The Experts below are selected from a list of 231 Experts worldwide ranked by ideXlab platform
Donna Sheng - One of the best experts on this subject based on the ideXlab platform.
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Many-body localization and Mobility edge in a disordered Heisenberg spin ladder
Physical Review B, 2015Co-Authors: Elliott Baygan, S. P. Lim, Donna ShengAbstract:We examine the interplay of interaction and disorder for a Heisenberg spin ladder system with random fields. We identify many-body localized states based on the entanglement entropy scaling, where delocalized and localized states have volume and area laws, respectively. We first establish the quantum phase transition at a critical random field strength $h_c \sim 8.5\pm 0.5$, where all energy eigenstates are localized beyond that value. Interestingly, the entanglement entropy and fluctuation of the bipartite magnetization show distinct probability distributions which characterize different quantum phases. Furthermore, we show that for weaker $h$, energy eigenstates with higher energy density are delocalized while states at lower energy density are localized. This defines a Mobility edge and a Mobility Gap separating these two phases. By following the evolution of low energy eigenstates, we observe that the Mobility Gap grows with increasing the random field strength, which drives the system to the phase of the full many-body localization with increasing disorder strength.Comment: 6 pages, 4 figure
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Topologically protected extended states in disordered quantum spin-Hall systems without time-reversal symmetry
Physical Review B, 2012Co-Authors: L. Sheng, Emil Prodan, D. Y. Xing, Donna ShengAbstract:We demonstrate the existence of robust bulk extended states in the disordered Kane-Mele model with vertical and horizontal Zeeman fields, in the presence of a large Rashba coupling. The phase diagrams are mapped out by using level statistics analysis and computations of the localization length and spin-Chern numbers $C_\pm$. $C_\pm$ are protected by the finite energy and spin Mobility Gaps. The latter is shown to stay open for arbitrarily large vertical Zeeman fields, or for horizontal Zeeman fields below a critical strength or at moderate disorder. In such cases, a change of $C_\pm$ is necessarily accompanied by the closing of the Mobility Gap at the Fermi level. The numerical simulations reveal sharp changes in the quantized values of $C_\pm$ when crossing the regions of bulk extended states, indicating that the topological nature of the extended states is indeed linked to the spin-Chern numbers. For large horizontal Zeeman fields, the spin-Gap closes at strong disorder prompting a change in the quantized spin-Chern numbers without a closing of the energy Mobility Gap.
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Mobility Gap in fractional quantum Hall liquids: Effects of disorder and layer thickness
Physical Review B, 2005Co-Authors: Xin Wan, Donna Sheng, Edward Rezayi, Kun Yang, Ravindra N. Bhatt, Frederick D. HaldaneAbstract:We study the behavior of two-dimensional electron gas in the fractional quantum Hall regime in the presence of finite layer thickness and correlated disordered potential. Generalizing the Chern number calculation to many-body systems, we determine the Mobility Gaps of fractional quantum Hall states based on the distribution of Chern numbers in a microscopic model. We find excellent agreement between experimentally measured activation Gaps and our calculated Mobility Gaps, when combining the effects of both disordered potential and layer thickness. We clarify the difference between Mobility Gap and spectral Gap of fractional quantum Hall states and explain the disorder-driven collapse of the Gap and the subsequent transitions from the fractional quantum Hall states to the insulator
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Disorder-driven collapse of the Mobility Gap and transition to an insulator in the fractional quantum Hall effect.
Physical Review Letters, 2003Co-Authors: Donna Sheng, Xin Wan, Edward Rezayi, Kun Yang, Ravindra N. Bhatt, Frederick D. HaldaneAbstract:We study the ??=1/3 quantum Hall state in the presence of random disorder. We calculate the topologically invariant Chern number, which is the only quantity known at present to distinguish unambiguously between insulating and current carrying states in an interacting system. The Mobility Gap can be determined numerically this way and is found to agree with experimental value semiquantitatively. As the disorder strength increases towards a critical value, both the Mobility Gap and plateau width narrow continuously and ultimately collapse, leading to an insulating phase
Jacob Shapiro - One of the best experts on this subject based on the ideXlab platform.
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Strongly Disordered Floquet Topological Systems
Annales Henri Poincaré, 2019Co-Authors: Jacob Shapiro, Clément TauberAbstract:We study the strong disorder regime of Floquet topological systems in dimension two that describe independent electrons on a lattice subject to a periodic driving. In the spectrum of the Floquet propagator we assume the existence of an interval in which all states are localized—a Mobility Gap—extending previous studies which make the stronger spectral Gap assumption. We devise a new approach to define the topological invariants by way of stretching the Gap of a given system onto the whole circle. We show that such completely localized systems have natural indices that circumvent the relative construction and match with quantized magnetization and pumping observables from the physics literature. These indices obey a bulk-edge correspondence, which carries over to the stretched systems as well. Finally, these invariants are shown to coincide with those associated with the usual relative construction, which we also extend to the Mobility Gap regime.
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Strongly Disordered Floquet Topological Systems
Annales Henri Poincaré, 2019Co-Authors: Jacob Shapiro, Clément TauberAbstract:We study the strong disorder regime of Floquet topological systems in dimension two, that describe independent electrons on a lattice subject to a periodic driving. In the spectrum of the Floquet propagator we assume the existence of an interval in which all states are localized--a Mobility Gap. First we generalize the relative construction from spectral to Mobility Gap, define a bulk index for an infinite sample and an edge index for the half-infinite one and prove the bulk-edge correspondence. Second, we consider completely localized systems where the Mobility Gap is the whole circle, and define alternative bulk and edge indices that circumvent the relative construction and match with quantized magnetization and pumping observables from the physics literature. Finally, we show that any system with a Mobility Gap can be reduced to a completely localized one. All the indices defined throughout are equal.
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The Bulk-Edge Correspondence for Disordered Chiral Chains
Communications in Mathematical Physics, 2018Co-Authors: Gian Michele Graf, Jacob ShapiroAbstract:We study one-dimensional insulators obeying a chiral symmetry in the single-particle picture. The Fermi level is assumed to lie in a Mobility Gap. Topological indices are defined for infinite (bulk) or half-infinite (edge) systems, and it is shown that for a given Hamiltonian with nearest neighbor hopping the two indices are equal. We also give a new formulation of the index in terms of the Lyapunov exponents of the zero energy Schrödinger equation, which illustrates the conditions for a topological phase transition occurring in the Mobility Gap regime.
Stephen K. O’leary - One of the best experts on this subject based on the ideXlab platform.
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Spectral variations in the optical transition matrix element and their impact on the optical properties associated with hydrogenated amorphous silicon
Solid State Communications, 2011Co-Authors: Farida Orapunt, Stephen K. O’learyAbstract:Abstract Using an empirical model for the density of states functions associated with hydrogenated amorphous silicon, in conjunction with an elementary model for the optical transition matrix elements, we aim to explore how variations in the matrix elements impact upon the spectral dependence of the optical properties associated with this material. We also wish to ascertain as to whether or not the hydrogenated amorphous silicon Mobility Gap result suggested by Jackson et al. [W.B. Jackson, S.M. Kelso, C.C. Tsai, J.W. Allen, S.-J. Oh, Phys. Rev. B 31 (1985) 5187] is consistent with the results of the experiment. We find that the Mobility Gap value suggested by Jackson et al. is too large. An upper bound on the Mobility Gap associated with hydrogenated amorphous silicon of 1.68 eV is suggested instead. Electrical measurements performed on undoped hydrogenated amorphous silicon yield a Mobility Gap value that is consistent with this bound.
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Spectral dependence of the squared average optical transition matrix element associated with hydrogenated amorphous silicon
Applied Physics Letters, 2003Co-Authors: Stephen K. O’learyAbstract:Using an empirical model for the density of states functions, in conjunction with an elementary model for the optical transition matrix elements, the spectral dependence of the squared average optical transition matrix element associated with hydrogenated amorphous silicon was evaluated. It was predicted that this squared average matrix element saturates at and beyond the Mobility Gap, decreases sharply just below the Mobility Gap as the photon energy is diminished, and then saturates at sufficiently low photon energies. The value of the squared average optical transition matrix element at low photon energies depends on the density of localized electronic states. The results suggest that a careful experimental measurement of the spectral dependence of this matrix element will provide one with a direct means of determining the position of the Mobility Gap of this semiconductor.
Frederick D. Haldane - One of the best experts on this subject based on the ideXlab platform.
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Mobility Gap in fractional quantum Hall liquids: Effects of disorder and layer thickness
Physical Review B, 2005Co-Authors: Xin Wan, Donna Sheng, Edward Rezayi, Kun Yang, Ravindra N. Bhatt, Frederick D. HaldaneAbstract:We study the behavior of two-dimensional electron gas in the fractional quantum Hall regime in the presence of finite layer thickness and correlated disordered potential. Generalizing the Chern number calculation to many-body systems, we determine the Mobility Gaps of fractional quantum Hall states based on the distribution of Chern numbers in a microscopic model. We find excellent agreement between experimentally measured activation Gaps and our calculated Mobility Gaps, when combining the effects of both disordered potential and layer thickness. We clarify the difference between Mobility Gap and spectral Gap of fractional quantum Hall states and explain the disorder-driven collapse of the Gap and the subsequent transitions from the fractional quantum Hall states to the insulator
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Disorder-driven collapse of the Mobility Gap and transition to an insulator in the fractional quantum Hall effect.
Physical Review Letters, 2003Co-Authors: Donna Sheng, Xin Wan, Edward Rezayi, Kun Yang, Ravindra N. Bhatt, Frederick D. HaldaneAbstract:We study the ??=1/3 quantum Hall state in the presence of random disorder. We calculate the topologically invariant Chern number, which is the only quantity known at present to distinguish unambiguously between insulating and current carrying states in an interacting system. The Mobility Gap can be determined numerically this way and is found to agree with experimental value semiquantitatively. As the disorder strength increases towards a critical value, both the Mobility Gap and plateau width narrow continuously and ultimately collapse, leading to an insulating phase
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disorder driven collapse of the Mobility Gap and transition to an insulator in the fractional quantum hall effect
Physical Review Letters, 2003Co-Authors: D N Sheng, Xin Wan, Edward Rezayi, Kun Yang, Ravindra N. Bhatt, Frederick D. HaldaneAbstract:We study the $\ensuremath{\nu}=1/3$ quantum Hall state in the presence of random disorder. We calculate the topologically invariant Chern number, which is the only quantity known at present to distinguish unambiguously between insulating and current carrying states in an interacting system. The Mobility Gap can be determined numerically this way and is found to agree with experimental value semiquantitatively. As the disorder strength increases towards a critical value, both the Mobility Gap and plateau width narrow continuously and ultimately collapse, leading to an insulating phase.
Shun-qing Shen - One of the best experts on this subject based on the ideXlab platform.
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Localization and Mobility Gap in the topological Anderson insulator
Physical Review B, 2012Co-Authors: Yan-yang Zhang, Rui-lin Chu, Fu-chun Zhang, Shun-qing ShenAbstract:It has been proposed that disorder may lead to a new type of topological insulator, called topological Anderson insulator (TAI). Here we examine the physical origin of this phenomenon. We calculate the topological invariants and density of states of disordered model in a super-cell of 2-dimensional HgTe/CdTe quantum well. The topologically non-trivial phase is triggered by a band touching as the disorder strength increases. The TAI is protected by a Mobility Gap, in contrast to the band Gap in conventional quantum spin Hall systems. The Mobility Gap in the TAI consists of a cluster of non-trivial subGaps separated by almost flat and localized bands.