented: (1) via the modern theory of polarization (Berry phase) and (2) via the velocity representation. Both approaches are found to be equivalent for a system of liquid (S)-methyloxirane with the computational settings used. Resulting non-resonance and resonance Raman spectra from the dynamic AIMD/RT-TDDFT approach are compared to the spectra of one gas phase molecule in the harmonic approximation highlighting finite temperature and solvation effects. Using RT-TDDFT to calculate the full frequency-dependent Placzek-type polarizability within one set of simulations covers the non-resonance, near-resonance, and on-resonance regimes on equal footing, thus allowing the calculation of full Raman excitation profiles.

Maxwellian electromagnetism describes the wave features of the light and related subjects. Its original formulation was established 150 years ago. One of the four Maxwell's equations is Gauss's law, which states significant facts regarding magnetic flux through surfaces. It was also observed that optical media provided surface electromagnetism around 60 years ago. This observation leads to improve new techniques on nano-photonics, metamaterials, and plasmonics. The goal of this manuscript is to suggest novel accurate and local conditions for defining magnetic flux surfaces for the inextensible Heisenberg antiferromagnetic flow in the binormal direction. The theoretical accuracy of the methodology is verified through the evolution of magnetic vector fields and the anti-symmetric Lorentz force field operator. On the other hand, the numerical accuracy and efficiency are developed in detail by considering the conformable fractional derivative method when these fields are transformed under the traveling wave hypothesis. © 2021. All Rights Reserved.

The massless Dirac fermions and the ease to introduce spatial and magnetic confinement in graphene provide us unprecedented opportunity to explore confined relativistic matter in this condensed-matter system. Here we report the interplay between the confinement induced by external electric fields and magnetic fields of the massless Dirac fermions in graphene. When the magnetic length lB is larger than the characteristic length of the confined electric potential lV, the spatial confinement dominates and a relatively small critical magnetic field splits the spatial-confinement-induced atomic-like shell states by switching on a pi Berry phase of the quasiparticles. When the lB becomes smaller than the lV, the transition from spatial confinement to magnetic confinement occurs and the atomic-like shell states condense into Landau levels (LLs) of the Fock-Darwin states in graphene. Our experiment demonstrates that the spatial confinement dramatically changes the energy spacing between the LLs and generates large electron-hole asymmetry of the energy spacing between the LLs. These results shed light on puzzling observations in previous experiments, which hitherto remained unaddressed., Comment: 4 Figures in main text

We address the question of different representation of Bloch states for lattices with a basis, with a focus on topological systems. The representations differ in the relative phase of the Wannier functions corresponding to the diffferent basis members. We show that the phase can be chosen in such a way that the Wannier functions for the different sites in the basis both become eigenstates of the position operator in a particular band. A key step in showing this is the extension of the Brillouin zone. When the distance between sites within a unit cell is a rational number, $p/q$, the Brillouin extends by a factor of $q$. For irrational numbers, the Brillouin zone extends to infinity. In the case of rational distance, $p/q$, the Berry phase "lives" on a cyclic curve in the parameter space of the Hamiltonian, on the Brillouin zone extended by a factor of $q$. For irrational distances the most stable way to calculate the polarization is to approximate the distance as a rational sequence, and use the formulas derived here for rational numbers. The use of different bases are related to unitary transformations of the Hamiltonian, as such, the phase diagrams of topological systems are not altered, but each phase can acquire different topological characteristics when the basis is changed. In the example we use, an extended Su-Schrieffer-Heeger model, the use of the diagonal basis leads to toroidal knots in the Hamiltonian space, whose winding numbers give the polarization.

We illustrate the geometric phase associated with the cyclic dynamics of a classical system of coupled oscillators. We use an analogy between a classical coupled oscillator and a two-state quantum mechanical system to represent the evolution of the oscillator on an equivalent Hilbert space, which may be represented as a trajectory on the surface of a sphere. The cyclic evolution of the system leads to a change in phase, which consists of a dynamic phase along with an additional phase shift dependent on the geometry of the evolution. A simple experiment suitable for advanced undergraduate students is designed to study the geometric phase incurred during cyclic evolution of a coupled oscillator., Comment: 13 pages, 10 figures

In this article, we study spherical optical Lorentz flux of spherical S t − optical flows with a spherical frame on the spherical optical Heisenberg space S H 2 . We get optical new conditions for spherical S t − optical Lorentz Heisenberg flux with spherical fields. Thus, we define spherical Lorentz Heisenberg flux for optical magnetic fields. We provide new construction for optical spherical curvatures of spherical S t − flows with spherical Landau Lifshitz condition. Additionally, magnetic optical flux surface is constructed in certain uniform optical surfaces with numerical and analytical results by spherical Landau Lifshitz condition.

Recently, intensive studies have revealed fascinating physics, such as charge density wave and superconducting states, in the newly synthesized kagome-lattice materials $A$V$_3$Sb$_5$ ($A$=K, Rb, Cs). Despite the rapid progress, fundamental aspects like the magnetic properties and electronic correlations in these materials have not been clearly understood yet. Here, based on the density functional theory plus the single-site dynamical mean-field theory calculations, we investigate the correlated electronic structure and the magnetic properties of the KV$_3$Sb$_5$ family materials in the normal state. We show that these materials are good metals with weak local correlations. The obtained Pauli-like paramagnetism and the absence of local moments are consistent with recent experiment. We reveal that the band crossings around the Fermi level form three groups of nodal lines protected by the spacetime inversion symmetry, each carrying a quantized $\pi$ Berry phase. Our result suggests that the local correlation strength in these materials appears to be too weak to generate unconventional superconductivity, and non-local electronic correlation might be crucial in this kagome system., Comment: 6 pages, 4 figures