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The dependence of the Hall and bend resistances on a perpendicular magnetic field and on vacancy defects in a four-terminal phosphorene single layer Hall bar is investigated. A tight-binding model in combination with the Landauer-Buttiker formalism is used to calculate the energy spectrum, the lead-to-lead transmissions, and the Hall and bend resistances of the system. It is shown that the terminals with zigzag edge orientation are responsible for the absence of quantized plateaus in the Hall resistance and peaks in the longitudinal resistance. A negative bend resistance in the ballistic regime is found due to the presence of high- and low-energy transport modes in the armchair and zigzag terminals, respectively. The system density of states, with single vacancy defects, shows that the presence of in-gap states is proportional to the number of vacancies. Quantized plateaus in the Hall resistance are only formed in a sufficiently clean system. The effects of different kinds of vacancies where the plateaus are destroyed and a diffusive regime appears in the bend resistance are investigated.

The spin Hall torque induced by DC current was studied experimentally. A Pt/Co/Pt structure with perpendicular magnetic anisotropy was grown, and magnetization reversal due to the spin Hall effect was observed. An extra magnetic field perpendicular to the sample was applied in addition to a constant bias field. It was found that the switching current shifted in proportion to the additional perpendicular field. The spin Hall angle was estimated from this relation, and the small perpendicular magnetic field can be measured accurately based on this effect.

It is well known that superconducting films made of a type-I material can demonstrate a type-II magnetic response, developing stable vortex configurations in a perpendicular magnetic field. Here we show that the superconducting state of a type-I nanowire undergoes more complex transformations, depending on the nanowire thickness. Sufficiently thin nanowires deviate from type I and develop multiquantum vortices and vortex clusters similar to intertype (IT) vortex states in bulk superconductors between conventional superconductivity types I and II. When the nanowire thickness decreases further, the quasi-one-dimensional vortex matter evolves towards type II so that the IT vortex configurations gradually disappear in favor of the standard Abrikosov lattice (chain) of single-quantum vortices. However, type II is not reached. Instead, an ultrathin nanowire re-enters abruptly the type-I regime while vortices tend to be suppressed by the boundaries, eventually becoming one-dimensional phase-slip centers. Our results demonstrate that arrays of nanowires can be used to construct composite superconducting materials with a widely tunable magnetic response.

The Peierls substitution in the energy functions of a carbon nanotube's sub-bands is carried out for a carbon nanotube of arbitrary chiral indices subjected to a perpendicular uniform magnetic field. The Peierls substitution represents a zeroth-order term of the asymptotically convergent power series in the magnetic field. It provides a very good approximation for the electron energy spectrum of a carbon nanotube subjected to a perpendicular uniform magnetic field, for magnetic fields currently accessible in laboratories.

By measuring the thermoelectric effect in high-mobility quantum wells with two occupied subbands in perpendicular magnetic field, we detect magnetophonon oscillations due to interaction of electrons with acoustic phonons. These oscillations contain specific features identified as combined resonances caused by intersubband phonon-assisted transitions of electrons in the presence of Landau quantization. The quantum theory of phonon-drag magnetothermoelectric effect, generalized to the case of multi-subband occupation, describes our experimental findings., 7 pages, 6 figures

By measuring magnetoresistance and Hall effect in classically moderate perpendicular magnetic field in Si-MOSFET-type macroscopic antidot array we found a novel effect: nonlinear with field, temperature- and density-dependent Hall resistivity. We discuss qualitative explanation of the phenomenon and suggest that it might originate from strong temperature dependence of the resistivity and mobility in the shells of the antidots., 4 pages, 7 figures

The effect of a perpendicular magnetic field on the quantized current induced by a surface acoustic wave in a quasi-one-dimensional channel is studied. The channel was defined in a GaAs heterostructure by a shallow-etching technique. The quantized current in this constriction displayed superior precision (\ifmmode\pm\else\textpm\fi{}60 ppm) and robustness to dc bias relative to that observed previously in Schottky-gate-defined channels. In a perpendicular magnetic field commensurability oscillations were observed in the interval of current between quantized plateaus. The phase of the oscillations changes when a plateau is approached, which leads to an oscillatory change in the slope of the plateaus.

In a quasi-two-dimensional ~2D! electron system under a perpendicular magnetic field, we have observed resonant interaction between intersubband Bernstein modes and coupled intersubband-plasmon–LO-phonon modes. By changing parameters of the 2D electron system, a transition from strong to weak regimes of coupling between the plasmon and LO phonon was considered. In the strong-coupling regime, we have observed a double-resonance splitting of the first intersubband Bernstein mode with both intersubbandplasmon–LO-phonon modes, whereas in the weak-coupling regime only a single resonance splitting with the intersubband-plasmon-like mode has been found.

Microwave frequency conductivity $\mathrm{Re}({\ensuremath{\sigma}}_{\mathrm{xx}})$ of high quality two-dimensional hole systems (2DHS) in a large perpendicular magnetic field (B) is measured with the carrier density ${(n}_{s})$ of the 2DHS controlled by a backgate bias. The high-$B$ insulating phase of the 2DHS exhibits a microwave resonance that remains well defined, but shifts to higher peak frequency ${(f}_{\mathrm{pk}})$ as ${n}_{s}$ is reduced. In different regimes, ${f}_{\mathrm{pk}}$ vs ${n}_{s}$ can be fit to ${f}_{\mathrm{pk}}\ensuremath{\propto}{n}_{s}^{\ensuremath{-}1/2}$ or to ${f}_{\mathrm{pk}}\ensuremath{\propto}{n}_{s}^{\ensuremath{-}3/2}.$ The data clearly indicate that both carrier-carrier interactions and disorder are indispensable in determining the dynamics of the insulator. The ${n}_{s}$ dependence of ${f}_{\mathrm{pk}}$ is consistent with a weakly pinned Wigner crystal in which domain size increases with ${n}_{s},$ due to larger carrier-carrier interaction.

We present a detailed investigation of excitonic absorption in $Zn_{0.69}Cd_{0.31}Se/ZnSe$ quantum wells under the application of a perpendicular magnetic field. The large energy separation between heavy- and light-hole excitons allows us to clearly resolve and identify magneto-excitonic absorption resonant with the continuum edge of the 1S heavy-hole exciton. Experimental values of the exciton binding energy are compared with results of a theoretical model that includes the exciton-phonon interaction. The remarkable agreemeent found unambiguously indicates the predominant polaronic character of excitons in ZnSe-based heterostructures.

Extending a model we previously used to calculate magnetization hysteresis arising from the geometrical barrier in a flat, bulk-pinning-free type-II superconducting strip subjected to a perpendicular magnetic field ${H}_{a},$ we here calculate the contribution, arising from screening currents on the top and bottom surfaces, to the magnetic-field-dependent critical current ${I}_{c}{(H}_{a})$ due to surface barriers, including both the geometrical barrier and the Bean-Livingston barrier.

Closed Green-function expressions for the third-order response of semiconductors are derived by mapping the two-band model onto the much simpler molecular ~Frenkel! Hamiltonian. The signatures of two-exciton resonances are incorporated through the exciton scattering matrix, totally avoiding the explicit calculation of two-exciton states. Exact expressions for the nonlinear optical response of two-dimensional semiconductor nanostructures in a strong perpendicular magnetic field are derived by truncating at the n51 Landau level, and using the symmetry of the system and a group-theoretical analysis. We find that the nonlinear optical response depends crucially on asymmetries between particle-particle and particle-hole Coulomb interactions. @S0163-1829~98!03732-1#

A two-dimensional (2D) electron system in a modulation potential and a weak uniform perpendicular magnetic field is studied by a molecular-dynamics simulation method. The simulation results clearly demonstrate some interesting oscillations in the diffusion coefficient, which we interpret in terms of the orbital motion of the electrons on the modulated 2D system.

A double-layer system in a strong perpendicular magnetic field is considered. Assuming a random potential in each layer to be smooth, we calculate the positions of the delocalized states within a wide range of the tunneling strengths. We show that each delocalized state is composed of alternating pieces of equipotentials from different layers. These combined equipotentials form a percolation network, the nodes of which are the regions where equipotentials from different layers nearly touch each other.

Optical spectra of type-II superlattices are presented, including Coulomb interaction and continuum states. We clarify the relative importance of above- and below-barrier transitions. By gradually increasing the band-gap modulation, we visualize the transition from a bulk semiconductor to a type-I or type-II superlattice. We show that transitions that dominate the spectrum of a type-II superlattice are absent in the spectrum of a type-I superlattice and vice versa. The interplay of size and Landau quantization in the optical absorption is studied for both a type-I superlattice and a type-II superlattice in a perpendicular magnetic field. {copyright} {ital 1997} {ital The American Physical Society}

A method of full quantum-mechanical calculation of the energy bands with the use of the S matrix is developed in antidot lattices subjected to a uniform perpendicular magnetic field. It can simplify the calculations considerably in comparison with other methods because only several traveling and a few evanescent modes are sufficient to give accurate results. The resulting energy bands are extremely complicated for realistic antidots. Calculated density of states are analyzed semiclassically in terms of the periodic orbit theory. \textcopyright{} 1996 The American Physical Society.

We investigate the magnetic interface states of graphene quantum dots that contain $p$-$n$ junctions. Within a tight-binding approach, we consider rectangular quantum dots in the presence of a perpendicular magnetic field containing $p$-$n$ as well as $p$-$n$-$p$ and $n$-$p$-$n$ junctions. The results show the interplay between the edge states associated with the zigzag terminations of the sample and the snake states that arise at the $p$-$n$ junction due to the overlap between electron and hole states at the potential interface. Remarkable localized states are found at the crossing of the $p$-$n$ junction with the zigzag edge having a dumb-bell-shaped electron distribution. The results are presented as a function of the junction parameters and the applied magnetic flux.

The intraband light absorption between conduction-band states in symmetric semiconductor quantum wells in the presence of a perpendicular magnetic field is discussed. By theoretical analysis three types of transitions are found: bound bound, bound free, and free free. Numerical calculations are given for a rectangular GaAs quantum well in bulk ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As. The absorption in this structure strongly depends on structure parameters (well thickness, mole fraction, and effective masses), and also on temperature and external magnetic field. Analysis and numerical results such as those presented here may be important for the design of infrared detectors.

The diagrammatic linear response formalism for the Coulomb drag in two--layer systems is developed. This technique can be used to treat both elastic disorder and intralayer interaction effects. In the absence of intralayer electron--electron correlations we reproduce earlier results, obtained using the kinetic equation and the memory--function formalism. In addition we calculate weak--localization corrections to the drag coefficient and the Hall drag coefficient in a perpendicular magnetic field. As an example of the intralayer interaction effects we consider a situation where one (or both) layers are close to (but above) the superconducting transition temperature. Fluctuation corrections, analogous to the Aslamazov--Larkin corrections, to the drag coefficient are calculated. Although the fluctuation corrections do not enhance the drag coefficient for normal--superconductor systems, a dramatic enhancement is found for superconductor--superconductor structures., 15 double--pages, self--extracting compressed ps file, landscape format

We have experimentally studied the superconducting behavior of one-dimensional aluminum wires of various lengths. Each wire had much wider two-dimensional contact pads on both sides. At a temperature [ital T] below [ital T][sub [ital c]], when the wide pads are driven normal by a perpendicular magnetic field, only samples longer than a critical length, [ital L][sub [ital c]][congruent][pi][xi]([ital T]), show evidence for superconductivity. This is a direct confirmation of the prediction by Liniger for a normal-metal--superconductor--normal-metal structure with clean interfaces.

We study the density of states (DOS) for a periodically modulated two-dimensional (2D) electronic system in a perpendicular magnetic field in the presence of a smooth random potential. We find an exact analytical solution for the DOS which is valid under the conditions that both the period of modulation and the correlation length of random potential are larger than the magnetic length. The magnetocapacitance, calculated with the use of this DOS, fits nicely the experimental data by Weiss et al. for the case of one-dimensional periodic potential. The fit of experimental data by Ismail et al. for magnetocapacitance of the samples with two-dimensional periodic modulation is also presented.

Comprehension of the origins of asymmetric behavior during the magnetization reversal is an outstanding issue in the studies of exchange bias (EB). By far, two intrinsic origins of the asymmetric magnetization reversal behavior (AMRB) have been found in different systems separately. The compatibility of the two origins has not been proved-yet. Here, we report on the AMRBs derived from cooperation between the two AMRB origins. Novel AMRBs, including the odd shape of the hysteresis loops and a positive EB, were found in the Co/FeMn bilayers grown under a perpendicular magnetic field. The striking AMRBs we observed could be explained by a model based on spin incoherent rotation and antiferromagnetic interfacial coupling. It suggests that the two AMRB origins are indispensable in the development of these unique AMRBs.

We analyze the four-dimensional Hamiltonian proposed to describe the band structure of the single-Dirac-cone family of topological insulators in the presence of a uniform perpendicular magnetic field. Surface Landau level(LL) states appear, decoupled from the bulk levels and following the quantized energy dispersion of a purely two-dimensional surface Dirac Hamiltonian. A small hybridization gap splits the degeneracy of the central n=0 LL with dependence on the film thickness and the field strength that can be obtained analytically. Explicit calculation of the spin and charge densities show that surface LL states are localized within approximately one quintuple layer from the surface termination. Some new surface-bound LLs are shown to exist at a higher Landau level index., Comment: 8 pages, 4 figures

We put forward a two-terminal valley filter based on a bulk graphene sheet under the modulations of both a local perpendicular magnetic field and a substrate strain. When only one of the two modulations is present, no valley polarization can be generated. A combination of the two modulations leads to a different (but not opposite) shifts of the K and K' valleys, which could be utilized to generate a valley-polarized current. The degree of the valley polarization can be tuned by the strain strength and the inclusion of a scalar potential. The valley polarization changes its polarity as the local magnetic field switches its direction.

Two quantized charge pumps are operated in parallel. The total current generated is shown to be far more accurate than the current produced with just one pump operating at a higher frequency. With the application of a perpendicular magnetic field the accuracy of quantization is shown to be $l20\text{ }\text{ppm}$ for a current of 108.9 pA. The scheme for parallel pumping presented in this work has applications in quantum information processing, the generation of single photons in pairs and bunches, neural networking, and the development of a quantum standard for electrical current. All these applications will benefit greatly from the increase in output current without the characteristic decrease in accuracy as a result of high-frequency operation.

We describe the effects of vacancies on the electronic properties of a graphene sheet in the presence of a perpendicular magnetic field: from a single defect to an organized vacancy lattice. An isolated vacancy is the minimal possible inner edge, showing an antidotlike behaviour, which results in an extra level between consecutive Landau levels. Two close vacancies may couple to each other, forming a vacancy molecule tuned by the magnetic field. We show that a vacancy lattice introduce an extra band in between Landau levels with localization properties that could lead to extra Hall resistance plateaus., 6 pages, 4 figures, few comments added after referees - accepted to publication in Phys. Rev. B

Magneto-optical imaging was used to observe flux dendrites with opposite polarities simultaneously penetrate superconducting, ring-shaped $\mathrm{Mg}{\mathrm{B}}_{2}$ films. By applying a perpendicular magnetic field, branching dendritic structures nucleate at the outer edge and abruptly propagate deep into the rings. When these structures reach close to the inner edge, where flux with opposite polarity has penetrated the superconductor, they occasionally trigger anti-flux-dendrites. These antidendrites do not branch, but instead trace the triggering dendrite in the backward direction. Two trigger mechanisms, a nonlocal magnetic and a local thermal mechanism, are considered as possible explanations for this unexpected behavior. Increasing the applied field further, the rings are perforated by dendrites which carry flux to the center hole. Repeated perforations lead to a reversed field profile and new features of dendrite activity when the applied field is subsequently reduced.

In a two-dimensional quantum wire in a perpendicular magnetic field with a smooth embedded repulsive scattering potential we find in the multimode conductance resonances caused by bound states with negative binding energy. These resonances are the counterexamples to well-known dips in the conductance and evanescent states caused by quasibound states of attractive scattering centers in the wire.

It is rigorously proved that the Green's function of a uniform two-dimensional interacting electron gas in a perpendicular magnetic field is diagonal with respect to single-particle states in the Landau gauge. The implication of this theorem is briefly discussed.

The latent heat of vortex lattice melting transition in a two-dimensional superconductor at high perpendicular magnetic field is calculated within the framework of the Ginzburg-Landau functional integral approach. The result is found to be smaller than that obtained from various numerical simulations, which tend to overestimate the latent heat due to finite-size effect.

We have numerically investigated the dynamics of vortices in a clean layered superconductor placed in a perpendicular magnetic field. We describe the energetics using a Ginzburg-Landau free energy functional in the lowest Landau level approximation. The dynamics are determined using the time-dependent Ginzburg-Landau approximation, and thermal fluctuations are incorporated via a Langevin term. The c-axis conductivity at nonzero frequencies, as calculated from the Kubo formalism, shows a strong but not divergent increase as the melting temperature $T_M$ is approached from above, followed by an apparently discontinuous drop at the vortex lattice freezing temperature. The discontinuity is consistent with the occurrence of a first-order freezing. The calculated equilibrium properties agree with previous Monte Carlo studies using the same Hamiltonian. We briefly discuss the possibility of detecting this fluctuation conductivity experimentally., Comment: To be published in Phys. Rev. B

It was recently observed [van der Beek et al., Phys. Rev. B 54, R792 (1996)] that irradiated layered high-T c superconductors subject to perpendicular magnetic field manifest two similar scaling behaviors corresponding totwo different critical temperatures. We show that this phenomenon is explained within the framework of the Ginzburg-Landau theory, In the weak field region, the scaling function differs from that of a clean sample mainly because of the renormalization of the critical temperature, due to defects. In the strong field region, defects are effectively suppressed and the scaling function, as well as the critical temperature, are the same as in a clean superconductor. The theory presented here agrees quite satisfactory with experiment.

In non-interacting or weakly-interacting 2D electron systems, the energy of the extended states increases as the perpendicular magnetic field approaches zero: the extended states "float up" in energy, giving rise to an insulator. However, in those 2D systems where metallic conductivity has been recently observed in zero magnetic field, the energy of the extended states remains constant or even decreases as B -> 0, thus allowing conduction in the limit of zero temperature. Here we show that aligning the electrons' spins causes the extended states to once more "float up" in energy in the vanishing perpendicular magnetic field, as they do for non- or weakly-interacting electrons. The difference between extended states that float up (an insulator) or remain finite (a metal) is thus tied to the existence of the spins.

The magnetoresistance of sub-0.4-\ensuremath{\mu}m-diam Au and ${\mathrm{Au}}_{60}$${\mathrm{Pd}}_{40}$ rings was measured in a perpendicular magnetic field at temperatures as low as 5 mK in search of simple, periodic resistance oscillations that would be evidence of flux quantization in normal-metal rings. However, instead of simple oscillations, a very complex structure developed in the magnetoresistance at low temperatures. Fourier analysis of all the data did not reveal convincing evidence for flux quantization in the rings. Complex structure similar to that observed in the rings was also found in the magnetoresistance of short, narrow, Au and ${\mathrm{Au}}_{60}$${\mathrm{Pd}}_{40}$ lines. This structure appears to be associated with the small size of the devices.

The excitation energies of the noninteracting two-dimensional electron gas in a strong perpendicular magnetic field are multiples of \ensuremath{\Elzxh}${\ensuremath{\omega}}_{c}$. We show that in the presence of interactions there are inter-Landau-level excitation modes which exactly repeat the intra-Landau-level spectrum when shifted by \ensuremath{\Elzxh}${\ensuremath{\omega}}_{c}$. .AE

We study the fractional boundary charges (FBCs) occurring in nanowires in the presence of periodically modulated chemical potentials and connect them to the FBCs occurring in a two-dimensional electron gas in the presence of a perpendicular magnetic field in the integer quantum Hall effect (QHE) regime. First, we show that in nanowires the FBCs take fractional values and change linearly as a function of phase offset of the modulated chemical potential. This linear slope takes quantized values determined by the period of the modulation and depends only on the number of the filled bands. Next, we establish a mapping from the one-dimensional system to the QHE setup, where we again focus on the properties of the FBCs. By considering a cylinder topology with an external flux similar to the Laughlin construction, we find that the slope of the FBCs as function of flux is linear and assumes universal quantized values, also in the presence of arbitrary disorder. We establish that the quantized slopes give rise to the quantization of the Hall conductance. Importantly, the approach via FBCs is valid for arbitrary flux values and disorder. The slope of the FBCs plays the role of a topological invariant for clean and disordered QHE systems. Our predictions for the FBCs can be tested experimentally in nanowires and in Corbino disk geometries in the integer QHE regime., 14 pages, 12 figures