Commensurability Oscillations Research Articles

Modulation of Landau levels by a one-dimensional periodic potential

We have studied the magnetoresistance of short-period one-dimensional lateral superlattices with strong modulation at low temperatures. Striking interference was seen between commensurability oscillations and the Shubnikov–de Haas effect. This cannot be explained within the usual semiclassical theory and a quantum mechanical explanation is proposed.

Composite fermions in a weakly density modulated 2DEG: direct evidence of a periodic magnetic field around [formula omitted

We investigate the magnetoresistance of a weakly density modulated high mobility two-dimensional electron system around filling factor ν= 1 2 . The density modulation with periods a between 300 nm and 500 nm was generated by in situ interferometric illumination. At low B we found commensurability oscillations of the magnetoresistance characteristic for transport in weak electrostatic potentials with minima positions on the magnetic field axis given by 2 R C=( λ−1/4) a. Here 2 R C is the electron cyclotron diameter at the Fermi-energy and λ an integer. In contrast, we find clear magnetic commensurability features around filling factor ν= 1 2 with a pronounced minimum for a composite fermion cyclotron radius R C,CF matching 1.25 a. This gives direct evidence that the density modulation results in a modulated effective magnetic field for composite fermions. The experimental ρ xx-traces around ν= 1 2 are well described by novel model calculations, based on a semiclassical solution of the Boltzmann equation, taking into account anisotropic scattering.

Minibands, magnetic breakdown, and novel magnetoresistance oscillations in short-period lateral superlattices

Novel 1/ B periodic low-field oscillations observed in the magnetoresistance of short-period lateral superlattices with weak electrostatic modulation are analyzed as being due to the formation of minibands. The energy gaps caused by the weak superlattice potential distort the Fermi circle of the unmodulated two-dimensional electron system (2DES) at the Brillouin-zone boundaries and form smaller closed Fermi contours giving rise to the novel oscillations. We discuss the periodicity of these novel oscillations for one-dimensional (1D) and two-dimensional (2D) lateral modulation and compare their dependence on the electron density with the well-known classical commensurability oscillations.

Spin-resolved commensurability oscillations

We report the observation of commensurability oscillations, induced by a one-dimensional periodic potential, in a high-mobility GaAs two-dimensional hole system confined to a triangular quantum well. The measured oscillations exhibit two frequencies that agree well with those calculated from the Fermi contours of the two spin-split hole subbands, providing clear evidence for the observation of spin-resolvedcommensurability oscillations.

Effect of oxygen stoichiometry on the out-of-plane anisotropy of YBa2Cu3O7- single crystals near optimal doping

We have performed magnetic measurements on pure detwinned YBa2Cu3O7- single crystals in order to investigate the influence of variations in the oxygen stoichiometry on the out-of-plane anisotropy ck in the region close to optimal doping (6.90 < 7- < 6.98). The anisotropy is estimated using the anisotropic London model from the period of the commensurability oscillations of the hysteretic magnetization as observed for fields applied parallel to the a-b-planes. For a variation in the oxygen deficiency by as much as 300%, we find that ck decreases but only slightly (less than 12%) with decreasing oxygen deficiency. The possibility of a temperature-dependent ck is also discussed.

Potential modulation by strain in lateral surface superlattices

We have measured the magnitude of the potential modulation below gated one-dimensional lateral surface superlattices fabricated with periods between 60 and 600 nm on a range of GaAs/AlGaAs heterostructures. The magnitude of the modulation was obtained by studying the amplitude of the commensurability oscillations in magnetoresistance, and confirmed by analysis of the low field positive magnetoresistance step. Without gate bias applied, the modulation is generated by strain in the gates, coupled piezoelectrically to the two-dimensional electron gas. Both magnitude and harmonic content of the potential are in reasonable agreement with a recent theoretical calculation of this coupling, over the full range of periods and for all the structures studied. Away from zero gate bias electrostatic modulation adds to the piezoelectric component. This differs according to the sign of the applied bias. In depletion it increases roughly linearly with bias and is in good agreement with theoretical estimates, whereas in positive bias it tends to saturate as strong screening in the donor layers develops.

Spin-resolved ballistic transport of GaAs two-dimensional holes

We report the observation of commensurability oscillations, induced by a one-dimensional periodic potential, in high-mobility GaAs two-dimensional hole system confined to a triangular quantum well. The measured commensurability oscillations exhibit two frequencies which agree well with those calculated from the Fermi contours of the two spin-split hole subbands, providing clear evidence for the observation of spin-resolved ballistic transport.

Commensurability oscillations and a new phase transition in YBa2Cu3Oy single crystals

Magnetization oscillations due to the commensurability of the vortex and crystal lattice periods in YBa2Cu3Oy (y=6.97±0.02) single crystals are investigated using a high angular resolution magnetometer. A sharp peak in the temperature dependence of the oscillation amplitude as well as other features in the behavior of the oscillation amplitude and of the irreversible magnetization are observed at T f ∼60 K. It is inferred that T f is the temperature of a transition of the solid vortex state to a smectic phase.

Commensurability oscillations in a stripe-shaped two-dimensional electron gas

We have studied the commensurability oscillations for a nonplanar, two-dimensional electron gas which is confined to a surface spatially modulated both in the transverse and longitudinal directions. We show, numerically, that coupling the drift in both directions causes the motion to be chaotic. The channeling tori, responsible for conduction along the stripes, are destroyed and the averaged squared drift velocities decrease.

Giant commensurability oscillations in a stressed surface superlattice

We have fabricated a novel type of lateral surface superlattice device comprising parallel, stressed ribs of In0.2Ga0.8As on a GaAs/Al0.3Ga0.7As heterostructure containing a high mobility two-dimensional electron gas (2DEG). Magnetotransport measurements were used to deduce the form and magnitude of the potential modulation. These experiments, supported by our calculations, indicate the importance of both piezoelectric coupling of stress to the electrons and the repulsive potential induced in the 2DEG by the removal of layers from the surface to define the superlattice.

Antidot shape dependence of the commensurability oscillation of magnetoresistance in two-dimensional antidot arrays

We have studied commensurability oscillations in magnetoresistance (MR) of antidot arrays by changing the antidot shape. For the bar-shaped antidot array, we found the clear dependence of the amplitude of commensurability oscillations on the current direction. This feature was successfully reproduced by numerical calculations. Based on these results, we discuss the origin of the commensurability oscillations. We have also studied antidot arrays with other antidot shapes experimentally and numerically.

Two-dimensional electron gas under a spatially modulated magnetic field: A test ground for electron-electron scattering in a controlled environment

We have studied the electronic transport in a two-dimensional electron gas (2DEG) subjected to a spatially modulated magnetic field and electrostatic potential. Independent control of the magnetic field components parallel and perpendicular to the 2DEG plane allows us to manipulate the amplitude of the magnetic modulation independently of the normal field component relevant to the magnetotransport in the 2DEG. The amplitudes of the magnetic and electrostatic modulations can be evaluated from an analysis of the commensurability oscillation of magnetoresistance. The increase of resistivity in the presence of a modulated magnetic field at a zero uniform magnetic field is found to be quadratic in the modulation amplitude and to vary as ${\mathrm{AT}}^{2}+C$ at low temperatures. This is a signature of the electron-electron scattering in the presence of a spatially modulated magnetic field. The present system provides an ideal test ground for theories of electron-electron-scattering-induced resistivity.

Tunable Spin-Splitting and Spin-Resolved Ballistic Transport in GaAs/AlGaAs Two-Dimensional Holes

We report quantitative experimental and theoretical results revealing the tunability of spin splitting in high-mobility two-dimensional GaAs hole systems, confined to either a square or a triangular quantum well, via the application of a surface-gate bias. The spin splitting depends on both the hole density and the symmetry of the confinement potential and is largest for the highest densities in asymmetric potentials. In the triangular well, when the spin splitting is sufficiently large, our measured commensurability oscillations, induced by a one-dimensional periodic potential, exhibit two frequencies providing clear evidence for spin-resolved ballistic transport.

Ballistic transport in a two-subband two-dimensional electron system

We report a quantitative study of ballistic transport, via measurements of commensurability oscillations (CO's), in a two-dimensional electron system confined to a wide square quantum well with two electric subbands occupied. The Fourier power spectrum of the CO's shows two clear-frequency components that correspond to ballistic transport in the upper and lower subbands. Through inverse Fourier transformation of each individual frequency component, we reconstruct the CO's of ballistic electrons in different subbands and extract their scattering times.

Thermodynamic properties of a two-dimensional electron gas in the presence of a weak spatially modulated periodic potential

A systematic investigation on the influence of an additional periodic modulation potential which is weak, either electric or magnetic in nature, and spatially modulated along one dimension, on the equilibrium thermodynamic properties of a two-dimensional electron gas in an externally applied magnetic field is presented. The application of such an additional modulation potential results in a broadening of the Landau level energy spectrum into bands whose widths oscillate as a function of the externally applied magnetic field. Such oscillations are found to reflect the commensurability of the two different length scales present in the system, namely the cyclotron diameter at the Fermi level and the period of the modulation. We show that such commensurability effects are also to be found in all thermodynamic quantities of the system. They appear at low magnetic fields as an amplitude modulation of the well-known de Haas-van Alphen-type oscillations, familiar from the homogeneous two-dimensional electron gas system in an external magnetic field, which may or may not be resolved depending on temperature and are only weakly dependent on temperature. Their origin lies in the oscillations occurring in the bandwidths and they are consequently completely different in origin from the usual de Haas-van Alphen-type oscillations. In particular, we show that commensurability oscillations are to be found in the chemical potential, Helmholtz free energy, internal energy, electronic entropy, electronic specific heat, orbital magnetization and orbital magnetic susceptibility of such weakly modulated systems. We find that the resulting commensurability oscillations in each thermodynamic function exhibit well-defined phase relations between the electric and magnetic modulations except in the case of the orbital magnetization and the orbital magnetic susceptibility. Explicit asymptotic expressions for the chemical potential, Helmholtz free energy and orbital magnetization, in the quasi-classical limit of small magnetic fields and small but finite temperatures, are also given.

Giant magnetoresistance and possible miniband effects in periodic magnetic fields

We have investigated the magnetoresistance (MR) of high mobility, near surface two-dimensional electron gases that are subject to a periodic magnetic field of amplitude up to 0.3 T. The fields are produced by sub-micron arrays of ferromagnetic stripes on the surface of the heterostructures. For small applied external magnetic fields we observe an MR of up to 1500% in applied fields of ∼100 mT. At low temperatures we observe both commensurability and Shubnikov-de Haas oscillations in the same field range. The SdH oscillations are strongly modulated by the 1D periodic magnetic potential. The observed behaviour is not consistent with semiclassical models. A new type of MR is observed on increasing the amplitude of the modulation. In this case, the MR amplitude increases as T 2. This provides evidence of an electron–electron scattering contribution to the resistivity possibly due to the presence of minibands.

Zero-field spin splitting in GaAs/AlGaAs 2D holes

From Fourier analysis of the low-magnetic-field Shubnikov–de Haas oscillations, we quantitatively determine the spin splitting, in the limit of zero magnetic field, for high-mobility two-dimensional hole systems confined to GaAs/AlGaAs heterostructures. The spin-splitting can be tuned continuously from large values to nearly zero in a square quantum well whose charge distribution can be controlled from being asymmetric to symmetric via the application of a front-gate bias. In a triangular well with an asymmetric potential, we always observe substantial spin splitting. In the latter system, our measured commensurability oscillations, induced by a one-dimensional periodic potential, reveal two frequencies, providing clear evidence for spin-resolved ballistic transport.

Commensurability oscillations by runaway and pinned electrons

We report on an investigation of commensurability oscillations in antidot square-lattices, and show that the commensurate peaks in resistivity ρxxderive from two kinds of electron: runaway and quasipinned electrons. The runaway electrons, which skip away along the antidot arrays, increase the value of conductivity σxx; and the quasipinned electrons, which orbit some antidots for a long time, decrease the value of σxx. Therefore, by competition between the two different types of electron, the conductivity σxxis determined. The conductivity σyxin the antidot lattice always has dips at the peaks in ρxx. As a result, by combining the of values of σxxand σyx, the resistivity is determined through the orthodox relation of ρxx= σxx/ (σxx2 + σyx2).

Envelope of Weiss oscillations and the role of disorder in surface superlattices

We study the magnitude of the Weiss magnetoresistance commensurability oscillations in surface superlattices, in samples with a long sequence of such features. The high index oscillations are suppressed faster than the conventional exponential term---apparently by a term of the form $\mathrm{exp}{\ensuremath{-}{(B}_{0}{/B)}^{3}}$. We discuss the role of small-angle scattering in the suppression of these oscillations and suggest a heuristic derivation of this envelope function.

Higher order magnetoresistance commensurability oscillations in low aspect ratio antidot lattice and focusing structures

We observe unusually strong magnetoresistance commensurability oscillations in two different types of artificial arrays of scattering centers, multiparallel focusing slits and a square antidot lattice, both fabricated on a two-dimensional electron gas by electron-beam lithography and damageless wet etching. The strength of the magnetoresistance peaks is attributed to a high reflection specularity and a small effective antidot cross section. The absence of commensurability effects near Landau level filling factor υ=3/2 is attributed to the composite fermion mean free path being smaller than the slit and antidot spacings. The mechanism for the observed commensurability is discussed.