Quantized dissipation of the quantum Hall effect at high currents

Quantized dissipative voltage states are observed when large currents are passed through a high-quality quantized Hall resistance device. These dissipative states are interpreted as occurring when electrons are excited to higher Landau levels and then return to the original Landau level. The author shows that the quantization is more complicated than previously thought. For example, the quantization can be a function of magnetic field. Therefore, the dissipative voltage quantization can, in general, be difficult to verify and determine     

Possible mechanisms of the external magnetic field influence on the exchange coupling

Possible mechanisms of the external magnetic field influence on exchange coupling in ultrathin M/N/M film structures are discussed. It is shown that the most reasonable mechanism is due to variation of the translational motion of spacer electrons in the external magnetic field. In this case in-plane components of the electron momentum should be quantized according to Landau levels. The most drastic effect should be observed in the case when magnetic field is perpendicular to the film plane. Comparison of calculations according to the proposed model with the experimental data is presented, showing very good correlation for the cases of presence and absence of external magnetic field.     

Nanocontact magnetoresistance and quantized conductance

The behavior of the magnetoresistance (MR) effect in a ferromagnetic Ni nanocontact is investigated in the regime of conductance quantization (1/12900 /spl Omega//sup -1/). The giant MR effect is observed in the case that the nanocontact with quantized conductance is fabricated. We sometimes observe that the conductance discretely changes by the quantization unit of e/sup 2//h and that the quantized conductance is switched by the application of magnetic field. There exists a close relationship between nanocontact MR and quantized conductance.     

Calculating the Effects of Longitudinal Resistance in Multi-Series-Connected Quantum Hall Effect Devices

Many ac quantized Hall resistance experiments have measured significant values of ac longitudinal resistances under temperature and magnetic field conditions in which the dc longitudinal resistance values were negligible. We investigate the effect of non-vanishing ac longitudinal resistances on measurements of the quantized Hall resistances by analyzing equivalent circuits of quantized Hall effect resistors. These circuits are based on ones reported previously for dc quantized Hall resistors, but use additional resistors to represent longitudinal resistances. For simplification, no capacitances or inductances are included in the circuits. The analysis is performed for many combinations of multi-series connections to quantum Hall effect devices. The exact algebraic solutions for the quantized Hall resistances under these conditions of finite ac longitudinal resistances provide corrections to the measured quantized Hall resistances, but these corrections do not account for the frequency dependences of the ac quantized Hall resistances reported in the literature.     

Irradiated bilayer graphene

We describe the gated bilayer graphene system when it is subjected to intense terahertz frequency electromagnetic radiation. We examine the electron band structure and density of states via exact diagonalization methods within Floquet theory. We find that dynamical states are induced which lead to modification of the band structure. We first examine the situation where there is no external magnetic field. In the unbiased case, dynamical gaps appear in the spectrum which manifest as dips in the density of states. For finite inter-layer bias (where a static gap is present in the band structure of unirradiated bilayer graphene), dynamical states may be induced in the static gap. These states can show a high degree of valley polarization. When the system is placed in a strong magnetic field, the radiation induces coupling between the Landau levels which allows dynamical levels to exist. For strong fields, this means the Landau levels are smeared to form a near-continuum of states.     

Can a repulsive potential in graphene have boundstates in a magnetic field?

We consider Klein tunneling through a repulsive and cylindrical potential with range R and strength V. Recently it was found that, in the strong coupling regime R/l < 1, the repulsive potential can have bound states peaked inside the potential with tails extending over l mean square root of 2(N+1), where N is Landau level (LL) index and f is the magnetic length. The presence of these bound states is a consequence of a subtle interplay between Klein tunneling and quantization effect of magnetic fields. Because of the presence of these bound states the effective coupling between the repulsive potential and an electron can be attractive. Here we show that this effect is a consequence of singular interaction between the repulsive potential and an electron that cannot be captured in perturbative approaches.     

Modulation effects on Landau levels in a monolayer graphene

Magnetoelectronic properties of a single-layer graphene are studied by the Peierls tight-binding model. A new numerical technique is developed to obtain a band-like Hamiltonian matrix. A spatially modulated magnetic field B' could drastically alter the Landau levels due to a uniform magnetic field B. The modulation effects include enhancement in dimensionality, change of energy dispersions, destruction of state degeneracy and creation of band-edge states. The dispersionless Landau levels, those at the Fermi levels excepted, become the 1D parabolic bands. The density of states thus exhibits many pairs of asymmetric prominent peaks. The height, frequency and number of pronounced peaks strongly depend on the modulation strength. These characteristics are hardly affected by the period and direction when B' is much weaker than B. The predicted results could be verified by experimental measurements on magneto-optical absorption spectra.     

Analyzing the Effects of Capacitances-to-Shield in Sample Probes on AC Quantized Hall Resistance Measurements

We analyze the effects of the large capacitances-to-shields existing in all sample probes on measurements of the ac quantized Hall resistance R_H. The object of this analysis is to investigate how these capacitances affect the observed frequency dependence of R_H. Our goal is to see if there is some way to eliminate or minimize this significant frequency dependence, and thereby realize an intrinsic ac quantized Hall resistance standard. Equivalent electrical circuits are used in this analysis, with circuit components consisting of: capacitances and leakage resistances to the sample probe shields; inductances and resistances of the sample probe leads; quantized Hall resistances, longitudinal resistances, and voltage generators within the quantum Hall effect device; and multiple connections to the device. We derive exact algebraic equations for the measured R_H values expressed in terms of the circuit components. Only two circuits (with single-series “offset” and quadruple-series connections) appear to meet our desired goals of measuring both R_H and the longitudinal resistance R_x in the same cool-down for both ac and dc currents with a one-standard-deviation uncertainty of 10⁻⁸ R_H or less. These two circuits will be further considered in a future paper in which the effects of wire-to-wire capacitances are also included in the analysis.     

Effect of level broadening on the photoelectric emission from a single quantum well in ultrathin film under the influence of a quantizing magnetic field

The photoelectric emission from a quasi-two-dimensional electron gas (Q2DEG) in a single quantum well (SQW) formed in wide-gap semiconductor films has been theoretically investigated, under magnetic quantization incorporating Landau level broadening arising due to electron impurity scattering. The photoelectric current density has been computed for a Q2DEG formed in n-type GaAs film and is found to be modified in the presence of level broadening. The photoemission from a quasi-zero-dimensional electron gas (QODEG) formed in the ultrathin film under the influence of a quantizing magnetic field applied normal to the film has also been compared with that for the QODEG formed in a quantum box.     

Possible Mechanism of a New Type of Three-Dimensional Quantized Hall Effect in Layered Semiconductors Bi2−xSnxTe3

We have found a new type of three-dimensional quantized Hall effect (QHE) in layered semiconductors Bi₂–xSn_xTe₃ (x0.0125) single crystals. The Hall resistivity is not expressed in a universal relation applicable for a conventional QHE and depends appreciably on the doped Sn concentration x. The flat Hall plateaus are visible at higher Landau levels but are rather suppressed at lower regions. The calculated Landau levels of the upper valence band (UVB) with the best-fit band parameters are in excellent agreement with the experiments, including spin splitting. For Bi₂–xSn_xTe₃, the Sn-originated impurity band (IB) has resonant nature and enhances the density of states at the Fermi level of UVB. The charge transfer occurs between the quantized UVB and the resonant IB or the lower valence band (LVB) for Bi₂–xSn_xTe₃ or Bi₂Te₃, respectively, and the Landau levels are enhanced appreciably. We have revealed that the quasi-localized states are formed in quantized three-dimensional density of state spectra. We have proposed a possible model for the present QHE, which is a modification of Mani's model, where the quasi-localized state is formed at the disorder-originated tail of each Landau level. In the quasi-localized regime, the IB or LVB are responsible for the carrier reservoir to regulate the Hall resistivity.     

Low-temperature thermodynamics of the two-dimensional orbital antiferromagnet

We consider the low-temperature properties of a two-dimensional orbital anti-ferromagnet (OAF), which is one of the possible states of the weakly interacting electron system with a half-filled band on a square lattice. Such a state can result from anisotropic electron-hole pairing due to the nesting property of the Fermi surface, and is characterized by nonzero local currents violating translational symmetry of the underlying lattice. Within a simple mean-field model, we show that, in the low-energy limit, the 2D OAF is described by (2+1)-dimensional quantum field theory of gapless fermion excitations associated with zeros of the gap function. The relativistic Landau quantization of the spectrum in external magnetic field shows up in unusual behavior of the magnetic susceptibility. Strong diamagnetism of the OAF is found in the perpendicular field, changing to paramagnetism upon the decreasing of the angle between the field and the plane. When the angle approaches zero, the susceptibility shows an oscillatory angle dependence.     

Hybrid silicon/molecular FETs: a study of the interaction of redox-active molecules with silicon MOSFETs

Redox-active molecular monolayers were incorporated in silicon MOSFETs to obtain hybrid silicon/molecular FETs. Cyclic voltammetry and FET characterization techniques were used to study the properties of these hybrid devices. The redox-active molecules have tunable charge states, which are quantized at room temperature and can be accessed at relatively low voltages. The discrete molecular states were manifested in the drain current and threshold voltage characteristics of the device, confirming the presence of distinct energy levels within the molecules at room temperature. This study demonstrates the modulation of Si-MOSFETs' drain currents via redox-active molecular monolayers. The single-electron functionality provided by the redox-active molecules is ultimately scalable to molecular dimensions, and this approach can be extended to nanoscale field-effect devices including those based on carbon nanotubes. The molecular states coupled with CMOS devices can be utilized for low-voltage, multiple-state memory and logic applications and can extend the impact of silicon-based technologies.     

Flux Rule, <Emphasis Type="Italic">U</Emphasis>(1) Instanton,and Superconductivity

We examine some consequences of the duality that a U(1) phase factor added on a wave function describes a whole system motion and also plays the role of a U(1) gauge potential. First, we show that the duality solves a long-standing puzzling problem that the ‘flux rule’ (the Faraday’s induction formula) and the Lorentz force calculation for an emf emerging in an electron system moving in a magnetic field give the same result (Feynman et al. 1963). Next, we examine a U(1) phase factor induced on the wave function for an electron system due to the single-valuedness requirement of the wave function with respect to the electron coordinates, and its consequential appearance of a U(1) instanton. This instanton explains the Meissner effect, supercurrent generation, flux quantization in the units of \({{h} \over {2e}}\), and the voltage quantization in the units of \({{hf} \over {2e}}\) across the Josephson junction in the presence of a radiation field with frequency f. In the experiment, a radiation field must be present to have a finite voltage across the Josephson junction; but a clear explanation for it has been lacking. The present work provides an explanation for it, and also explains the high precision of the quantized voltage as due to a topological effect.     

Quantized magnetoresistance in atomic-size contacts

When the dimensions of a metallic conductor are reduced so that they become comparable to the de Broglie wavelengths of the conduction electrons, the absence of scattering results in ballistic electron transport and the conductance becomes quantized. In ferromagnetic metals, the spin angular momentum of the electrons results in spin-dependent conductance quantization and various unusual magnetoresistive phenomena. Theorists have predicted a related phenomenon known as ballistic anisotropic magnetoresistance (BAMR). Here we report the first experimental evidence for BAMR by observing a stepwise variation in the ballistic conductance of cobalt nanocontacts as the direction of an applied magnetic field is varied. Our results show that BAMR can be positive and negative, and exhibits symmetric and asymmetric angular dependences, consistent with theoretical predictions.     

On the quantization of the electromagnetic field in conducting media

In this work we investigate the quantization of electromagnetic waves propagating through homogeneous conducting linear media with no charge density. We use Coulomb's gauge to reduce the problem to that of a time-dependent harmonic oscillator, which is described by the Caldirola–Kanai Hamiltonian. Furthermore, we obtain the corresponding exact wave functions with the help of quadratic invariants and of the dynamic invariant method. These wave functions are written in terms of a particular solution of the Milne–Pinney equation. We also construct coherent and squeezed states for the quantized electromagnetic waves and evaluate the quantum fluctuations in coordinates and momentum as well as the uncertainty product for each mode of the electromagnetic field.     

Coupling of surface and lowest Landau level states in a rectangular graphene dot

A rectangular graphene dot with two zigzag edges and two armchair edges have electronic states in the presence of a magnetic field that are localized on the zigzag edges with non zero values of the wavefunction inside the dot. We have investigated the dependence of these wavefunctions on the size of the dot, and explain the physical origin of them in terms of surface and the lowest Landau level (LLL) states of infinitely long nanoribbons. We find that the armchair edges play a crucial role by coupling the surface and LLL states.     

Production of Macroscopic Schrödinger Cat States from Weak Quantized Cavity Fields Interacting with Atoms Driven by Classical Fields

Abstract

We show that macroscopic superposition (Schrödinger cat) states of a quantized single-mode cavity field can be produced via the interaction of this field with a two-level atom which is driven by a classical field even for small initial intensities of the quantized cavity mode. We show that with a properly chosen driving field an almost pure superposition state with arbitrary amplitudes and phases of component states can be produced.     

The damping of helicon waves in a tipped magnetic field

The damping of helicon waves in indium was measured under nonlocal conditions with a variable angle between the wave vectorq and the magnetic field. In contrast to the predictions of the free-electron theory, the damping was not a monotonic function of the angle and exhibits considerable structure, which is attributed to minima in the Landau damping for certain orientations of the magnetic field. Minima in the damping are to be expected for such field directions as give rise to cyclotron orbits having a substantial number of electron states with orbital velocities perpendicular toq. In simple situations the critical orientations of the magnetic field may be deduced from a given Fermi surface by a geometrical construction. The construction has been extended to indium, and the tipping angles found are in reasonable agreement with the experiment.Based on a thesis to be submitted to the Senate of the Technion, Israel Institute of Technology, in partial fulfillment of the requirements for D.Sc. degree.     

Graphene Acoustic Phonon‐Mediated Pseudo‐Landau Levels Tailoring Probed by Scanning Tunneling Spectroscopy

Graphene has attracted great interests in various areas including optoelectronics, spintronics, and nanomechanics due to its unique electronic structure, a linear dispersion with a zero bandgap around the Dirac point. Shifts of Dirac cones in graphene creates pseudo‐magnetic field, which generates an energy gap and brings a zero‐magnetic‐field analogue of the quantum Hall effect. Recent studies have demonstrated that graphene pseudo‐magnetic effects can be generated by vacancy defects, atom adsorption, zigzag or armchair edges, and external strain. Here, a larger than 100 T pseudo‐magnetic field is reported that generated on the step area of graphene; and with the ultrahigh vacuum scanning tunneling microscopy, the observed Landau levels can be effectively tailored by graphene phonons. The zero pseudo‐Landau level is suppressed due to the phonon‐mediated inelastic tunneling, and this is observed by the scanning tunneling spectroscopy spectrum and confirmed by the Vienna ab initio simulation package calculation, where graphene phonons modulate the flow of tunneling electrons and further mediate pseudo‐Landau levels. These observations demonstrate a viable approach for the control of pseudo‐Landau levels, which tailors the electronic structure of graphene, and further ignites applications in graphene valley electronics.