Showing papers on "Landau quantization published in 1999"
TL;DR: In this paper, the Pfaffian quantum Hall states, which can be viewed as involving pairing either of spin-polarized electrons or of composite fermions, are generalized by finding the exact ground states of certain Hamiltonians with $k+1$-body interactions, for all integers $kg~1.
Abstract: The Pfaffian quantum Hall states, which can be viewed as involving pairing either of spin-polarized electrons or of composite fermions, are generalized by finding the exact ground states of certain Hamiltonians with $k+1$-body interactions, for all integers $kg~1.$ The remarkably simple wave functions of these states involve clusters of k particles, and are related to correlators of parafermion currents in two-dimensional conformal field theory. The $k=2$ case is the Pfaffian. For $kg~2,$ the quasiparticle excitations of these systems are expected to possess non-Abelian statistics, like those of the Pfaffian. For $k=3,$ these ground states have large overlaps with the ground states of the (two-body) Coulomb-interaction Hamiltonian for electrons in the first excited Landau level at total filling factors $\ensuremath{
u}=2+3/5,2+2/5.$
702 citations
TL;DR: In this paper, strong anisotropies and nonlinearities of the longitudinal resistivity ρxx were observed at the ground state or first excited Landau level but begin abruptly in the third level.
Abstract: Magnetotransport experiments on high mobility two-dimensional electron gases in GaAs/AlGaAs heterostructures have revealed striking anomalies near half filling of several spin-resolved, yet highly excited, Landau levels. These anomalies include strong anisotropies and nonlinearities of the longitudinal resistivity ρxx which commence only below about 150 mK. These phenomena are not seen in the ground state or first excited Landau level but begin abruptly in the third level. Although their origin remains unclear, we speculate that they reflect the spontaneous development of a generic anisotropic many-electron state.
414 citations
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TL;DR: In this paper, the authors present more recent data obtained with a very high mobility sample, and reiterate that an anisotropic state develops in high Landau levels at very low temperatures.
Abstract: We recently reported [PRL 82, 394 (1999)] large transport anisotropies in a two-dimensional electron gas in high Landau levels. These observations were made utilizing both square and Hall bar sample geometries. Simon recently commented [cond-mat/9903086] that a classical calculation of the current flow in the sample shows a magnification of an underlying anisotropy when using a square sample. In this reply we present more recent data obtained with a very high mobility sample, and reiterate that, with or without magnification, an anisotropic state develops in high Landau levels at very low temperatures.
311 citations
TL;DR: In this article, the effects of quantum and thermal fluctuations about such a state and show that they can lead to a set of electronic liquid crystalline states, particularly a stripe-nematic phase, which is stable at $Tg 0.$
Abstract: Mean-field calculations for the two-dimensional electron gas in a large magnetic field with a partially filled Landau level with index $Ng~2$ consistently yield ``stripe-ordered'' charge-density wave ground states, for much the same reason that frustrated phase separation leads to stripe-ordered states in doped Mott insulators. We have studied the effects of quantum and thermal fluctuations about such a state and show that they can lead to a set of electronic liquid crystalline states, particularly a stripe-nematic phase, which is stable at $Tg0.$ Recent measurements of the longitudinal resistivity of a set of quantum Hall devices have revealed that these systems spontaneously develop, at low temperatures, a very large anisotropy. We interpret these experiments as evidence for a stripe nematic phase, and propose a general phase diagram for this system.
231 citations
TL;DR: In this article, it was shown that low-temperature, electronic transport in Landau levels N > 1 of a two-dimensional electron system is strongly anisotropic, and the transport anisotropies may be indicative of a new many particle state, which forms exclusively in higher landau levels.
228 citations
TL;DR: The Quantum Hall Effect (QHE) is one of the most remarkable condensed-matter phenomena discovered in the second half of the 20th century as mentioned in this paper, and it rivals superconductivity in its fundamental significance as a manifestation of quantum mechanics.
Abstract: The Quantum Hall Effect (QHE) is one of the most remarkable condensed-matter phenomena discovered in the second half of the 20th century. It rivals superconductivity in its fundamental significance as a manifestation of quantum mechanics on macroscopic scales. The basic experimental observation is the nearly vanishing dissipation σ xx → 0 (1.1) and the quantization of the Hall conductance
$$\sigma _{xy} =
u \frac{{e^2 }}{h}$$
(1.2)
of a real (as opposed to some theorist’s fantasy) transistor-like device (similar in some cases to the transistors in computer chips) containing a two-dimensional electron gas subjected to a strong magnetic field. This quantization is universal and independent of all microscopic details such as the type of semiconductor material, the purity of the sample, the precise value of the magneticfield, and so forth. As a result, the effect is now used to mantain the standard of electrical resistance by metrology laboratories around the world. In addition, since the speed of light is now defined, a measurement of e 2/h equivalent to a measurement of the fine structure constant of fundamental importance in quantum electrodynamics.
191 citations
TL;DR: In this paper, an acute sensitivity of the anisotropic longitudinal resistivity of two-dimensional electron systems in half-filled high Landau levels to the magnitude and orientation of an in-plane magnetic field was observed.
Abstract: We report the observation of an acute sensitivity of the anisotropic longitudinal resistivity of two-dimensional electron systems in half-filled high Landau levels to the magnitude and orientation of an in-plane magnetic field. In the third and higher Landau levels, at filling fractions ν = 9/2, 11/2, etc., the in-plane field can lead to a striking interchange of the “hard” and “easy” transport directions. In the second Landau level the normally isotropic resistivity and the weak ν = 5/2 quantized Hall state are destroyed by a large in-plane field and the transport becomes highly anisotropic.
165 citations
TL;DR: In this paper, the influence of screw dislocation on the energy spectrum of an electron in the magnetic field was studied in a continuum theory of defects that is isomorphic to three-dimensional gravity.
Abstract: We study electrons moving in a magnetic field in the presence of a screw dislocation. We focus on the influence of the screw dislocation on the energy spectrum of the electron (or hole) in the magnetic field, in a continuum theory of defects that is isomorphic to three-dimensional gravity. We find exact expressions for the eigenfunctions and eigenvalues of the energy and verify that the infinite degeneracy of the Landau levels is broken by the unusual boundary conditions imposed by the defect.
147 citations
TL;DR: In this article, microscopic images of the local electron compressibility, electrostatic potential, and current-induced Hall voltage of a two-dimensional sheet of electrons in the quantum Hall regime are acquired using a single-electron transistor as a scanned probe.
135 citations
TL;DR: In this article, it was shown that charge can be measured independently of conductance in the fractional quantum Hall regime, generalizing previous observations of fractionally charged quasiparticles.
Abstract: 1-3 of this behaviour invokes strong Coulomb interactions among the electrons that give rise to fractionally charged quasiparticles which can be regarded as non- interacting current carriers 1-5 . Previous studies 4,5 have demon- strated the existence of quasiparticles with one-third of an electron's charge, the same fraction as that of the respective fractional state. An outstanding ambiguity is therefore whether these studies measured the charge or the conductance. Here we report the observation of quasiparticles with a charge of e/5 in the 2/5 fractional state, from measurements of shot noise in a two- dimensional electron gas 4 . Our results imply that charge can be measured independently of conductance in the fractional quantum Hall regime, generalizing previous observations of fractionally charged quasiparticles. In the fractional quantum Hall (FQH) regime, the first Landau level is partly populated, or 'fractionally filled'. Laughlin's explana- tion of the FQH effect 1-3 involved the emergence of new, fractionally charged, quasiparticles. Shot-noise measurements 4,5 have confirmed
133 citations
TL;DR: The phase structures of Nambu-Jona-Lasinio models with one or two flavors have been investigated at non-zero values of µ and H, where H is an external magnetic field and µ is the chemical potential.
Abstract: The phase structures of Nambu–Jona-Lasinio models with one or two flavours have been investigated at non-zero values of µ and H, where H is an external magnetic field and µ is the chemical potential. In the phase portraits of both models there arise infinitely many massless chirally symmetric phases, as well as massive ones with spontaneously broken chiral invariance, reflecting the existence of infinitely many Landau levels. Phase transitions of first and second orders and a lot of tricritical points have been shown to exist in phase diagrams. In the massless case, such a phase structure leads unavoidably to the standard van Alphen–de Haas magnetic oscillations of some thermodynamical quantities, including magnetization, pressure and particle density. In the massive case we have found an oscillating behaviour not only for thermodynamical quantities, but also for a dynamical quantity as the quark mass. Besides, in this case we have non-standard, i.e. non-periodic, magnetic oscillations, since the frequency of oscillations is an H-dependent quantity.
TL;DR: In this article, an energy analyzer that accounts for rf fluctuations in plasma potential was constructed, and it was shown that Landau-accelerated electrons are too sparse to explain the ionization efficiency.
Abstract: The uncommonly high rf absorption efficiency of helicon discharges has been thought to be caused by Landau damping of helicon waves and the concomitant acceleration of primary electrons. By constructing an energy analyzer that accounts for rf fluctuations in plasma potential, it is shown that Landau-accelerated electrons are too sparse to explain the ionization efficiency. Instead, rf absorption and ionization are found to be consistent with the mechanism of mode coupling to Trivelpiece-Gould modes at the plasma boundary.
TL;DR: In this paper, it was shown that phonons dominate the transresistance at very low temperatures and that plasmon excitations are important at temperatures T> 0 : 1 T F, with TF the Fermi temperature.
Abstract: The advances in the techniques used for fabrication and lithography of semiconductors have made it possible to study bi-layer systems made of two electronic layers separated by distances of several hundred angstrIn this situation the electrons in layer 1 are distinguishable from those in layer 2, and can communicate through the direct inter-layer Coulomb interaction. In particular, if a current is applied to one of the layers, the electrons in the second will be dragged, giving rise to a transresistance D. In this article we review recent theoretical and experimental developments in the understanding of this effect. At very low temperatures it turns out that phonons dominate the transresistance. The direct Coulomb interaction and plasmon excitations are important at temperatures T> 0 : 1 T F, with TF the Fermi temperature. If a magnetic field is applied, the transresistance is increased, in a very interesting interplay between D and Landau quantization. The non-dissipative drag is also reviewed.
TL;DR: In this article, the first-order phase transitions in n = 2 and 4 quantum Hall states confined to a wide gallium arsenide quantum well were studied and the observed hysteretic behaviour and anomalous temperature dependence in the longitudinal resistivity indicate the occurrence of a transition between the two distinct ground states of an Ising quantum-Hall ferromagnet.
Abstract: The single-particle energy spectrum of a two-dimensional electron gas in a perpendicular magnetic field consists of equally-spaced spin-split Landau levels, whose degeneracy is proportional to the magnetic field strength. At integer and particular fractional ratios between the number of electrons and the degeneracy of a Landau level (filling factors n) quantum Hall effects occur, characterised by a vanishingly small longitudinal resistance and quantised Hall voltage. The quantum Hall regime offers unique possibilities for the study of cooperative phenomena in many-particle systems under well-controlled conditions. Among the fields that benefit from quantum-Hall studies is magnetism, which remains poorly understood in conventional material. Both isotropic and anisotropic ferromagnetic ground states have been predicted and few of them have been experimentally studied in quantum Hall samples with different geometries and filling factors. Here we present evidence of first-order phase transitions in n = 2 and 4 quantum Hall states confined to a wide gallium arsenide quantum well. The observed hysteretic behaviour and anomalous temperature dependence in the longitudinal resistivity indicate the occurrence of a transition between the two distinct ground states of an Ising quantum-Hall ferromagnet. Detailed many-body calculations allowed the identification of the microscopic origin of the anisotropy field.
TL;DR: In this paper, the authors studied the quantum mechanics of a scalar particle in the background of a magnetic cosmic string and a chiral cosmic string, and showed that the wave functions, the phase shifts, and scattering amplitudes associated with the particle depend on the global features of those spacetimes.
Abstract: Using Kaluza-Klein theory we study the quantum mechanics of a scalar particle in the background of a magnetic cosmic string and in the background of a chiral cosmic string. We show that the wave functions, the phase shifts, and scattering amplitudes associated with the particle depend on the global features of those spacetimes. These dependences represent gravitational analogues of the well-known Aharonov-Bohm effect. In addition, we discuss the Landau levels in the presence of a cosmic string in the framework of Kaluza-Klein theory.
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TL;DR: In this article, the authors studied the quantum mechanical motion of a charged particle moving in a half plane subject to a uniform constant magnetic field B directed along the z-axis and to an arbitrary impurity potential W_B, assumed to be weak in the sense that ||W_B||_\infty < \delta B, for some δ small enough.
Abstract: We study the quantum mechanical motion of a charged particle moving in a half plane (x>0) subject to a uniform constant magnetic field B directed along the z-axis and to an arbitrary impurity potential W_B, assumed to be weak in the sense that ||W_B||_\infty < \delta B, for some \delta small enough. We show rigorously a phenomenon pointed out by Halperin in his work on the quantum Hall effect, namely the existence of current carrying and extended edge states in such a situation. More precisely, we show that there exist states propagating with a speed of size B^{1/2} in the y-direction, no matter how fast W_B fluctuates. As a result of this, we obtain that the spectrum of the Hamiltonian is purely absolutely continuous in a spectral interval of size \gamma B (for some \gamma <1) between the Landau levels of the unperturbed system (i.e. the system without edge or potential), so that the corresponding eigenstates are extended.
TL;DR: The intriguing reentrant integer quantized Hall states recently discovered in high Landau levels of high-mobility 2D electron systems are found to exhibit extremely nonlinear transport as mentioned in this paper.
Abstract: The intriguing re-entrant integer quantized Hall states recently discovered in high Landau levels of high-mobility 2D electron systems are found to exhibit extremely nonlinear transport. At small currents these states reflect insulating behavior of the electrons in the uppermost Landau level. At larger currents, however, a discontinuous and hysteretic transition to a conducting state is observed. These phenomena, found only in very narrow magnetic field ranges, are suggestive of the depinning of a charge density wave state, but other explanations can also be constructed.
TL;DR: In this article, numerical studies of two-dimensional electron systems in the presence of a perpendicular magnetic field, with a high Landau level index (N > 1) half filled by electrons, are presented.
Abstract: We report on numerical studies of two-dimensional electron systems in the presence of a perpendicular magnetic field, with a high Landau level index (N > 1) half filled by electrons. Strong and sharp peaks are found in the wave vector dependence of both static density susceptibility and equal-time density-density correlation function, in finite-size systems with up to twelve electrons. Qualitatively different from partially filled lowest (N=0) Landau level, these results are suggestive of a tendency toward charge density wave ordering in these systems. The ordering wave vector is found to decrease with increasing N.
TL;DR: In this article, the Mourre theory of positive commutators is applied to prove absolute continuity of the energy spectrum well in between Landau levels, corresponding to edge states, for a two-dimensional electron gas confined to a halfplane.
Abstract: Properties of eigenstates of one-particle Quantum Hall Hamiltonians localized near the boundary of a two-dimensional electron gas - so-called edge states - are studied. For finite samples it is shown that edge states with energy in an appropriate range between Landau levels remain extended along the boundary in the presence of a small amount of disorder, in the sense that they carry a non-zero chiral edge current. For a two-dimensional electron gas confined to a half-plane, the Mourre theory of positive commutators is applied to prove absolute continuity of the energy spectrum well in between Landau levels, corresponding to edge states.
TL;DR: In this article, the authors examined the magnetic catalysis of chiral symmetry breaking due to interactions of massless fermions in their lowest Landau level in the context of chirally symmetric models with short ranged interactions.
Abstract: The hypothesis that the magnetic catalysis of chiral symmetry breaking is due to interactions of massless fermions in their lowest Landau level is examined in the context of chirally symmetric models with short ranged interactions. It is argued that, when the magnetic field is sufficiently large, even an infinitesimal attractive interaction in the appropriate channel will break chiral symmetry. {copyright} {ital 1999} {ital The American Physical Society}
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TL;DR: In this article, the results of theoretical analysis of the oscillation spectrum of a plasma placed in a very strong quantizing magnetic field are presented, and it is shown that in ultraquantum limit, when all particles occupy the first Landau level, in an inhomogeneous quantized two-component plasma, volume quantum drift waves arise.
Abstract: The results of theoretical analysis of the oscillation spectrum of a plasma placed in a very strong quantizing magnetic field are presented. It is shown that in ultra-quantum limit, when all particles occupy the first Landau level, in an inhomogeneous quantized two-component plasma, volume quantum drift waves arise. These waves become unstable under some circumstances.
TL;DR: In this article, the authors construct effective field theories for fractional quantum Hall states, such as the Pfaffian state, which exhibit non-abelian statistics, which rely on a Meissner construction which increases the level of a nonabelian Chem-Simons theory while simultaneously projecting out the unwanted degrees of freedom of a concomitant enveloping abelian theory.
TL;DR: In this paper, the basal-plane resistivity ρa(T,H) was measured on pyrolitic graphite, with magnetic field H∥c-axis in the temperature interval 2-300K and fields up to 8 T, providing evidence for both field-induced and zero-field superconducting instabilities.
Abstract: Measurements of the basal-plane resistivity ρa(T,H) performed on highly oriented pyrolitic graphite, with magnetic field H∥c-axis in the temperature interval 2–300K and fields up to 8 T, provide evidence for the occurrence of both field-induced and zero-field superconducting instabilities. Additionally, magnetization M(T,H) measurements suggest the occurrence of Fermi surface instabilities which compete with the superconducting correlations.
TL;DR: In this paper, the Hartree-Fock calculations of the UCDW orientation energy induced by a tilted magnetic field were performed on two-dimensional (2D) electron systems with valence Landau level index (LLEI).
Abstract: Recently reported giant anisotropy in the longitudinal resistivity of a two-dimensional (2D) electron system with valence Landau level index $Ng~2$ has been interpreted as a signal of unidirectional charge density wave (UCDW) ground states. We report on detailed Hartree-Fock calculations of the UCDW orientation energy induced by a tilted magnetic field. We find that for current experimental samples, stripes are oriented perpendicular to the in-plane field, consistent with experiment. For wider 2D electron systems, we predict tilt-induced stripe states with variable anisotropy energy sign.
TL;DR: In this article, the anisotropy of the underlying sheet resistivities is correctly represented by Hall bar resistance measurements but shows up exponentially enhanced in resistance measurements on square samples due to simple geometric effects.
Abstract: In a recent letter M. Lilly et al [PRL 82, 394 (1999)] have shown that a highly anisotropic state can arise in certain two dimensional electron systems. In the large square samples studied, resistances measured in the two perpendicular directions are found to have a ratio that may be 60 or larger at low temperature and at certain magnetic fields. In Hall bar measurements, the anisotropy ratio is found to be much smaller (roughly 5). In this comment we resolve this discrepancy by noting that the anisotropy of the underlying sheet resistivities is correctly represented by Hall bar resistance measurements but shows up exponentially enhanced in resistance measurements on square samples due to simple geometric effects. We note, however, that the origin of this underlying resistivity anisotropy remains unknown, and is not addressed here.
TL;DR: In this article, a random Schrodinger operator in an external magnetic field is considered, where the random potential consists of delta functions of random strengths situated on the sites of a regular two-dimensional lattice.
Abstract: We consider a random Schrodinger operator in an external magnetic field. The random potential consists of delta functions of random strengths situated on the sites of a regular two-dimensional lattice. We characterize the spectrum in the lowest N Landau bands of this random Hamiltonian when the magnetic field is sufficiently strong, depending on N. We show that the spectrum in these bands is entirely pure point, that the energies coinciding with the Landau levels are infinitely degenerate and that the eigenfunctions corresponding to energies in the remainder of the spectrum are localized with a uniformly bounded localization length. By relating the Hamiltonian to a lattice operator we are able to use the Aizenman–Molchanov method to prove localization.
TL;DR: In this paper, it was shown that the total Hamiltonian has a continuous spectrum in some intervals in between the Landau levels provided that both the amplitude and spatial variation of the impurity potential are sufficiently weak.
Abstract: We consider an electron in two dimensions submitted to a magnetic field and to the potential of impurities. We show that when the electron is confined to a half-space by a planar wall described by a smooth increasing potential, the total Hamiltonian necessarily has a continuous spectrum in some intervals in between the Landau levels provided that both the amplitude and spatial variation of the impurity potential are sufficiently weak. The spatial decay of the impurity potential is not needed. In particular, this proves the occurrence of edge states in semi-infinite quantum Hall systems.
TL;DR: The conduction band parameters of two-dimensional (2D) electrons in high density GaN/AlGaN heterojunctions were studied using the cyclotron resonance and magnetotransport techniques in high magnetic fields (24 T) and low temperatures (300 mK) as discussed by the authors.
Abstract: The conduction band parameters of two-dimensional (2D) electrons in high density GaN/AlGaN heterojunctions were studied using the cyclotron resonance and magnetotransport techniques in high magnetic fields (24 T) and low temperatures (300 mK) The Landau level splitting determined from the cyclotron resonance experiment yielded the effective mass of 2D carriers, m*=0242±0002 m0 The Lande g factor for the 2D electrons (g=206±004) was determined from the angular dependence of the amplitude of Shubnikov–de-Haas oscillations experiments in tilted magnetic field
TL;DR: In this paper, the relation between the conventional Fermion-Chern-Simons (FCS) theory of the half-filled Landau level and alternate descriptions that are based on the notion of neutral quasiparticles that carry electric-dipole moments was investigated.
Abstract: In this paper we study the relation between the conventional Fermion-Chern-Simons (FCS) theory of the half-filled Landau level $(\ensuremath{
u}=1/2),$ and alternate descriptions that are based on the notion of neutral quasiparticles that carry electric-dipole moments. We have previously argued that these two approaches are equivalent, and that, e.g., the finite compressibility obtained in the FCS approach is also obtained from the alternate approach, provided that one properly takes into account a peculiar symmetry of the dipolar quasiparticles---the invariance of their energy to a shift of their center of mass momentum. Here, we demonstrate the equivalence of these two approaches in detail. We first study a model where the charge and flux of each fermion is smeared over a radius ${Q}^{\ensuremath{-}1}$ where results can be calculated to leading order in the small parameter ${Q/k}_{\mathrm{F}}.$ We study two dipolar-quasiparticle descriptions of the $\ensuremath{
u}=1/2$ state in the small-$Q$ model and confirm that they yield the same density-response function as in the FCS approach. We also study the single-particle Green's function and the effective mass, for one form of dipolar quasiparticles, and find the effective mass to be infrared divergent, exactly as in the FCS approach. Finally, we propose a form for a Fermi-liquid theory for the dipolar quasiparticles, which should be valid in the physical case where Q is infinite.