Showing papers on "Landau quantization published in 1996"
TL;DR: In this article, the ground state of a clean two-dimensional electron liquid in a weak magnetic field where lower Landau levels are completely filled and the upper level is partially filled was studied.
Abstract: We study the ground state of a clean two-dimensional electron liquid in a weak magnetic field where $N\ensuremath{\gg}1$ lower Landau levels are completely filled and the upper level is partially filled. It is shown that the electrons at the upper Landau level form domains with filling factors equal to 1 and zero. The domains alternate with a spatial period of order of the cyclotron radius, which is much larger than the interparticle distance at the upper Landau level. The one-particle density of states, which can be probed by tunneling experiments, is shown to have a gap linearly dependent on the magnetic field in the limit of large $N$.
337 citations
TL;DR: It is shown that when the filling factor of the upper Landau level is close to one-half, the domains have the form of parallel stripes alternating with a spatial period close to three cyclotron radii, and the density of states has a pseudogap linearly dependent on the magnetic field in the limit of large N.
Abstract: We consider a clean two-dimensional electron liquid in a weak magnetic field where N\ensuremath{\gg}1 lower Landau levels are completely filled, while the upper level is only partially filled. Due to a screening by the lower Landau levels, the repulsive interaction between any two electrons at the upper level as a function of the separation between the guiding centers of their cyclotron orbits abruptly drops at the distance of two cyclotron radii. Such a ``box-like'' component in the interaction potential makes the uniform distribution of the electron density at the upper Landau level unstable, and domains with filling factor equal to one and zero are formed. The shape of domains is studied both analytically and numerically. We show that when the filling factor of the upper Landau level is close to one-half, the domains have the form of parallel stripes alternating with a spatial period close to three cyclotron radii. Away from a small interval around half-filling, a ``bubble'' phase is more favorable. We investigate the implications of the proposed ground state for the one-particle density of states, which can be probed by tunneling experiments. For the stripe phase, the density of states is shown to have a pseudogap linearly dependent on the magnetic field in the limit of large N. \textcopyright{} 1996 The American Physical Society.
255 citations
TL;DR: The accuracy of the Hartree-Fock approximation for potentials with a nonzero range such as the Coulomb interaction is discussed, and the unidirectional charge-density wave at zero temperature is discussed and it is argued that quantum fluctuations are unimportant in the large-{ital n} limit.
Abstract: We study a two-dimensional electron system in a magnetic field with a fermion hard-core interaction and without disorder. Projecting the Hamiltonian onto the {ital n}th Landau level, we show that the Hartree-Fock theory is exact in the limit {ital n}{r_arrow}{infinity}, for the high-temperature, uniform density phase of an infinite system; for a finite-size system, it is exact at all temperatures. In addition, we show that a charge-density wave arises below a transition temperature {ital T}{sub {ital t}}. Using Landau theory, we construct a phase diagram which contains both unidirectional and triangular charge-density wave phases. We discuss the unidirectional charge-density wave at zero temperature and argue that quantum fluctuations are unimportant in the large-{ital n} limit. Finally, we discuss the accuracy of the Hartree-Fock approximation for potentials with a nonzero range such as the Coulomb interaction. {copyright} {ital 1996 The American Physical Society.}
255 citations
TL;DR: The rapid decay of spin alignment over small changes to both higher and lower magnetic field provides experimental evidence for the presence of Skyrmion excitations where exchange energy dominates Zeeman energy in the quantum Hall regime at 0ex-0ex=1.
Abstract: A dramatic reduction in the spin polarization of a two-dimensional electron gas in a magnetic field is observed when the Fermi energy moves off the midpoint of the spin gap of the lowest Landau level, $\ensuremath{
u}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$. The spin polarization is measured by magnetoabsorption spectroscopy which distinguishes the occupancy of the two electron spin states. The rapid decay of spin alignment over small changes to both higher and lower magnetic field provides experimental evidence for the presence of Skyrmion excitations where exchange energy dominates Zeeman energy in the quantum Hall regime at $\ensuremath{
u}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$.
144 citations
TL;DR: In this paper, a numerical model of the Landau levels in a quasi-two-dimensional metal was used to simulate the de Haas-van Alphen oscillations observed in high magnetic field measurements.
Abstract: Departures from standard Lifshitz-Kosevich behavior observed in the oscillatory magnetization and magnetoresistance of bis(ethylenedithio)tetrathiafulvalene (BEDT-TTF) charge-transfer salts in high magnetic fields are investigated using a numerical model of the Landau levels in a quasi-two-dimensional metal. The numerical model enables oscillations in the chemical potential to be treated, as well as the effects of finite temperature, Landau level broadening, and the presence of additional quasi-one-dimensional Fermi surface sheets. The numerical calculations reproduce experimental magnetization data successfully, and allow several phenomena observed in the experiments to be investigated. It is found that pinning of the chemical potential to the Landau levels is responsible for the apparent anomalously low effective masses of the higher harmonics of the de Haas--van Alphen oscillations observed in recent experiments. In addition, the quasi-one-dimensional components of the Fermi surface are found to have a pronounced influence on the wave form of the oscillations in the model, providing a means by which their density of states can be estimated from experimental results. Whilst the magnetization is a thermodynamic function of state, calculations of the behavior of the magnetoresistance are much more model dependent. In this paper, recent theoretical models for the longitudinal magnetoresistance in semiconductor superlattices have been modified for use with the BEDT-TTF salts and are shown to successfully reproduce the form of the experimental data. The strongly peaked structure of the magnetoresistance, which comes about when the chemical potential is situated in or close to the gap between adjacent Landau levels, is found to be responsible for the apparent strong increase of the effective mass which has recently been reported in high field transport measurements. \textcopyright{} 1996 The American Physical Society.
83 citations
TL;DR: It is found that, for such a weakly coupled ring in a uniform magnetic field, not only do the electron states in different subbands of the ring produce different AB frequencies, the clockwise and anticlockwise moving states in the same subband also lead to two differentAB frequencies.
Abstract: We propose an exactly soluble model for a ring with finite width. Exact energy spectra and wave functions are obtained analytically for a ring in the presence of both a uniform perpendicular magnetic field and a thin magnetic flux through the ring center. We use the model to study the Aharonov-Bohm (AB) effect in an ideal annular ring that is weakly coupled to both the emitter and the collector. It is found that, for such a weakly coupled ring in a uniform magnetic field, not only do the electron states in different subbands of the ring produce different AB frequencies, the clockwise and anticlockwise moving states in the same subband also lead to two different AB frequencies. Therefore, when many subbands in the ring are populated, the large number of different AB frequencies generally result in an aperiodic AB oscillation. More striking is that, even when only one subband is populated, the two AB frequencies corresponding to the states moving in opposite directions also cause beating in the AB oscillations. We have obtained explicit expressions for all these AB frequencies. Our results produce a clear explanation for the recent experimental observation of Liu and co-workers. \textcopyright{} 1996 The American Physical Society.
83 citations
TL;DR: Low temperature heat capacity (C) data on a multiple-quantum-well GaAs/AlGaAs sample in the quantum Hall regime are reported, attributing the large C to a Skyrmion-induced, strong coupling of the nuclear spin system to the lattice.
Abstract: We report low temperature (T) heat capacity (C) data on a multiple-quantum-well GaAs/AlGaAs sample in the quantum Hall regime. Relative to its low field magnitude, C exhibits up to similar to 10(5)-fold enhancement near v = 1 where Skyrmions are the ground state of the confined two-dimensional electrons. We attribute the large C to a Skyrmion-induced, strong coupling of the nuclear spin system to the lattice. The data are consistent with the Schottky nuclear heat capacity of Ga and As atoms in the quantum wells, except at very low T where C vs T exhibits a remarkably sharp peak, suggestive of a phase transition in the electronic system.
77 citations
TL;DR: The tunneling between two parallel two-dimensional electron gases (2DEGs) has been investigated as a function of temperature T, carrier density n, and the applied perpendicular magnetic field B, and various theoretical predictions have been examined.
Abstract: The tunneling between two parallel two-dimensional electron gases (2DEGs) has been investigated as a function of temperature T, carrier density n, and the applied perpendicular magnetic field B. In zero magnetic field the equilibrium resonant line shape is Lorentzian, reflecting the Lorentzian form of the spectral functions within each layer. From the width of the tunneling resonance the lifetime of the electrons within a 2DEG has been measured as a function of n and T, giving information about the density dependence of the electron-impurity scattering and the temperature dependence of the electron-electron scattering. In a magnetic field there is a general suppression of equilibrium tunneling for fields above B=0.6 T. A gap in the tunneling density of states has been measured over a wide range of magnetic fields and filling factors, and various theoretical predictions have been examined. In a strong magnetic field, when there is only one partially filled Landau level in each layer, the temperature dependence of the conductance characteristics has been modeled with a double-Gaussian spectral density. \textcopyright{} 1996 The American Physical Society.
59 citations
TL;DR: In this article, a microscopic theory of the Skyrmion states which occur in the quantum Hall regime was proposed based on the identification of skyrmions states in this system with zero-energy eigenstates of a hard core model Hamiltonian.
Abstract: We report on a microscopic theory of the Skyrmion states which occur in the quantum Hall regime. The theory is based on the identification of Skyrmion states in this system with zero-energy eigenstates of a hard-core model Hamiltonian. We find that for $N_{\phi}$ orbital states in a Landau level, a set of Skyrmions states with orbital degeneracy $N_{\phi}-K$ and spin quantum number $S = N/2 -K$ exists for each nonnegative integer $K$. The energetic ordering of states with different $K$ depends on the interaction potential.
58 citations
TL;DR: A qualitatively different character of dHvA oscillations has been found in a multiband (quasi)two dimensional Fermi liquid with a fixed fermion density compared with an open system where the chemical potential $\mu$ is kept fixed (grand canonical ensemble).
Abstract: A qualitatively different character of dHvA oscillations has been found in a multiband (quasi)two dimensional Fermi liquid with a fixed fermion density $n_{e}$ (canonical ensemble) compared with an open system where the chemical potential $\mu$ is kept fixed (grand canonical ensemble). A new fundamental period $P_{f}$ appears when $n_{e}$ is fixed, a damping of the Landau levels is relatively small and a background density of states is negligible. $P_{f}$ is determined by the total density rather than by the partial densities of carriers in different bands: $P_{f}=1/(2n_{e}\phi)$ for spin-split Landau levels and $P_{f}=1/(n_{e}\phi)$ in the case of spin degenerate levels where $\phi$ is the flux quantum.
58 citations
TL;DR: Electron transport in crystals in intense parallel electric and magnetic fields is investigated and Stark-cyclotron resonance (SCR) condition is investigated, showing how elastic tunneling transport between Landau levels belonging to neighboring crystal sites becomes possible.
Abstract: Electron transport in crystals in intense parallel electric and magnetic fields is investigated. Current resonances are shown for particular ratios of electric and magnetic fields satisfying the Stark-cyclotron resonance (SCR) condition. At SCR, the potential drop per period is an integer multiple of the magnetic quantization energy and elastic tunneling transport between Landau levels belonging to neighboring crystal sites becomes possible. Unambiguous demonstration of SCR in an appropriately tailored heterojunction superlattice is given for transitions involving up to four Landau-level index changes.
TL;DR: Landau-level lifetimes are determined from saturation cyclotron resonance measurements on an InAs/GaSb double heterojunction using a picosecond far-infrared free-electron laser, and show minima at NHBar omega(c) = HBAR omega(LO), a direct observation of the magnetophonon effect.
Abstract: Landau-level lifetimes are determined from saturation cyclotron resonance measurements on an InAs/GaSb double heterojunction using a picosecond far-infrared free-electron laser. Strong nonparabolicity of the conduction band truncates the equidistant Landau-level ladder, and saturation is achieved at all wavelengths. The Landau-level lifetimes show minima at NHBAR omega(c) = HBAR omega(LO), a direct observation of the magnetophonon effect. Observed picosecond lifetimes are due to LO-phonon emission which dominates electron-electron scattering at the magnetophonon resonance condition.
TL;DR: In this paper, a torque magnetometer was used to measure de Haas van Alphen oscillations in the magnetization of two-dimensional electrons in GaAs/AlGaAs heterostructures and multiple-quantum-well systems for temperatures ranging from 0.125 K to 4.2 K and in magnetic fields of up to 15 T.
Abstract: We have used a torque magnetometer to measure de Haas - van Alphen oscillations in the magnetization of two-dimensional electrons in GaAs/AlGaAs heterostructures and multiple-quantum-well systems for temperatures ranging from 0.125 K to 4.2 K and in magnetic fields of up to 15 T. Our results indicate that for high magnetic fields the density of states can be described by a series of Lorentzian-broadened Landau levels with a broadening that is independent of the magnetic field, B, and Landau level index, n. However, at low magnetic fields the Lorentzian-broadened density of states becomes indistinguishable from a Gaussian one with a broadening that is proportional to . The high-field behaviour of the Landau level line-shape is shown to differ appreciably from the low-field case as reported by other workers using both magnetization and other experimental methods. The reliability of this and other experimental techniques is discussed.
TL;DR: The localization properties in the transition from a two-dimensional electron gas at zero magnetic field into an integer quantum Hall (QH) liquid are studied and it is found that the extended state energy for each Landau level (LL) is linear in magnetic field.
Abstract: We investigate the transition of a two-dimensional electron gas from the regime of the quantum Hall effect to the regime of weak magnetic fields for a tight-binding model. Unlike previous work, we find the following: (1) the linear field dependence of the extended-state energies is not affected by disorder, although the total density of states below each level of extended states increases with disorder strength; (2) for each Landau band and disorder strength there exists a critical field ${B}_{c}$ below which the extended level disappears, with ${B}_{c}$ smaller for lower Landau bands. We show how the experimental findings of level flotation and direct transition from high Landau level states to the Anderson insulating phase may be explained in light of our results.
TL;DR: In this article, the scaling properties of the specific heat of the high T c superconductor YBa 2 Cu 3 O 6.93 (YBCO) are studied using a large crystal (0.29 g) at optimal doping.
Abstract: The scaling properties of the specific heat of the high- T c superconductor YBa 2 Cu 3 O 6.93 (YBCO) are studied. We used a large crystal (0.29 g) at optimal doping. The measurements are performed with a high-resolution (∼10 −4 ) quasi-adiabatic continuous heating type calorimeter in magnetic fields up to 16 T. Rather than scaling the electronic specific heat, we scale the derivatives versus field and versus temperature of the total specific heat. This new approach is less sensitive to arbitrary background subtraction and/or normalization. It is found unexpectedly that the low-field 3D- XY model is valid at high fields for H > 1 T, and that the lowest Landau level (3D-LLL) approximation is a poor description if H c2 ( T ) is taken to be linear in T . But if we take into account the experimentally observed curvature of H c 2 (T) ∝ |T − T c | 4 3 , then 3D-LLL scaling is also satisfied for H > 1 T. With this modification, both descriptions are valid in the same range of fields. Measurements of the magnetization confirm this result. The shape of the scaling function agrees with that predicted in the modified 3D-LLL approximation.
18 Dec 1996
TL;DR: In this paper, the authors derived analytic formulae for the stability limit when the detunings are linear combinations of the two betatron action variables, which represents the lowest contribution of magnetic octupoles to the detuning with amplitude and is of special interest for the stabilization of transverse oscillation modes at collision energy.
Abstract: We discuss Landau damping of the rigid dipole oscillations for a beam with amplitude-dependent betatron tunes. In particular, we derive analytic formulae for the stability limit when the detunings are linear combinations of the two betatron action variables. Such linear dependence represents the lowest contribution of magnetic octupoles to the detuning with amplitude and is of special interest for the stabilization of transverse oscillation modes at collision energy in the LHC. When the detuning coefficients have opposite signs, we find that the case of two-dimensional betatron spread is qualitatively different from the one-dimensional case: for a Gaussian distribution in the two transverse planes, the beam transfer function has tails both in the positive and negative tune directions and collective rigid dipole oscillations can be Landau damped for any real coherent tune shift caused by the impedance. The stability limit exhibits complicated pathologies for a truncated Gaussian distribution and, to obtain quantitative results concerning the loss of Landau damping for a given real coherent tune shift, we discuss the case of a “quasi-parabolic” distribution in the two transverse planes.
TL;DR: In this paper, effective masses derived from the low-field Shubnikov-de Haas oscillations in high mobility GaAs/AlGaAs samples are found to decrease systematically with density.
TL;DR: Calculations of hole Landau levels, cyclotron masses, and far-infrared spectra for strained asymmetric p-type Ge quantum wells in a perpendicular magnetic field are presented to interpret recent experimental results by Engelhardt et al.
Abstract: We present calculations of hole Landau levels, cyclotron masses, and far-infrared spectra for strained asymmetric p-type Ge-${\mathrm{Si}}_{\mathit{x}}$${\mathrm{Ge}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$ quantum wells in a perpendicular magnetic field in order to interpret recent experimental results by Engelhardt et al. [Solid State Electron. 37, 949 (1994)]. Self-consistent hole subband calculations are combined with calculations of the Landau levels using a 6\ifmmode\times\else\texttimes\fi{}6 k\ensuremath{\cdot}p Hamiltonian for the topmost ${\mathrm{\ensuremath{\Gamma}}}_{8}$ and ${\mathrm{\ensuremath{\Gamma}}}_{7}$ bulk valence bands. Our results are in very good agreement with the experimental data. Taking into account the coupling to the split-off band turns out to be important. The complex spectra of hole Landau levels in strained quantum wells remind one of the well known quantum resonance spectra of bulk p-type Ge under uniaxial stress. \textcopyright{} 1996 The American Physical Society.
TL;DR: The Kubo formalism is used to calculate the transresistivity of $\rho_{21}$ for carriers in coupled quantum wells in a large perpendicular magnetic field and finds that it is enhanced by approximately 50--100 times over that of the B=0 case in the interplateau regions of the integer quantum Hall effect.
Abstract: We use the Kubo formalism to calculate the transresistivity $\rho_{21}$ for carriers in coupled quantum wells in a large perpendicular magnetic field $B$. We find that $\rho_{21}$ is enhanced by approximately 50--100 times over that of the B=0 case in the interplateau regions of the integer quantum Hall effect. The presence of both electron--electron interactions and Landau quantization results in (i) a twin-peaked structure of $\rho_{21}(B)$ in the inter-plateau regions at low temperatures, and, (ii) for the chemical potential at the center of a Landau level band, a peaked temperature dependence of $\rho_{21}(T)/T^2$.
TL;DR: In this paper, the Schrodinger equation of magnetoexcitons is solved numerically to describe their magnetic-field behavior and to deduce the relevant excitonic and band parameters in dependence on the Cd content in the well.
Abstract: Magnetoabsorption on high-quality ${\mathrm{Zn}}_{\mathit{x}}$${\mathrm{Cd}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$Se/ZnSe multiple quantum wells grown by molecular-beam epitaxy is used to study systematically the major excitonic properties. The small inhomogeneous width of the exciton lines allows us to observe Landau levels arising from higher heavy-hole exciton transitions as well as to analyze in detail the spin splitting and diamagnetic shift of the ground state. The Schr\"odinger equation of magnetoexcitons is solved numerically to describe their magnetic-field behavior and to deduce the relevant excitonic and band parameters in dependence on the Cd content in the well. Anticrossing features at higher Landau levels and the magnetic-field dependence of the light-hole exciton ground-state energy signify a complex valence-band structure due to heavy-light hole coupling. \textcopyright{} 1996 The American Physical Society.
TL;DR: In this paper, measurements in a perpendicular magnetic field of the frictional drag between two closely spaced, but electrically isolated, two-dimensional electron gases have been performed, showing that when the Fermi energy lies at the centre of a Landau level, the drag can be enhanced by two orders of magnitude over the zero field signal.
Abstract: We present measurements in a perpendicular magnetic field of the frictional drag between two closely spaced, but electrically isolated, two-dimensional electron gases. At high temperatures, when the Landau level structure is smeared out, the transresistivity shows a magnetic field dependence and an approximately linear temperature dependence. As the temperature is lowered below 20 K, the transresistivity shows structure reflecting the formation of Landau levels and, in general, the drag is more sensitive to the spin splitting of the Landau levels than the Shubnikov - de Haas oscillations. When the Fermi energy lies at the centre of a Landau level, the drag can be enhanced by two orders of magnitude over the zero field signal. In contrast, when lies between Landau levels in the quantum Hall regime, the drag signal tends to zero. We have also measured the transverse voltage in the drag layer and find no evidence for a Hall transresistance.
TL;DR: An analysis of spin-textures in Quantum Hall droplets, for filling factors ν ≃ 1.40, addressing the two previously mentioned restrictions of present theories.
Abstract: We present an analysis of spin-textures in Quantum Hall droplets, for filling factors ν ≃ 1. Analytical wavefunctions with well defined quantum numbers are given for the low-lying states of the system which result to be either bulk skyrmions or edge spin excitations. We compute dispersion relations and study how skyrmions become ground states of the Quantum Hall droplet at ν > 1. A Hartree-Fock approximation is recovered and discussed for those spin textures. PACS number: 73.40.Hm Spin excitations of a two-dimensional (2D) electron gas in the filling factor ν = 1 regime are the subject of increasing interest due to the experimental observation [1–3] of skyrmions. [4–9] They have been analyzed both by a classical nonlinear-σ model (CNLSM) [5,7] and by a Hartree-Fock (HF) approximation. [6,9] These descriptions ignore quantum fluctuations; furthermore quantum numbers as modulus (S 2 ) and third component (Sz) of the spin, and total (M) and center-of-mass (MCM) angular momenta are not well described. A superposition of mean-field wavefunctions has been proposed [10] which have well defined M and Sz but still neither MCM nor S 2 are represented adequately. Current descriptions of spintextures have always been considered in infinite [5–7,9] or periodic (sphere) [4,7,10] systems. Therefore, they can not be directly used to analyze available experimental information for small systems. [11–13] In this letter we address the two previously mentioned restrictions of present theories: 1) We analyze spin-textures in a system of N electrons moving in 2D, in the presence of both a high perpendicular magnetic field B and a confinement potential (Quantum Hall droplets (QHD)). 2) We obtain analytical many-body wavefunctions of spin excitations with all quantum numbers (M, MCM, S 2 and Sz) properly described, i.e. we present a microscopic description including quantum fluctuations. We also obtain the energies of these excitations, which turn out to be low-lying excitations at ν = 1, some of them becoming the ground state (GS) close to ν = 1. We consider interacting electrons moving in the xy plane, confined by a parabolic potential (characterised by a bare frequency ω0). We assume that B is high enough as to project the Hamiltonian H onto the lowest Landau level with both spin up and down. In symmetric gauge, Vm1m2m3m4 2 c
TL;DR: In this article, a qualitative picture of the metamagnetic transition in the Anderson lattice model of heavy fermion Ce compounds is described and a strong coupling spin fluctuation theory of the high field state is presented.
Abstract: A qualitative picture of the metamagnetic transition in the Anderson lattice model of heavy fermion Ce compounds is described and a strong coupling spin fluctuation theory of the high field state is presented. The field dependence of the minority spin quasiparticle mass is calculated and the onset of the metamagnetic transition with decreasing field is discussed. The theory of the high field state is extended to include Landau levels and the oscillatory behaviour of the spin self-energy as a function of the inverse applied field is investigated. For the heavy fermion model considered such oscillations of the self-energy lead to significant modifications in the standard theory of the de Haas - van Alphen effect. The possible relevance to anomalous experimental results on CeRu2Si2 is discussed.
TL;DR: In this paper, a single-band approximation to the random Schrodinger operator in an external magnetic field is considered, where the random potential is taken to be constant on unit squares and i.i.d. on each square with a bounded distribution.
Abstract: We consider a single‐band approximation to the random Schrodinger operator in an external magnetic field. The random potential is taken to be constant on unit squares and i.i.d. on each square with a bounded distribution. We prove that the eigenstates corresponding to energies at the edges of the Landau band are localized. This is an important ingredient in the theory of the Quantum Hall Effect.
TL;DR: In this article, it was shown that at small Zeeman energies, the charged excitations in the vicinity of 1 3 filled Landau level are skyrmions of composite fermions.
Abstract: A prescription is provided for constructing the Hall curve including both integral (I)- and fractional (F)-quantum Hall effects (QHE) that is based upon the iterative application of particular transformations simultaneously to the Hall resistance (Rxy) and magnetic field (B) axes of a template constructed from the elementary (integral quantum) Hall curve to filling factor v = 1. The construction shows that scaled copies of the elementary Hall curve reappear in various parts of the constructed curve upon increasing the magnification, resulting in FQHE sequences in higher Landau bands, and novel FQHE sequences between main sequence FQHE’s in the lowest Landau band. The self similarity observed in the constructed Hall curve helps to draw a connection between FQHE’s and the classical problem of an electronin-a-periodic-potential-subjected-to-a-magnetic-field (‘Hofstadter’s butterfly’), and suggests that fractional quantum Hall effects constitute another manifestation of fractal geometry in nature—one that might also be viewed as a signature of transport in a Wigner crystal.
TL;DR: In this article, the curvature of the surface on which a two-dimensional (2D) electron gas is placed is studied and the most significant effect in an external magnetic field (which for 2D electrons becomes effectively nonuniform) is the lifting of the degeneracy of the Landau levels.
Abstract: A number of effects associated with the curvature of the surface on which a two-dimensional (2D) electron gas is placed are studied. The most significant effect in an external magnetic field (which for 2D electrons becomes effectively nonuniform) is the lifting of the degeneracy of the Landau levels. The intensity and shape of the cyclotron resonance line (inhomogeneously broadened) for different polarizations and the corrections to the Hall constant are found for the example of a circular cylinder. A picture of the quantization of the conductance that is qualitatively different from the case of a flat strip is obtained for a quasi-one-dimensional quantum wire in the form of a hollow cylinder. It is shown that in contradistinction to the planar case the spectrum of 2D electrons on the curved surface is sensitive to the sign of the spin-orbit coupling constant (for a fixed sign of the curvature). For hetero-junctions, for example, this opens up new possibilities for extracting information about their “hidden parameters.”
TL;DR: In this article, a new field theory for studying quantum Hall systems is introduced, which is a modified version of the bosonic operator introduced by Read, and it does not work in the lowest Landau level alone, and leads to a much simpler formalism.
Abstract: We introduce a new field theory for studying quantum Hall systems. The quantum field is a modified version of the bosonic operator introduced by Read. In contrast to Read's original work we do not work in the lowest Landau level alone, and this leads to a much simpler formalism. We identify an appropriate canonical conjugate field, and write a Hamiltonian that governs the exact dynamics of our bosonic field operators. We describe a Lagrangian formalism, derive the equations of motion for the fields and present a family of mean-field solutions. Finally, we show that these mean field solutions are precisely the Laughlin states. We do not, in this work, address the treatment of fluctuations.
TL;DR: In this paper, the spectra for both the Coulomb and generic short-range interactions are found algebraically, and the one-dimensional bosonization of edge excitations in the limit of a large number of particles is proved.