Edge states and quantized Hall resistance in quantum wires containing a periodic potential

Transport in a strip of finite width containing a weak periodic potential in a strong magnetic field is studied numerically. In the case of a strip connected to ideal leads, some edge states are confined in the periodic potential region and form quasidiscrete bound states. The transmission probability has resonance peaks or antiresonance dips at these energies. Edge states moving in directions opposite to each other sometimes appear in pairs at the outermost period of the strip due to effects of the confining potential. The presence of these pairs can make the Hall resistance in a Hall bar geometry different from that expected in an infinite system.