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Register a new userRelevance of multiple-quasiparticle tunneling between edge states at u =p/(2np+1)
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We present an explanation for the anomalous behavior in tunneling conductance and noise through a point contact between edge states in the Jain series $ u=p/(2np+1)$, for extremely weak-backscattering and low temperatures [Y.C. Chung, M. Heiblum, and V. Umansky, Phys. Rev. Lett. {bf{91}}, 216804 (2003)]. We consider edge states with neutral modes propagating at finite velocity, and we show that the activation of their dynamics causes the unexpected change in the temperature power-law of the conductance. Even more importantly, we demonstrate that multiple-quasiparticles tunneling at low energies becomes the most relevant process. This result will be used to explain the experimental data on current noise where tunneling particles have a charge that can reach $p$ times the single quasiparticle charge. In this paper we analyze the conductance and the shot noise to substantiate quantitatively the proposed scenario.
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We study the magneto-conductance of a $1.4~mathrm{mu m}$-wide quantum dot in the fractional quantum Hall regime. For a filling factor $approx 2/3$ and $gtrsim 1/3$ in the quantum dot the observed Coulomb resonances show a periodic modulation in magnetic field. This indicates a non-trivial reconstruction of the 2/3 fractional quantum Hall state in the quantum dot. We present a model for the charge stability diagram of the system assuming two compressible regions separated by an incompressible stripe of filling factor $2/3$ and $1/3$, respectively. From the dependence of the magnetic field period on total magnetic field we construct the zero-field charge density distribution in the quantum dot. The tunneling between the two compressible regions exhibits fractional Coulomb blockade. For both filling factor regions, we extract a fractional charge $e^*/e = 0.32 pm 0.03$ by comparing to measurements at filling factor 2. With their close relation to quantum Hall Fabry-P{e}rot interferometers, our investigations on quantum dots in the fractional quantum Hall regime extend and complement interference experiments investigating the nature of anyonic fractional quantum Hall quasiparticles.
We study the heat transport along an edge state of a two-dimensional electron gas in the quantum Hall regime, in contact to two reservoirs at different temperatures. We consider two exactly solvable models for the edge state coupled to the reservoirs. The first one corresponds to filling $ u=1$ and tunneling coupling to the reservoirs. The second one corresponds to integer or fractional filling of the sequence $ u=1/m$ (with $m$ odd), and capacitive coupling to the reservoirs. In both cases we solve the problem by means of non-equilibrium Green function formalism. We show that heat propagates chirally along the edge in the two setups. We identify two temperature regimes, defined by $Delta$, the mean level spacing of the edge. At low temperatures, $T< Delta$, finite size effects play an important role in heat transport, for both types of contacts. The nature of the contacts manifest themselves in different power laws for the thermal conductance as a function of the temperature. For capacitive couplings a highly non-universal behavior takes place, through a prefactor that depends on the length of the edge as well as on the coupling strengths and the filling fraction. For larger temperatures, $T>Delta$, finite-size effects become irrelevant, but the heat transport strongly depends on the strength of the edge-reservoir interactions, in both cases. The thermal conductance for tunneling coupling grows linearly with $T$, whereas for the capacitive case it saturates to a value that depends on the coupling strengths and the filling factors of the edge and the contacts.
We present a comprehensive numerical study of a microscopic model of the fractional quantum Hall system at filling fraction $ u = 5/2$, based on the disc geometry. Our model includes Coulomb interaction and a semi-realistic confining potential. We also mix in some three-body interaction in some cases to help elucidate the physics. We obtain a phase diagram, discuss the conditions under which the ground state can be described by the Moore-Read state, and study its competition with neighboring stripe phases. We also study quasihole excitations and edge excitations in the Moore-Read--like state. From the evolution of edge spectrum, we obtain the velocities of the charge and neutral edge modes, which turn out to be very different. This separation of velocities is a source of decoherence for a non-Abelian quasihole/quasiparticle (with charge $pm e/4$) when propagating at the edge; using numbers obtained from a specific set of parameters we estimate the decoherence length to be around four microns. This sets an upper bound for the separation of the two point contacts in a double point contact interferometer, designed to detect the non-Abelian nature of such quasiparticles. We also find a state that is a potential candidate for the recently proposed anti-Pfaffian state. We find the speculated anti-Pfaffian state is favored in weak confinement (smooth edge) while the Moore-Read Pfaffian state is favored in strong confinement (sharp edge).
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