Screw dislocation-induced influence of transverse modes on Hall conductivity

The Hall conductivity of an electron gas on an interface showing a topological defectcalled screw dislocation is investigated. This kind of defect induces a singular torsionon the medium which in turn induces transverse modes in the quantum Hall effect. It isshown that this topology decreases the plateaus’ widths and shifts the steps in the Hallconductivity to lower magnetic fields. The Hall conductivity is neither enhanced nordiminished by the presence of this kind of defect alone. We also consider the presence oftwo defects on a sample, a screw dislocation together with a disclination. For a specificvalue of deficit angle, there is a reduction in the Hall conductivity. For an excess ofangle, the steps shift to higher magnetic fields and the Hall conductivity is enhanced.Our work could be tested only in common semiconductors but we think it opens a road to theinvestigation on how topological defects can influence other classes of Hall effect.     

On the Singular Effects in the Relativistic Landau Levels in Graphene with a Disclination

The effect of a pseudo Aharonov-Bohm (AB) magnetic field generated by a disclination on a two-dimensional electron gas in graphene is addressed in the continuum limit within the geometric approach. The influence of the coupling between the spinor fields and the singular conical curvature is investigated, which shows that singularities have pronounced impact in the Hall conductivity. Moreover, the degeneracy related to the Dirac valleys is broken for negative values of the angular momentum quantum numbers, l, includingl ≡ 0. In this case, a Hall plateau develops at the null filling factor. Obtaining the Hall conductivity by summing over the positive and the negative l's, the null Landau level is recovered and the plateau at the null filling factor disappears. In any case, the standard plateaus, which are seen in a flat graphene are not obtained with these curvature and singular effects.     

Gap generation for Dirac fermions on Lobachevsky plane in a magnetic field

We study symmetry breaking and gap generation for fermions in the 2D space of constant negative curvature (the Lobachevsky plane) in an external covariantly constant magnetic field in a four-fermion model. It is shown that due to the magnetic and negative curvature catalyses phenomena the critical coupling constant is zero and there is a symmetry breaking condensate in the chiral limit even in free theory. We analyze solutions of the gap equation in the cases of zero, weak, and strong magnetic fields. As a byproduct, we calculate the density of states and the Hall conductivity for noninteracting fermions that may be relevant for studies of graphene.     

Magnetotransport in a semconductor superlattice with transverse magnetic field

Magnetotransport in a semiconductor superlattice (SL) under transverse magnetic field has been investigated. It is shown that in weak magnetic and electric fields there is negative magnetoresistivity along the SL layers and positive magnetoresistivity along the SL axis. The Hall resistivity is much less than the usual semiconductor value. With an increase of electric field, there appears a negative differential conductivity (NDC) along the SL layers, and the Hall voltage depends nonlinearly on current density. In higher electric field, destroying the miniband structure, the magnetoresistivity along the SL axis is negative. The magnetoresistivity along the SL axis in strong magnetic field is positive for any current density. The Hall resistivity in strong magnetic (electric) field equals the classical value.     

Electric- and magnetic-field-tuned Landau levels and Hall conductivity in AA-stacked bilayer graphene

We theoretically study the combined effect of magnetic and electric fields on the Landau levels and Hall conductivity in AA-stacked bilayer graphene. From the analytic expressions derived, we obtain explicit criterions for determining the zero-energy Landau level and different level crossings in the graphene bilayer. For providing a scheme of experimental verification, we further explore the quantum Hall effect in such a biased bilayer. It is found that the zero-conductance Hall plateau in this system can vanish at certain specific combinations of magnetic and electric fields, accompanying with the occurrence of resonance Hall conductivity steps.     

Spin polarization in carbon nanostructures with disclinations

We performed ab initio calculations, using density functional theory, to study spin polarization in carbon nanostructures with disclinations. The results indicate that compounds with positive and negative Gaussian curvature may exhibit a net magnetic moment in the ground state. Additionally, we can conclude that, carbon compounds that display an odd number of pentagons and heptagons, present polarization in the ground state.     

Zur anschaulichen Diskussion der qualitativen Eigenschaften der galvanomagnetischen Koeffizienten

The dependence of the different components of the conductivity resp. the resistivity tensor upon the strength and direction of an external magnetic field is discussed qualitatively. — In metals, in which the Fermi surface is simply closed, the changes in longitudinal and transversal resistance and the Hall coefficients are large if the anisotropies of the Fermi surface resp. of the scattering mechanism in the planes perpendicular to magnetic field direction are large, and vice versa. In fields, in which this effect already clearly is marked, the changes in transversal resistance in addition increase with increasing anisotropies ink-space perpendicular to Hall field direction, whereas by equal set in of current and Hall field direction the Hall coefficients now show a tendency to decrease with increasing anisotropies perpendicular to magnetic field direction. The order of Hall coefficients may change in high magnetic fields. In contrast to the changes in resistance the Hall coefficients decrease with increasing strength of magnetic field. — In the presence of open Fermi surfaces the transversal resistance doesn't saturate in the direction of the open orbits. If open orbits exist in more than one direction, saturation returns and the Hall coefficients now vanish proportional to 1/B ². In considering open Fermi surfaces it is not allowed to neglect scattering in strong magnetic fields.     

Vertical hall effect in GaAs quantum wells

Applying orthogonal in-plane electric and magnetic fields in a 2D system leads to the development of a Hall voltage across the width of the quantum well when the cyclotron orbit is greater than the well width. Tang and Butcher [1] have calculated the developed Hall voltage for a parabolic quantum well where they find that the Hall voltage is dependent on the frequency associated with the harmonic potential in the well. The limitation of this model is that it does not enable one to determine the well width dependence of the Hall Voltage, nor is it a particularly good model for a quantum well. It is also difficult to compare their model with the bulk result which would apply at large well widths. In this work we present a model calculation which considers a square quantum well and hence is able to predict the well width dependence of the Hall Voltage and compare the large well width case to the bulk result. An electro-optic probing method previously used to measure bulk Hall voltages [2] is shown to be capable of measuring the Hall 'voltage across a quantum well, and therefore can be used to confirm the prediction of the model presented here.     

Motion of Charged Particle in Electric and Magnetic Fields in 3D Noncommutative Spaces and Related Problems

In three-dimensional noncommutative phase space, the energy spectrum and wave functions for the motion of a charged particle in a magnetic field are derived. Due to the momentum–momentum noncommutativity, the particle feels an effective magnetic field in a new direction. When an external electric field perpendicular to this effective magnetic field is applied, the Hall conductivity can be calculated. To get the Hall conductivity, one should define the electric currents from the probability currents in quantum mechanics rather than extending the classical electric currents to quantum mechanics directly. When the electric field is not perpendicular to the effective magnetic field, it is difficult to define the Hall conductivity.     

Quantum Hall effect in intentionally disordered two‐dimensional electron systems

In this work intentionally disordered two‐dimensional electron systems in modulation doped GaAs/GaAlAs heterostructures are studied by magnetotransport experiments. The disorder is provided by a δ‐doped layer of negatively charged beryllium acceptors. In low magnetic fields a strong negative magnetoresistance is observed that can be ascribed to magnetic‐field‐induced delocalization. At increased magnetic fields the quantum Hall effect exhibits broad Hall plateaus whose centers are shifted to higher magnetic fields, i.e. lower filling factors. This shift can be explained by an asymmetric density of states. Consistently, the transition into the insulating state of quantum Hall droplets in high magnetic fields occurs at critical filling factors around ν_c=0.4, i.e. well below the value 1/2 that is expected for symmetric disorder potentials. The insulator transition is characterized by the divergence of both the longitudinal resistance as well as the Hall resistance. This is contrary to other experiments which observe a finite Hall resistance in the insulating regime and has not been observed previously. According to recent theoretical studies the divergence of the Hall resistance points to quantum coherent transport via tunneling between quantum Hall droplets. The magnetotransport experiments are supplemented by simulations of potential landscapes for random and correlated distributions of repulsive scatterers, which enable the determination of percolation thresholds, densities of states, and oscillator strengths for far‐infrared excitations. These simulations reveal that the strong shift of the Hall plateaus and the observed critical filling factor for the insulator transition in high magnetic fields require an asymmetric density of states that can only be generated by a strongly correlated beryllium distribution. Cyclotron resonance on the same samples also indicates the possibility of correlations between the beryllium acceptors.     

Quantum transport in topological semimetals under magnetic fields

Topological semimetals are three-dimensional topological states of matter, in which the conduction and valence bands touch at a finite number of points, i.e., the Weyl nodes. Topological semimetals host paired monopoles and antimonopoles of Berry curvature at the Weyl nodes and topologically protected Fermi arcs at certain surfaces. We review our recent works on quantum transport in topological semimetals, according to the strength of the magnetic field. At weak magnetic fields, there are competitions between the positive magnetoresistivity induced by the weak anti-localization effect and negative magnetoresistivity related to the nontrivial Berry curvature. We propose a fitting formula for the magnetoconductivity of the weak anti-localization. We expect that the weak localization may be induced by inter-valley effects and interaction effect, and occur in double-Weyl semimetals. For the negative magnetoresistance induced by the nontrivial Berry curvature in topological semimetals, we show the dependence of the negative magnetoresistance on the carrier density. At strong magnetic fields, specifically, in the quantum limit, the magnetoconductivity depends on the type and range of the scattering potential of disorder. The high-field positive magnetoconductivity may not be a compelling signature of the chiral anomaly. For long-range Gaussian scattering potential and half filling, the magnetoconductivity can be linear in the quantum limit. A minimal conductivity is found at the Weyl nodes although the density of states vanishes there.     

Electrical properties of bilayer heterojunctions in a strong magnetic field

The electrical properties of bilayer heterojunctions in a strong magnetic field at low temperatures have been considered. It has been shown that both the ohmic and Hall conductivities decrease exponentially due to the formation of neutral pairs if the electric fields in the two layers are parallel. In the antiparallel fields, the Hall conductivity is still determined by the activation energy of the excited electrons and decreases exponentially, but the ohmic conductivity decreases much slower, proportional to the temperature square.     

Hall quantum Hamiltonians and electric 2D-curvature

For the Dirac 2D-operator in a constant magnetic field with perturbing electric potential, we derive Hamiltonians describing the quantum quasiparticles (Larmor vortices) at Landau levels. The discrete spectrum of this Hall-effect quantum Hamiltonian can be computed to all orders of the semiclassical approximation by a deformed Planck-type quantization condition on the 2D-plane; the standard magnetic (symplectic) form on the plane is corrected by an ??electric curvature?? determined via derivatives of the electric field. The electric curvature does not depend on the magnitude of the electric field and vanishes for homogeneous fields (i.e., for the canonical Hall effect). This curvature can be treated as an effective magnetic charge of the inhomogeneous Hall 2D-nanosystem.     

Gap opening in the zeroth Landau level in gapped graphene: pseudo-Zeeman splitting in an angular magnetic field

We present a theoretical study of gap opening in the zeroth Landau level in gapped graphene as a result of pseudo-Zeeman interaction. The applied magnetic field couples with the valley pseudospin degree of freedom of the charge carriers leading to the pseudo-Zeeman interaction. To investigate its role in transport at the charge neutrality point (CNP), we study the integer quantum Hall effect in gapped graphene in an angular magnetic field in the presence of pseudo-Zeeman interaction. Analytical expressions are derived for the Hall conductivity using the Kubo-Greenwood formula. We also determine the longitudinal conductivity for elastic impurity scattering in the first Born approximation. We show that pseudo-Zeeman splitting leads to a minimum in the collisional conductivity at high magnetic fields and a zero plateau in the Hall conductivity. Evidence for activated transport at CNP is found from the temperature dependence of the collisional conductivity.     

Electron magnetotransport in carbon nanotubes and negative magnetoresistance: The density matrix method

A solution (stationary and linear in electric field) to the kinetic equation for a one-electron density matrix in an arbitrary magnetic field is found for deformation-potential scattering in the approximation of a small deviation of the electron gas from equilibrium. An expression for the nanotube conductivity is obtained in the form of a sum over magnetic-quantization states. In the absence of a magnetic field, this expression coincides with the corresponding classical relations. In weak magnetic fields, the magnetoresistance of a multilayer nanotube is positive for high electron mobilities and negative for low mobilities. In intermediate fields, it reverses sign with increasing field strength. The magnetoresistance of a one-layer nanotube is always positive.     

Topological nature of the phonon Hall effect

We provide a topological understanding of the phonon Hall effect in dielectrics with Raman spin-phonon coupling. A general expression for phonon Hall conductivity is obtained in terms of the Berry curvature of band structures. We find a nonmonotonic behavior of phonon Hall conductivity as a function of the magnetic field. Moreover, we observe a phase transition in the phonon Hall effect, which corresponds to the sudden change of band topology, characterized by the altering of integer Chern numbers. This can be explained by touching and splitting of phonon bands.     

Magnetic fields in 2D and 3D sphere

In this note we study the Landau–Hall problem in the 2D and 3D unit sphere, that is, the motion of a charged particle in the presence of a static magnetic field. The magnetic flow is completely determined for any Riemannian surface of constant Gauss curvature, in particular, the unit 2D sphere. For the 3D case we consider Killing magnetic fields on the unit sphere, and we show that the magnetic flowlines are helices with the given Killing vector field as its axis.     

A direct connection between quantum Hall plateaus and exact pair states in a 2D electron gas

It is previously found that the two-dimensional (2D) electron-pair in a homogeneous magnetic field has a set of exact solutions for a denumerably infinite set of magnetic fields. Here we demonstrate that as a function of magnetic field a band-like structure of energy associated with the exact pair states exists. A direct and simple connection between the pair states and the quantum Hall effect is revealed by the band-like structure of the hydrogen “pseudo-atom”. From such a connection one can predict the sites and widths of the integral and fractional quantum Hall plateaus for an electron gas in a GaAs-Al _x Ga_1−x As heterojunction. The results are in good agreement with the existing experimental data.     

High-field magnetoresistance and Hall effect in Bi2Sr2CuO x single crystals

We investigated the in-plane magnetoresistance and the Hall effect of high-quality Bi₂Sr₂CuO_x single crystals with T _c (midpoint) = 3.7–9.6 K in dc magnetic fields up to 23 T. For T < 10 K, the crystals show the classical positive magnetoresistance. Starting at T ≈ 14 K, an anomalous negative magnetoresistance appears at low magnetic fields; for T ≥ 40 K, the magnetoresistance is negative in the whole studied range of magnetic fields. Temperature and magnetic field dependences of the negative-magnetoresistance single crystals are qualitatively consistent with the electron interaction theory developed for simple semiconductors and disordered metals. As is observed in other cuprate superconductors, the Hall resistivity is negative in the mixed state and changes its sign with increasing field. The linear T-dependence of cotθ_H for the Hall angle in the normal state closely resembles that of the normal-state resistivity as expected for a Fermi liquid picture.