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J. T. Chalker - One of the best experts on this subject based on the ideXlab platform.
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Density of quasiparticle states for a two-dimensional disordered system: Metallic, insulating, and critical behavior in the class-D thermal quantum Hall effect
Physical Review B, 2007Co-Authors: A. Mildenberger, Ferdinand Evers, Alexander D. Mirlin, J. T. ChalkerAbstract:We investigate numerically the quasiparticle density of states $\ensuremath{\varrho}(E)$ for a two-dimensional, disordered superconductor in which both time-reversal and spin-rotation symmetries are broken. As a generic single-particle description of this class of systems (symmetry class D), we use the Cho-Fisher version of the network model. This has three phases: a thermal insulator, a thermal metal, and a quantized thermal Hall conductor. In the thermal metal, we find a Logarithmic Divergence in $\ensuremath{\varrho}(E)$ as $E\ensuremath{\rightarrow}0$, as predicted from sigma model calculations. Finite-size effects lead to superimposed oscillations, as expected from random-matrix theory. In the thermal insulator and quantized thermal Hall conductor, we find that $\ensuremath{\varrho}(E)$ is finite at $E=0$. At the plateau transition between these phases, $\ensuremath{\varrho}(E)$ decreases toward zero as $\ensuremath{\mid}E\ensuremath{\mid}$ is reduced, in line with the result $\ensuremath{\varrho}(E)\ensuremath{\sim}\ensuremath{\mid}E\ensuremath{\mid}\mathrm{ln}(1∕\ensuremath{\mid}E\ensuremath{\mid})$ derived from calculations for Dirac fermions with random mass.
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density of quasiparticle states for a two dimensional disordered system metallic insulating and critical behavior in the class d thermal quantum hall effect
Physical Review B, 2007Co-Authors: A. Mildenberger, Ferdinand Evers, Alexander D. Mirlin, J. T. ChalkerAbstract:We investigate numerically the quasiparticle density of states $\varrho(E)$ for a two-dimensional, disordered superconductor in which both time-reversal and spin-rotation symmetry are broken. As a generic single-particle description of this class of systems (symmetry class D), we use the Cho-Fisher version of the network model. This has three phases: a thermal insulator, a thermal metal, and a quantized thermal Hall conductor. In the thermal metal we find a Logarithmic Divergence in $\varrho(E)$ as $E\to 0$, as predicted from sigma model calculations. Finite size effects lead to superimposed oscillations, as expected from random matrix theory. In the thermal insulator and quantized thermal Hall conductor, we find that $\varrho(E)$ is finite at E=0. At the plateau transition between these phases, $\varrho(E)$ decreases towards zero as $|E|$ is reduced, in line with the result $\varrho(E) \sim |E|\ln(1/|E|)$ derived from calculations for Dirac fermions with random mass.
A. Mildenberger - One of the best experts on this subject based on the ideXlab platform.
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Density of quasiparticle states for a two-dimensional disordered system: Metallic, insulating, and critical behavior in the class-D thermal quantum Hall effect
Physical Review B, 2007Co-Authors: A. Mildenberger, Ferdinand Evers, Alexander D. Mirlin, J. T. ChalkerAbstract:We investigate numerically the quasiparticle density of states $\ensuremath{\varrho}(E)$ for a two-dimensional, disordered superconductor in which both time-reversal and spin-rotation symmetries are broken. As a generic single-particle description of this class of systems (symmetry class D), we use the Cho-Fisher version of the network model. This has three phases: a thermal insulator, a thermal metal, and a quantized thermal Hall conductor. In the thermal metal, we find a Logarithmic Divergence in $\ensuremath{\varrho}(E)$ as $E\ensuremath{\rightarrow}0$, as predicted from sigma model calculations. Finite-size effects lead to superimposed oscillations, as expected from random-matrix theory. In the thermal insulator and quantized thermal Hall conductor, we find that $\ensuremath{\varrho}(E)$ is finite at $E=0$. At the plateau transition between these phases, $\ensuremath{\varrho}(E)$ decreases toward zero as $\ensuremath{\mid}E\ensuremath{\mid}$ is reduced, in line with the result $\ensuremath{\varrho}(E)\ensuremath{\sim}\ensuremath{\mid}E\ensuremath{\mid}\mathrm{ln}(1∕\ensuremath{\mid}E\ensuremath{\mid})$ derived from calculations for Dirac fermions with random mass.
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density of quasiparticle states for a two dimensional disordered system metallic insulating and critical behavior in the class d thermal quantum hall effect
Physical Review B, 2007Co-Authors: A. Mildenberger, Ferdinand Evers, Alexander D. Mirlin, J. T. ChalkerAbstract:We investigate numerically the quasiparticle density of states $\varrho(E)$ for a two-dimensional, disordered superconductor in which both time-reversal and spin-rotation symmetry are broken. As a generic single-particle description of this class of systems (symmetry class D), we use the Cho-Fisher version of the network model. This has three phases: a thermal insulator, a thermal metal, and a quantized thermal Hall conductor. In the thermal metal we find a Logarithmic Divergence in $\varrho(E)$ as $E\to 0$, as predicted from sigma model calculations. Finite size effects lead to superimposed oscillations, as expected from random matrix theory. In the thermal insulator and quantized thermal Hall conductor, we find that $\varrho(E)$ is finite at E=0. At the plateau transition between these phases, $\varrho(E)$ decreases towards zero as $|E|$ is reduced, in line with the result $\varrho(E) \sim |E|\ln(1/|E|)$ derived from calculations for Dirac fermions with random mass.
Ferdinand Evers - One of the best experts on this subject based on the ideXlab platform.
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Density of quasiparticle states for a two-dimensional disordered system: Metallic, insulating, and critical behavior in the class-D thermal quantum Hall effect
Physical Review B, 2007Co-Authors: A. Mildenberger, Ferdinand Evers, Alexander D. Mirlin, J. T. ChalkerAbstract:We investigate numerically the quasiparticle density of states $\ensuremath{\varrho}(E)$ for a two-dimensional, disordered superconductor in which both time-reversal and spin-rotation symmetries are broken. As a generic single-particle description of this class of systems (symmetry class D), we use the Cho-Fisher version of the network model. This has three phases: a thermal insulator, a thermal metal, and a quantized thermal Hall conductor. In the thermal metal, we find a Logarithmic Divergence in $\ensuremath{\varrho}(E)$ as $E\ensuremath{\rightarrow}0$, as predicted from sigma model calculations. Finite-size effects lead to superimposed oscillations, as expected from random-matrix theory. In the thermal insulator and quantized thermal Hall conductor, we find that $\ensuremath{\varrho}(E)$ is finite at $E=0$. At the plateau transition between these phases, $\ensuremath{\varrho}(E)$ decreases toward zero as $\ensuremath{\mid}E\ensuremath{\mid}$ is reduced, in line with the result $\ensuremath{\varrho}(E)\ensuremath{\sim}\ensuremath{\mid}E\ensuremath{\mid}\mathrm{ln}(1∕\ensuremath{\mid}E\ensuremath{\mid})$ derived from calculations for Dirac fermions with random mass.
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density of quasiparticle states for a two dimensional disordered system metallic insulating and critical behavior in the class d thermal quantum hall effect
Physical Review B, 2007Co-Authors: A. Mildenberger, Ferdinand Evers, Alexander D. Mirlin, J. T. ChalkerAbstract:We investigate numerically the quasiparticle density of states $\varrho(E)$ for a two-dimensional, disordered superconductor in which both time-reversal and spin-rotation symmetry are broken. As a generic single-particle description of this class of systems (symmetry class D), we use the Cho-Fisher version of the network model. This has three phases: a thermal insulator, a thermal metal, and a quantized thermal Hall conductor. In the thermal metal we find a Logarithmic Divergence in $\varrho(E)$ as $E\to 0$, as predicted from sigma model calculations. Finite size effects lead to superimposed oscillations, as expected from random matrix theory. In the thermal insulator and quantized thermal Hall conductor, we find that $\varrho(E)$ is finite at E=0. At the plateau transition between these phases, $\varrho(E)$ decreases towards zero as $|E|$ is reduced, in line with the result $\varrho(E) \sim |E|\ln(1/|E|)$ derived from calculations for Dirac fermions with random mass.
Alexander D. Mirlin - One of the best experts on this subject based on the ideXlab platform.
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Density of quasiparticle states for a two-dimensional disordered system: Metallic, insulating, and critical behavior in the class-D thermal quantum Hall effect
Physical Review B, 2007Co-Authors: A. Mildenberger, Ferdinand Evers, Alexander D. Mirlin, J. T. ChalkerAbstract:We investigate numerically the quasiparticle density of states $\ensuremath{\varrho}(E)$ for a two-dimensional, disordered superconductor in which both time-reversal and spin-rotation symmetries are broken. As a generic single-particle description of this class of systems (symmetry class D), we use the Cho-Fisher version of the network model. This has three phases: a thermal insulator, a thermal metal, and a quantized thermal Hall conductor. In the thermal metal, we find a Logarithmic Divergence in $\ensuremath{\varrho}(E)$ as $E\ensuremath{\rightarrow}0$, as predicted from sigma model calculations. Finite-size effects lead to superimposed oscillations, as expected from random-matrix theory. In the thermal insulator and quantized thermal Hall conductor, we find that $\ensuremath{\varrho}(E)$ is finite at $E=0$. At the plateau transition between these phases, $\ensuremath{\varrho}(E)$ decreases toward zero as $\ensuremath{\mid}E\ensuremath{\mid}$ is reduced, in line with the result $\ensuremath{\varrho}(E)\ensuremath{\sim}\ensuremath{\mid}E\ensuremath{\mid}\mathrm{ln}(1∕\ensuremath{\mid}E\ensuremath{\mid})$ derived from calculations for Dirac fermions with random mass.
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density of quasiparticle states for a two dimensional disordered system metallic insulating and critical behavior in the class d thermal quantum hall effect
Physical Review B, 2007Co-Authors: A. Mildenberger, Ferdinand Evers, Alexander D. Mirlin, J. T. ChalkerAbstract:We investigate numerically the quasiparticle density of states $\varrho(E)$ for a two-dimensional, disordered superconductor in which both time-reversal and spin-rotation symmetry are broken. As a generic single-particle description of this class of systems (symmetry class D), we use the Cho-Fisher version of the network model. This has three phases: a thermal insulator, a thermal metal, and a quantized thermal Hall conductor. In the thermal metal we find a Logarithmic Divergence in $\varrho(E)$ as $E\to 0$, as predicted from sigma model calculations. Finite size effects lead to superimposed oscillations, as expected from random matrix theory. In the thermal insulator and quantized thermal Hall conductor, we find that $\varrho(E)$ is finite at E=0. At the plateau transition between these phases, $\varrho(E)$ decreases towards zero as $|E|$ is reduced, in line with the result $\varrho(E) \sim |E|\ln(1/|E|)$ derived from calculations for Dirac fermions with random mass.
Angel Rubio - One of the best experts on this subject based on the ideXlab platform.
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dielectric screening in two dimensional insulators implications for excitonic and impurity states in graphane
Physical Review B, 2011Co-Authors: Pierluigi Cudazzo, I V Tokatly, Angel RubioAbstract:For atomic thin layer insulating materials we provide an exact analytic form of the two-dimensional (2D) screened potential. In contrast to three-dimensional systems where the macroscopic screening can be described by a static dielectric constant, in 2D systems the macroscopic screening is nonlocal ($q$ dependent) showing a Logarithmic Divergence for small distances and reaching the unscreened Coulomb potential for large distances. The crossover of these two regimes is dictated by 2D layer polarizability that can be easily computed by standard first-principles techniques. The present results have strong implications for describing gap-impurity levels and also exciton binding energies. The simple model derived here captures the main physical effects and reproduces well, for the case of graphane, the full many-body $\mathrm{GW}$ plus Bethe-Salpeter calculations. As an additional outcome we show that the impurity hole-doping in graphane leads to strongly localized states, which hampers applications in electronic devices. In spite of the inefficient and nonlocal two-dimensional macroscopic screening we demonstrate that a simple $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ approach is capable to describe the electronic and transport properties of confined 2D systems.
