Two-dimensional Lateral Surface Superlattices Research Articles

Two-dimensional lateral surface superlattices in GaAs heterostructures with independent control of carrier density and modulation potential

We present a double-layer design for two-dimensional lateral surface superlattice systems in GaAs-AlGaAs heterostructures. Unlike previous studies, our device (1) uses an in situ gate, which allows a very short period superlattice in high mobility, shallow heterostructures and (2) enables independent control of the carrier density and the superlattice modulation potential amplitude over a wide range. We characterize this device design using low-temperature magneto-transport measurements and show that the fabrication process caused minimal damage to the system. We demonstrate the tuning of potential modulation from weak (much smaller than Fermi energy) to strong (larger than the Fermi energy) regimes.

Probing the ladder spectrum arising from motion in a two-dimensional lattice driven by in-plane constant forces

The coherent interband dynamics of optically excited two-dimensional lateral surface superlattices (quantum-dot arrays), driven by an in-plane static electric field, has been investigated. Linear absorption and a spectrally resolved four-wave mixing signals are obtained. When the rational condition ${E}_{x}{/E}_{y}=p/q,$ with p and q prime to each other, is fulfilled, it is found that p peaks appear within the frequency interval ${\ensuremath{\omega}}_{\mathrm{Bx}}{=eE}_{x}a/\ensuremath{\Elzxh}$ in both linear absorption and degenerate four-wave mixing signals with different time delays. These findings are consistent with the recent spectral results [Phys. Rev. Lett. 86, 3116 $(2001)]$, hence providing a method for probing the coherent dynamics of quantum particles in two-dimensional lattices.

Inverse flux quantum periodicity in the amplitudes of commensurability oscillations in two-dimensional lateral surface superlattices

We report strong, amplitude modulated, commensurability oscillations in the magnetoresistance of short period, square, two-dimensional, lateral surface superlattices with symmetric potentials. The amplitude of the oscillations is strongly enhanced when one magnetic-flux quantum (h/e) passes through an integral number of cells of the superlattice. The temperature dependence of the strong oscillations agrees with the theory for commensurability oscillations in one-dimensional superlattices, but the smaller oscillations between these are more rapidly attenuated by increasing temperature. Although the structure we observe has the same flux periodicity as expected for the Landau-level substructure known as the Hofstadter butterfly, such substructure will not be resolved at the temperatures of measurement (1-10 K). We compare our data instead to a recent theoretical model which treats exactly this case, and find significant points of agreement.

Switching of guiding center-drift direction in asymmetric two-dimensional lateral surface superlattices

We have investigated commensurability oscillations (CO's) in the magnetoresistances of stressed rectangular two-dimensional lateral surface superlattices. Devices were realized by shallow etching of holes, arranged on rectangular grids, into ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ heterostuctures. Changing the gate bias on these devices was observed to change the period of the CO's. This phenomenon was predicted by a recent semiclassical theory based on the guiding center-drift concept, and corresponds to the switching of the drift direction in the superlattice as the dominant Fourier component changes. When different Fourier components in the potential were approximately equal, then switching of the drift direction for varying magnetic fields was also observed.

Importance of symmetry breaking in two-dimensional lateral-surface superlattices

We have investigated commensurability oscillations in the magnetoresistances of two-dimensional lateral surface superlattices with square patterns and periods of 100 nm. In some of our samples the symmetry of the potential was broken by the presence of stress and strong piezoelectric effects. Oscillations were weak in symmetric samples, but became much stronger for transport along the $[011\ifmmode\bar\else\textasciimacron\fi{}]$ direction [on a (100) wafer] when the symmetry was broken. For transport along the $[010]$ and $[001]$ directions in the asymmetric samples, the dominant Fourier component in the potential was at an angle of $45\ifmmode^\circ\else\textdegree\fi{}$ to the transport direction, and the commensurability oscillations had an effective period of $100/\sqrt{2}$ nm. All of these observations are fully in accord with a recent semi-classical theory based on the guiding center drift concept.

Commensurability oscillations due to pinned and drifting orbits in a two-dimensional lateral surface superlattice

We have simulated conduction in a two-dimensional electron gas subject to a weak two-dimensional periodic potential, $V_x \cos(2\pi x/a) + V_y \cos(2\pi y/a)$. The usual commensurability oscillations in $\rho_{xx}(B)$ are seen with $V_x$ alone. An increase of $V_y$ suppresses these oscillations, rather than introducing the additional oscillations in $\rho_{yy}(B)$ expected from previous perturbation theories. We show that this behavior arises from drift of the guiding center of cyclotron motion along contours of an effective potential. Periodic modulation in the magnetic field can be treated in the same way.

Dynamic conductivity of a lateral-surface superlattice in a magnetic field

Results are presented of a theoretical and experimental investigation of the dynamic conductivity in the microwave region of a two-dimensional lateral-surface superlattice. A theoretical analysis based on the solution of the Boltzmann kinetic equation for 2D electrons in a laterally modulating potential, an external magnetic field and a microwave field shows that the components of the dynamic conductivity tensor have an oscillatory character of various types. A preliminary experimental study of the dynamic conductivity in the microwave region is presented. Measurements of the reflection coefficient of the microwave radiation (f=38 GHz) from a GaAs/AlGaAs lateral superlattice have been carried out. For the first time Weiss-type oscillations have been observed in a dynamic regime.

Magnetoresistance in dotlike and antidotlike structures.

The magnetotransport in a two-dimensional electron gas in strongly modulated potentials is investigated. For dotlike and antidotlike lateral surface superlattices, a well-defined negative-differential-magnetoresistance behavior is observed followed by a large peak at low magnetic fields. Calculating the electron drift in the modulated potential by taking the external electric fields and the Hall field explicitly into account, two different groups of electrons are obtained, which are in a detailed balance. As only one of these groups contributes to the current flow, the occurrence of the negative differential magnetoresistance in two-dimensional lateral surface superlattices is thus explained. Moreover, the observed maximum in the magnetoresistance is also obtained from this model.

Single-electron states and conductance in lateral-surface superlattices.

The electronic properties of a two-dimensional lateral-surface superlattice are simulated by using the split-operator technique based on the solution of the time-dependent Schr\"odinger equation involving the propagation of the wave functions in the imaginary time domain. The two-dimensional dispersion relation and the density of states are derived and the transport characteristics of the system are calculated in linear-response theory. The results compare well with recent experimental data and show clear evidence of single-electron states in the system.

Guiding-center-drift resonance of two-dimensional electrons in a grid-gate superlattice potential

We have studied the low-field magnetoresistance of the two-dimensional electron gas in GaAs/<m1;&33>AlxGa1−xAs in the presence of a two-dimensional lateral surface superlattice (2D LSSL) potential, and observed, for the first time, the guiding-center drift resonance, previously reported for one-dimensional LSSL structures. The 2D LSSL potential is created by applying a voltage Vg to a 200 nm period grid-gate structure fabricated on top of the sample and can be tuned continuously from being repulsive to attractive by tuning Vg.

Fabrication of coupled quantum dot arrays with a 100–150 nm period

This paper demonstrates a novel method for fabricating two-dimensional lateral surface superlattices. The technique involves etching a grid into a GaAs/GaAlAs modulation-doped heterostructure using a mask consisting of an array of 50-nm diam Ni/Au dots with a 100–150 nm period. Bias applied to a Schottky gate deposited over the structured surface varies the coupling strength between dots. The devices can be tuned to operate in the superlattice (weak and strong coupling) or the quantum dot (no coupling) regimes. Low-temperature characterization of the superlattices fabricated specifically for transport and capacitance measurements reveal novel magnetic field effects.

Oscillatory density-of-states of Landau bands in a two-dimensional lateral surface superlattice

A new oscillatory phenomenon is observed in the magneto-capacitance between the high mobility two-dimensional electron gas in a GaAs/AlGaAs heterostructure and a metal grid gate of 200nm periodicity. The observed minima reflect the minima in the density-of-states of Landau bands resulting from removal of the Landau level degeneracy by the grid gate potential. A model calculation is carried out and the results agree with the experimental observation.

Resonant magnetoconductance in a two-dimensional lateral-surface superlattice.

We have investigated magnetoconductance in a two-dimen- sional lateral-surface superlattice on modulation-doped GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As heterostructure, at 50 mKT1.5 K and 0B13.5 T. The superlattice potential modulation is formed and controlled by a metal grid gate with 200-nm periodicity. This modulation can be made larger than the Fermi energy and cyclotron energy depending on the grid-gate bias. Conductance oscillations as a function of gate bias in the presence of a magnetic field have been observed. The magnetic-field dependence of the amplitude and position of the oscillations indicates that the effect of the magnetic field is to sharpen the superlattice potential modulation.