Quantum Field Theory Description of Tunneling in the Integer Quantum Hall Effect

Abstract

We study the tunneling between two quantum Hall systems, along a quasi one-dimensional interface. A detailed analysis relates microscopic parameters, characterizing the potential barrier, with the effective field theory model for the tunneling. It is shown that the phenomenon of fermion number fractionalization is expected to occur, either localized in conveniently modulated barriers or in the form of free excitations, once lattice effects are taken into account. This opens the experimental possibility of an observation of fractional charges with internal structure, close to the magnetic length scale. The coupling of the system to external gauge fields is performed, leading us to the exact quantization of the Hall conductivity at the interface. The field theory approach is well supported by a numerical diagonalization of the microscopic Hamiltonian.