Spontaneous Edge Currents for the Dirac Equation in Two Space Dimensions |
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Authors: | Michael J Gruber Marianne Leitner |
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Institution: | 1. Institut für Physik, Theoretische Physik II, Universit?t Augsburg, Augsburg, Germany 2. School of Theoretical Physics, Dublin Institute for Advanced Studies, Dublin, Ireland
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Abstract: | Spontaneous edge currents are known to occur in systems of two space dimensions in a strong magnetic field. The latter creates
chirality and determines the direction of the currents. Here we show that an analogous effect occurs in a field-free situation
when time reversal symmetry is broken by the mass term of the Dirac equation in two space dimensions. On a half plane, one
sees explicitly that the strength of the edge current is proportional to the difference between the chemical potentials at
the edge and in the bulk, so that the effect is analogous to the Hall effect, but with an internal potential. The edge conductivity
differs from the bulk (Hall) conductivity on the whole plane. This results from the dependence of the edge conductivity on
the choice of a selfadjoint extension of the Dirac Hamiltonian. The invariance of the edge conductivity with respect to small
perturbations is studied in this example by topological techniques
Mathematics Subject Classification (2000). 81Q10, 58J32 |
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Keywords: | Dirac operator boundary condition Hall effect spectral flow |
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