Edge currents in the absence of edges

Pavel Exner (1) , Alain Joye (2) , H. Kovařík (3)

1 Nuclear Physics Institute [Prague]
2 IF - Institut Fourier
3 Faculty of Mathematics and Physics [Praha/Prague]

We investigate a charged two-dimensional particle in a homogeneous magnetic field interacting with a periodic array of point obstacles. We show that while Landau levels remain to be infinitely degenerate eigenvalues, between them the system has bands of absolutely continuous spectrum and exhibits thus a transport along the array. We also compute the band functions and the corresponding probability current.

Domaines: Mathématiques [math]

Pavel Exner, Alain Joye, H. Kovařík. Edge currents in the absence of edges. Physics Letters A, 1999, 264 (2-3), pp.124-130. ⟨10.1016/S0375-9601(99)00804-X⟩. ⟨hal-01233232⟩