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We apply the exact Wentzel–Kramers–Brillouin (WKB) analysis to a couple of 1D Schrödinger-type equations reduced from the Stark effect of hydrogen in a uniform electric field. By introducing Langer's modification and incorporating the Stokes graphs, we prove the exactness of the Bohr–Sommerfeld quantization conditions for the Borel-resummed quantum WKB periods in the specific parameter regions of the electric field intensity and magnetic quantum number. It is also found these quantization conditions get modified with an additional suppressed contribution when the parameters vary beyond the specific regions. We also present thermodynamic Bethe ansatz (TBA) equations governing the quantum periods in the absence of Langer's modification and discuss its wall-crossing and analytic continuation. Numerical calculations are conducted to compare the complex resonant frequencies from our quantization conditions against ones from the Riccati–Padé method; the TBA equations are also confirmed by comparing its expansions with all-order quantum periods. [ABSTRACT FROM AUTHOR]

The angular momentum of any quantum system should be unambiguously quantized. We show that such a quantization fails for a pure Dirac monopole due to a previously overlooked field angular momentum from the monopole-electric charge system coming from the magnetic field of the Dirac string and the electric field of the charge. Applying the point-splitting method to the monopole-charge system yields a total angular momentum which obeys the standard angular momentum algebra, but which is gauge variant. In contrast it is possible to properly quantize the angular momentum of a topological 't Hooft–Polyakov monopole plus charge. This implies that pure Dirac monopoles are not viable – only 't Hooft–Polyakov monopoles are theoretically consistent with angular momentum quantization and gauge invariance. [ABSTRACT FROM AUTHOR]

In this study, we address the electronic properties of conducting films constituted of an array of randomly distributed few layer graphene patches and investigate on their most salient galvanometric features in the moderate and extreme disordered limit. We demonstrate that, in annealed devices, the ambipolar behaviour and the onset of Landau level quantization in high magnetic field constitute robust hallmarks of few-layer graphene films. In the strong disorder limit, however, the magnetotransport properties are best described by a variable-range hopping behaviour. A large negative magneto-conductance is observed at the charge neutrality point, in consistency with localized transport regime. [ABSTRACT FROM AUTHOR]

The interplay between ferromagnetism and topological properties of electronic band structures leads to a precise quantization of Hall resistance without any external magnetic field. This so-called quantum anomalous Hall effect (QAHE) is born out of topological correlations, and is oblivious of low-sample quality. It was envisioned to lead towards dissipation-less and topologically protected electronics. However, no clear framework of how to design such an electronic device out of it exists. Here we construct an ultra-low power, non-volatile, cryogenic memory architecture leveraging the QAHE phenomenon. Our design promises orders of magnitude lower cell area compared with the state-of-the-art cryogenic memory technologies. We harness the fundamentally quantized Hall resistance levels in moiré graphene heterostructures to store non-volatile binary bits (1, 0). We perform the memory write operation through controlled hysteretic switching between the quantized Hall states, using nano-ampere level currents with opposite polarities. The non-destructive read operation is performed by sensing the polarity of the transverse Hall voltage using a separate pair of terminals. We custom design the memory architecture with a novel sensing mechanism to avoid accidental data corruption, ensure highest memory density and minimize array leakage power. Our design provides a pathway towards realizing topologically protected memory devices. [ABSTRACT FROM AUTHOR]

Abstract We theoretically investigate multiphonon resonance Raman scattering between the Landau levels in graphene on the polar substrate using the Huang-Rhys's model. We not only present the single and multiple surface optical (SO) phonons scattering, but also propose the combined multiphonon scattering, which is composed of the SO phonon and longitudinal acoustic phonon. We find that the combined multiphonon scattering has a blue-shift behavior with increasing the magnetic field, differing from these SO phonon resonance scattering occurred at specific magnetic field values. This behavior may be used to explain the changing shoulder of the Raman spectrum of optical phonon resonance scattering in experiments. The theoretical model could be expanded to analyze the fine structure of Raman spectrum in two-dimensional materials. Graphical abstract The distribution of Landau levels in graphene in a strong magnetic field. The possible multiphonon resonance Raman processes are occurred between these Landau levels. Image 1 [ABSTRACT FROM AUTHOR]

We examine the recently introduced idea of Spin-Field Correspondence (SFC) focusing on the example of the spin system described by the XXZ Heisenberg model with external magnetic field. The Hamiltonian of the resulting nonlinear scalar field theory is derived for arbitrary value of the anisotropy parameter Δ. We show that the linear scalar field theory is reconstructed in the large spin limit. For Δ = 1 , a nonrelativistic scalar field theory satisfying the Born reciprocity principle is recovered. As expected, for the vanishing anisotropy parameter Δ → 0 , the standard relativistic Klein–Gordon field is obtained. Various aspects of the obtained class of the scalar fields are studied, including the fate of the relativistic symmetries and the properties of the emerging interaction terms. We show that, in a certain limit, the so-called polymer quantization of the field variables is recovered. This and other discussed properties suggest a possible relevance of the considered framework in the context of quantum gravity. [ABSTRACT FROM AUTHOR]

Developing alternative paradigms of electronics beyond silicon technology requires the exploration of fundamentally new physical mechanisms, such as the valley-specific phenomena in hexagonal two-dimensional materials. We realize ballistic valley Hall kink states in bilayer graphene and demonstrate gate-controlled current transmission in a four-kink router device. The operations of a waveguide, a valve, and a tunable electron beam splitter are demonstrated. The valley valve exploits the valley-momentum locking of the kink states and reaches an on/off ratio of 8 at zero magnetic field. A magnetic field enables a full-range tunable coherent beam splitter. These results pave a path to building a scalable, coherent quantum transportation network based on the kink states. [ABSTRACT FROM AUTHOR]

In metals, orbital motions of conduction electrons on the Fermi surface are quantized in magnetic fields, which is manifested by quantum oscillations in electrical resistivity. This Landau quantization is generally absent in insulators. Here, we report a notable exception in an insulator—ytterbium dodecaboride (YbB12). The resistivity of YbB12, which is of a much larger magnitude than the resistivity in metals, exhibits distinct quantum oscillations. These unconventional oscillations arise from the insulating bulk, even though the temperature dependence of the oscillation amplitude follows the conventional Fermi liquid theory of metals with a large effective mass. Quantum oscillations in the magnetic torque are also observed, albeit with a lighter effective mass. [ABSTRACT FROM AUTHOR]

In this letter, we have discussed the implications of nonlocal-in-time kinetic energy approach recently introduced by Suykens on the dynamics of charge particles spin in a magnetic field with spin. It was observed that both the Landau quantization of the energy and their levels positions are modified. Besides, massive photons are generated in magnetic materials similar to the one encountered in massive quantum electrodynamics. These massive photons depend on the electron mass and on the nonlocal relaxation time. For solid copper, we found M ≈ 3.4 × 10 - 20 α - 2 eV / c 2 where α is a real free parameter. [ABSTRACT FROM AUTHOR]

We prove a criterion for a "magnetic" Weyl operator to be trace-class by extending a method developed by Cordes, Kato and Arsu. Using the Calderon-Vaillancourt type Theorem for magnetic Weyl operators and an interpolation argument we also give a criterion for a "magnetic" Weyl operator to be in a Schatten-von Neumann class with 1 < p < ∞. [ABSTRACT FROM AUTHOR]

Quantum states have been calculated analytically; the dynamics of a wave packet in a magnetic field has been investigated, and the optical absorption coefficient has been calculated for surface states in 3D topological insulators of the Bi2Te3 family. We have detected a qualitative effect of the hexagonal warping of the spectrum on the structure of wavefunctions at the Landau levels, its manifestation in the features of the wave packet dynamics in a quantizing magnetic field, as well as in the frequency dependence of the optical absorption coefficient, in which new peaks that are absent in the isotropic model of the spectrum appear depending on the polarization of the incident wave. The effects considered here can be manifested in the optical and transport experiments with topological insulators, which makes it possible to determine the parameters of their band structure. [ABSTRACT FROM AUTHOR]

Dirac Fermions with different helicities exist on the top and bottom surfaces of topological insulators, offering a rare opportunity to break the degeneracy protected by the no-go theorem. Through the application of Co clusters, quantum Hall plateaus were modulated for the topological insulator BiSbTeSe2, allowing an optimized surface transport. Here, using renor-malization group flow diagrams, we show the extraction of two sets of converging points in the conductivity tensor space, revealing that the top surface exhibits an anomalous quantization trajectory, while the bottom surface retains the 1/2 quantization. Co clusters are believed to induce a sizeable Zeeman gap ( > 4.8 meV) through antiferromagnetic exchange coupling, which delays the Landau level hybridization on the top surface for a moderate magnetic field. A quasi-half-integer plateau also appears at -7.2 Tesla. This allows us to study the interesting physics of parity anomaly, and paves the way for further studies simulating exotic particles in condensed matter physics. [ABSTRACT FROM AUTHOR]

We report experiments on the two-terminal conductance of a long disordered quantum wire in a perpendicular magnetic field. Pronouncedly enhanced magnetoconductance in magnetic fields of intermediate strength is observed in the Coulomb blockade regime, which is well explained using the boundary roughness scattering and the subband quantization of the quantum wire, by modeling the disordered quantum wire as that of a quantum dot defined in a quantum wire. Assuming a parabolic constriction in the disordered quantum wire, we further obtained the magnetic field dependence of high energy levels in the quantum dot and the gate voltage dependence of the effective width of the quantum wire. Our results may provide useful information for further studies on integrated structures in on-chip laboratories. [ABSTRACT FROM AUTHOR]

The quantum description of an atom with a magnetic quadrupole moment in the presence of a time-dependent magnetic field is analysed. It is shown that the time-dependent magnetic field induces an electric field that interacts with the magnetic quadrupole moment of the atom and gives rise to a Landau-type quantization. It is also shown that a time-independent Schrödinger equation can be obtained, i.e., without existing the interaction between the magnetic quadrupole moment of the atom and the time-dependent magnetic field, therefore, the Schrödinger equation can be solved exactly. It is also analysed this system subject to scalar potentials. [ABSTRACT FROM AUTHOR]

In the present work, we have investigated the effect of trapping as a microscopic phenomenon on the formation of solitary structures in the presence of a quantizing magnetic field in an electronpositron-ion (e-p-i) plasma having degenerate electrons and positrons, whereas ions are taken to be classical and cold. We have found that positron concentration, quantizing magnetic field, and finite electron temperature effects not only affect the linear dispersion characteristics of the electrostatic waves under consideration but also have a significant bearing on the propagation of solitary structures in the nonlinear regime. Importantly, the system under consideration has been found to allow the formation of compressive solitary structures only. The work presented here may be beneficial to understand the propagation of nonlinear electrostatic structures in dense astrophysical environments and in intense-laser plasma interactions. [ABSTRACT FROM AUTHOR]

Kinematics and dynamics of a particle moving on a torus knot poses an interesting problem as a constrained system. In the first part of the paper we have derived the modified symplectic structure or Dirac brackets of the above model in Dirac’s Hamiltonian framework, both in toroidal and Cartesian coordinate systems. This algebra has been used to study the dynamics, in particular small fluctuations in motion around a specific torus. The spatial symmetries of the system have also been studied. In the second part of the paper we have considered the quantum theory of a charge moving in a torus knot in the presence of a uniform magnetic field along the axis of the torus in a semiclassical quantization framework. We exploit the Einstein–Brillouin–Keller (EBK) scheme of quantization that is appropriate for multidimensional systems. Embedding of the knot on a specific torus is inherently two dimensional that gives rise to two quantization conditions. This shows that although the system, after imposing the knot condition reduces to a one dimensional system, even then it has manifested non-planar features which shows up again in the study of fractional angular momentum. Finally we compare the results obtained from EBK (multi-dimensional) and Bohr–Sommerfeld (single dimensional) schemes. The energy levels and fractional spin depend on the torus knot parameters that specifies its non-planar features. Interestingly, we show that there can be non-planar corrections to the planar anyon-like fractional spin. [ABSTRACT FROM AUTHOR]

The photoluminescence spectra of exciton polaritons in microcavities under conditions of three-dimensional quantization are studied as a factor of the density of the optical excitation and magnetic field. The behavior of the degree of circular polarization of the exciton luminescence in a magnetic field shows that, when the concentration of excitons increases, they condense at the lowest Zeeman sublevel. [ABSTRACT FROM AUTHOR]

For nonparabolic dispersion law determined by the density of the energy states in a quantizing magnetic field, the dependence of the density of energy states on temperature in quantizing magnetic fields is studied with the nonquadratic dispersion law. Experimental results obtained for PbTe were analyzed using the suggested model. The continuous spectrum of the energy density of states at low temperature is transformed into discrete Landau levels. [ABSTRACT FROM AUTHOR]

We investigate the influence of external electric fields on the spins of a ballistic nanowire in terms of variations of the Rashba parameter and modification of the confinement potential. For a weak Rashba effect, the spins along the confinement direction in a given subband nearly assume full quantization. In the presence of a perpendicular magnetic field, the state of quantization can be manipulated using a transverse electric. This process requires modifications in the spin textures. If an in-plane magnetic field is applied, spins suffer rigid displacement to one edge of the wire and their expectation value becomes independent of the transverse electric field. [ABSTRACT FROM AUTHOR]

Ballistic electron transport is a key requirement for existence of a topological phase transition in proximitized InSb nanowires. However, measurements of quantized conductance as direct evidence of ballistic transport have so far been obscured due to the increased chance of backscattering in one-dimensional nanowires. We show that by improving the nanowire-metal interface as well as the dielectric environment we can consistently achieve conductance quantization at zero magnetic field. Additionally we study the contribution of orbital effects to the sub-band dispersion for different orientation of the magnetic field, observing a near-degeneracy between the second and third sub-bands. [ABSTRACT FROM AUTHOR]

Quantized conductance is observed at zero magnetic field and room temperature in metal-insulator-metal structures with graphene submicron-sized nanoplatelets embedded in a 3-hexylthiophene (P3HT) polymer layer. In devices with medium concentration of graphene platelets, integer multiples of G = 2 e/ h (=12.91 kΩ), and in some devices partially quantized including a series of with ( n/7) × G, steps are observed. Such an organic memory device exhibits reliable memory operation with an on/off ratio of more than 10. We attribute the quantized conductance to the existence of a 1-D electron waveguide along the conductive path. The partial quantized conductance results likely from imperfect transmission coefficient due to impedance mismatch of the first waveguide modes. [ABSTRACT FROM AUTHOR]

We study the quantum capacitance in the objects with completely discrete structure of electron states as a result of both dimensional quantization and applied magnetic field. The capacitance is analyzed in such objects as nanoplates of metal, semiconductor and semimetal. Factors which define the form of the dependence of on the position of the Fermi level or potential bias, and magnetic field, are analyzed. [ABSTRACT FROM AUTHOR]

Novel quantization properties related to the state vectors and the energy spectrum of a two-dimensional system of free particles are obtained in the framework of noncommutative (NC) quantum mechanics (QM) supported by the Weyl–Wigner formalism. Besides reproducing the magnetic field aspect of a Zeeman-like effect, the momentum space NC parameter introduces mutual information properties quantified by the quantum purity related to the relevant coordinates of the corresponding Hilbert space. Supported by the QM in the phase-space, the thermodynamic limit is obtained, and the results are extended to three-dimensional systems. The noncommutativity imprints on the thermodynamic variables related to free particles are identified and, after introducing some suitable constraints to fix an axial symmetry, the analysis is extended to two- and- three dimensional quantum rotor systems, for which the quantization aspects and the deviation from standard QM results are verified. [ABSTRACT FROM AUTHOR]

We present a theoretical description of the process of therahertz emission in biased semiconductor superlattices that follows an ultra-fast interband excitation. The results show that the average current performs Bloch oscillations whose amplitude depends on the intrinsic characteristic of the superlattice as well as on the light pulse parameters. In these calculations we use a fully three-dimensional picture and include the excitonic effects. We also studied the terahertz intensity when the sample is subjected to a magnetic field parallel to its axis. We considered in detail the high magnetic field regime, where the in-plane motion is frozen in Landau orbits spectrally well separated. In this regime, a set of quasi one-dimensional Bloch oscillators can be ideally generated (oscillators with decoupled vertical and lateral electron motions), making the terahertz emission more intense and more coherent. [ABSTRACT FROM AUTHOR]

This work describes coherent states for a physical system governed by a Hamiltonian operator, in two-dimensional space, of spinless charged particles subject to a perpendicular magnetic field B , coupled with a harmonic potential. The underlying s u ( 1 , 1 ) Lie algebra and Barut–Girardello coherent states are constructed and discussed. Then, the Berezin–Klauder–Toeplitz quantization, also known as coherent state (or anti-Wick) quantization, is discussed. The thermodynamics of such a quantum gas system is elaborated and analyzed. [ABSTRACT FROM AUTHOR]

The energy of magnetic moment of the persistent current circulating in superconducting loop in an externally produced magnetic field is not taken into account in the theory of quantization effects because of identification of the Hamiltonian with the energy. This identification misleads if, in accordance with the conservation law, the energy of a state is the energy expended for its creation. The energy of magnetic moment is deduced from a creation history of the current state in magnetic field both in the classical and quantum case. But taking this energy into account demolishes the agreement between theory and experiment. Impartial consideration of this problem discovers the contradiction both in theory and experiment. [ABSTRACT FROM AUTHOR]

Within the framework of perturbation theory formulas are derived that estimate effective hole masses in a Ge single crystal in a strong quantizing magnetic field in the vicinity of the point k = 0 when the magnetic field is oriented along the [001] direction. Values of effective hole masses for some Landau levels (n = 2-6) are calculated. [ABSTRACT FROM AUTHOR]

The spectrum of allowed energy of electron in graphene superlattice in the quantizing magnetic field is investigated. Such spectrum consists of number of so-called magnetic minibands. The width of these minibands depends on the superlattice barriers power and on the magnetic field intensity. The explicit form of electron spectrum is derived in the case of weak magnetic field. The possibility of electron-electron and electron-phonon bound states is shown. The binding energies of these states are calculated. The binding energy is shown to be the function of magnetic field intensity. [ABSTRACT FROM AUTHOR]

Topological properties of the spin-1/2 dimerized Heisenberg ladder are investigated focusing on the plateau phase in the magnetic field whose magnetization is half of the saturation value. Although the applied magnetic field removes most of the symmetries of the system, there is a symmetry protected topological phase supported by the spatial inversion symmetry. The Z2 Berry phase associated with a symmetry respecting boundary and quantized into 0 and π is used as a symmetry protected topological order parameter. Edge states are also analyzed to confirm the bulk-edge correspondence. In addition, a symmetry breaking boundary is considered. Then, we observe a unique type of quantization of the Berry phase, a quantization into ±π/2 of the Berry phase. In this case, the bulk-edge correspondence is also unique, namely, there emerge "polarized" edge states for the case with ±π/2 quantization. We also evaluate the entanglement entropy by the infinite time-evolving block decimation (iTEBD) to complement the Berry phase based arguments. Further, a different type of the topological order parameter is extracted from the matrix product state representation of the ground state given by the iTEBD. [ABSTRACT FROM AUTHOR]

The photogalvanic effect is studied in electron gas over the liquid He surface with the presence of quantizing magnetic field. The gas is affected by the weak alternating microwave electric field tilted towards the surface normal. Both linear and circular photogalvanic effects are studied. The current occurs via indirect phototransition with the participation of ripplons emission or absorption. The photogalvanic tensor has strong resonances at the microwave frequency ω approaching to the frequencies of transitions between size-quantized subbands. The resonances are symmetric or antisymmetric, depending on a tensor component. Other resonances appear at ω ≈ nω, where n being integer and ω is the cyclotron frequency. It is found that the latter resonances split to two peaks connected with emission or absorption of ripplons. The calculated photogalvanic coefficients are in accord with the experimental observed values. [ABSTRACT FROM AUTHOR]

The energy spectrum and wave functions of holes in the valence band in semiconductor nanosystems, including quantum wells, quantum wires, and quantum dots, in an external magnetic field are theoretically investigated. The dependence of Zeeman splitting of the hole ground state upon variation in the size-quantization parameters with regard to the complex structure of the valence band and magnetic field-induced mixing of hole states is traced. Analytical formulas for describing the Zeeman effect in the valence band in the limiting cases of a quantum disk, spherically symmetric quantum dot, and quantum wire are presented. It is demonstrated that the g-factor of a hole is extremely sensitive to the hole-state composition (heavy or light hole) and, consequently, to the geometry of the size-quantization potential. [ABSTRACT FROM AUTHOR]

We report a nearly ideal quantum anomalous Hall effect in a three-dimensional topological insulator thin film with ferromagnetic doping. Near zero applied magnetic field we measure exact quantization in the Hall resistance to within a part per 10 000 and a longitudinal resistivity under 1 Ω per square, with chiral edge transport explicitly confirmed by nonlocal measurements. Deviations from this behavior are found to be caused by thermally activated carriers, as indicated by an Arrhenius law temperature dependence. Using the deviations as a thermometer, we demonstrate an unexpected magnetocaloric effect and use it to reach near-perfect quantization by cooling the sample below the dilution refrigerator base temperature in a process approximating adiabatic demagnetization refrigeration. [ABSTRACT FROM AUTHOR]

We report on the magnetic trapping of an ultracold ensemble of 87Rb atoms close to a superconducting ring prepared in different states of quantized magnetic flux. The niobium ring of 10 μm radius is prepared in a flux state n Φ0, where Φ0 = h/2e is the flux quantum and n varying between ±6. An atomic cloud of 250 nK temperature is positioned with a harmonic magnetic trapping potential at ~18 μm distance below the ring. The inhomogeneous magnetic field of the supercurrent in the ring contributes to the magnetic trapping potential of the cloud. The induced deformation of the magnetic trap impacts the shape of the cloud, the number of trapped atoms, as well as the center-of-mass oscillation frequency of Bose-Einstein condensates. When the field applied during cooldown of the chip is varied, the change of these properties shows discrete steps that quantitatively match flux quantization. [ABSTRACT FROM AUTHOR]

Electronic properties of surface areas decoupled from graphite are studied using scanning tunneling microscopy and spectroscopy. We show that it is possible to identify the decoupled graphene monolayer, the Bernal bilayer, and the Bernal trilayer on a graphite substrate according to their tunneling spectra in a high magnetic field. The decoupled monolayer and bilayer exhibit Landau quantization of massless and massive Dirac fermions, respectively. The substrate generates a sizable band gap ~35 meV in the Bernal bilayer, therefore, the eightfold degenerate Landau level at the charge neutrality point is split into two valley-polarized quartets polarized on each layer. In the decoupled Bernal trilayer, we find that both massless and massive Dirac fermions coexist and its low-energy band structure can be described quite well by taking into account only the nearest-neighbor intra- and interlayer hopping parameters. A strong correlation between the Fermi velocity of the massless Dirac fermions and the effective mass of the massive Dirac fermions is observed in the graphene trilayer. Our result demonstrates that the surface of graphite provides a natural ideal platform to probe the electronic spectra of graphene layers. [ABSTRACT FROM AUTHOR]

In the present investigation, linear and nonlinear propagation of low frequency (ω≪&#937;ci) electrostatic waves have been studied in a spatially inhomogeneous degenerate plasma with one dimensional electron trapping in the presence of a quantizing magnetic field and finite temperature effects. Using the drift approximation, formation of 1 and 2D drift ion solitary structures have been studied both for fully and partially degenerate plasmas. The theoretical results obtained have been analyzed numerically for the parameters typically found in white dwarfs for illustrative purpose. It is observed that the inclusion of Landau quantization significantly changes the expression of the electron number density of a dense degenerate plasma which affects the linear and nonlinear propagation of drift acoustic solitary waves in such a system. The present work may be beneficial to understand the propagation of drift solitary structures with weak transverse perturbation in a variety of physical situations, such as white dwarfs and laser-induced plasmas, where the quantum effects are expected to dominate. [ABSTRACT FROM AUTHOR]

We compute static equilibria of white dwarf stars containing strong poloidal magnetic field, and present the modification of white dwarf mass–radius relation caused by the magnetic field. We find that a maximum white dwarf mass of about 1.9 M⊙ may be supported if the interior field is as strong as approximately 1010 T. This mass is over 30 per cent larger than the traditional Chandrasekhar Limit. The equation of state of electron degenerate matter can be strongly modified due to Landau quantization at such high magnetic fields. We find, however, that this does not significantly affect the structure of the white dwarf. [ABSTRACT FROM AUTHOR]

We analyze the quantum phenomenon arising from the interaction of a spinless charged particle with a rotating cosmic string, under the action of a static and uniform magnetic field parallel to the string. We calculate the energy levels of the particle in the non-relativistic approach, showing how these energies depend on the parameters involved in the problem. In order to do this, we solve the time independent Schrödinger equation in the geometry of the spinning cosmic string, taking into account that the coupling between the rotation of the spacetime and the angular momentum of the particle is very weak, such that makes sense to apply the Schrödinger equation in a curved background whose metric has an off diagonal term which involves time and space. It is also assumed that the particle orbits sufficiently far from the boundary of the region of closed timelike curves which exist around this topological defect. Finally, we find the Landau levels of the particle in the presence of a spinning cosmic string endowed with internal structure, i.e. , having a finite width and uniformly filled with both material and vacuum energies. [ABSTRACT FROM AUTHOR]

We study the influence of a background uniform magnetic field and boundary conditions on the vacuum of a quantized charged massive scalar matter field confined between two parallel plates; the magnetic field is directed orthogonally to the plates. The admissible set of boundary conditions at the plates is determined by the requirement that the operator of one-particle energy squared be self-adjoint and positive-definite. We show that, in the case of a weak magnetic field and a small separation of the plates, the Casimir force is either attractive or repulsive, depending on the choice of a boundary condition. In the case of a strong magnetic field and a large separation of the plates, the Casimir force is repulsive, being independent of the choice of a boundary condition, as well as of the distance between the plates. [ABSTRACT FROM AUTHOR]

Abstract: We investigate the modification of the pion self-energy at finite temperature due to its interaction with a low-density, isospin-symmetric nuclear medium embedded in a constant magnetic background. To one loop, for fixed temperature and density, we find that the pion effective mass increases with the magnetic field. For the , interestingly, this happens solely due to the trivial Landau quantization shift , since the real part of the self-energy is negative in this case. In a scenario in which other charged particle species are present and undergo an analogous trivial shift, the relevant behavior of the effective mass might be determined essentially by the real part of the self-energy. In this case, we find that the pion mass decreases by for a magnetic field , which favors pion condensation at high density and low temperatures. [Copyright &y& Elsevier]

Bound and resonance states of quantum dots play a significant role in photo-absorption processes. In this work, we analyse a cylindrical quantum dot, its spectrum and, in particular, the behaviour of the lowest resonance state when a magnetic field is applied along the symmetry axis of the cylinder. To obtain the energy and width of the resonance we use the complex rotation method. As expected, the structure of the spectrum is strongly influenced by the Landau levels associated to the magnetic field. We show how this structure affects the behaviour of the resonance state and that the binding of the resonance has a clear interpretation in terms of the Landau levels and the probability of localization of the resonance state. The localization probability and the fidelity of the lowest energy state allow identification of two different physical regimes, a large field–small quantum dot radius regime and a small field–large quantum dot radius, where the binding of the resonance is dominated by the field strength or the potential well, respectively. [ABSTRACT FROM AUTHOR]

Analysis of properties of an electron (electrons) in a periodic two-dimensional potential and quantised magnetic field is presented. The key role in this description is played by the symmetry of the model determined by the magnetic translation group, together with the symmetric and unitary group according to the duality of Weyl. The magnetic translation group is described in detail along with its irreducible representations which form the Brillouin zone in magnetic field. Together with the other two mentioned groups, it allows to characterize the system providing some good quantum numbers. These groups facilitate determination of the band structure through the diagonalisation of the eigenvalue problem in the base adapted to the considered symmetry. The difference between the Brillouin zone with and without magnetic field is pointed out. Discussion is concentrated on the finite two-dimensional systems, closed by use of Born-von Karman boundary conditions. [ABSTRACT FROM AUTHOR]

Theoretical research has predicted that a ripple of graphene generates an effective gauge field on its low-energy electronic structure and could lead to Landau quantization. Here, we demonstrate using a combination of an experimental method (scanning tunneling microscopy) and a theoretical approach (tight-binding approximation) that Landau levels will form when the effective pseudomagnetic flux per ripple Φ~(h²/la)Φ0 is larger than the flux quantum Φ0 (here, h is the height, l is the width of the ripple, and a is the nearest C-C bond length). The strain-induced gauge field in the ripple only results in one-dimensional (1D) Landau-level quantization along the ripple. Such 1D Landau quantization does not exist in two-dimensional systems in an external magnetic field. Its existence offers a unique opportunity to realize interesting electronic properties in strained graphene. [ABSTRACT FROM AUTHOR]

We present measurements of the electron transport in top-gated InAs spin-filter cascades. The cascades consist of a first filter stage that acts as a polarizer, a center wire, and a second filter stage that acts as an analyzer. Conductance quantization indicates quasi-ballistic transport in these rather large devices. Oscillations of the conductances of the second filter's outputs with the strength of an in-plane magnetic field perpendicular to the center wire provide evidence of the so-called zitterbewegung and substantiate the interpretation of the conductance imbalance at the second filter as the consequence of a spin polarization. [ABSTRACT FROM AUTHOR]

Formulas for the contribution of the conduction electrons to the polarization and magnetization are derived for disordered systems and within a one-particle framework. These results generalize known formulas for Bloch electrons and the presented proofs considerably simplify and strengthen prior justifications. The new formulas show that orbital polarization and magnetization are of geometric nature. This leads to quantization for a periodically driven Piezo effect as well as the derivative of the magnetization w.r.t. the chemical potential. It is also shown how the latter is connected to boundary currents in Chern insulators. The main technical tools in the proofs are an adaption of Nenciu's super-adiabatic theory to C*-dynamical systems and Bellissard's Ito derivatives w.r.t. the magnetic field. [ABSTRACT FROM AUTHOR]

We theoretically investigate the appearance of spatially modulated superconducting states in mesoscopic superconducting thin-wall cylinders in a magnetic field at low temperatures. Quantization of the electron motion around the circumference of the cylinder leads to a discontinuous evolution of the spatial modulation of the superconducting order parameter along the transition line Tc(H). We show that this discontinuity leads to the nonmonotonic behavior of the specific heat jump at the onset of superconductivity as a function of temperature and field. We argue that this geometry provides an excellent opportunity to directly and unambiguously detect distinctive signatures of the Fulde-Ferrell-Larkin-Ovchinnikov modulation of the superconducting order. [ABSTRACT FROM AUTHOR]

This review describes the results of investigations on charged particle dynamics in a magnetic field carried out over a number of years. The studies have unravelled the existence of some very surprising and unusual phenomena. Though existing on the macro-scale, they are found to be of quantum origin, and are thereby not covered by the Lorentz equation, which has been regarded conventionally as the descriptor of electrodynamic phenomena on the macro-scale. These novel phenomena have been found to be attributed to the ‘quantum modulation’ of the de Broglie wave along the magnetic field. This is brought about through the scattering-induced transition across Landau levels, leading to the modulation of the plane wave state along the field as a result of the entanglement between the parallel and perpendicular degrees of freedom. These findings were motivated by the predictions of a formalism developed by the author and include such unusual phenomena as (i) macro-scale matter wave interference effects and (ii) the detection of curl-free vector potential also on the macro-scale, both attributed to quantum modulation which is a matter wave on the macro-scale. The formalism is thus described as ‘macro-quantization of guiding centre motion’. [ABSTRACT FROM AUTHOR]

A non-commutative formula for the isotropic magneto-electric response of disordered insulators under magnetic fields is derived using the methods of non-commutative geometry. Our result follows from an explicit evaluation of the Ito derivative with respect to the magnetic field of the non-commutative formula for the electric polarization reported in Schulz-Baldes and Teufel (2012 arXiv:1201.4812v1). The quantization, topological invariance and connection to a second Chern number of the magneto-electric response are discussed in the context of three-dimensional, disordered, time-reversal or inversion symmetric topological insulators. [ABSTRACT FROM AUTHOR]

We show in elementary terms the equivalence in a general gauge of a U(1)-gauge theory of a scalar charged particle on a torus $\mathbb{T}^{n}=\mathbb{R}^{n}/\varLambda$ to the analogous theory on ℝ constrained by quasiperiodicity under translations in the lattice Λ. The latter theory provides a global description of the former: the quasiperiodic wavefunctions ψ defined on ℝ play the role of sections of the associated hermitean line bundle E on $\mathbb{T}^{n}$, since also E admits a global description as a quotient. The components of the covariant derivatives corresponding to a constant (necessarily integral) magnetic field B= dA generate a Lie algebra g and together with the periodic functions the algebra of observables $\mathcal {O}_{Q}$. The non-abelian part of g is a Heisenberg Lie algebra with the electric charge operator Q as the central generator; the corresponding Lie group G acts on the Hilbert space as the translation group up to phase factors. Also the space of sections of E is mapped into itself by g∈ G. We identify the socalled magnetic translation group as a subgroup of the observables' group Y. We determine the unitary irreducible representations of $\mathcal{O}_{Q},Y_{Q}$ corresponding to integer charges and for each of them an associated orthonormal basis explicitly in configuration space. We also clarify how in the n=2 m case a holomorphic structure and Theta functions arise on the associated complex torus. These results apply equally well to the physics of charged scalar particles on ℝ and on $\mathbb{T}^{n}$ in the presence of periodic magnetic field B and scalar potential. They are also necessary preliminary steps for the application to these theories of the deformation procedure induced by Drinfel'd twists. [ABSTRACT FROM AUTHOR]

The magnetotransport characteristics of quasi-two-dimensional electronic Corbino disks based on a wide GaAs quantum well with two filled subbands of size quantization are studied. At low temperatures and high magnetic fields, the Corbino disks exhibit the oscillations of differential conductivity, which are periodic with respect to dc electric field E. It is shown that the observed oscillations are related to the Zener tunneling induced by E. The tunneling occurs between the filled and empty Landau levels under conditions corresponding to the absence of the Hall field. [ABSTRACT FROM AUTHOR]

We have studied quantized transport in HgTe wells with inverted band structure corresponding to the two-dimensional topological insulator phase (2D TI) with locally controlled density allowing n-p-n and n-2D TI-n junctions. The resistance reveals the fractional plateau 2h/e2 in the n-p-n regime in the presence of the strong perpendicular magnetic field. We found that in the n-2D TI-n regime the plateaux in resistance in not universal and results from the edge state equilibration at the interface between chiral and helical edge modes. We provided the simple model describing the resistance quantization in n-2D TI-n regime. [ABSTRACT FROM AUTHOR]