Session A21: Semiconductors: 2D Electrons and Transport

Temperature dependence of microwave photoresistance in 2D electron systems

We report on studies of the temperature dependence of microwave- induced resistance oscillations in a high-mobility two- dimensional electron system. We find that the oscillations decay exponentially with increasing temperature, as $\exp(- \alpha T^2)$, where $\alpha$ scales with the inverse magnetic field. This observation suggests that the temperature dependence originates {\em primarily} from the modification of the single particle lifetime, likely through electron-electron interaction effects. The relevance of our findings to existing theories will be discussed.   

Temperature dependence of Hall-field induced resistance oscillations in 2D Electron Systems

A few years ago a new class of resistance oscillations was discovered in two-dimensional electron systems subject to weak magnetic fields and strong dc electric fields [1]. These oscillations, termed Hall field induced resistance oscillations (HIRO), are believed to originate from commensurability between the cyclotron diameter and real-space separation between Hall field tilted Landau levels. Here, we study temperature dependence of these oscillations in a very-high mobility two-dimensional electron system. Our results suggest that, in contrast to Shubnikov-de Haas effect, HIRO are sensitive to electron-electron interactions modifying the single particle lifetime. [1] C. L. Yang, J. Zhang, R. R. Du, J. A. Simmons, and J. L. Reno, Phys. Rev. Lett. {\bf 89}, 076801 (2002)   

Non-linear transport in microwave-irradiated 2D electron systems at the cyclotron resonance subharmonics

We study microwave photoresistivity oscillations in a high mobility two-dimensional electron system subject to strong dc electric fields. We find [1] that near the second subharmonic of the cyclotron resonance the frequency of the resistivity oscillations with dc electric field is twice the frequency of the oscillations at the cyclotron resonance, its harmonics, or in the absence of microwave radiation. This observation is discussed in terms of the microwave-induced sidebands in the density of states and the interplay between different scattering processes in the separated Landau level regime. [1] A.~T.~Hatke, H.-S. Chiang, M.~A.~Zudov, L.~N.~Pfeiffer, and K.~W.~West, Phys. Rev. Lett. accepted for publication.   

Observation of Fractional Microwave-Induced Resistance Oscillations using Co-Planar Waveguide on High-Mobility 2DES

The microwave-induced resistance oscillations (MIRO) are commonly observed in high-mobility GaAs 2D electron systems (2DES) irradiated by microwaves. Usually this is accomplished using an antenna or waveguide, where the electromagnetic components (E$_{\omega }$ and H$_{\omega })$ coincide with the 2DES plane. We explore MIRO in a co-planar waveguide (CPW) geometry, in which E$_{\omega }$ is the dominant excitation component in the 2DES plane. Our samples are Hall bars of high-mobility, $\mu $= (6 - 12) $\times $10$^{6}$ cm$^{2}$/Vs, GaAs/Al$_{x}$Ga$_{1-x}$As quantum wells with electron densities ranging from 3 to 5 $\times $10$^{11}$cm$^{-2}$. Microwaves from a tunable source (2 - 40 GHz) were fed in, via a semi-rigid coax cable, to an impedance-matched CPW across the length of the Hall bar, and brought out via a similar semi-rigid coax to a power sensor. Using this CPW geometry, we are able to simultaneously measure the photoconductivity and the microwave transmission across the sample. In a temperature range of 2.0 K - 5.0 K, we observed fractional MIRO associated with $\varepsilon $ =1/2, 1/3, 1/4, and 1/5, 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.   

Photoconductivity of a 2D electron gas at large filling factors

We study non-equilibrium dc conductivity of a 2D electron gas, placed in a classically strong perpendicular magnetic field in the presence of in-plane microwave field and generic Gaussian disorder potential. Focusing the consideration on the bilinear response in the microwave field, we identify four different mechanisms essential for the linear dc resistance. We employ two specific models of the disorder relevant for ultra-high mobility samples and show that the relative strength of the above mechanisms strongly depends on the spatial range of the disorder potential. In particular, when large angle scattering dominates the transport and temperature is sufficiently high, the contribution of the ``displacement'' mechanism can overcome the ``inelastic'' contribution, which is dominant at low temperature. For smooth disorder, characterized by small angle scattering, the ``displacement'' contribution is strongly suppressed. Other contributions are responsible for the microwave-induced corrections to the non-diagonal part of the conductivity tensor and only weakly depend on the nature of the disorder. We discuss the ways to distinguish experimentally the contributions of the above mechanisms according to their different polarization and temperature dependence.   

Warming in systems with discrete spectrum: spectral diffusion of two dimensional electrons in magnetic field

Warming in complex physical systems, in particular global warming, attracts significant contemporary interest. It is essential, therefore, to understand basic physical mechanisms leading to overheating. It is well known that application of an electric field to conductors heats electric charge carriers. Often an elevated electron temperature describes the result of the heating. This paper demonstrates that an electric field applied to a conductor with discrete electron spectrum produces a non-equilibrium electron distribution, which cannot be described by temperature. Such electron distribution changes dramatically the conductivity of highly mobile two dimensional electrons in a magnetic field, forcing them into a state with a zero differential resistance. Most importantly the results demonstrate that, in general, the effective overheating in the systems with discrete spectrum is significantly stronger than the one in systems with continuous and homogeneous distribution of the energy levels at the same input power.   

Effect of parallel magnetic field on the zero-differential resistance state

The non-linear zero-differential resistance state (ZDRS) that occurs for highly mobile two-dimensional electron systems in response to a dc bias in the presence of a strong magnetic field applied perpendicular to the electron plane is suppressed and disappears gradually as the magnetic field is tilted away from the perpendicular at fixed filling factor $\nu$. Good agreement is found with a model that considers the effect of the Zeeman splitting of Landau levels enhanced by the in-plane component of the magnetic field.   

Magnetoresistance of two-dimensional electrons in Si/SiGe quantum wells in in-plane magnet field at 20 mK

We have measured the magnetoresistance of two-dimensional electrons in two modulation-doped Si/SiGe quantum wells in an in-plane magnetic field at 20mK. It was found that the ratio of the saturation resistance in high in-plane magnetic field to the zero-magnetic-field resistance is dependent on the electron density. At high electron density, the ratio is approximately 1.8. As the electron density decreases and is close to the metal-insulator transition, the ratio is strongly enhanced and appears diverging at a sample dependent characteristic density. The field at which the magnetoresistance saturates as a function of density is linear at high density. It deviates from this linear dependence and appears to extrapolate to zero when the electron density is below $\sim $0.7x10$^{11}$/cm$^{2}$.   

Electron and Hole Transport in 40 MilliKelvin Germanium $<100>$

Ultrapure germanium at milliKelvin temperatures presents a charge transport regime which is rarely encountered. In this case, thermal phonons play a negligible role and the scattering of electrons and holes is dominated by spontaneous phonon emission. As these carriers are always hot, typical assumptions of thermal equilibrium are no longer valid. Furthermore, for fields of only a few $V/cm$, the emission of optical and intervalley phonons is highly inelastic such that carrier distributions may differ substantially from the form of a displaced Maxwellian. We present simulation results of transport processes of carriers in germanium $<100>$ at a temperature of $40 ~mK$. These studies were performed in order to provide a deeper understanding of processes occurring in detectors of the Cryogenic Dark Matter Search (CDMS), which seeks to detect weakly-interacting massive particles (WIMPs) in the halo of our galaxy. As CDMS measures both the ionized charge and the energy in non-thermalized phonons created by particle interactions, we will describe the applicability of these transport simulation results to a wide variety of measured phenomena.   

Magnetotransport in Zener Tunneling Regime in a High-Mobility Two-Dimensional Hole System

Magnetotransport in two-dimensional electron systems (2DES) under a DC-current bias has recently revealed a number of interesting phenomena, including current-induced Zener oscillations [1] and current-induced spin-polarization in Rashba 2DES. We have measured the DC-current induced magnetotransport in high-mobility 2D holes in a C-doped (100) GaAs/Al$_{0.4}$Ga$_{0.6}$As quantum well (QW). The QW has a width of 15 nm and a carrier density p $\sim $ 2 x 10$^{11}$/cm$^{2 }$and a mobility $\mu $= 7 x 10$^{5}$ cm$^{2}$/Vs at T = 300 mK. We observe sharp features in the differential resistance, which we interpret as the Zener tunneling peak and valley associated with commensuration transition of Landau orbits. In a gated Hall bar we are able to tune the carrier density to p $>$ 2.6 x 10$^{11}$/cm$^{2}$, and observe strong positive magnetoresistance, which can be attributed to the inter-subband scattering with light holes. We will discuss the roles that electron - electron scattering plays in the Zener oscillations observed in electron and hole systems. The work at Rice was supported by NSF DMR-0706634. [1] C. L. Yang et al, Phys. Rev. Lett. 89, 076801 (2002).   

Strongly Temperature-dependent Compressibility of Dilute 2D Holes near the Metal-Insulator Transition

We used the capacitance measurement to study the compressibility of dilute 2D holes in a 10nm wide GaAs quantum well for $T$=0.01-0.7K. The sample exhibits the $B$=0 metal-insulator transition (MIT) at a critical density $p_{c} \quad \sim $ 1.0 $\times $ 10$^{10 }$/cm$^{2}$. Deep in the metallic state, the sample capacitance decreases slowly as hole density $p$ increases, due to the (negative) exchange contribution to the compressibility of an interacting 2D system. As $p$ is reduced below $p_{c}$ at low-$T$, the capacitance of sample diminishes rapidly as a result of the incompressible nature of the insulator state, similar to previous studies (Dultz and Jiang, PRL 84, 4689 (2000); Allison et al., PRL 96, 216407 (2006)). On the other hand, we found that temperature has a strong effect near the MIT, in contrast to literature. In our system, the compressibility of insulator state increases with $T$ and remains positive, while the behavior of metallic phase is more complex. Notably, for metallic phase with $p$ slightly above $p_{c}$, the sign of compressibility can change from positive to negative as $T$ increases. This strongly $T$-dependent compressibility is possibly related to the competition between two phases with distinctive compressibility in our system, which is more strongly interacting than samples studied previously.   

Branched flow and caustics in random media with magnetic fields

Classical particles as well as quantum mechanical waves exhibit complex behaviour when propagating through random media. One of the dominant features of the dynamics in correlated, weak disorder potentials is the branching of the flow. This can be observed in several physical systems, most notably in the electron flow in two-dimensional electron gases {[}1], and has also been used to describe the formation of freak waves {[}2]. We present advances in the theoretical understanding and numerical simulation of classical branched flows in magnetic fields. In particular, we study branching statistics and branch density profiles. Our results have direct consequences for experiments which measure transport properties in electronic systems {[}3].\\ \\ {[}1] e.g. M. A. Topinka \emph{et al}., Nature \textbf{410}, 183 (2001), M. P. Jura \emph{et al.}, Nature Physics \textbf{3}, 841 (2007)\\ {[}2] E. J. Heller, L. Kaplan and A. Dahlen, J. Geophys. Res., \textbf{113}, C09023 (2008)\\ {[}3] J. J. Metzger, R. Fleischmann and T. Geisel, \emph{in preparation}   

Possible competing ground states in high mobility electron-hole bilayers

Recently it has become possible to fabricate independently contacted high mobility electron-hole bilayers (EHBL) with densities $<5\times10^{10}{\rm cm}^{-2}$ and a separation 10-20 nm in a GaAs/AlGaAs system. In these EHBLs the interlayer interaction can be stronger than the intralayer interactions. Excitonic superfluidity in such EHBLs was first predicted almost forty years ago. Since then theoretical works have indicated the possibility of a very rich phase diagram, containing a superfluid, charge density waves, Wigner crystals and a BCS-BEC crossover. However this system has been extremely difficult to fabricate in practice. Very recent experiments have revealed novel features in the interlayer scattering (Coulomb drag) below $\sim 1{\rm K}$. The Coulomb drag shows strong non-monotonic deviations from a $\sim T^2$ behaviour expected for Fermi-liquids at low temperatures. Simultaneously an insulating behaviour in the single layer resistances also appears in both layers inspite of electron mobilities $> 10^6{\rm cm}^{2}{\rm V}^{- 1}{\rm s}^{-1}$ and hole mobilities $> 10^5{\rm cm}^{2}{\rm V}^{-1}{\rm s}^{-1}$. The experimental results may indicate a competition between an excitonic ground state and charge-density- waves. [J. Keogh {\it et al} APL, 87,202104 (2005). A.F.Croxall {\it et al} arXiv:0807.0117 (to appear in JAP), A.F. Croxall {\it et al} arXiv:0807.0134v3 (to appear in PRL)]   

Anomalous plateau formation and improved quantization in charge pumping under the application of a perpendicular magnetic field

We present experimental results of high frequency quantized charge pumping through a quantum dot formed by the electric field arising from applied voltages in a GaAs/AlGaAs system in the presence of a perpendicular magnetic field $B$. Improved quantization and robustness in gate voltage are seen as $B$ is increased. Under application of even higher $B$ fields, the formation of anomalous plateaus in the pumped current are seen.   

Thermal transport size effects in self-assembled Germanium quantum dots in single-crystal silicon

Superlattices with low thermal conductivity have been used to design 1-D thermoelectric materials. With them, it is challenging to obtain a thermoelectric figure of merit \textit{ZT} $>$ 1. Self-assembly is used to fabricate Ge quantum-dot (QD) arrays. High \textit{ZT} is expected in these self-assembled Ge QDs arrays in Si since they are single crystals. We prove that high-density 3-D Ge QD arrays in diamond-cubic Si exhibit low thermal conductivity. This property can be used to design 3-D thermoelectric devices. To study the thermal behavior of these 3-D `phononic crystal' nanocomposites, we create an atomistic model of a supercell consisting of Si unit cells. Inside each supercell, we substitute Si atoms with Ge atoms to form a QD. The thermal conductivity has been shown to reduce below 0.2 W/m/K. Such a result is realized by ensuring minimum group velocities. Further reduction is expected from multiple scattering. We are concerned with the size dependence of the thermal conductivity upon the Ge volumic composition $f$. From preliminary results with constant $f$, we obtain an exponential-like thermal-conductivity decrease when the supercell size is increased.