  The quantum spin Hall effect has been observed in topological insulators
using spin-orbit coupling as the probe, but it has not yet been observed in a
metal. An experiment is proposed to measure the quantum spin Hall effect of an
electron or hole in a two-dimensional (2D) metal by using the previously
unexplored but relativistically generated 2D quantum spin Hall Hamiltonian, but
without using spin-orbit coupling. A long cylindrical solenoid lies normally
through the inner radius of a 2D metallic Corbino disk. The current $I_S$
surrounding 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) a potential difference $\Delta v$ or (b)
a radial charge current ${\bm I}$ across its inner and outer radii. Combined
changes in $I_S$ and in either $\Delta v$ or ${\bm I}$ generate 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 experiments (a) and (b) are both
solved exactly. A method to control the Joule heating is presented, which could
potentially allow the quantum spin Hall measurements to be made at room
temperature. Extensions of this design to an array of thermally-managed
solenoids, each surrounded by thermally-managed stacks of 2D metallic Corbino
disks, could function as a quantum computer that could potentially operate at
room temperature.
