Bulletin of the American Physical Society
2006 APS March Meeting
Monday–Friday, March 13–17, 2006; Baltimore, MD
Session V1: Quantum Hall Edges |
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Sponsoring Units: DCMP Chair: Woowon Kang, University of Chicago Room: Baltimore Convention Center Ballroom IV |
Thursday, March 16, 2006 11:15AM - 11:51AM |
V1.00001: Bending the quantum Hall effect: Novel metallic and insulating states in one dimension Invited Speaker: One-dimensional conductors are the wires that will connect the circuits of tomorrow's nanoworld, so it is important to characterize their possible conducting phases. We study a novel one-dimensional wire state which arises at the corner of two quantum Hall systems joined at a 90 degree angle, and observe one-dimensional metallic and insulating states. Such non-planar confinement structures are unconventional for the quantum Hall effect and reveal the striking observation of a macroscopic one- dimensional state whose conductance increases with decreasing temperature. This single system can map out generic properties of disordered one-dimensional conductors since the metallic, critical, or insulating character is tunable with an external parameter, the magnetic field. [Preview Abstract] |
Thursday, March 16, 2006 11:51AM - 12:27PM |
V1.00002: Coupled Luttinger Liquid State in Quantum Hall Line Junction Invited Speaker: We report on tunneling spectroscopy of quantum Hall tunnel junctions that juxtaposes two counterpropagating edge states across a high quality tunnel barrier. As the only current-carrying excitation of quantum Hall effect, edge states possess a unique ability to form robust one-dimensional electronic state along the perimeter of two-dimensional electron system. In our tunnel junctions, produced by cleaved edge overgrowth, the two edge states are laterally separated by an in-plane semiconductor barrier on the order of magnetic length and interact strongly over a junction that is $\sim 100 \mu m$ long. Due to the quality of the tunnel barrier and the ballistic property of the edge states, inter-edge electron-electron interaction effects become predominant and disorder plays a negligible role to the leading order. Tunneling strongly mix the single particle states from two chiral one-dimensional systems, and the inter- edge correlation transforms the two counterpropagating edge states into a system of coupled, non- chiral Luttinger liquid whose Luttinger liquid properties are continuously tuned by magnetic field through the filling factor $\nu$ of the bulk quantum Hall state. The tunneling density of states of this many-body state possesses a power- law dependence on energy with an exponent $\alpha$, that is inversely proportional to the bulk filling factor, $\alpha \sim 1/\nu$. Inter-edge correlation also manifests in a series of quantum critical points between successive strong and weak tunneling regimes that are reminiscent of the plateau-transitions in quantum Hall effect. Tunneling spectroscopy consequently provides a direct probe of the quantum order underlying within these highly correlated one-dimensional states. [Preview Abstract] |
Thursday, March 16, 2006 12:27PM - 1:03PM |
V1.00003: Universality of the Edge-Tunneling Exponent of Fractional Quantum Hall Liquids Invited Speaker: Fractional quantum Hall states are characterized by their topological order. For example, the edge physics is uniquely determined by the bulk and gives a non-Ohmic relation $I\propto V^\alpha$ for tunneling into the edge, where the exponent $\alpha$ is a universal constant. In the simplest case of filling factors $\nu=n/(np+1)$, ($n$ and $p$ are integers $>0$, $p$ even) the exponent is $p+1$. However, experiments show substantial deviations. In a microscopic model of fractional quantum Hall liquids, we calculate the edge Green’s function by exact diagonalization and obtain the exponent $\alpha$. We consider the 1/3 and 2/3 states with the Coulomb interaction and a variety of edge confining potentials. We find that the form of the confinement, such as sharpness of the edge and/or the strength of the confining potential which could lead to edge reconstruction, may cause deviations from universality in the edge-tunneling I-V exponent. We study two types of edge potentials: a sharp edge induced by a cut-off of angular momentum beyond $m_{max}$) and one induced by a uniform neutralizing background charge (a distance $d$ from the 2-d layer). Without the background charge, the exponent retains its universal value for soft edges (large $m_{max}$) but is non-universal for hard edges. In the presence of background charge and strong confinement (small $d$), the exponent is universal even for hard edges; for weak confinement and hard edges there is a deviation from the universal value while for soft edges there are finite-size corrections to $\alpha$, consistent with the edge reconstruction scenario. The relation of these results to experiments will be discussed. [Preview Abstract] |
Thursday, March 16, 2006 1:03PM - 1:39PM |
V1.00004: Particle-hole symmetry and Luttinger liquids in a quantum Hall circuit Invited Speaker: I shall present recent experimental results on edge-state transport through quantum point contacts in the quantum Hall (QH) regime. Finite-bias backscattering measurements between edge channels at filling factor $\nu=1$ will be presented at different temperatures. Transport through the constriction displays a non-linear Luttinger-like behavior even in the integer QH regime in contrast with the linear tunneling predicted for integer edge states [1,2]. Both zero-bias enhancement and suppression of the inter-edge tunneling will be shown in a controllable way as a function of gate bias [2,3,4]. The observed evolution is connected to the local charge depletion in the constriction region and offers new insight into the link between QH charge-conjugation and Luttinger liquid description of edge channels [2]. I shall discuss the relevance of these experimental results in the context of the dynamics of the highly-correlated edge channels in the fractional QH regime [5]. Finally I shall demonstrate how charge-conjugation can be exploited in the design of new QH circuits where the transport properties of the hole component of a partially filled Landau level can be directly addressed. \newline \newline [1] X.-G. Wen, Phys. Rev. Lett. {\bf 62}, 2206 (1990); P. Fendley {\em et al.} Phys. Rev. Lett. {\bf 74}, 3005 (1995). \newline [2] S. Roddaro, V. Pellegrini, F. Beltram, L. N. Pfeiffer, K. W. West, Phys. Rev. Lett. {\bf 95}, 156804 (2005). \newline [3] S. Roddaro, V. Pellegrini, F. Beltram, G. Biasiol, L. Sorba., Phys. Rev. Lett. {\bf 93}, 046801 (2004). \newline [4] S. Roddaro, V. Pellegrini, F. Beltram, G. Biasiol, L. Sorba, R. Raimondi, G. Vignale, Phys. Rev. Lett. {\bf 90}, 046805 (2003). \newline [5] A. M. Chang, Rev. Mod. Phys. {\bf 75}, 1449 (2003). [Preview Abstract] |
Thursday, March 16, 2006 1:39PM - 2:15PM |
V1.00005: Edge State Tunneling in Split Hall Bar Models Invited Speaker: Edge states of Quantum Hall systems offer a rich ground for testing theoretical predictions on the properties of 1D strongly interacting fermionic systems. More importantly they are considered clean realizations the Luttinger Liquid description. In the past two years we [1,2,3,4] have examined a number of models that attempt to describe coupled edge density waves in the quantum Hall regime in various different geometries and to confront the large number of experimental observations that are at odds with the models that have been thought to apply in the past. Work that is currently in progress attempts to explain experimental results of the Pisa experimental group in which tunneling through a constriction between incompressible quantum Hall edge states is tuned from relevance to irrelevance by adjusting a gate voltage. This property is explained in terms of an interplay of the change in the connectivity of multi-mode edge magnetosplasmon and the role played by the metallic gates on the structure of the edge state, as well as the interactions between the edges. I will talk also for unresolved questions that have appeared in recent experiments in quantum Hall systems divided by thin cleaved-edge-overgrowth barriers. An important difficulty that arises in interpreting transport properties of QH line junction systems is the uncertainty about the strength and sometimes even the sign of these interactions, which can be difficult to estimate because of subtleties in understanding their relationship to underlying Coulombic interactions, because of edge reconstruction or because of the role played by the nearby metallic gates. We propose theoretical ideas and experimental measurements to obtain the required information. 1. E. Papa, and A. H. MacDonald, Phys. Rev. Lett. 93, 126801 (2004) 2. E. Papa, and A. H. MacDonald, Phys. Rev. B 72, 045324 (2005) 3. W.-C. Lee, N. A. Sinitsyn, E. Papa, and A. H. MacDonald, Phys. Rev. B 72, 121304 (2005) 4. E. Papa, and T. Stroh, in preparation [Preview Abstract] |
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