Type-II quantum spin Hall effect in two-dimensional metals

The quantum spin Hall (QSH) effect has been observed in topological insulators and long quantum wells using spin-orbit coupling as the probe, but it has not yet been observed in a metal. An experiment is proposed to measure the different Type-II QSH effect of an electron or hole in a two-dimensional (2D) metal by using the previously unexplored but relativistically gauge-invariant form of the generated 2D QSH Hamiltonian. Instead of using the electric field in the surface of the spin-polarized bands of a topological insulator or across the quantum well width as the probe, ones uses an applied azimuthal vector potential and an applied radial electric field as the tools to generate a spontaneously quantized spin current in an otherwise spin unpolarized 2D metal. A long cylindrical solenoid lies normally through the inner radius of a 2D metallic Corbino disk. The currentISsurrounding the solenoid produces an azimuthal magnetic vector potential but no magnetic field in the disk. In addition, a radial electric field is generated across the disk by imposing either a potential differenceΔvor a radial charge currentacross its inner and outer radii. Combined changes inISand in eitherΔvorgenerate spontaneously quantized azimuthal charge and spin currents. The experiment is designed to measure these quantized azimuthal charge and spin currents in the disk consistently. The quantum Hamiltonians for both experiments are solved exactly. A method to control the Joule heating is presented, which could potentially allow the Type-II QSH measurements to be made at room temperature.