Surface Interband Transitions Research Articles

Signatures of surface Majorana modes in the magnetic response of topological superconductors

We study the magnetic susceptibility of a two-dimensional cone of Majorana modes localised at the surface of a three-dimensional time-reversal invariant topological superconductor belonging to class DIII. A field parallel to the surface tilts the surface Majorana cone along the supercurrent direction. For fields larger than a critical threshold field $H^*$, $H>H^*$, a transition from type I to type II Dirac cone occurs and a finite current carried by the Majorana modes start to flow, leading to an additional diamagnetic contribution to the surface magnetization. On a curved surface interband transitions are promoted by the Majorana spin connection that couples to the external field, giving rise to a finite frequency magnetic susceptibility.

Surface plasmon dispersion on sputtered and nanostructured Ag(001)

The surface plasmon dispersion of ion bombarded Ag(001) is investigated by angle resolved high resolution electron energy loss spectroscopy. We find it to be parabolic and dominated by the quadratic term, contrary to the case of flat Ag(001) where the linear term is dominant. The case is reminiscent of surface plasmon dispersion on the oxygen covered, missing row reconstructed Ag(001) surface, for which case the change of the dispersion from nearly linear to quadratic was attributed to the removal of a surface plasmon decay channel associated to the surface interband transition at $\overline{X}.$ We show moreover, that for the sputtered surface, slope and curvature of the dispersion depend on surface morphology at the nanoscale. When sputtering is performed at low crystal temperature and no ordered superstructure forms, the quadratic term coincides with the isotropic value dictated by bulk properties, reported for flat Ag(110) and Ag(111) and for reconstructed Ag(001). When on the contrary sputtering is performed at room temperature and the checkerboard superstructure develops, the quadratic term becomes twice as large.

Substrate reconstruction and electronic surface states: Ag(0 0 1)

We present the result of a combined ab initio theoretical study and ultraviolet photoemission spectroscopy experiment of the electronic surface states of the clean and of the oxygen covered, unreconstructed and missing-row reconstructed, Ag(0 0 1) surface. For the clean and for the unreconstructed oxygen covered surface, theory and experiment find an electronic surface state at about 0.4 eV below the Fermi energy ( E F) at the X ̄ point of the surface Brillouin zone. At the same point, theory predicts the existence of an empty state at +3 eV. Upon reconstruction, the photoemission signal of the filled state is strongly reduced and, according to calculations, the state shifts in energy above E F. The surface interband transition (SIT) between the two states exists thus only for the unreconstructed surfaces and nearly matches the surface plasmon energy. Our investigation confirms therefore the correlation between the presence of this SIT and the anomaly of the surface plasmon dispersion curve of unreconstructed Ag(0 0 1).

Effect of surface interband transitions on surface plasmon dispersion: O/Ag(001)

The effect of surface interband transitions (SIT) on surface plasmon dispersion was investigated by high-resolution electron-energy-loss spectroscopy for Ag(001). We demonstrate that the anomalous linear dispersion on this face, which is at variance with the parabolic form present for the other low Miller index surfaces, is due to a SIT between Shockley states that nearly matches the surface plasmon frequency. The anomaly is eliminated when the substrate undergoes a missing-row reconstruction induced by oxygen adsorption that removes the SIT.

Plasmon damping and surface interband transitions on Ag(001) and (011)

The dependence of surface-plasmon damping versus plasmon momentum and energy has been measured for the Ag(011) surface with angle-resolved electron energy loss spectroscopy. The data are compared with previous results obtained for Ag(001). At small transferred momenta, q‖, we observe a nearly linear dependence of the energy loss width with q‖ due to the growing phase space available for e-h pair creation. However the very efficient damping mechanism observed for q‖ beyond 0.10 Å−1 is not present for Ag(011). We demonstrate that it is due the onset of interband transitions between filled and empty surface states. Two such states are indeed present near the X point of Ag(001) as demonstrated by inverse photoemission experiments and electronic band structure calculations. The energy gap between the two bands can thus be determined by EELS with a greater precision than by photoemission.

Effect of optical resonances on the second harmonic response from Ag(111) and Ag(110) in solution

The wavelength dependence of the second harmonic response from native single crystal silver electrodes is examined for Ag(111) and Ag(110). Both the rotational anisotropy and potential dependence of the second harmonic response are significantly different at the two wavelengths examined, 1064 nm and 532 nm excitation. These differences are attributed to optical resonances between the incident or outgoing radiation and surface electronic or bulk electronic transitions of the native metal. The anisotropy at 532 nm reflects the increased contribution of surface interband transitions as this higher excitation energy. It is proposed that the potential dependence at 532 nm excitation involves resonances with surface electronic states on the metal.

Interfacial relaxation via s-polarized electroreflectance

The problem of the microscopic interpretation of plasma electroreflectance is revisited. A simple analytical expression is derived for electroreflectance of s-polarized light on the basis of an extension of Aspnes and McIntyre's model with no account of electromodulation of surface interband transitions. The extension allows for relaxation of the distance of closest approach of the solvent molecules to the electrode with charging. In order to illustrate this formula, experimental data are treated for indium and lead in contact with surface-inactive electrolytes. The results obtained so far exhibit qualitative features of interfacial relaxation which are in line with the conclusions of the jellium electronic theory.