Uniform Perpendicular Magnetic Field Research Articles

Landau levels of multilayer graphene ribbons

The low-energy Landau levels of multilayer graphene ribbons with AB-stacking in the presence of a uniform perpendicular magnetic field ( B) are investigated by the Peierls coupling tight-binding model. They are dominated by the B-field strength, the interlayer interactions, and the ribbon width. Many dispersionless Landau levels and parabolic energy bands exist along k x and k z directions respectively. The former are doubly degenerate, while state degeneracy is absent for the latter. The occupied valence bands are asymmetric to the unoccupied conduction bands about the Fermi level ( E F). Such features are directly reflected in density of states (DOS). DOS exhibits a lot of asymmetric prominent peaks because of 1D curving bands. Meanwhile, the Landau-level energies following the simple relation E c , v ∝ B are observed. The predicted magnetoelectronic properties could be examined by the experimental measurements on transport conductance and absorption spectra.

Edge disorder and localization regimes in bilayer graphene nanoribbons

A theoretical study of the magnetoelectronic properties of zigzag and armchair bilayer graphene nanoribbons (BGNs) is presented. Using the recursive Green's function method, we study the band structure of BGNs in uniform perpendicular magnetic fields and discuss the zero-temperature conductance for the corresponding clean systems. The conductance is quantized as $2(n+1){G}_{0}$ for the zigzag edges and $n{G}_{0}$ for the armchair edges with ${G}_{0}=2{e}^{2}/h$ being the conductance unit and $n$ an integer. Special attention is paid to the effects of edge disorder. As in the case of monolayer graphene nanoribbons (GNR), a small degree of edge disorder is already sufficient to induce a transport gap around the neutrality point. We further perform comparative studies of the transport gap ${E}_{g}$ and the localization length $\ensuremath{\xi}$ in bilayer and monolayer nanoribbons. While for the GNRs ${E}_{g}^{\text{GNR}}\ensuremath{\sim}1/W$, the corresponding transport gap ${E}_{g}^{\text{BGN}}$ for the bilayer ribbons shows a more rapid decrease as the ribbon width $W$ is increased. We also demonstrate that the evolution of localization lengths with the Fermi energy shows two distinct regimes. Inside the transport gap, $\ensuremath{\xi}$ is essentially independent on energy and the states in the BGNs are significantly less localized than those in the corresponding GNRs. Outside the transport gap $\ensuremath{\xi}$ grows rapidly as the Fermi energy increases and becomes very similar for BGNs and GNRs.

Low-energy Landau levels of Bernal zigzag graphene ribbons

Low-energy Landau levels of Bernal zigzag graphene ribbons in the presence of a uniform perpendicular magnetic field (B) are investigated by the Peierls coupling tight-binding model. State energies and associated wave functions are dominated by the B-field strength and the kz-dependent inter-ribbon interactions. The occupied valence bands are asymmetric to the unoccupied conduction bands about the Fermi level. Many doubly degenerate Landau levels and singlet curving magnetobands exist along the kx and kz directions, respectively. The kz-dependent inter-ribbon interactions dramatically modify the magnetobands, such as the lift of double degeneracy, the change in state energies, and the production of two groups of curving magnetobands. They also change the characteristics of the wave functions and cause the redistribution of the charge-carrier density. The kz-dependent wave functions are further used to predict the selection rule of the optical transition.

Polaronic effects in one-dimensional quantum antidot arrays

We study the effect of polaronic corrections arising from the electron-longitudinal optical phonon interaction on the energy spectrum of a two-dimensional electron system with a one-dimensional periodic antidot array geometry created by a weak electrostatic modulation potential, and subjected to a weak magnetic field modulation as well as a uniform strong perpendicular static magnetic field. To incorporate the effects of electron-phonon interactions within the framework of Frohlich polaron theory, we first apply a displaced-oscillator type unitary transformation to diagonalise the relevant Frohlich Hamiltonian, and we then determine the parameters of this transformation together with the parameter included in the electronic trial wave function . On the basis of this technique, it has been shown that the polaronic corrections have non-negligible effects on the electronic spectrum of a two-dimensional electron system with a quantum antidot array, since switching such an interaction results in shifting the degeneracy restoring points of Landau levels wherein the flatband condition is fulfilled, thus suppressing the Weiss oscillations.

Magneto-electronic properties of graphene nanoribbons in the spatially modulated electric field

The Peierls tight-binding model with the nearest-neighbor interactions is used to calculate the magneto-electronic structure of graphene nanoribbons under a spatially modulated electric field along the y-axis. A uniform perpendicular magnetic field could make energy dispersions change into the quasi-Landau levels. Such levels are composed of the dispersionless and parabolic energy bands. A spatially modulated electric field would further induce a lot of oscillating parabolic bands with several band-edge states. It drastically modifies energy dispersions, alters subband spacings, destroys symmetry of energy spectrum about k x = 0 , and changes features of band-edge states (number and energy). The above-mentioned magneto-electronic structures are directly reflected in density of states (DOS). The modulation effect changes shape, number, positions, and intensities of peaks in DOS. The predicted result could be tested by the optical measurements.

Hybrid ferrohydrodynamic instability: Coexisting peak and labyrinthine patterns

We present an experimental study of a different pattern-forming instability occurring when a ferrofluid droplet is immersed in a thin layer of a nonmagnetic fluid, and subjected to a uniform perpendicular magnetic field. The formation of intriguing interfacial structures is observed, and the development of a hybrid-type ferrohydrodynamic instability is verified, where peak and labyrinthine ferrofluid patterns coexist and share a coupled dynamic evolution. Based on our experimental findings we have identified the occurrence of three well defined regimes for the evolution of the miscible Rosensweig peak in which it first grows rapidly, and then gradually decays, to ultimately reimmerse into the surrounding nonmagnetic solvent layer. This unique scenario for the rise and fall of the Rosensweig peak implies the simultaneous emergence of peculiar labyrinthine structures induced by an outward radial flow within the thin nonmagnetic layer. A variety of possible morphologies is revealed (labyrinth, broken tentaclelike fingers, etc.), which result from the interplay between magnetic, diffusive, and convective effects. These free surface flow labyrinthine structures are contrasted to alternative interfacial designs obtained when the experimental system is spatially confined.

Influence of dephasing on the quantum Hall effect and the spin Hall effect

We study the influence of the phase relaxation process on Hall resistance and spin Hall current of a mesoscopic two-dimensional four-terminal Hall cross bar with or without Rashba spin-orbit interaction (SOI) in a perpendicular uniform magnetic field. We find that the plateaus of the Hall resistance with even number of edge states can survive for very strong phase relaxation when the system size is much longer than the phase coherence length. On the other hand, the odd integer Hall resistance plateaus arising from the SOI are easily destroyed by the weak phase relaxation during the competition between the magnetic field and the SOI which delocalize the edge states. In addition, we have also studied the transverse spin Hall current and found that it exhibits resonant behavior whenever the Fermi level crosses the Landau band of the system. The phase relaxation process weakens the resonant spin Hall current and enhances the nonresonant spin Hall current.

Magnetoelectronic properties of bilayer Bernal graphene

The Peierls Hamiltonian band matrix is developed to investigate magnetoelectronic properties of bilayer Bernal graphene. A uniform perpendicular magnetic field creates many dispersionless Landau levels (LLs) at low and high energies and some oscillatory LLs at moderate energy. State degeneracy of the low LLs is two times as much as that of the high LLs. Wave functions and state energies are dominated by the interlayer atomic interactions and field strength $({B}_{0})$. The former induce two groups of LLs, more low LLs, the asymmetric energy spectrum about the Fermi level, and the change of level spacing. Two sets of effective quantum numbers, ${n}_{1}^{\mathit{eff}}$'s and ${n}_{2}^{\mathit{eff}}$'s, are required to characterize all the wave functions. They are determined by the strongest oscillation modes of the dominant carrier densities; furthermore, they rely on the specific interlayer atomic hoppings. The dependence of the quite low Landau-level energies on ${B}_{0}$ and ${n}_{1}^{\mathit{eff}}$ is approximately linear. An energy gap is produced by the magnetic field and interlayer atomic hoppings. ${E}_{g}$ grows with increasing field strength, while it is reduced by the Zeeman effect. The main features of magnetoelectronic structures are directly reflected in the density of states. The predicted electronic properties could be verified by the experimental measurements on absorption spectra and transport properties.

Geometric Phases for Wave Packets of the Landau Problem

The Landau problem of a charged particle in a plane with a uniform perpendicular magnetic field is analysed in two oscillator modes. The coherent states for the problem have been found out using a general definition of displaced states. The time evolution and the associated nonadiabatic geometric phase for both initially displaced and non-displaced wave packets have been studied. The path integral is derived in a simple way through the calculation of Gaussian integrals via the concept of coherent state wavefunctions.

Unusual critical states in type-II superconductors

We give a theoretical description of the general critical states in which the critical currents in type-II superconductors are not perpendicular to the local magnetic induction. Such states frequently occur in real situations, e.g., when the sample shape is not sufficiently symmetric or the direction of the external magnetic field changes in some complex way. Our study is restricted to the states in which flux-line cutting does not occur. The properties of such general critical states can essentially differ from the well-known properties of the usual Bean critical states. To illustrate our approach, we analyze several examples. In particular, we consider the critical states in a slab placed in a uniform perpendicular magnetic field and to which two components of the in-plane magnetic field are then applied successively. We also analyze the critical states in a long thin strip placed in a perpendicular magnetic field which then is tilted towards the axis of the strip.

Low-Field Phase Diagram of the Spin Hall Effect in the Mesoscopic Regime

When a mesoscopic two dimensional four-terminal Hall cross bar with spin-orbit interaction (SOI) is subjected to a perpendicular uniform magnetic field B, both integer quantum Hall effect (IQHE) and mesoscopic spin Hall effect (MSHE) may exist when disorder strength W in the sample is weak. We have calculated the low field "phase diagram" of MSHE in the (B,W) plane for disordered samples in the IQHE regime. For weak disorder, MSHE conductance G(sH) and its fluctuations rms(G(sH)) vanish identically on even numbered IQHE plateaus, they have finite values on those odd numbered plateaus induced by SOI, and they have values G(sH)=1/2 and rms(G(sH))=0 on those odd numbered plateaus induced by Zeeman energy. At larger disorders, the system crosses over into a regime where both G(sH) and rms(G(sH)) are finite, a chaotic regime, and finally a localized regime.

Superconducting properties of mesoscopic squares

We apply the complete nonlinear Time Dependent Ginzburg Landau (TDGL) equations to study the vortex dynamics in a mesoscopic type II superconductor using the numerical method based on the technique of gauge invariant variables. The solution of these equations shows how the vorticity penetrates into and goes out of the superconductor through the surface boundary. We calculate the spatial distribution of the superconducting electron density and the phase of the superconducting order parameter in a mesoscopic superconducting square sample containing two holes in the presence of a uniform perpendicular magnetic field. The dynamics of different vortex states are studied as a function of the external magnetic field.

Weak Localization in Multiwall Carbon Nanotubes in a Perpendicular Magnetic Field

The weak-localization (WL) effect on electron transport is studied for multiwall carbon nanotubes in a uniform perpendicular magnetic field. The influence of a magnetic field on the WL effect is determined by its component normal to the rolled surface of nanotubes, so an effective magnetic field is nonuniform. We adopt a disordered two-dimensional electron system rolled into a cylinder as a minimal model, and obtain the WL correction to conductivity taking account of the cylindrical structure and the spatial nonuniformity of an effective magnetic field. The result is compared with the WL correction in a two-dimensional strip in a uniform perpendicular magnetic field. It is shown that their magnetic-field dependences are qualitatively equivalent to each other. However, it is also shown that the magnetic-field dependence in a cylinder is quantitatively less pronounced than that in a strip reflecting the nonuniformity of an effective magnetic field as well as the cylindrical structure.

Analytic and numeric Green’s functions for a two-dimensional electron gas in an orthogonal magnetic field

We have derived closed analytic expressions for the Green’s function of an electron in a two-dimensional electron gas threaded by a uniform perpendicular magnetic field, also in the presence of a uniform electric field and of a parabolic spatial confinement. A workable and powerful numerical procedure for the calculation of the Green’s functions for a large infinitely extended quantum wire is considered exploiting a lattice model for the wire, the tight-binding representation for the corresponding matrix Green’s function, and the Peierls phase factor in the Hamiltonian hopping matrix element to account for the magnetic field. The numerical evaluation of the Green’s function has been performed by means of the decimation–renormalization method, and quite satisfactorily compared with the analytic results worked out in this paper. As an example of the versatility of the numerical and analytic tools here presented, the peculiar semilocal character of the magnetic Green’s function is studied in detail because of its basic importance in determining magneto-transport properties in mesoscopic systems.

Coherent states attached to Landau levels on the Poincaré disc

We construct a family of generalized coherent states attached to Landau levels of a charged particle moving in the Poincare disc under a perpendicular uniform magnetic field. The corresponding coherent state transforms enable us to connect, by an integral transform, spaces of bound states of the particle with the space of square integrable functions on the real line. The established connection provides us with a new way to obtain hyperbolic Landau states.

Coherent states attached to landau levels on the riemann sphere

We construct a family of generalized coherent states attached to Landau levels of a charged particle moving in the Riemann sphere under a perpendicular uniform magnetic field. Bound states of the particle are then characterized as coherent state transforms of polynomial functions. This provides us with a new characterization of spherical Landau states.

Non-linear ring currents: effect of strong magnetic fields on π-electron circulation

Finite-field calculations of non-linear induced current density in representative [4 n + 2] and [4 n] π systems, benzene and flat cyclooctatetraene (COT), show that a strong uniform perpendicular magnetic field enhances benzene π-diatropicity and decreases COT π-paratropicity. The non-linear current is stronger by two orders of magnitude in COT, but still small: at 1 a 0 height and in a field of 25 T, third-order effects contribute −5 ppm to the first-order π ring current. Classical arguments based on radial contraction of charge density rationalise the non-linear response of benzene, but that of COT depends on a specific orbital-rotation effect, characteristic of paratropic π systems.

Characterization of two-dimensional Euclidean Landau states by coherent state transforms

We construct a family of generalized coherent states attached to Landau levels of a charged particle moving in the two-dimensional Euclidean plane under a perpendicular uniform magnetic field. We prove that the ranges of the corresponding coherent state transforms coincide with spaces of bound states of the particle. This provides us with a new characterization of two-dimensional Euclidean Landau states.

Transport in ferromagnet/semiconductor 2DEG hybrid network structure

We have investigated transport in a network of narrow two-dimensional electron gas (2DEG) channel under a gradient magnetic field which is generated by a network of cobalt film deposited on the surface. Resistance of the 2DEG network changed with the magnetization of the cobalt network. The gradient magnetic field breaks the symmetry of the system with respect to the direction along the channel. We have found that the differential resistance under a finite DC bias current depends on the current direction. Magnetoresistance as a function of uniform perpendicular magnetic field while keeping the gradient field constant exhibits an overall shift and modulation of Shubnikov de-Haas oscillations.

SUPERINTEGRABLE SYSTEMS, MULTI-HAMILTONIAN STRUCTURES AND NAMBU MECHANICS IN AN ARBITRARY DIMENSION

A general algebraic condition for the functional independence of 2n-1 constants of motion of an n-dimensional maximal superintegrable Hamiltonian system has been proved for an arbitrary finite n. This makes it possible to construct, in a well-defined generic way, a normalized Nambu bracket which produces the correct Hamiltonian time evolution. Existence and explicit forms of pairwise compatible multi-Hamiltonian structures for any maximal superintegrable system have been established. The Calogero–Moser system, motion of a charged particle in a uniform perpendicular magnetic field and Smorodinsky–Winternitz potentials are considered as illustrative applications and their symmetry algebras as well as their Nambu formulations and alternative Poisson structures are presented.