Position-dependent mass effects in the electronic transport of two-dimensional quantum systems

In this work, we investigate the electronic transport properties of curved two-dimensional quantum systems with a position-dependent mass (PDM). We found the Schr\"odinger equation for a general surface following the da Costa approach, obtaining the geometrical potential for systems with PDM. We obtained expressions for the transmittance and reflectance for a general surface of revolution. As a first application of the general results obtained here, we investigate the transport properties of deformed nanotubes, since the variation of the effective mass with the radius of the nanotubes has been dis-considered in previous studies of this system and experimentally a change of the effective mass is observed for different radii. We found that the inclusion of the position-dependent mass, particularly a radial change in the mass distribution, can induce a significant change in the transport properties of the system, which reveals that the transport properties of two dimensional quantum systems are sensitive to the PDM and when modeling electronic transport in surfaces this effects should be considered.