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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 current I across its inner and outer radii. Combined changes inISand in eitherΔvor 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 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., (© 2022 IOP Publishing Ltd.)

To construct a microscopic theory of electrons and holes in anisotropic conductors that self-consistently treats their band effective mass anisotropy with their interactions with applied electric and magnetic fields, the Dirac equation is extended for an electron or hole in an orthorhombically-anisotropic conduction band. Its covariance is established both by a modified version of the Klemm-Clem transformations to a space in which it is isotropic, and also in its fully anisotropic form by making the most general proper and improper Lorentz transformations, proving its validity in both the relativistic and non-relativistic limits. The appropriate Foldy-Wouthuysen transformations are extended to expand about the non-relativistic Hamiltonian limit to fourth order in the inverse of the particle's Einstein rest energy. The results have important consequences for magnetic measurements of many classes of clean anisotropic semiconductors, metals, and superconductors. In all of these cases, the Zeeman interaction is found to depend strongly upon the effective mass anisotropy. When an electron or hole is traveling in an atomically thin one-dimensional conduction band, its Zeeman, spin-orbit, and quantum spin Hall interactions are vanishingly small. Accurate expressions for the Zeeman, spin-orbit and quantum spin Hall interactions for two-dimensional conductors are provided.

We have carried out density-functional theory (DFT) calculations for the chromium pnictide BaCr 2 P 2 , which is structurally analogous to BaFe 2 As 2 , a parent compound for iron-pnictide superconductors. Evolutionary methods combined with DFT predict that the chromium analog has the same crystal structure as the latter. DFT also predicts Néel antiferromagnetic order on the chromium sites. Comparison with a simple electron-hopping model over a square lattice of chromium atoms suggests that it is due to residual nesting of the Fermi surfaces. We have confirmed the DFT predictions directly after the successful synthesis of polycrystalline samples of BaCr 2 P 2 . X-ray diffraction recovers the predicted crystal structure to high accuracy, while magnetic susceptibility and specific-heat measurements are consistent with a transition to an antiferromagnetically ordered state below [Formula: see text] K.