Richard A. Klemm

The influence of the Zeeman energy and the Landau levels (LLs) arising from an applied magnetic field B upon the critical temperature T_c is studied using a fully quantum mechanical method within the framework of the Bardeen–Cooper–Schrieffer (BCS) theory of superconductivity that forms from an ultraclean metal. As in semiclassical treatments, we found that two electrons can form Cooper pairs with opposite spins and momenta in the B direction while either in the same or in neighboring LLs. However, the fully quantum mechanical treatment of the LLs causes T _c (B) for electrons paired on the same LL to oscillate about the critical temperature of the BCS theory, similar to that of the de Haas-van Alphen effect. The Zeeman energy causes T _c (B) to decrease in an oscillatory fashion with increasing B for electrons paired either on the same or on neighboring LLs. For the Zeeman g > 1, pairing on neighboring LLs results in the highest T _c (B). For g < 1, pairing on the same LLs gives the highest T _c (B). In addition, T _c (B) for electrons paired on neighboring LLs exhibits an apparent symmetry around g = 2, as the oscillatory critical temperature behaviors are nearly identical for g = 2 ± δ .

The exponential of an operator or matrix is widely used in quantum theory, but it sometimes can be a challenge to evaluate. For non-commutative operators X and Y, according to the Campbell-Baker-Hausdorff-Dynkin theorem, e ^X+Y is not equivalent to e ^X e ^Y , but is instead given by the well-known infinite series formula. For a Lie algebra of a basis of three operators {X, Y, Z}, such that [X, Y] = κ Z for scalar κ and cyclic permutations, here it is proven that e ^{a X+b Y} is equivalent to e ^{p Z} e ^{q X} e^{−p Z} for scalar p and q. Extensions for e ^{a X+b Y+c Z} are also provided. This method is useful for the dynamics of atomic and molecular nuclear and electronic spins in constant and oscillatory transverse magnetic and electric fields.

Highly-sensitive broadly-tunable detectors are needed for future multi-domain sensing and quantum-information systems. Layered graphene with “magic” twist-angle between 2 - 4 sheets is superconducting below 2 K. Demonstrated Josephson junctions in this material feature very high dynamic resistance at the maximum zero-voltage current. Biased at this current, a small microwave voltage across the junction shifts the voltage-current step, which results in a large DC output voltage. A suitable antenna driven by external radiation can source the desired AC voltage across the junction. As a non-thermal mechanism, such detectors may in principle be fast, as well as sensitive. Additionally, there is a bolometric response, whose temperature coefficient of resistance we estimate to be 300%/K. Design, fabrication, response, and twist-angle tolerance for antenna-coupled, superconducting-graphene, Josephson-junction detectors of mm-wave and THz radiation are discussed.

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 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 potential difference Δ v or a radial charge current I across its inner and outer radii. Combined changes in I S and in either Δ v or 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.