## Details

Originalsprache | Englisch |
---|---|

Seiten (von - bis) | 25-37 |

Seitenumfang | 13 |

Fachzeitschrift | Letters in mathematical physics |

Jahrgang | 75 |

Ausgabenummer | 1 |

Publikationsstatus | Veröffentlicht - 1 Jan. 2006 |

Extern publiziert | Ja |

## 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.

## ASJC Scopus Sachgebiete

- Physik und Astronomie (insg.)
**Statistische und nichtlineare Physik**- Mathematik (insg.)
**Mathematische Physik**

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**Spontaneous edge currents for the dirac equation in two space dimensions.**/ Gruber, Michael J.; Leitner, Marianne.

in: Letters in mathematical physics, Jahrgang 75, Nr. 1, 01.01.2006, S. 25-37.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

*Letters in mathematical physics*, Jg. 75, Nr. 1, S. 25-37. https://doi.org/10.1007/s11005-005-0036-4

*Letters in mathematical physics*,

*75*(1), 25-37. https://doi.org/10.1007/s11005-005-0036-4

}

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 -