Session U37: Transport Properties of Semiconductors: 2-D Systems

Resistance oscillations in two-dimensional electron systems due to resonant acoustic phonon scattering

A few years ago a new class of resistance oscillations was discovered in two-dimensional electron systems subject to weak magnetic fields and elevated temperatures [1]. It was proposed that oscillations originate from resonant interaction with acoustic phonons made possible by virtue of a special selection rule which favors electron backscattering. In contrast to other types of magneto-resistance oscillations, such as those appearing under application of microwave or dc electric fields, phonon-induced resistance oscillations (PIRO) have not received much attention and remain poorly understood. Of particular interest are the period and the phase of PIRO, relative contribution and nature of different phonon modes, and the effect of temperature and sample parameters. This talk will briefly review prior and new experimental results and discuss open issues. \newline [1] M.A. Zudov, I.V. Ponomarev, A.L. Efros, R.R. Du, J.A. Simmons, and J.L. Reno, Phys. Rev. Lett. {\bf 86}, 3614 (2001)   

Effect of dc electric field on resonant acoustic phonon scattering in two-dimensional electron systems

We study [1] the effect of dc electric field on transport properties of two-dimensional electron systems in which resonant acoustic phonon scattering dominates linear response resistivity. We observe that dc electric field strongly modifies phonon resonances, transforming resistance maxima into minima and back into maxima. Further, phonon resonances are enhanced dramatically in the non-linear dc response and can be detected even at low temperatures. Most of our observations can be explained by dc-induced (de)tuning of the acoustic phonon resonances and intra-Landau level impurity scattering. We also observe a dc-induced zero-differential resistance state and a resistance maximum which occurs when the electron drift velocity approaches the speed of sound. \newline [1] W. Zhang, M.A. Zudov, L.N. Pfeiffer, and K.W. West, arXiv:0711.1547v1, Phys. Rev. Lett. (accepted for publication).   

Effect of electron-phonon scattering on magneto-transport in 2DES

We evaluate the contribution of electron-phonon scattering to the non-linear magneto-resistance of two-dimensional electron systems (2DES). Both linear [1] and differential [2] magneto-resistances show oscillatory dependence on the applied magnetic field in high mobility 2DES. These oscillations originate from the relation between the change of electron energy in a scattering event and the cyclotron frequency. In case of electron scattering with phonons in dc electric fields, the change in electron energy is equal to the sum of the energy of an emitted or absorbed phonon and the change of the electrostatic electron energy due to the shift of an electron cyclotron trajectory. We show that the electrostatic contribution in sufficiently strong fields moves the position of maxima and minima of the differential magnetoresistance. We also explain why the phonon-induced magneto-oscillations exist in the linear response regime only at moderately high temperatures, but appear at significantly lower temperatures in stronger electric fields. [1] M.A. Zudov, et al., Phys. Rev. Lett. {\bf 86}, 3614 (2001). [2] W. Zhang, et al., arXiv:0711.1547v1 (2007).   

Non-linear dc response in microwave-irradiated two-dimensional electron systems: interplay between ac and dc induced effects

\def\eac{\epsilon^{\mbox{{\scriptsize ac}}}} We study nonlinear dc response of a high-mobility two- dimensional electron system subject to microwave (ac) excitation and weak magnetic fields. Recent experiments [1] studied resistance at different dc excitations as a function of the ratio of the microwave frequency to the cyclotron frequency, $\eac$. Here, we examine oscillations in microwave photoconductivity as a function of dc excitation, at different values of $\eac$. We find that, for the most part, the oscillation period is the same as in the dark resistivity, and the phase is determined by microwave-induced oscillations at zero dc bias, consistent with the earlier results. However, at some excitation values previously associated with resistance maxima, this approach revealed resistance minima indicating saddle points in the resistivity. We further observed that the oscillation amplitude itself oscillates as a function of $\eac$, with the oscillations strongly suppressed near half-integral values. These findings indicate the limitations of the simplified resonant condition proposed in Ref. 1 and might stimulate further theoretical studies. \newline [1] W. Zhang, M.A. Zudov, L.N. Pfeiffer, and K.W. West, Phys. Rev. Lett. {\bf 98}, 106804 (2007)   

Zero differential resistance state in 2D dimensional electron system in strong magnetic field.

We report the observation of a zero differential resistance state (ZDRS) in response to direct current above a threshold value $I>I_{th}$ applied to a two-dimensional system of electrons at low temperatures in a strong magnetic field. Entry into the ZDRS, which is not observable above several Kelvins, is accompanied by a sharp dip in the differential resistance. Additional analysis reveals instability of the electrons for $I>I_{th}$ and an inhomogeneous, non-stationary pattern of the electric current. We suggest that the dominant mechanism leading to the new electron state is a redistribution of electrons in energy space induced by the direct current.   

Influence of a Parallel Magnetic Field on the Microwave-Induced Resistance and Photovoltaic Oscillations

Microwave induced photovoltaic (PV) and resistance oscillations (MIRO) were studied in high-mobility ($\mu >$ 8$\times $10$^{6}$ cm$^{2}$/V s) 2D electron gas in GaAs/Al$_{x}$Ga$_{1-x}$As Hall bar samples employing a two-axis magnet system (perpendicular field B$_{\bot }$ and parallel field B//). Consistent with the previous results, strong MIRO were observed and were found to diminish under a B// $\sim $ 1 T. We observed two types of PV oscillations: 1) PV oscillations that are periodic in 1/B$_{\bot }$, with a periodicity similar to MIRO, but are anti-symmetric with respect to B$_{\bot }$ = 0; and, 2) PV oscillations due to edge magnetoplasmon modes, which are periodic in B$_{\bot }$ and are symmetric with respect to B$_{\bot }$ = 0. Characteristically, the 1/B$_{\bot }$ oscillations in PV were completely suppressed by a B// $\sim $ 1 T, whereas the B$_{\bot }$-periodic oscillations retain their main features even in B// = 2 T. Experimental data and a brief discussion will be presented. The work at Rice was supported by NSF DMR-0706634.   

Microwave-Induced Resistance Oscillations in Non-Faraday Configurations

The microwave-induced resistance oscillations (MIRO) are commonly observed in high-mobility GaAs 2D electron systems (2DES), typically using a Faraday configuration. In a Faraday configuration, the electromagnetic components (E$_{\omega }$ and H$_{\omega })$ coincide with the 2DES plane. We explore MIRO in a microstrip line geometry, in which the dominant excitation component in the 2DES plane is H$_{\omega }$. Our samples were 100 or 200 $\mu $m wide Hall bars of very-high mobility ($\mu \quad >$ 8 $\times $ 10$^{6}$ cm$^{2}$/Vs) GaAs/Al$_{x}$Ga$_{1-x}$As heterojunctions or quantum wells with electron density ranging from 2.1 - 7.0 $\times $ 10$^{11}$/cm$^{2}$. Microwaves from a tunable source (2 GHz - 40 GHz) were fed via a semi-rigid coax cable to the microstrip line over the length of the Hall bar. In a temperature range of 0.3 K -- 2.0 K, we observed strong MIRO in all the samples measured. We have studied the fractional MIRO using both the microstrip line and dipole antenna geometries. By increasing the MW power, MIRO features associated with $\varepsilon $ = 1/2, 1/3, and 1/4 emerged, where $\varepsilon =\omega $/$\omega _{c}$, and $\omega _{c}$ is the cyclotron frequency. Experimental data as well as a brief discussion will be presented. The work at Rice was funded by NSF DMR-0706634.   

Low Temperature Scanning Hall Probe Microscopy of 2D Electron Nanostructures

Current distribution can provide key information on microscopic properties of 2D electron systems (2DES) in the regime of quantum transport. However, imaging coherent electron flow is proven to be experimentally challenging. We developed a method to image current distribution by using low temperature (0.3K), high spatial resolution ($<1\mu m)$ scanning Hall probe. We imaged the local magnetic field component perpendicular to the 2DES in GaAs/AlGaAs samples, and then used Fast Fourier Transform (FFT) technique to recover the current distribution from the data of magnetic field. As an example, we will present the data and a brief discussion of imaging geometrical resonance in anti-dot lattices patterned on a very high mobility 2DES. The research at Rice was supported by NSF DMR-0706634.   

Spin-Orbit Interaction in High-$\kappa $ Dielectric Gated Rashba-2D Electron Gas and Mesoscopic Rings

There is increasing current interest in the quantum interference effect in mesoscopic devices fabricated on a Rashba-2D electron gas (2DEG), where the spin-orbit interaction parameters can be tuned by a potential gate. We explore ring structures that use a gate consisting of thin (5nm-50nm) high-$\kappa $ dielectric Al$_{2}$O$_{3}$ or HfO$_{2}$ layer and nano-patterned metals. The 2DEG is provided by lattice-matched $In_{0.52} Al_{0.48} As/In_{0.53} Ga_{0.47} As/In_{0.52} Al_{0.48} As$ quantum wells that have a typical electron density n of $1.5\times 10^{12}/cm^2$ and mobility $\mu \ge 2\times 10^4cm^2/Vs$. The dielectric material was grown by atomic layer deposition. We will present the gate characteristics of Hall bars as well as magnetic transport data from gated mesoscopic rings. The work at Rice is funded by NSF DMR-0706634. Reference: M. Konig et al, Phys. Rev. Lett. 96, 076804 (2006); T. Bergsten et al, Phys. Rev. Lett. 97, 196803 (2006); B. Grbic et al, Phys. Rev. Lett. 99, 176803 (2007).   

Novel interaction-induced magneto-oscillations in ac conductivity of 2D electron gas

We demonstrate that electron-electron interactions in a high-mobility 2D electron gas give rise to the {\em oscillatory} correction, $\delta\sigma^{int}(\omega)$, to the ac magnetoconductivity, $\sigma(\omega)$. Similarly to the conventional single-particle harmonics of the cyclotron resonance, the oscillating correction is periodic in $\omega_c^{-1}$, where $\omega_c$ is the cyclotron frequency. However, unlike the single-particle oscillations, which are periodic with $\omega$, the interaction correction is periodic with $\omega^{3/2}$. Oscillatory behavior of the interaction-induced magnetoconductivity develops at very low magnetic fields, $\omega_c\ll\omega$; at such fields the conventional harmonics are suppressed by the disorder. The underlying physical process of the new effect is {\em double} backscattering of an electron from the impurity-induced Friedel oscillations. Unlike the case of single-particle oscillations, the electron travels only a {\em small portion} of the Larmour circle during the time $\sim\omega^{-1}$ between the two backscattering events.   

Many-body local field corrections to spin Coulomb drag in a quasi-two-dimensional electron system

We investigate the effect of exchange and correlation on spin Coulomb drag in a quasi-two-dimensional electron gas of finite transverse width. We find that the finite transverse width of the electron gas causes a significant reduction of the spin Coulomb drag. This reduction, however, is largely compensated by the enhancement coming from the inclusion of many-body local field corrections beyond the random phase approximation. Our calculations are in very good agreement with and confirm the experimental observations of the spin Coulomb drag by C. P. Weber \textit{et al.}, Nature, \textbf{437}, 1330 (2005).   

Evidence of Coulomb Drag between Anderson Insulators

We report observations of Coulomb drag between 200 Angstrom thick co-sputtered insulating amorphous silicon-niobium alloy films, separated by a thin silicon-oxide barrier. An apparent linear-response regime for the transresistance is found to only exist over a narrow range of layer separations ($\sim $100 Angstroms) and material parameters (niobium concentrations $\sim $ 7{\%}) at low driving currents ($\sim $1nA) and temperatures below $\sim $20 Kelvin. The temperature dependence, as well as the magnitude, of the transresistance in this regime is consistent with predictions for that between Anderson insulators with long ranged intra-layer Coulomb interactions, provided that the density of states of the silicon-niobium layers are taken to be that of effectively 3-dimensional systems. This is in contrast with measurements of the temperature dependence of the dc layer-conductivity in such bilayer systems, which suggest that transport should be effectively 2-dimensional at these energies. We will discuss the fabrication and characterization of bilayer samples, as well as possible explanations for the observed magnitude and temperature dependence of the transresistance.   

Scaling of thermoelectric voltage induced by microwave radiation at the boundary between two-dimensional electron systems

We report measurements of the rectification of microwave radiation ($0.7$-$20$ GHz) at the boundary between two- dimensional electron systems created by a narrow gap split gate on a silicon surface for different temperatures, electron densities and microwave power. For frequencies above $4$ GHz and different temperatures, the rectified voltage $V_{dc}$ as a function of microwave power $P$ can be collapsed onto a single universal curve $V_{dc}^{*}=f^*(P^{*})$ using two scaling parameters. The scaled voltage, $V_{dc}^{*}$, is a linear function of power, $P^{*}$, for small power and proportional to $(P^*)^{1/2}$ at higher power. A theory is developed which attributes the observed voltage to the thermoelectric response associated with local heating by the microwave radiation of adjacent two-dimensional electron systems with different densities $n_1$ and $n_2$. Excellent quantitative agreement is obtained between theory and experiment. *The work at the City College of New York was supported by DOE grant DOE-FG02-84-ER45153. The work at International Center of Condensed Matter Physics, Brasilia, was supported by IBEM fund from Brazilian Ministry of Science and Technology.   

Charged Excitations of a Two Dimensional Electron System

Despite the central role that the tunneling (or single-particle) particle density of states (TDOS) plays in our theories of many- body systems, it has proven a difficult quantity to access experimentally in two dimensional electron systems (2DES). We have developed a technique, time domain capacitance spectroscopy, which allows measurement of the TDOS over a range of 30 meV centered about the Fermi surface, revealing the detailed structure present in these systems far from the Fermi energy. Remarkably, we observe a long-lived excitation in the 2DES whose creation requires more energy than is needed to eject an electron from the most tightly bound state in the 2DES. Based on its energy as a function of the 2D electron density and behavior when a magnetic field is applied, we identify this excitation as a hole in the 2DES coupled to a plasmon. Such a ``plasmaron'' has been predicted in calculations of the density of states for 3D [1] and 2D [2] electron gases, but it has never been definitively observed. These spectra may represent the first observation of this long-predicted quasiparticle in the 2DES. [1] L. Hedin, B.I. Lundqvist, and S. Lunqvist. Solid State Comm. 5, 237–239 (1967). [2] P. von Allmen. Phys. Rev. B 46, 13345 (1992).   

Effects of finite layer thickness on the differential capacitance of electron bilayers

We have calculated the effects of the finite thickness of electron or hole layers in double-quantum-well systems on the complete set of differential capacitances that can be measured in double-layer electron systems, with or without separately contactable layers.~ We~present results for~the regime of negligible interlayer tunneling, zero applied magnetic field, and low layer densities, when the compressibility of~one or~both layers is negative.