  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.
