Details
| Original language | English |
|---|---|
| Pages (from-to) | 25-37 |
| Number of pages | 13 |
| Journal | Letters in mathematical physics |
| Volume | 75 |
| Issue number | 1 |
| Publication status | Published - 1 Jan 2006 |
| Externally published | Yes |
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.
Keywords
- Boundary condition, Dirac operator, Hall effect, Spectral flow
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematics(all)
- Mathematical Physics
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In: Letters in mathematical physics, Vol. 75, No. 1, 01.01.2006, p. 25-37.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Spontaneous edge currents for the dirac equation in two space dimensions
AU - Gruber, Michael J.
AU - Leitner, Marianne
PY - 2006/1/1
Y1 - 2006/1/1
N2 - 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.
AB - 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.
KW - Boundary condition
KW - Dirac operator
KW - Hall effect
KW - Spectral flow
UR - http://www.scopus.com/inward/record.url?scp=32344443650&partnerID=8YFLogxK
U2 - 10.1007/s11005-005-0036-4
DO - 10.1007/s11005-005-0036-4
M3 - Article
AN - SCOPUS:32344443650
VL - 75
SP - 25
EP - 37
JO - Letters in mathematical physics
JF - Letters in mathematical physics
SN - 0377-9017
IS - 1
ER -