Session V24: Low-Dimensional Semiconductors

1/f Noise in Delta Doped GaAs/AlGaAs Heterostructures

We studied $1/f$ noise of a two-dimensional electron gases (2DEG) in $\delta$-doped $GaAs/Al_{x}Ga_{1-x}As$ heterostructures. Three samples that we measured were identical except for the $\delta$-doping concentration: $9.1\times10^{18}(cm^{-2})$(high), $1.3\times10^{18}(cm^{-2})$(medium), $0.3\times10^{18}(cm^{-2})$(low). These $\delta$-doping layers are located in the $Al_{x}Ga_{1-x}As$ region, $800\AA$ above the $GaAs$ and $Al_{x}Ga_{1-x}As$ interface. We fabricated Corbino and Hall bar structures with different sizes. Carrier density was varied by the persistent photoconductivity effect at low temperature (4.2K). Initially, the samples did not exhibit measurable $1/f$ noise. The high $\delta$-doping concentration samples exhibited parallel conduction. As we increased the carrier concentration in the high and medium-doped samples, $1/f$ noised increased initially, but disappeared as the photo current was saturated. The low-doped samples did not exhibit $1/f$ noise as the carrier concentration was increased. We conclude that $1/f$ noise is caused by the remote ionized impurities in the $\delta$-doped region. Also, changing the DX-center configuration changes the density of the ionized impurities, which then changes the magnitude of $1/f$ noise.   

Conductance noise in a strongly disordered 2D electron system in Si MOSFETs

Studies have shown that the metal-insulator transition (MIT) in a 2DES in Si MOSFETs is closely related to the glassy freezing of electrons as temperature $T\rightarrow0$. However, no glassy relaxations were seen after a $T$ quench. Here we first study the effect of cooling in detail: the carrier density $n_s$ is changed at a high $T\approx 20$~K, the system is then cooled to a desired $T$ with a fixed $n_s$, and fluctuations of conductance $G$ with time are measured. The analysis of the noise power spectra $S_G \propto 1/f^{\alpha}$ gives evidence for the onset of slow, glassy dynamics near the MIT as $T\rightarrow0$, supporting conclusions obtained with a different protocol. While these noise measurements were done in the Ohmic regime, we have also explored the effect of high excitation voltages, deep into the nonlinear regime, on the noise statistics. The results will be discussed in detail. Finally, we show that sweeping $n_s$ at low enough $T$ results in a reproducible fluctuation pattern of $G(n_s)$. Such a pattern, which reflects a particular realization of disorder, does not change even after warming up to 30~K. This demonstrates that the disorder does not change at low $T$, and that the observed non-Gaussianity of the noise reflects the intrinsic glassiness of the 2DES.   

Extended States and Critical Behavior in 2D and 3D Amorphous Conductors

With a tight binding treatment for one, two and three dimensional systems, we calculate and analyze electronic states in a conductor with topological disorder, or no correlations among the positions of the hopping sites. The Inverse Participation Ratio (IPR) is used to characterize carrier wave functions with respect to localization. We consider an exponentially decaying hopping integral with range (or ``Bohr radius'') $l$. Using two complementary finite size scaling techniques to extrapolate to the bulk limit (both methods exploit critical behavior in different ways to locate the energy marking the boundary between extended and localized wave functions) which nevertheless yield identical results, we obtain phase diagrams showing regions where states are extended and domains of localized states. We find exclusively localized wave functions for 1D geometries, irrespective of $l$. In the 2D case, states are localized below a threshold length scale $l_{c} \approx 1.0$, with a finite fraction of states extended for $l > l_{c}$. For 3D systems, the extended phase is flanked by regions of localized states and bounded by two mobility edges. The swath of extended states, broad for $l \sim 1$, becomes narrower with decreasing $l$, scaling asymptotically as $e^{-A/l}$ for $l \ll 1$.   

The disappearance of weak localization in a strongly correlated 2D hole system

The origin of Metal-Insulator Transition (MIT) in strongly correlated two-dimensional (2D) electrons or holes in semiconductors has long been of great interest. We will present the low temperature (down to 0.05K) transport properties of 10nm GaAs quantum wells with metallic hole densities near the critical point of the 2D MIT (critical density p$_{c }\approx $ 0.8 $\times $ 10$^{10}$cm$^{-2})$. We found that 2D holes exhibit a negative magneto-resistance in small perpendicular magnetic fields, which has been attributed to weak localization in the literature. On the other hand, the magnitude of this negative magneto-resistance is much smaller than conventional 2D weak localization. What is more surprising is that the weak localization induced negative magneto-resistance peak around B=0 becomes weaker at lower temperature, suggesting there is a mechanism causing quasiparticles to lose coherence as temperature decreases.   

Strong negative magnetoresistance in high-mobility 2D electron systems

This talk reports on a remarkably strong negative magnetoresistance effect in high mobility GaAs/AlGaAs heterostructures and quantum wells. The effect is the strongest at about 1 kG where a deep and strongly temperature dependent minimum is observed. At low temperature, the resistivity at this minimum is a small fraction of the zero field resistivity. The talk will discuss the effects of temperature and in-plane magnetic field on this negative magnetoresistance and compare experimental findings with existing theories. A portion of this work was performed at the National High Magnetic Field Laboratory, which is supported by NSF Cooperative Agreement No. DMR-0654118, by the State of Florida, and by the DOE and at the Center for Integrated Nanotechnologies, a U.S. Department of Energy, Office of Basic Energy Sciences user facility. The work at Minnesota was supported by the NSF Grant No. DMR-0548014 and by the DOE Grant No. DE-SC002567. The work at Princeton was partially funded by the Gordon and Betty Moore Foundation and the NSF MRSEC Program through the Princeton Center for Complex Materials (DMR-0819860) and the work at Sandia was supported by the Sandia Corporation under Contract No. DE-AC04-94AL85000. Sandia National Laboratories is a multi-program laboratory managed.   

Nonlinear response of magnetoplasmon resonance

Magnetoplasmon resonances have been observed in microwave photoresistance of Hall bar-shaped two-dimensional electron systems more than two decateds ago. This talk will report on such a resonance in a very high mobility two-dimensional electron gas where it appears as a distinct photoresistivity peak superimposed on a microwave-induced zero-resistance state. In particular, we will discuss the response of this peak to dc electric field. A portion of this work was performed at the National High Magnetic Field Laboratory which is supported by NSF Cooperative Agreement No. DMR-0654118, by the State of Florida, and the DOE. The work at Minnesota was supported by DOE Grant No. DE-SC002567 and NSF Grant No. DMR-0548014. The work at Purdue was supported by DOE grant de-sc0006671.   

Interference effect in magneto-oscillations in two-dimensional system under bichromatic irradiation

We report on the studies of magneto-oscillations caused by bichromatic irradiation in perpendicular magnetic field. Using quantum kinetic method, we have studied the case of $\omega$, $2\omega$, and the case of $\omega$, $3\omega$ frequencies. In the latter case the interference part is shown to produce a phase-sensitive contribution. Also, the final answer depends on the polarizations of the two waves.   

Quantum lifetime of 2D electron in magnetic field

The lifetime of two dimensional electrons in GaAs quantum wells, placed in weak quantizing magnetic fields, is measured using a simple transport method in broad range of temperatures from 0.3 K to 20 K. The temperature variations of the electron lifetime are found to be in good agreement with conventional theory of electron-electron scattering in 2D systems.   

Hall viscosity in lattice models

We present results from our investigations of the Hall viscosity in lattice models. We use the insight gained from these calculations to comment on using the Hall viscosity to characterize gapped quantum fluids.   

Rank Saturation in finite size Entanglement Spectrum for Quantum Hall states

We investigate analytically in finite size the entanglement spectrum arising from real-space cuts for fractional quantum Hall states. We provide a proof that the rank of the reduced density matrix is saturated for the Laughlin state even on finite sizes.   

Magnetic field spectra and many-body correlations of spin 3/2 holes confined to GaAs quantum well

We consider two dimensional spin $3/2$ hole liquid in the presence of a perpendicular magnetic field. Single particle states of Luttinger Hamiltonian are calculated. For the semiclassical limit, the Hamiltonian is separated into the time-symmetric part treated exactly and time-antisymmetric part treated perturbatively. The angular momentum (spin) $3/2$ states are characterized by the Landau level index and parity with respect to reflection about the growth direction. The single-particle spectrum exhibits level-crossings as magnetic field is varied, with or without Rashba and Dresselhaus interactions. The numerical calculations were performed for infinite barrier well, finite size barrier, well doped on one side, symmetrically doped well and parabolic well. Cyclotron mass was calculated and its dependence of the type of structure, magnetic field and symmetry of states is discussed and compared with experimental values. Land\`{e} effective factor is defined and evaluated. Shubnikov-de Haas oscillations are calculated. Electron-electron interactions are accounted using (time-dependent) mean field theories. An interesting effect is a single-well non-homogeneous spin-texture state. Possible implications of shape of hole spectra for fractional quantum Hall states are explored.   

Tunneling spectroscopy of 5/2 fractional quantum Hall excitations in etch defined quantum point contacts

Ever since its discovery the fractional quantum Hall (FQH) state at the even denominator filling fraction v=5/2 has generated immense interests among researchers. 5/2 FQH excitations are believed to obey non-Abelian statistics and posses topological properties making them an ideal candidate for the proposed fault tolerant topological quantum computation. Theoretical proposals to characterize the topological properties of the5/2 state are usually based on confined geometries. In this work we report the characterization of the 5/2 state using quasiparticle tunneling experiments in quantum point contacts (QPC). We have successfully fabricated QPCs on high mobility GaAs/AlGaAs heterostructures using conventional photolithography followed by etching and evaporation of Cr/Au depletion gates. Our samples show very stable FQH plateaus at v = 7/3, 5/2 and 8/3 filling fractions. Tunneling experiments are performed in the QPCs at various temperatures and also at various pinch-off voltages to characterize the effective charge and Coulomb interaction parameters of the quasiparticles. (Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000).   

Quasiparticles and excitons for the Pfaffian quantum Hall state

We propose trial wave functions for quasiparticle and exciton excitations of the Moore-Read Pfaffian fractional quantum Hall states, both for bosons and for fermions, and study these numerically. Our construction of trial wave functions employs a picture of the bosonic Moore-Read state as a symmetrized double layer composite fermion state. We obtain the number of independent angular momentum multiplets of quasiparticle and exciton trial states for systems of up to $20$ electrons. We find that the counting for quasielectrons at large angular momentum on the sphere matches that expected from the CFT which describes the Moore-Read state's boundary theory. In particular, the counting for quasielectrons is the same as for quasiholes, in accordance with the idea that the CFT describing both sides of the FQH plateau should be the same. We also show that our trial wave functions have good overlaps with exact wave functions obtained using various interactions, including second Landau level Coulomb interactions and the $3$-body delta interaction for which the Pfaffian states and their quasiholes are exact ground states.   

Exact results for a fermion chain with fractionalized excitations

We present a number of exact results for a fermion chain with center of mass conservation at $1/3$ filling. The ground state of our model, which is three-fold degenerate even in the case of site dependent interactions, show striking similarities with the superconducting BCS wave functions, the AKLT spin chain, and in particular, with the Laughlin state describing the fractional quantum Hall effect. This state supports exact zero modes with fractional charge slightly below $1/3$ filling, and it has a matrix product representation which enables us to analytically calculate correlation functions, excitation gaps, and the entanglement spectrum. Reference: M. Nakamura, Z.-Y. Wang and E. J. Bergholtz, arXiv:1110.5033   

Polaronic effects in a single modulation doped GaAs quantum well

Absolute magneto-optical transmission measurements have been performed in the far-infra-red range under magnetic fields up to 32 T and at a temperature of 1.8 K on a single modulation doped GaAs quantum well (QW) with a width dw = 13 nm. This QW is sandwiched between two GaAs/AlAs superlattices, the whole epilayer being lift-off from the GaAs substrate and deposited on a wedged Si substrate. The carrier concentration Ns= 3.8 10$^{11}$ cm$^{-2}$ and has a mobility exceeding 10$^{6}$ cm$^{2}$/V/sec at low temperatures. Due to the absence of the GaAs substrate, the magneto-transmission of the sample, mainly governed by the cyclotron (CR) absorption line, can be followed continuously over the whole range of energies. It reveals a strong polaronic interaction with the LO GaAs-phonon: the results can be interpreted quantitatively using the FHIP model [1] and the related conductivity response [2]. \\[4pt] [1] R.P. Feynman, R.W. Hellwarth, C.K. Iddings and P.M. Platzman, Phys. Rev., 127 , 1004 (1962. \\[0pt] [2] F.M. Peeters and J.T. Devreese, Phys. Rev. B, \textbf{28}, 6051 (1983).