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This study measures three critical exponents (κ, p, γ) of the quantum Hall effect in graphene. It reveals the inelastic scattering exponent (p) varies with magnetic field, unlike prior assumptions.

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Area of Science:

  • Condensed matter physics
  • Quantum mechanics
  • Materials science

Background:

  • The quantum Hall (QH) effect is a key 2D phenomenon.
  • Scaling theory describes QH plateau-plateau transitions using exponents κ, p, and γ.
  • Previous studies assumed a constant p=2, limiting understanding.

Purpose of the Study:

  • To measure all three scaling exponents (κ, p, γ) within a single device.
  • To determine the inelastic scattering exponent (p) across different magnetic field regimes.
  • To investigate the variation of p in graphene and 2D electron systems.

Main Methods:

  • Utilized a single graphene device and a conventional 2D electron system.
  • Employed analytical methods including weak localization, plateau-plateau transitions, and variable range hopping.
  • Measured exponents κ, p, and γ directly.

Main Results:

  • Successfully determined all three exponents (κ, p, γ) in both graphene and 2D electron systems.
  • Found that the inelastic scattering exponent p varies significantly with magnetic field in graphene.
  • Observed p transitions from 1 in low magnetic fields to 2 in the QH regime.

Conclusions:

  • The inelastic scattering exponent p is not constant and depends on the magnetic field regime.
  • Graphene exhibits a field-dependent p, challenging previous assumptions.
  • This work provides a more comprehensive understanding of QH effect scaling theory.