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Consider an external electric field propagating through a homogeneous medium. When the electric field crosses the surface boundary of the medium, it undergoes a discontinuity. The electric field can be resolved into normal and tangential components. The amount by which the field changes at any boundary is given by the difference between the field components above and below the surface boundary.
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Spontaneous Localization at a Potential Saddle Point from Edge State Reconstruction in a Quantum Hall Point Contact.

Liam A Cohen1, Noah L Samuelson1, Taige Wang2,3

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We found that quantum Hall edge states can localize at unstable points in graphene quantum point contacts due to Coulomb interactions. This unexpected behavior is driven by soft confinement potentials, demonstrating Coulomb-driven reconstruction.

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Area of Science:

  • Condensed Matter Physics
  • Mesoscopic Physics
  • Graphene Physics

Background:

  • Quantum point contacts (QPCs) are fundamental building blocks in mesoscopic electronic devices.
  • Understanding quantum Hall edge mode transmission is crucial for quantum electronics.

Purpose of the Study:

  • Investigate quantum Hall edge mode transmission through a gate-defined QPC in monolayer graphene.
  • Characterize the nature and location of localized states within the QPC.

Main Methods:

  • Fabrication and measurement of a gate-defined QPC in monolayer graphene.
  • Analysis of transmission spectra, including resonant tunneling peaks and nonlinear conductance.
  • In-plane electric polarizability measurements.
  • Theoretical modeling using a self-consistent Thomas-Fermi approach.

Main Results:

  • Observed resonant tunneling peaks and Coulomb-blockaded localized states in the QPC.
  • Electric polarizability measurements indicated localization at a classically unstable electrostatic saddle point.
  • Theoretical model confirmed that soft confinement favors localization at the saddle point.

Conclusions:

  • Demonstrated Coulomb-driven reconstruction of quantum Hall edge states at a boundary.
  • Identified a novel mechanism for state localization in graphene QPCs.
  • Provided insights into the interplay between confinement potential and Coulomb interactions in quantum systems.