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In the presence of spin-orbit coupling, electron scattering off impurities depends on both spin and orbital angular momentum of electrons -- spin-orbit scattering. Although some transport properties are subject to spin-orbit scattering, experimental techniques directly accessible to this effect are limited. Here we show that a signature of spin-orbit scattering manifests itself in quasiparticle interference (QPI) imaged by spectroscopic-imaging scanning tunneling microscopy. The experimental data of a polar semiconductor BiTeI are well reproduced by numerical simulations with the $T$-matrix formalism that include not only scalar scattering normally adopted but also spin-orbit scattering stronger than scalar scattering. To accelerate the simulations, we extend the standard efficient method of QPI calculation for momentum-independent scattering to be applicable even for spin-orbit scattering. We further identify a selection rule that makes spin-orbit scattering visible in the QPI pattern. These results demonstrate that spin-orbit scattering can exert predominant influence on QPI patterns and thus suggest that QPI measurement is available to detect spin-orbit scattering.
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A superconductor-semiconducting nanowire-superconductor heterostructure in the presence of spin orbit coupling and magnetic field can support a supercurrent even in the absence of phase difference between the superconducting electrodes. We investigate this phenomenon, the anomalous Josephson effect, employing a model capable of describing many bands in the normal region. We discuss geometrical and symmetry conditions required to have finite anomalous supercurrent and in particular we show that this phenomenon is enhanced when the Fermi level is located close to a band opening in the normal region.
Although recent experiments and theories have shown a variety of exotic transport properties of non-equilibrium quasiparticles (QPs) in superconductor (SC)-based devices with either Zeeman or exchange spin-splitting, how QP interplays with magnon spin currents remains elusive. Here, using non-local magnon spin-transport devices where a singlet SC (Nb) on top of a ferrimagnetic insulator (Y3Fe5O12) serves as a magnon spin detector, we demonstrate that the conversion efficiency of magnon spin to QP charge via inverse spin-Hall effect (iSHE) in such an exchange-spin-split SC can be greatly enhanced by up to 3 orders of magnitude compared with that in the normal state, particularly when its interface superconducting gap matches the magnon spin accumulation. Through systematic measurements with varying the current density and SC thickness, we identify that superconducting coherence peaks and exchange spin-splitting of the QP density-of-states, yielding a larger spin excitation while retaining a modest QP charge-imbalance relaxation, are responsible for the giant QP iSHE. The latter exchange-field-modified QP relaxation is experimentally proved by spatially resolved measurements with varying the separation of electrical contacts on the spin-split Nb.
When an electron or hole is in a conduction band of a crystal, it can be very different from 2, depending upon the crystalline anisotropy and the direction of the applied magnetic induction ${bf B}$. In fact, it can even be 0! To demonstrate this quantitatively, the Dirac equation is extended for a relativistic electron or hole in an orthorhombically-anisotropic conduction band with effective masses $m_j$ for $j=1,2,3$ with geometric mean $m_g=(m_1m_2m_3)^{1/3}$. The appropriate Foldy-Wouthuysen transformations are extended to evaluate the non-relativistic Hamiltonian to $O({rm m}c^2)^{-4}$, where ${rm m}c^2$ is the particles Einstein rest energy. For ${bf B}||hat{bf e}_{mu}$, the Zeeman $g_{mu}$ factor is $2{rm m}sqrt{m_{mu}}/m_g^{3/2} + O({rm m}c^2)^{-2}$. While propagating in a two-dimensional (2D) conduction band with $m_3gg m_1,m_2$, $g_{||}<<2$, consistent with recent measurements of the temperature $T$ dependence of the parallel upper critical induction $B_{c2,||}(T)$ in superconducting monolayer NbSe$_2$ and in twisted bilayer graphene. While a particle is in its conduction band of an atomically thin one-dimensional metallic chain along $hat{bf e}_{mu}$, $g<<2$ for all ${bf B}={bf abla}times{bf A}$ directions and vanishingly small for ${bf B}||hat{bf e}_{mu}$. The quantum spin Hall Hamiltonian for 2D metals with $m_1=m_2=m_{||}$ is $K[{bf E}times({bf p}-q{bf A})]_{perp}sigma_{perp}+O({rm m}c^2)^{-4}$, where ${bf E}$ and ${bf p}-q{bf A}$ are the planar electric field and gauge-invariant momentum, $q=mp|e|$ is the particles charge, $sigma_{perp}$ is the Pauli matrix normal to the layer, $K=pmmu_B/(2m_{||}c^2)$, and $mu_B$ is the Bohr magneton.
In this article we review recent work on van der Waals (vdW) systems in which at least one of the components has strong spin-orbit coupling. We focus on a selection of vdW heterostructures to exemplify the type of interesting electronic properties that can arise in these systems. We first present a general effective model to describe the low energy electronic degrees of freedom in these systems. We apply the model to study the case of (vdW) systems formed by a graphene sheet and a topological insulator. We discuss the electronic transport properties of such systems and show how they exhibit much stronger spin-dependent transport effects than isolated topological insulators. We then consider vdW systems in which the layer with strong spin-orbit coupling is a monolayer transition metal dichalcogenide (TMD) and briefly discuss graphene-TMD systems. In the second part of the article we discuss the case in which the vdW system includes a superconducting layer in addition to the layer with strong spin-orbit coupling. We show in detail how these systems can be designed to realize odd-frequency superconducting pair correlations. Finally, we discuss twisted graphene-NbSe2 bilayer systems as an example in which the strength of the proximity-induced superconducting pairing in the normal layer, and its Ising character, can be tuned via the relative twist angle between the two layers forming the heterostructure.
The cuprate high-temperature superconductors are known to host a wide array of effects due to interactions and disorder. In this work, we look at some of the consequences of these effects which can be visualized by scanning tunneling spectroscopy. These interaction and disorder effects can be incorporated into a mean-field description by means of a self-energy appearing in the Greens function. We first examine the quasiparticle scattering interference spectra in the superconducting state at optimal doping as temperature is increased. Assuming agreement with angle-resolved photoemission experiments which suggest that the scattering rate depends on temperature, resulting in the filling of the $d$-wave gap, we find that the peaks predicted by the octet model become progressively smeared as temperature is increased. When the scattering rate is of the same order of magnitude as the superconducting gap, the spectral function shows Fermi-arc-like patterns, while the power spectrum of the local density of states shows the destruction of the octet-model peaks. We next consider the normal state properties of the optimally-doped cuprates. We model this by adding a marginal Fermi liquid self-energy to the normal-state propagator, and consider the dependence of the QPI spectra on frequency, temperature, and doping. We demonstrate that the MFL self-energy leads to a smearing of the caustics appearing in the normal-state QPI power spectrum as either temperature or frequency is increased at fixed doping. The smearing is found to be more prominent in the MFL case than in an ordinary Fermi liquid. We also consider the case of a marginal Fermi liquid with a strongly momentum-dependent self-energy which gives rise to a visible nodal-antinodal dichotomy at the normal state, and discuss how the spectra as seen in ARPES and STS differ from both an isotropic metal and a broadened $d$-wave superconductor.
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