Uniform Perpendicular Magnetic Field Research Articles

Landau levels for charged particles with anisotropic mass

The problem of the two-dimensional motion of a charged particle with constant mass in the presence of a uniform constant perpendicular magnetic field features in several undergraduate and graduate quantum physics textbooks. This problem is very important to studies of two-dimensional materials that manifest quantum Hall behavior, as evidenced by several major discoveries over the last few years. Many real experimental samples are more complicated due to the anisotropic mass of the electrons. In this work, we provide the exact solution to this problem by means of a clever scaling of coordinates. Calculations are done for a symmetric gauge of the magnetic field. This study allows a broad audience of students and teachers to understand the mathematical techniques that lead to the solution of this quantum problem.

The guiding center role in defining the eigenstates of an electron in the fractional quantum Hall effect regime: ladder operators approach

The quantum problem of a two-dimensional electron in a uniform perpendicular magnetic field is considered. Using the formalism of ladder operators, the electron eigenfunctions are derived for all quantum numbers n and m, where n denotes the Landau level and m the eigenvalue of the angular momentum L z , with m taking all possible eigenvalues. We note that existing one-electron orbitals, in most of the known literature on the fractional quantum Hall effect (FQHE), correspond to a restricted range of possible eigenvalues m, some are missing. Similarly detailed calculations using ladder operator techniques show that for a state ∣n, m〉, the quantum number (n − m) represents a precise physical quantity, that is the distance from the origin to the center of the electron orbit. This finding allowed us to obtain, for this known quantum problem, a new set of basis states for which both quantum numbers have a physical meaning namely n and (n − m).

A Charged Particle with Anisotropic Mass in a Perpendicular Magnetic Field–Landau Gauge

The loss of any symmetry in a system leads to quantum problems that are typically very difficult to solve. Such a situation arises for particles with anisotropic mass, like electrons in various semiconductor host materials, where it is known that they may have an anisotropic effective mass. In this work, we consider the quantum problem of a spinless charged particle with anisotropic mass in two dimensions and study the resulting energy and eigenstate spectrum in a uniform constant perpendicular magnetic field when a Landau gauge is adopted. The exact analytic solution to the problem is obtained for arbitrary values of the anisotropic mass using a mathematical technique that relies on the scaling of the original coordinates. The characteristic features of the energy spectrum and corresponding eigenstate wave functions are analyzed. The results of this study are expected to be of interest to quantum Hall effect theory.

Transformation of a skyrmionium to a skyrmion through the thermal annihilation of the inner skyrmion

Skyrmioniums are doughnutlike topological spin textures in chiral magnets, which are able to move with zero skyrmion Hall effect. The annihilation of a skyrmionium involves the topological transition through singularity formation at the continuum level. Here we analytically and numerically study a type of thermal annihilation of a skyrmionium under the framework of micromagnetism. The skyrmionium initially exists in an ultrathin ferromagnetic film in the exchange-dominated regime and is stabilized under a uniform perpendicular magnetic field. The thermal annihilation of the “skyrmion” inside the skyrmionium results in the transformation of the skyrmionium to a skyrmion. We derive an analytical formula in the Arrhenius form describing the annihilation rate of this process. We find that the analytical solutions agree well with the micromagnetic simulation results. Besides, from the large deviation point of view, we derive the dynamical path for the collapse of a skyrmionium. Our results are useful for understanding the thermal stability of skyrmioniums and may lead to spintronic applications based on the thermal manipulation of skyrmioniums. Published by the American Physical Society 2024

Strain engineering of magneto-optical properties in C[formula omitted]B/C[formula omitted]N van der Waals heterostructure

Carbon-based bilayer van der Waals (vdW) materials are attracting much attention due to their predicted interesting physical properties. Here, we theoretically investigate electronic and optical properties of C3B/C3N vdW heterostructure (HTS) under external magnetic field and mechanical strain. The tight-binding model of the system is constructed to include the strain-induced modification of the hopping interactions. The influence of a uniform perpendicular magnetic field is included by using the Peierls substitution method. We observe the intriguing electronic and optical characteristics of the HTS under mechanical strain, covering the band inversion, alteration of band gap and optical gap, distortion of band-edge states, as well as significant enhancement of optical absorption. Furthermore, the interplay between external magnetic field and biaxial strain leads to exotic features of quantization and optical spectra. This work provides important information for the comprehension of the engineering of materials by external effects. Our study suggests that C3B/C3N vdW HTS is a promising candidate for next-generation electronic and optoelectronic devices.

Interaction potential between coplanar uniformly charged disk and ring

We consider a system made up of a uniformly charged disk and a uniformly charged ring that are coplanar with each other. The disk and ring have arbitrary radii and contain arbitrary amounts of net charge that is spread uniformly over area and length, respectively. This study is seen as the first necessary step towards a classical model treatment of a two-dimensional system of electrons in a weak perpendicular magnetic field. In this scenario, the uniformly charged disk represents the neutralizing background in a jellium approximation while a uniformly charged ring is viewed as a classical approximation to the cyclotron motion of the electron in presence of a uniform perpendicular magnetic field. In this work, we obtain an exact integral expression for the interaction potential energy of the system as a function of the separation distance between the centers of the two bodies and discuss various emerging features of this model.

Inversion symmetry breaking in spin–orbit torque-induced magnetization switching to improve the recording density of multi-level magnetoresistive random-access memory

In this study, we prepared a multi-layer Tb–Fe/Pt/Tb–Fe wire to develop a multi-level magnetic memory. By applying current, magnetizations of the Tb–Fe layers were inversion symmetrically switched by spin– orbit torque (SOT) generated from the middle Pt layer. Measurements of SOT showed that its efficiency had opposite polarities in the top and bottom Tb–Fe layers. The switching current density of the top and bottom Tb–Fe layers shifted in opposite directions under a uniform perpendicular magnetic field. Because the perpendicular magnetic field broke the inversion symmetry of SOT generated from the middle Pt layer, it could be used to control the switching current. Our results prove that the additional uniform and perpendicular magnetic field can enhance the controllability of the magnetization state in case of multi-level SOT-induced magnetization switching.

Band Structure and Quantum Transport of Bent Bilayer Graphene.

We investigate the band structures and transport properties of a zigzag-edged bent bilayer graphene nanoribbon under a uniform perpendicular magnetic field. Due to its unique geometry, the edge and interface states can be controlled by an electric field or local potential, and the conductance exhibits interesting quantized behavior. When Zeeman splitting is considered, the edge states are spin-filtered, and a weak quantum spin Hall (WQSH) phase appears. In the presence of an electric field or local potential, a WQSH-QH junction or WQSH-spin-unbalanced QSH junction can be achieved, respectively, while fully spin-polarized currents appear in the interface region. Zeeman splitting lifts the spin degeneracy, leading to a WQSH around zero energy with a quantized two-terminal conductance of 4e2/h, which is robust against weak nonmagnetic disorder. These results provide a way to manipulate the band structures and transport properties of the system using an electric field, local potential, and Zeeman splitting.

Skyrmion motion and partitioning of domain wall velocity driven by repulsive interactions

Magnetic skyrmions, as a whirling spin texture with axisymmetry, cannot be propelled directly by a uniform perpendicular magnetic field. Therefore, reported skyrmion motions have been induced using other sorts of stimuli — typically, electric currents in magnetic metals. Here, we propose to drive skyrmion motion, in a uniform perpendicular field, by intrinsic repulsive interactions among an outer domain wall (DW) and magnetic skyrmions. Through micromagnetic simulations, we demonstrate that the uniform perpendicular magnetic field can indeed displace magnetic skyrmions alongside the leading DW. At a fixed field strength, the velocity of the skyrmion train evolves according to a 1 / (Ns + 1) relation with Ns denoting the number of skyrmions. Based on the Thiele equation, we elucidate, analytically, the mechanism of the driven magnetic skyrmion motion as well as the velocity equipartition phenomenon and reveal that the skyrmion–DW and inter-skyrmion repulsive interactions offer the driving force for skyrmion motion. This study underlines the role of spin textures’ interaction in skyrmion dynamics, and opens an alternative route for skyrmion manipulation especially relevant to insulating magnets. Given the correspondence between ferromagnetism and ferroelectricity, we anticipate that the scheme should also work for polar skyrmions in ferroelectrics.

Giant diamagnetism of a quantum charged particle after inversion of the magnetic field

We consider a quantum charged particle moving in the $xy$ plane under the action of a uniform perpendicular time-dependent magnetic field, in the presence of a parabolic binding potential. The time-dependent probability distribution of the magnetic moment is calculated analytically and numerically in the case of initial thermodynamic equilibrium state. In the high-temperature regime, the initial distribution is almost symmetric, resulting in a tiny mean diamagnetism. However, if the magnetic field eventually changes its sign, the fragile balance between the diamagnetic and paramagnetic ``wings'' of the probability distribution becomes broken, resulting in a giant mean diamagnetic moment, exceeding the initial one by several orders of magnitude. The final mean value of the magnetic moment is inversely proportional to the strength of the binding potential, and it does not depend on the Planck constant in the high-temperature regime. Strong fluctuations of the magnetic moment (described in terms of the variance) exist in all temperature regimes.

Creating and detecting a magnetic bimeron by magnetic force microscope probe

A magnetic bimeron is a version of skyrmion, which is predicted for the in-plane magnetized thin films with interfacial Dzyaloshinskii-Moriya interaction. Here we theoretically investigate the possibility to create individual bimeron using stray field of magnetic force microscope (MFM) tip. We demonstrate that a local magnetization reversal of the film by localized MFM field in combination with an additional uniform perpendicular magnetic field enables the stable bimeron formation. The possibilities for detection of the bimeron by the methods of magnetic force microscopy, Lorentz transmission electron microscopy and magnetic resonance force spectroscopy are discussed.

Modulation of persistent current in graphene quantum rings

We investigate the effect of long-range impurity potentials on the persistent current of graphene quantum rings in the presence of an uniform perpendicular magnetic field. The impurity potentials are modeled as finite regions of the ring with a definite length. We show that, due to the relativistic and massless character of the charge carriers in graphene, the effect of such non-uniform potentials on the energy spectrum and on the persistent current of the rings can be reliably modeled by assuming a non-perturbed ring and including an additional phase due to the interaction of the charge carriers with the potential. In addition, the results show the presence of localized states in the impurity regions. Moreover, we show that for the case of a potential created by a p-n-p junction, the persistent current can be modulated by controlling the voltage at the junction.

Holographic Abrikosov lattice: Vortex matter from black hole

The $\mathrm{AdS}/\mathrm{CFT}$ correspondence provides a unique way to study the vortex matter phases in superconductors. We solve the dynamical evolution of a superconductor in $2+1$ dimensions at a finite temperature subjected to a magnetic field quench in terms of a gravitational ``hairy black hole'' dual living in an asymptotic ${\mathrm{AdS}}_{4}$ space. We exploit this to determine the nature of the equilibrium states realized at long times after the quench of this two dimensional type II superconductor in a perpendicular external uniform magnetic field ${B}_{0}$. This holographic superconductor exhibits the generic lower (${B}_{c1}(T)$) and upper (${B}_{c2}(T)$) critical fields. For ${B}_{0}<{B}_{c1}(T)$ the magnetic field is completely expelled revealing the Meissner phase, while the superconductivity is destroyed when ${B}_{0}>{B}_{c2}(T)$. Abrikosov lattices appear in the range ${B}_{c1}(T)<{B}_{0}<{B}_{c2}(T)$ that realize various configurations in the form of hexagonal, square and slightly irregular square lattices pending the magnetic field strength and the influence of finite size boundaries. We show this to be consistent with the expectations of Ginzburg-Landau theory where the upper and lower critical fields are associated with the inverse squares of the coherence length and magnetic penetration depth, respectively.

Magnetoresistance of electrons in quantum ring with Rashba spin-orbit interaction

The influence of Rashba spin-orbit interaction on the transport properties of the two-dimensional quantum ring with finite width has been investigated in the presence of the uniform perpendicular magnetic field. The dependence of magnetoresistance on the magnetic field and Rashba spin-orbit coupling parameter in quantum ring with finite width are investigated. It was shown that in the presence Rashba spin-orbit interaction that the beating pattern is destroyed.

Solving Dirac oscillator in commutative and noncommutative planes by supersymmetry structures

Based on the supersymmetry structures, we propose to solve the model of a charged Dirac oscillator interacting with a uniform perpendicular magnetic field on both commutative and noncommutative planes in a unified way by employing unitary transformations. The unitary operators are constructed out of the generators of the supersymmetry structures of the model.

Temperature-Induced Plasmon Excitations for the α-T3 Lattice in Perpendicular Magnetic Field.

We have investigated the – model in the presence of a mass term which opens a gap in the energy dispersive spectrum, as well as under a uniform perpendicular quantizing magnetic field. The gap opening mass term plays the role of Zeeman splitting at low magnetic fields for this pseudospin-1 system, and, as a consequence, we are able to compare physical properties of the the – model at low and high magnetic fields. Specifically, we explore the magnetoplasmon dispersion relation in these two extreme limits. Central to the calculation of these collective modes is the dielectric function which is determined by the polarizability of the system. This latter function is generated by transition energies between subband states, as well as the overlap of their wave functions.

Current distribution and group velocities for electronic states on lattice ribbons in a magnetic field

We study the group velocities of electronic states and distributions of currents in lattice ribbons under a uniform perpendicular magnetic field. Using the effective low-energy model we analyze all possible simple configurations of lattice termination with zigzag and armchair boundaries. We show that the edge current depends on the type of zigzag termination, and can be zero or finite near the edge. Also similar dependence is observed in the case of armchair termination and is related to the size of the ribbon. The nonzero current flowing along the edge can be used a signature of formation of propagating edge states. In addition, we show the qualitative difference in the distribution of the edge current between the case of α = 1 (dice model) and other values of model parameter α ≠ 1 for armchair-terminated ribbons.

Supersymmetric structures of Dirac oscillators in commutative and noncommutative spaces* *Project supported by the National Natural Science Foundation of China (Grant No. 11465006).

The supersymmetric properties of a charged planar Dirac oscillator coupling to a uniform perpendicular magnetic field are studied. We find that there is an N = 2 supersymmetric structure in both commutative and noncommutative cases. We construct the generators of the supersymmetric algebras explicitly and show that the generators of the supersymmetric algebras can be mapped onto ones which only contain the left or right-handed chiral phonons by unitary transformations.

The effect of disorder on local electron temperature in quantum Hall systems

The local electron temperature distribution is calculated considering a two dimensional electron system in the integer quantum Hall regime in presence of disorder and uniform perpendicular magnetic fields. We solve thermo-hydrodynamic equations to obtain the spatial distribution of the local electron temperature in the linear-response regime. It is observed that, the variations of electron temperature exhibit an antisymmetry regarding the center of the sample in accordance with the location of incompressible strips. To understand the effect of sample mobility on the local electron temperature we impose a disorder potential calculated within the screening theory. Here, long range potential fluctuations are assumed to simulate cumulative disorder potential depending on the impurity atoms. We observe that the local electron temperature strongly depends on the number of impurities in narrow samples. The electron temperature $$T_e$$ versus position calculated for different values of the modulation potential $$V_0$$ . The calculations are done at $$T_\mathrm{L} = 0.04 \,E_F^0/k_B$$ lattice temperature considering impurity $$N_l = 6600$$ and repeated for three different values of magnetic field $$\hbar \omega _c/E_F^0 = 0.80$$ , 0.85 and 0.90. The insets show the enlarged region for the left side.

Magnetic-moment probability distribution of a quantum charged particle in thermodynamic equilibrium

We consider a quantum charged particle moving in the $xy$ plane under the action of a uniform perpendicular constant magnetic field, in the presence of a parabolic binding potential. The magnetic-moment operator has a continuous spectrum, and its eigenfunctions in the momentum representation are expressed in terms of modified Bessel functions. The probability distribution of the magnetic moment in the thermodynamic equilibrium state is calculated. At zero temperature, it has a simple exponential form in the diamagnetic region, with a sharp jump to zero at the origin. With an increase of temperature, a paramagnetic wing of the distribution becomes more and more pronounced. In the high-temperature regime, the diamagnetic and paramagnetic wings of the distribution have almost identical forms, described with a high precision by simple exponential functions with very large extensions. Therefore, diamagnetic and paramagnetic contributions almost cancel each other. The remaining non-zero diamagnetic value is due to a small asymmetry of the distribution nearby the origin, where some nonexponential fine structure is observed. The total width of the distribution function strongly depends on the strength of the binding potential. Strong fluctuations of the magnetic moment (described in terms of the variance) are discovered in all temperature regimes.