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Register a new userProposal For A Quantum Hall Pump
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Authors
Steven H. Simon
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A device is proposed that is similar in spirit to the electron turnstile except that it operates within a quantum Hall fluid. In the integer quantum Hall regime, this device pumps an integer number of electrons per cycle. In the fractional regime, it pumps an integer number of fractionally charged quasiparticles per cycle. It is proposed that such a device can make an accurate measurement of the charge of the quantum Hall effect quasiparticles.
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A seminal gedankenexperiment by Laughlin describes the charge transport in quantum Hall systems via the pumping of flux. Here, we propose an optical scheme which probes and manipulates quantum Hall systems in a similar way: When light containing orbital angular momentum interacts with electronic Landau levels, it acts as a flux pump which radially moves the electrons through the sample. We investigate this effect for a graphene system with Corbino geometry, and calculate the radial current in the absence of any electric potential bias. Remarkably, the current is robust against the disorder which is consistent with the lattice symmetry, and in the weak excitation limit, the current shows a power-law scaling with intensity characterized by the novel exponent 2/3.
The three-dimensional (3D) quantum Hall effect (3DQHE) was initially proposed to be realized in systems with spontaneous charge-density-wave (CDW) or spin-density-wave (SDW), which has stimulated recent experimental progress in this direction. Here, instead of such intrinsic scenarios, we propose to realize the 3DQHE in a synthetic semiconductor superlattice. The superlattice is engineered along one direction, which is modeled by the Kronig-Penney type periodic potential. By applying a magnetic field along this direction, quantized 3D Hall conductivity can be achieved in certain parameter regimes, along with a vanishing transverse conductivity. We show that such results are robust against the disorder effect and can be hopefully realized by state-of-the-art fabrication techniques. Our work opens a new research avenue for exploring the 3DQHE in electronic superlattice structures.
The quantum spin Hall edge is predicted to reliably produce Majorana zero modes on the border between magnetic insulator- and superconductor-proximitized regions of the edge. The direction of magnetization determines the size of the induced magnetic gap and can control the resulting tunnel barrier. Here we propose a way to avoid magnetic manipulations of the material and use electric-only local control of the barrier. We follow with a design of a charging-energy-protected qubit and a layout of a quantum computer based on the quantum spin Hall effect. We estimate relevant scales and show that they allow for testing of these ideas in the near future.
We show how a quantum dot with a ballistic single-channel point contact to a superconductor can be created by means of a gate electrode at the edge of a quantum spin Hall insulator (such as an InAs/GaSb quantum well). A weak perpendicular magnetic field traps a Majorana zero-mode, so that it can be observed in the gate-voltage-averaged differential conductance <dI/dV> as a 4e^2/h zero-bias peak above a (2/3{pi}^2 - 4)e^2/h background. The one-dimensional edge does not permit the braiding of pairs of Majorana fermions, but this obstacle can be overcome by coupling opposite edges at a constriction, allowing for a demonstration of non-Abelian statistics.
We propose a theoretical scenario for pumping of fractionally charged quasi-particle in the context of $ u=1/3$ fractional quantum Hall liquid. We consider quasi-particle pumping across an anti-dot level tuned close to the resonance. Fractional charge pumping is achieved by slow and periodic modulation of coupling of the anti-dot level to left and right moving edges of a Hall bar set-up. This is attained by periodically modulating the gate voltages controlling the couplings. In order to obtain quantization of pumped charge in the unit of the electronic charge fraction ($ u e$) per pumping cycle in the adiabatic limit, we argue that the only possibility is to tune the quasi-particle operator to be irrelevant from being relevant in the renormalization group sense, which can be accomplished by invoking quantum Hall line junctions into the Hall bar geometry. We also comment on possibility for experimental realization of the above scenario.
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