Transport through constricted quantum Hall edge systems: beyond the quantum point contact

Abstract

Motivated by surprises in recent experimental findings, we study transport in a model of a quantum Hall edge system with a gate-voltage controlled constriction. A finite backscattered current at finite edge-bias is explained from a Landauer-Buttiker analysis as arising from the splitting of edge current caused by the difference in the filling fractions of the bulk (${\nu }_1$) and constriction (${\nu }_2$) quantum Hall fluid regions. We develop a hydrodynamic theory for bosonic edge modes inspired by this model. The constriction region splits the incident long-wavelength chiral edge density-wave excitations among the transmitting and reflecting edge states encircling it. The competition between two interedge tunneling processes taking place inside the constriction, related by a quasiparticle-quasihole (qp-qh) symmetry, is accounted for by computing the boundary theories of the system. This competition is found to determine the strong coupling configuration of the system. A separatrix of qp-qh symmetric gapless critical states is found to lie between the relevant RG flows to a metallic and an insulating configuration of the constriction system. This constitutes an interesting generalisation of the Kane-Fisher quantum impurity model. The features of the RG phase diagram are also confirmed by computing various correlators and chiral linear conductances of the system. In this way, our results find excellent agreement with many recent puzzling experimental results for the cases of ${\nu }_1=1/3,1$. We also discuss and make predictions for the case of a constriction system with ${\nu }_2=5/2$.

18 pages, 9 figures

References in corpus (46)

• Bosonization and Strongly Correlated Systems
• Topological orders and Edge excitations in FQH states
• An Electronic Mach-Zehnder Interferometer
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Exact Conductance through Point Contacts in the $\nu =1/3$ Fractional Quantum Hall Effect
• Exact non-equilibrium transport through point contacts in quantum wires and fractional quantum Hall devices
• Impurity scattering and transport of fractional Quantum Hall edge state
• Resonant Tunneling Between Quantum Hall Edge States
• Tunneling in Quantum Wires: a Boundary Conformal Field Theory Approach
• Junctions of three quantum wires and the dissipative Hofstadter model
• Decoherence and single electron charging in an electronic Mach-Zehnder interferometer
• Entanglement, Dephasing, and Phase Recovery via Cross-Correlation Measurements of Electrons
• Incompressible strips in dissipative Hall bars as origin of quantized Hall plateaus
• Junction of several weakly interacting quantum wires: a renormalization group study
• Scattering of Bunched Fractionally Charged Quasiparticles
• Fractional quantum Hall effect in a quantum point contact at filling fraction 5/2
• Universal structure of the edge states of the fractional quantum Hall states
• Inter-Edge interaction in the Quantum Hall Effect
• Landauer-type transport theory for interacting quantum wires: Application to carbon nanotube Y junctions
• Inter-edge strong-to-weak scattering evolution at a constriction in the fractional quantum Hall regime
• The Hanbury Brown and Twiss Experiment with Fermions
• Interactions suppress Quasiparticle Tunneling at Hall Bar Constrictions
• Particle-hole symmetric Luttinger liquids in a quantum Hall circuit
• Bunching of Fractionally-Charged Quasiparticles Tunneling through High Potential Barriers
• Open Luttinger liquids
• Andreev reflection in the fractional quantum Hall effect
• Effective action of a compressible QH state edge: application to tunneling
• Renormalization group study of the conductances of interacting quantum wire systems with different geometries
• Critical points in edge tunneling between generic FQH states
• Self-consistent calculation of the electron distribution near a Quantum-Point Contact in the integer Quantum Hall Effect
• Duality Near Quantum Hall Transitions
• Transport through quasi-ballistic quantum wires: the role of contacts
• Coulomb interactions and delocalization in quantum Hall constrictions
• Tunneling through two resonant levels: fixed points and conductances
• Boundary Field Theory Approach to the Renormalization of SQUID Devices
• Edge State Tunneling in a Split Hall Bar Model
• Strong-coupling branching of FQHL edges
• Transport properties of a two-dimensional electron liquid at high magnetic field
• Conductance through contact barriers of a finite length quantum wire
• Non-equilibrium tunneling into general quantum Hall edge states
• Interplay of Short-Range Interactions and Quantum Interference Near the Integer Quantum Hall Transition
• Electrostatics of Edge States of Quantum Hall Systems with Constrictions: Metal--Insulator Transition Tuned by External Gates
• Metal-Insulator Transition Tuned by External Gates in Hall Systems with Constrictions
• On transport in quantum Hall systems with constrictions
• Edge state transmission, duality relation and its implication to measurements

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