Optimization of edge state velocity in the integer quantum Hall regime

Abstract

Observation of interference in the quantum Hall regime may be hampered by a small edge state velocity due to finite phase coherence time. Therefore designing two quantum point contact (QPCs) interferometers having a high edge state velocity is desirable. Here, we present a new simulation method for realistically modeling edge states near QPCs in the integer quantum Hall effect (IQHE) regime. We calculate the filling fraction in the center of the QPC and the velocity of the edge states, and predict structures with high edge state velocity. The 3D Schrödinger equation is split into 1D and 2D parts. Quasi-1D Schrödinger and Poisson equations are solved self-consistently in the IQHE regime to obtain the potential profile near the edges, and quantum transport is used to solve for the edge state wavefunctions. The velocity of edge states is found to be $⟨E⟩/B$, where $⟨E⟩$ is the expectation value of the electric field for the edge state. Anisotropically etched trench gated heterostructures with double sided delta doping have the highest edge state velocity among the structures considered.

12 pages, 11 figures

References in corpus (8)

• Non-Abelian Anyons and Topological Quantum Computation
• Edge-State Velocity and Coherence in a Quantum Hall Fabry-Perot Interferometer
• Time-of-Flight Measurements of Single-Electron Wave Packets in Quantum-Hall Edge States
• Quantum transport in electron Fabry-Perot interferometers
• Suppression of interference in quantum Hall Mach-Zehnder geometry by upstream neutral modes
• Realistic modelling of quantum point contacts subject to high magnetic fields and with current bias at out of linear response regime
• Dephasing of an Electronic Two-Path Interferometer
• Combination of equilibrium and non-equilibrium carrier statistics into an atomistic quantum transport model for tunneling hetero-junctions

Cited by in corpus (10)

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• Impact of bulk-edge coupling on observation of anyonic braiding statistics in quantum Hall interferometers
• Anyons in Quantum Hall Interferometry
• Exchange coupling in a linear chain of three quantum-dot spin qubits in silicon
• The self-consistent quantum-electrostatic problem in strongly non-linear regime
• Half-integer conductance plateau at the $\nu =2/3$ fractional quantum Hall state in a quantum point contact
• Reconciling edge states with compressible stripes in a ballistic mesoscopic conductor
• Anyonic braiding via quench dynamics in fractional quantum Hall liquids
• Single electron interference and capacitive edge mode coupling generates ${\Phi }_0/2$ flux periodicity in Fabry-Perot interferometers