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.

Lateral-surface superlattices in systems with spin-orbit coupling: Quantum states and bloch oscillations in an electric field

The quantum states of a two-dimensional electron gas with spin-orbit coupling located in the periodic potential of a lateral-surface superlattice are studied. The spin-split energy bands and the distribution of spin projections in the Brillouin zone are constructed. Bloch oscillations accompanied by spin precession in superlattices with spin-orbit coupling located in a constant electric field are studied.

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.

Quantum Hall effect in ap-type heterojunction with a lateral surface superlattice

The quantization of Hall conductance in a p-type heterojunction with lateral surface quantum dot superlattice is investigated. The topological properties of the four-component hole wavefunction are studied both in r- and k-spaces. New method of calculation of the Hall conductance in a 2D hole gas described by the Luttinger Hamiltonian and affected by lateral periodic potential is proposed, based on the investigation of four-component wavefunction singularities in k-space. The deviations from the quantization rules for Hofstadter "butterfly" for electrons are found, and the explanation of this effect is proposed. For the case of strong periodic potential the mixing of magnetic subbands is taken into account, and the exchange of the Chern numbers between magnetic subands is discussed.

Commensurability oscillations on lateral surface superlattices with large periods

We present for the first time, an investigation of commensurability oscillations (COs) on lateral surface superlattice devices with large periods (1 and 2 μm). The observed values of the COs positions are compared with the predicted peaks. In forward bias clear COs are observed. It is noticed that the COs have a strong dominant third harmonic content. The COs are found to vanish with increasing negative bias.

Commensurability effects in lateral surface-doped superlattices

We fabricate density-modulated two-dimensional electron systems by shallow compensation doping the donor layer of a modulation-doped heterostructure. Zinc acceptor atoms are diffused from the sample surface which is heated by a focused laser beam. Low-temperature magnetotransport experiments provide evidence that high-quality lateral surface superlattices can be fabricated. In weak periodic one-dimensional potentials, commensurability oscillations are recovered, whereas in strong periodic two-dimensional potentials the semiclassically expected antidot resistance resonances are found to dominate the low-field transport. Additionally, the homogeneity of the laser-induced doping is confirmed by magnetic focusing experiments.

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.

Large positive magnetoresistance in periodically modulated two-dimensional electron gas formed on self-organized GaAs multiatomic steps

We study magneto-transport properties of two-dimensional electron gas (2DEG) subjected to a periodic potential with a period of 60–70 nm, where the potential modulation is realized by periodically corrugated InGaAs channel layer formed on self-organized GaAs multiatomic steps. We find a large positive magnetoresistance (MR) when the current is perpendicular to the potential modulation, while such positive resistance is not observed for the current parallel to the potential modulation. It is also found that the amplitude of MR oscillation for current perpendicular to the potential modulation is extremely large over 3.5 T, and is modulated in 2–3.5 T. In addition, we also find the anisotropy in electron mobility. The results can be explained by the large potential modulation in the lateral surface superlattice (LSSL) and associating modulation of Landau subbands in LSSL.

The Stark effect of excitons in corrugated lateral surface superlattices: the effect of centre-of-mass quantization

The quantum-confined Stark effect of excitons in GaAs/AlGaAs corrugated lateral surface superlattices (CLSSLs) is calculated. New absorption peaks with nearly equal energy spacing appear in the exciton absorption spectra due to the exciton centre-of-mass quantization by the periodically corrugated interfaces of the CLSSLs. The shift of the exciton optical absorption peaks and variation in its absorption strength with the applied electric field, as well the absorption selection rules for the CLSSLs, are 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.

Characterization of Potential Modulation in Novel Lateral Surface Superlattices Formed on GaAs Multiatomic Steps

We investigated the potential modulation in a novel lateral surface superlattice (LSSL) structure which was realized by utilizing multiatomic steps. The structure was grown by metalorganic vapor-phase epitaxy (MOVPE) on vicinal GaAs substrates to introduce periodic thickness modulation to the channel GaAs layer with spontaneously formed multiatomic steps. Devices having split gates were fabricated on the epitaxially grown LSSL structure. The potential modulation was investigated by a potential sweeping technique, where different bias voltages were applied to the split gates to change the minima of the potential across the multiatomic steps. We observed plateaus and oscillations of conductance as a function of the gate voltage. Systematic shifts of these positions were also observed when offset voltages between the two gates were applied and changed. These features are assumed to originate from the potential modulation induced by multiatomic steps.

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.

Formation and characterization of modulated two-dimensional electron gas on GaAs multiatomic steps grown by metalorganic vapor phase epitaxy

We used multiatomic steps spontaneously formed on vicinal surfaces during metalorganic vapor phase epitaxial (MOVPE) growth to introduce lateral potential modulation into two-dimensional electron gas (2DEG) and to realize a novel lateral surface superlattice (LSSL) with period of around 70 nm. Their electron transport properties were investigated at low temperatures and large anisotropies in the mobility and transconductance characteristics were found for the current parallel and perpendicular to the multiatomic steps. The potential modulation was further applied to form multiple quantum dots and tunnel junctions in combination with the squeezing of the width of the channel defined across the multiatomic steps. The Coulomb blockade type conductance oscillations were observed at low temperature transport measurement.

Theory of potential modulation in lateral surface superlattices. III. Two-dimensional superlattices and arbitrary surfaces

Abstract We have calculated the potential energy induced in a two-dimensional electron gas by a two-dimensional array of gates on the surface of a heterostructure. Differential thermal contraction of the gates generates strain that couples to the electrons by the deformation potential and piezoelectric effect. The piezoelectric effect usually dominates and its angular dependence breaks the symmetry of the gate or array. For example, the potential under a circular gate on a (100) surface varies as sin 2θ where θ is measured from the [010] axis. This nulls the lowest Fourier components of the potential from a square array of gates aligned parallel to the principal axes. The lowest surviving component has a smaller period than the gates and is rotated with respect to them by 45◦. Arrays are usually aligned parallel to the {011} cleavage planes in practice, which causes a stronger potential without such cancellation. We also provide results for (110), (111), and (311) surfaces; (111) may be attractive because the piezoelectric effect is nearly isotropic. The potential due to a bias on the gates, and the limit of a one-dimensional array, are considered briefly. Our calculations are for the strain induced by metal gates but also apply to devices with stressors such as mismatched semiconductors.

Large periodic potential under lateral surface superlattices fabricated from heteroepitaxial stressor layers

We have fabricated lateral surface superlattices by etching a strained layer of In0.2Ga0.8As near the surface of a heterostructure. This provides strong modulation of the electron gas while retaining a high electron mobility. The potential arises mainly from strain and the piezoelectric effect, which depends on orientation, and from the change in the surface profile. The fundamental components of these two contributions cancel in one orientation to leave a dominant second harmonic. This effectively halves the period of the superlattice from its lithographic value and provides a promising technique for creating potentials with a period comparable to the Fermi wavelength.

The strong Stark effect of intersubband transitions in corrugated lateral surface superlattices

Intersubband electro-absorption and electro-refraction index spectra of GaAs/AlAs corrugated lateral surface superlattices (CLSSLs) are calculated. Large shifts of intersubband transition energies and Fermi energy levels in the electron occupied subbands induced by applied electric fields result in strong intersubband Stark effects and large refractive index variations in the CLSSLs that we considered with moderate electric fields . Strong intersubband absorptions with normally incident light due to the corrugated interfaces of the CLSSLs which break the in-plane translational symmetry of the systems are predicted. Broadenings of the intersubband electro-absorption and electro-refraction index spectra caused by structural fluctuations of the CLSSLs are discussed.

Infrared Optical Absorptions in Corrugated Lateral Surface Superlattices**The project supported by National Natural Science Foundation of China and the Science and Technology Foundation of High Education of China

The optical properties are investigated numerically in infrared (IR) regions for GaAs/AlAs corrugated lateral surface superlattices (CLSSLs) with short lateral periods. The calculations are carried out for refractive indexes and optical absorption coefficients with and without inclusion of electron interactions in an attempt to study the effects of intersubband plasmons on the IR optical properties of CLSSLs. As lateral periods of CLSSLs increase from 10 nm to 30 nm, their IR optical properties change from the behavior dominated by single electron transitions between conduction subbands to those dominated by intersubband plasmon excitations. Strong and sharp peaks in the optical absorption coefficients, large variations of the refractive indexes and strong anisotropic optical properties of CLSSLs are predicted in IR regions.