Session V12: Transport in 2-D Systems

In-Plane Field Magneto-transport in a Six-fold Degenerate Si-(111) 2DEG

In-plane magneto-transport is an effective tool for measuring sub-band occupancy and differentiating between effects such as the so-called ``reentrant Metal-Insulator Transition'' or a ferromagnetic to paramagnetic phase transition. Using a two-dimensional electron gas (2DEG) on high mobility (up to $100,000$ cm$^2/$Vs) hydrogen terminated Si-(111) surfaces [1], we have studied the magneto-resistance due to in-plane magnetic fields of this six-fold degenerate system. While high perpendicular field (up to 12 T) measurements indicate field-dependent valley splitting, parallel field data helps differentiate this dependence from spin dynamics. The application of an in-plane field polarizes the 2DEG into distinct sub-bands. I will present measurements of both spin and valley sub-band polarization in parallel magnetic fields from samples of various mobility ($10,000 - 100,000$ cm$^2/$Vs) and discuss these results in the context of the broader question of field-dependent valley splitting. In a simple picture of valley splitting on Si-(111) surfaces, one would expect two valley polarization fields in addition to the spin polarization. I will discuss how this interaction-free model fits with the perpendicular field measurements, and what we can learn about the six-fold degenerate system.\\[0pt] [1] R. N. McFarland et al., {\it Phys.~Rev.~B} {\bf 80} 161310R (2009)   

Zero Differential Resistance State in double GaAs quantum wells at high filling factors

Differential resistance $r_{xx}$ of 2D electrons was investigated in double GaAs quantum wells placed in magnetic fields $B<0.5$ (T) at temperatures $T=1.6-4.2$ (K). Electron state with Zero Differential Resistance (ZDR) is found in finite current range at maximums of inter-subband quantum oscillations. The experiment shows that the ZDR state exists at $2R_cE_H/ \hbar \omega_c < 1/2$, where $R_c$ is electron cyclotron radius at Fermi level, $E_H$ is Hall electric field, induced by the $dc$ bias, and $\omega_c$ is cyclotron frequency.\\[4pt] [1] A.A. Bykov, E. G. Mosulev and S. A. Vitkalov, JETP Letters v92, (2010) to be published   

Degenerate versus semi-degenerate transport in a correlated 2D hole system

It has been puzzling that the resistivity of high mobility two-dimensional (2D) carrier systems in semiconductors with low carrier density often exhibits a large increase followed by a decrease when the temperature ($T)$ is raised above a characteristic temperature comparable with the Fermi temperature ($T_{F})$. We find that the metallic 2D hole system (2DHS) in GaAs quantum well (QW) has a linear density ($p)$ dependent conductivity, \textit{$\sigma \approx $e$\mu $}$^{\ast }(p-p_{0})$, in both the degenerate ($T <T_{F})$ is originated from the reduced $p_{0}$, the density of immobile carriers in a two-phase picture. Quantum oscillations in the magneto-resistivity are also found to persist into the semi-degenerate regime in our strongly correlated 2DHS.   

Nonlinear transport in very high Landau levels of a high mobility quantum Hall systems

When a dc current is passed through a high-mobility two-dimensional electron system its differential resistivity exhibits oscillations with the applied magnetic field. The minima of these oscillations can extend all the way to zero leading to states with zero-differential resistance. This talk will discuss our recent experiments studying the evolution of the differential resistivity with temperature and with perpendicular and in-plane magnetic fields.   

Charge carrier velocity distribution in amorphous oxide field-effect transistors

Charge transport in field-effect transistors (FETs) and the underlying physical mechanisms have been the subjects of numerous studies. Many types of transistors have been studied utilizing organic/polymer, amorphous silicon, and thin-film inorganic active layers. Most of these studies involve the evaluation of charge carrier mobility from steady-state characteristics as a function of temperature, electric field, channel dimensions, etc. In this study, we describe a technique to measure the velocity distribution of charge carriers in a thin-film transistor. We use this technique to evaluate velocity distributions in zinc-tin oxide (ZTO) thin-film transistors at various temperatures. In ZTO FETs, we observe multiple distinct transport pathways, each with a distinct activation energy. In contrast, steady state measurements yield a single activation energy. This shows that new insights into charge transport mechanisms and phenomena can be obtained with such time-resolved transport measurements which are not possible with steady-state approaches.   

Electronic Transport Properties of Epitaxial ZnO Films by Electron Dephasing and Mobility Spectrum Analysis

Epitaxial ZnO films were grown by pulsed laser deposition on (111) Si substrates with bixbyite oxide buffers. Carrier transport properties were investigated using Hall measurements (4--300 K) under magnetic fields of 0--10 T, indicating mobility up to 113 cm$^{2}$/Vs. A diffusive Fermi surface (DFS) model incorporating electron dephasing theories was used to fit the abnormally positive magneto-conductivity observed below 150 K. Quantitative mobility spectrum analysis revealed the presence of a hole group at lower mobility accompanying the major electron group. Geometric distribution of the conducting groups was examined by capacitance-frequency experiments, while both temperature-dependent photoluminescence and mobility fitting confirmed a donor binding energy of $\sim$60 meV.   

Response of the Cyclotron Harmonic Spike to an In-Plane Magnetic Field

Microwave-induced resistance oscillations (MIRO) have been commonly observed in high- mobility GaAs/AlGaAs two-dimensional electrons systems (2DES) under microwave irradiations. In ultraclean GaAs/AlGaAs quantum wells (mobility $\sim 3.0\times 10^7cm^2/Vs)$ we have recently observed an extraordinary resistance spike at the second harmonic of cyclotron resonance. In order to elucidate its origin, we have studied the response of microwave photoresistances in a two-axis magnetic field configuration, where the perpendicular (B$_{perp})$ and the in-plane (B$_{//})$ components can be independently applied to the sample. The experiments reveal a distinctive response of the spike to the B$_{//}$ as compared with that of the MIRO. While the major MIRO peaks show an increasing phase-shift towards 0.25 in increasing B$_{//}$, the spike position shows an essentially zero shift. This finding lends additional support for the notion that the spike is a new effect in the microwave-driven 2DES.   

Conductivity kinks in the transport of ultra-dilute GaAs two-dimensional hole systems in zero field

Though Wigner crystal was first observed for electrons on helium in 1979, a Fermi Liquid-to-Wigner crystal transition has never been demonstrated. Important questions on how interaction drives such a transition and the nature of the transition remain unanswered. Apart from the complexity associated with the disorder which competes with or even dominates interaction by rendering the system into an Anderson insulator, an important question is whether there exists intermediate phases that hinder a direct first order transition. We report findings obtained via measuring ultra-high-purity GaAs two-dimensional hole systems with dilute charge concentrations down to 8x10$^{8}$ cm$^{-2}$. For fixed charge densities below 4x10$^{9}$cm$^{-2}$, a conductivity ($\sigma )$ kink is observed while sweeping the temperature across some characteristic value where the derivative d$\sigma $/dT exhibits a discontinuous step. For charge densities above 4x10$^{9}$cm$^{-2}$, the kink evolves into a dip which diminishes for charge densities beyond 7x10$^{9}$cm$^{-2}$. A possible first order phase transition will be discussed.   

The Zero-Resistance States in InN Films

InN is a narrow gap semiconductor which possesses interesting transport properties. Besides the 2D electron accumulation layer on the surface, low temperature zero-resistance states have been observed in InN thin films and attributed to superconductivity. In order to elucidate the origin of superconductivity, we have studied systematically the temperature and magnetic field dependences of resistance in InN films of various thicknesses. High quality InN film samples of thickness between 50 nm and 5 $\mu $m were grown by molecular beam epitaxy on Al$_{2}$O$_{3}$ substrate with a GaN buffer layer. Typically these films have an electron density of 3x10$^{17}$- 6 x10$^{18}$ cm$^{-3}$, and the mobility between 1000-2400 cm$^{2}$/Vs at 300 mK. Zero-resistance states were observed in films of thickness above 1 $\mu $m with the transition temperature of $\sim $ 1K, along with marked nonlinear I-V characteristics suggesting the presence of supercurrent. We observed anisotropic dependences of resistance on in-plane magnetic fields with respect to the direction of applied current. This work in Rice was supported by NSF DMR-0706634 and Welch Foundation C-1682, in Peking University was supported by the NSFC of China (Nos. 60990313, 10774001), and RFDP (No. 20090001120008).   

Electron interaction effects on Aharonov-Bohm resonances in an antidot-based quantum Hall interferometer

We theoretically study the electron interaction effects on Aharonov-Bohm resonances in an antidot-based quantum Hall interferometer in the integer quantum Hall regime. We introduce a general capacitive interaction model for an antidot with multiple bound modes of edge states, and find that the pattern of Aharonov-Bohm resonances is governed by the spectator behavior: The resonances of some modes disappear and instead are replaced by those of the other modes, due to charge relaxation between bound modes in the cotunneling regime. This behavior gives a reasonable understanding on the nontrivial features of previous experimental data, e.g., spectator behavior in an antidot molecule and resonance peaks in a single antidot with two, three, or four modes. References:\\[4pt] [1] W.-R. Lee and H.-S. Sim, Phys. Rev. Lett. 104, 196802 (2010);\\[0pt] [2] W.-R. Lee and H.-S. Sim, arXiv: 1009.1004.   

Effective interlayer charge transfer in an electron bilayer system

An electron bilayer system is realized in a wide GaAs quantum well. The chemical potentials of both layers can be tuned by intrinsic back and top gates. The Landau level spectrum for various charge distributions is probed by photoluminescence (PL), able to discriminate between both layers independently. The PL spectra show unambiguously how the system spontaneously deforms itself in strong magnetic fields as a consequence of energy minimization under Landau quantization and huge SAS energy gaps, reaching up to the cyclotron energy, become visible in the PL spectra [1]. \\[4pt] [1] V.V. Solovyev, S. Schmult, W. Dietsche, I.V. Kukushkin, PRB 80, 241310, 2009.   

Exciton condensates in Pfaffian Quantum Hall states

We apply recently developed (arXiv:1004.3657) conformal field theory techniques to describe exciton condensates in non-abeliann quantum Hall states of the Pfaffian type.   

Spin-full quantum Hall states: squeezing techniques

Despite the high magnetic field does the spin of the electron play an important role in the quantum Hall effect. Various spin (singlet) quantum Hall states have been proposed to explain various observed quantum Hall plateaux. In this talk, we present a method to generate spin-full quantum Hall states, by employing a squeezing procedure, as is used in the polarized state. This squeezing procedure also sheds additional light on the underlying (topological) structure of such states. By using connections between polarized and un-polarized states, one gains insight in the polarized state, as is the case for the Haffnian and Haldane-Rezayi states.   

Spin polarization measurement of the $\nu $ = 5/2 fractional quantum Hall state via NMR

The $\nu $ = 5/2 fractional quantum Hall state has attracted much interest due to its possible non-Abelian statistics, which are expected for the \textit{Pfaffian} state. While the \textit{Pfaffian} model assumes full spin polarization, recent optical experiments suggest a spin-unpolarized ground state at $\nu $ = 5/2 instead [1, 2], and have thus posed a new challenge for understanding the true nature of the 5/2 state. Here, we report a spin polarization measurement of the $\nu $ = 5/2 state using resistively-detected NMR and demonstrate its full polarization. The measurements were performed at $T$ = 10 mK on a gated 30-nm quantum well at 4.4 T. For the resistive read-out of the nuclear resonance frequencies, we used the $\nu $ = 2/3 spin transition by comparing its $R_{xx}$ prior to and after the application of an \textit{rf} pulse at $\nu $ = 5/2. The NMR spectrum at $\nu $ = 5/2 is shifted to lower frequencies from the one at $\nu $ = 2, where the system is unpolarized, indicating a nonzero polarization at $\nu $ = 5/2. Our analysis, which considers the changes of the sub-band wave function under a gate bias, indicates that the polarization at $\nu $ = 5/2 is very close to its maximal value. This, in turn, gives support for the Pfaffian state.\\[0pt] [1] T. D. Rhone, APS March Meeting 2010, Y2.00003 [2], M. Stern \textit{et al}., Phys. Rev. Lett. \textbf{105}, 096801 (2010).   

Observation of a Well-Developed $\nu $ = 5/2 Fractional Quantum Hall State in Low-Mobility Electron Systems

The fractional quantum Hall (FQH) state at filling factor 5/2 is currently one of the hottest issues in FQH physics. This is mainly due to the predicted non-Abelian statistics of its quasiparticles and their possible implementation in quantum computation. However, experimental efforts to explore the 5/2 FQH state are severely hampered by the extremely high sample quality required for its emergence. Indeed, well-developed 5/2 FQH states have been reported only in samples with an ultra high mobility in excess of 1x10$^{7}$ cm$^{2}$/Vs. Here, we report the observation of a fully developed 5/2 FQH state in a GaAs/Al$_{x}$Ga$_{1-x}$As quantum well with a mobility of 4.8x10$^{6}$ cm$^{2}$/Vs, which was established after illumination at low temperatures by a red LED. To clarify the mechanism underlying the emergence of the 5/2 state, we carried out a systematic study on a series of samples with different parameters. Our study unveils that the screening of the remote impurity (RI) potential by the nearby neutral donors in the modulation doping layer plays the essential role. We also find that while the emergence of the 5/2 state is governed by the RI potential, once this state has emerged, the energy gap at 5/2 is still limited by the background impurity potential. Based on the analysis of the transport and quantum lifetimes, the relation between the 5/2 gap and these parameters will be discussed.