Control of Spin Diffusion and Suppression of the Hanle Effect by the Coexistence of Spin and Valley Hall Effects

In addition to spin, electrons in many materials possess an additional pseudo-spin degree of freedom known as 'valley'. In materials where the spin and valley degrees of freedom are weakly coupled, they can be both excited and controlled independently. In this work, we study a model describing the interplay of the spin and valley Hall effects in such two-dimensional materials. We demonstrate the emergence of an additional longitudinal neutral current that is both spin and valley polarized. The additional neutral current allows to control the spin density by tuning the magnitude of the valley Hall effect. In addition, the interplay of the two effects can suppress the Hanle effect, that is, the oscillation of the nonlocal resistance of a Hall bar device with in-plane magnetic field. The latter observation provides a possible explanation for the absence of the Hanle effect in a number of recent experiments. Our work opens also the possibility to engineer the conversion between the valley and spin degrees of freedom in two-dimensional materials.Comment: 15 pages, 2 figure

Fermi sea and sky in the Bogoliubov-de Gennes equation

We develop a comprehensive logical framework for effectively handling the overcomplete basis set in the Bogoliubov-de Gennes equation that contains two orthonormal basis sets conjugate with each other, such as particle and hole orthonormal basis sets. We highlight the significant implications of our logical framework from theoretical concepts and experimental predictions. Firstly, we rigorously derive all many-body eigenfunctions of arbitrary nonuniform superconductors and uncover that the many-body eigenstates are full of superconducting spin clouds-the electron configuration within the Cooper-like pair of an arbitrary nonuniform superconductor. Secondly, we demonstrate a conjugate loop formed by the effective vacuum states of two orthonormal basis sets conjugate with each other, such as the Fermi sea and sky-the effective vacuum states of positive and negative orthonormal basis sets, respectively. Thirdly, we present a gate-, field-, and phase-tunable tunnel spectroscopy asymmetry arising from the imbalanced particle-hole distribution of the subgap quasiparticles in a quantum-dot Josephson junction. These findings underscore the power of our logical framework and its implications for advancing our understanding and utilization of solid-state devices based on superconductivity.Comment: 28 page, 6 figure