A straight quantum wave guide with mixed Dirichlet and Neumann boundary conditions in uniform magnetic fields

A straight quasi-one-dimensional Dirichlet wave guide with a Neumann window of length L on one or two confining surfaces is considered theoretically with and without perpendicular homogeneous magnetic field . It is shown that for the field-free case, a bound state in the continuum (BIC) for one Neumann window exists for some critical lengths only, while for the two Neumann segments symmetrically located on the opposite walls, due to the restored transverse symmetry of the system, BICs exist for the arbitrary L. Bound states lying below the fundamental propagation threshold of the Dirichlet strip survive any strength of the uniform magnetic field and do not depend on its direction. Moreover, an increasing field induces new bound states regularly arranged with the levels present at B = 0. For two Neumann windows, strong magnetic fields lead to the degeneracy of the adjacent odd and even bound states with their energies almost equal to each other and to their corresponding counterpart for one Neumann segment, which is explained by mapping the problem onto the field-free one or two purely attractive one-dimensional quantum wells with field-dependent depth. Miscellaneous magnetotransport characteristics of the structures are also considered; in particular, it is demonstrated that small fields applied to the channel with two Neumann windows destroy BICs by coupling them to the continuum states. This is manifested in the conductance-Fermi energy dependence by Fano resonances. Currents flowing in the wave guide are investigated too, and it is shown that current density patterns near the resonances form vortices which change their chirality as energy sweeps through the resonant region. Generalizations to any other arbitrary combination of the boundary conditions are provided. Comparison with other structures such as window-coupled Dirichlet wave guides, a bent strip or straight Dirichlet channel with electrostatic impurity inside, is performed.