SKYRMIONS IN QUANTUM HALL FERROMAGNETS

1999 ◽  
Vol 13 (05n06) ◽  
pp. 461-468 ◽  
Author(s):  
H. A. FERTIG
Keyword(s):  
Close Agreement ◽  
Filling Factor ◽  
Quantum Hall ◽  
Time Dependent ◽  
Square Lattice ◽  
Hartree Fock ◽  
Quantum Hall Systems ◽  
Spin Ordering ◽  
Lattice State ◽  
The Stability

Properties of skyrmions in quantum Hall systems are reviewed. It is shown that, using a Hartree-Fock technique, the size of skyrmions near filling factor ν=1 may be computed, yielding a result in close agreement with experiment. Finite densities of skyrmions are shown to lead to a crystal state with square symmetry due to the spin-dependent nature of their mutual interactions. The square lattice state has an unusual spin ordering which leads to a new gapless mode, analogous to spin waves in a two-dimensional XY antiferromagnet. The stability of the ordered spin state is assessed using a time-dependent Hartree-Fock approach, and a phase diagram is derived which shows the parameter range for which long-range spin ordering is destroyed by quantum fluctuations.

scholarly journals COULOMB GAP IN THE QUANTUM HALL INSULATOR

2001 ◽  
Vol 15 (10n11) ◽  
pp. 1369-1372 ◽  
Author(s):  
MICHAEL BACKHAUS ◽  
BODO HUCKESTEIN
Keyword(s):  
Filling Factor ◽  
Particle Density ◽  
Quantum Hall ◽  
Correct Treatment ◽  
Coulomb Gap ◽  
Hartree Fock ◽  
Strong Disorder ◽  
Single Particle Density ◽  
Lowest Landau Level ◽  
Classical Point

We calculate numerically the spectrum of disordered electrons in the lowest Landau level at filling factor 1/5 using the self-consistent Hartree-Fock approximation for systems containing up to 400 flux quanta. Special attention is paid to the correct treatment of the q=0 component of the Coulomb interaction. For sufficiently strong disorder, the system is an insulator at this filling factor. We observe numerically a Coulomb gap in the single-particle density of states (DOS). The DOS agrees quantitatively with the predictions for classical point charges.

FRACTIONAL QUANTUM HALL EFFECT: CONSTRUCTION OF THE HARTREE–FOCK STATE BY USING TRANSLATIONAL COVARIANCE

1994 ◽  
Vol 08 (05) ◽  
pp. 529-579 ◽  
Author(s):  
R. FERRARI
Keyword(s):  
Magnetic Field ◽  
Hall Effect ◽  
Landau Level ◽  
Quantum Hall Effect ◽  
Filling Factor ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Hartree Fock

The formalism introduced in a previous paper is used for discussing the Coulomb interaction of many electrons moving in two space-dimensions in the presence of a strong magnetic field. The matrix element of the Coulomb interaction is evaluated in the new basis, whose states are invariant under discrete translations (up to a gauge transformation). This paper is devoted to the case of low filling factor, thus we limit ourselves to the lowest Landau level and to spins all oriented along the magnetic field. For the case of filling factor νf = 1/u we give an Ansatz on the state of many electrons which provides a good approximated solution of the Hartree–Fock equation. For general filling factor νf = u′/u a trial state is given which converges very rapidly to a solution of the self-consistent equation. We generalize the Hartree–Fock equation by considering some correlation: all quantum states are allowed for the u′ electrons with the same translation quantum numbers. Numerical results are given for the mean energy and the energy bands, for some values of the filling factor (νf = 1/2, 1/3, 2/3, 1/4, 3/4, 1/5, 2/5, 3/5, 4/5). Our results agree numerically with the Charge Density Wave approach. The boundary conditions are shown to be very important: only large systems (degeneracy of Landau level over 200) are not affected by the boundaries. Therefore results obtained on small scale systems are somewhat unreliable. The relevance of the results for the Fractional Quantum Hall Effect is briefly discussed.

HARTREE–FOCK–BOGOLIUBOV STUDIES OF BILAYER ν = 2 QUANTUM HALL SYSTEMS

2005 ◽  
Vol 19 (11) ◽  
pp. 539-548 ◽  
Author(s):  
YUICHI SHIMODA ◽  
TATSUYA NAKAJIMA ◽  
ANJU SAWADA
Keyword(s):  
Ground State ◽  
Degrees Of Freedom ◽  
Rotational Symmetry ◽  
Quantum Hall ◽  
Excitation Spectra ◽  
Hartree Fock ◽  
Quantum Hall Systems ◽  
Spin Singlet ◽  
Spin Triplet ◽  
Bilayer Quantum Hall

Excitation spectra in bilayer quantum Hall systems at total Landau-level filling ν = 2 are studied by the Hartree–Fock–Bogoliubov (HFB) approximation. The systems have the spin degrees of freedom in addition to the layer degrees of freedom described in terms of pseudospin. On the excitation spectrum from the spin-singlet and pseudospin-polarized ground state, this approximation fully preserves the spin rotational symmetry and thus can give both spin-triplet and spin-singlet excitations systematically. It is also found that the ground state is pseudospin squeezed because of pseudospin correlations and that the HFB approximation can describe ground-state properties better than other approximations.

scholarly journals Coherence and Disorder in Bilayer Quantum Hall Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
H. A. Fertig ◽  
Ganpathy Murthy
Keyword(s):  
Thin Film ◽  
Finite Temperature ◽  
Filling Factor ◽  
Quantum Hall ◽  
Quantum Fluctuations ◽  
Low Energy ◽  
Quantum Hall Systems ◽  
Low Dissipation ◽  
Bilayer Quantum Hall

The quantum Hall bilayer at total filling factor displays a number of properties akin to superfluidity, most clearly apparent in its very low dissipation in tunneling and counterflow transport. Theoretical descriptions in terms of quantum Hall ferromagnetism or thin-film superfluidity can be developed to explain these phenomena. In either case, merons can be identified as important low energy excitations. We demonstrate that a model in which puddles of merons induced by disorder, separated by narrow regions of interlayer coherence—a coherence network—can naturally explain many of the imperfect superfluid finite temperature properties that are observed in these systems. The periodic realization of this model shows that there can be low energy excitations beyond the superfluid mode. These are associated with transitions between states of different meron number in the puddles, where we argue that merons should be unbound atanytemperature, and which can have important implications for the effect of quantum fluctuations on the system.

scholarly journals ZERO-BIAS CONDUCTANCE ANOMALY IN BILAYER QUANTUM HALL SYSTEMS

2002 ◽  
Vol 16 (20n22) ◽  
pp. 2936-2939
Author(s):  
Y. N. JOGLEKAR ◽  
A. H. MACDONALD
Keyword(s):  
Filling Factor ◽  
Quantum Hall ◽  
Tunneling Conductance ◽  
Coulomb Interactions ◽  
Zero Bias ◽  
Rich Variety ◽  
Quantum Hall Systems ◽  
Zero Bias Conductance ◽  
Quantum Hall System ◽  
Bilayer Quantum Hall

Bilayer quantum Hall system at total filling factor ν=1 shows a rich variety of broken symmetry ground states because of the competition between the interlayer and intralayer Coulomb interactions. When the layers are sufficiently close, a bilayer system develops spontaneous interlayer phase-coherence that manifests itself through a spectacular enhancement of the zero-bias interlayer tunneling conductance. We present a theory of this tunneling conductance anomaly, and show that the zero-bias conductance is proportional to the square of the quasiparticle tunneling amplitude.

scholarly journals Active topolectrical circuits

2021 ◽  
Vol 118 (32) ◽  
pp. e2106411118
Author(s):  
Tejas Kotwal ◽  
Fischer Moseley ◽  
Alexander Stegmaier ◽  
Stefan Imhof ◽  
Hauke Brand ◽  
...  
Keyword(s):  
Close Agreement ◽  
Quantum Hall ◽  
High Dimensional ◽  
Electric Signal ◽  
Electronic Systems ◽  
Two Dimensional ◽  
Electrical Circuits ◽  
Quantum Hall Systems ◽  
Self Organized ◽  
Global Signal

The transfer of topological concepts from the quantum world to classical mechanical and electronic systems has opened fundamentally different approaches to protected information transmission and wave guidance. A particularly promising emergent technology is based on recently discovered topolectrical circuits that achieve robust electric signal transduction by mimicking edge currents in quantum Hall systems. In parallel, modern active matter research has shown how autonomous units driven by internal energy reservoirs can spontaneously self-organize into collective coherent dynamics. Here, we unify key ideas from these two previously disparate fields to develop design principles for active topolectrical circuits (ATCs) that can self-excite topologically protected global signal patterns. Realizing autonomous active units through nonlinear Chua diode circuits, we theoretically predict and experimentally confirm the emergence of self-organized protected edge oscillations in one- and two-dimensional ATCs. The close agreement between theory, simulations, and experiments implies that nonlinear ATCs provide a robust and versatile platform for developing high-dimensional autonomous electrical circuits with topologically protected functionalities.

scholarly journals Optics with Quantum Hall Skyrmions

1998 ◽  
Vol 12 (01) ◽  
pp. 1-35 ◽  
Author(s):  
T. Portengen ◽  
J. R. Chapman ◽  
V. Nikos Nicopoulos ◽  
N. F. Johnson
Keyword(s):  
Optical Properties ◽  
Spin Density ◽  
Theoretical Investigation ◽  
Disordered Systems ◽  
Lower Energy ◽  
Filling Factor ◽  
Electron Gas ◽  
Quantum Hall ◽  
Quantum Hall Systems ◽  
Optical Signature

A novel type of charged excitation, known as a Skyrmion, has recently been discovered in quantum Hall systems with filling factor near ν=1. A Skyrmion — which can be thought of as a topological twist in the spin density of the electron gas — has the same charge as an electron, but a much larger spin. In this review we present a detailed theoretical investigation of the optical properties of Skyrmions. Our results provide means for the optical detection of Skyrmions using photoluminescence (PL) spectroscopy. We first consider the optical properties of Skyrmions in disordered systems. A calculation of the luminescence energy reveals a special optical signature which allows us to distinguish between Skyrmions and ordinary electrons. Two experiments to measure the optical signature are proposed. We then turn to the optical properties of Skyrmions in pure systems. We show that, just like an ordinary electron, a Skyrmion may bind with a hole to form a Skyrmionic exciton. The Skyrmionic exciton can have a lower energy than the ordinary magnetoexciton. The optical signature of Skyrmions is found to be a robust feature of the PL spectrum in both disordered and pure systems.

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