Finite difference method for transport properties of massless Dirac fermions

  • Tworzydlo J
  • Groth C
  • Beenakker C
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We adapt a finite difference method of solution of the two-dimensional
massless Dirac equation, developed in the context of lattice gauge
theory, to the calculation of electrical conduction in a graphene
sheet or on the surface of a topological insulator. The discretized
Dirac equation retains a single Dirac point (no ``fermion doubling{''}),
avoids intervalley scattering as well as trigonal warping, and preserves
the single-valley time-reversal symmetry (=symplectic symmetry) at
all length scales and energies-at the expense of a nonlocal finite
difference approximation of the differential operator. We demonstrate
the symplectic symmetry by calculating the scaling of the conductivity
with sample size, obtaining the logarithmic increase due to antilocalization.
We also calculate the sample-to-sample conductance fluctuations as
well as the shot-noise power and compare with analytical predictions.

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  • J Tworzydlo

  • C W Groth

  • C W J Beenakker

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