Bound in continuum states and induced transparency in a mesoscopic demultiplexer with two outputs

We investigate the electronic transport in a simple mesoscopic cross structure made of two wires (stubs) grafted at the same point along a quantum waveguide. We show that the structure may exhibit important phenomena such as bound in continuum (BIC) states. These states are transformed into electromagnetically induced transparency (EIT) resonance by detuning slightly the lengths of the stubs. The last phenomenon is used to propose and study a mesoscopic demultiplexer device with an input waveguide and two output waveguides. We give closed-form expressions of the geometrical parameters that allow a selective transfer of a given state in the first waveguide without perturbing the second waveguide. The effect of temperature on the transmission resonances is also examined by using Landauer-Buttiker formula. The analytical results of the dispersion relation and transmission and reflection coefficient are obtained using the Green's function method.