Energy spectrum and current-phase relation of a nanowire Josephson junction close to the topological transition

A semiconducting nanowire proximitized by an $s$-wave superconductor can be tuned into a topological state by an applied magnetic field. This quantum phase transition is marked by the emergence of Majorana zero modes at the ends of the wire. The fusion of Majorana modes at a junction between two nanowires results in a $4\pi$-periodic Josephson effect. We elucidate how the $4\pi$-periodicity arises across the topological phase transition in a highly-transparent short nanowire junction. Owing to a high transmission coefficient, Majorana zero modes coming from different wires are strongly coupled, with an energy scale set by the proximity-induced, field-independent pairing potential. At the same time, the topological spectral gap---defined by competition between superconducting correlations and Zeeman splitting---becomes narrow in the vicinity of the transition point. The resulting hybridization of the fused Majorana states with the spectral continuum strongly affects the electron density of states at the junction and its Josephson energy. We study the manifestations of this hybridization in the energy spectrum and phase dependence of the Josephson current. We pinpoint the experimentally observable signatures of the topological phase transition, focusing on junctions with weak backscattering.Comment: 26 pages, 11 figure

Short-wavelength out-of-band EUV emission from Sn laser-produced plasma

We present the results of spectroscopic measurements in the extreme ultraviolet (EUV) regime (7-17 nm) of molten tin microdroplets illuminated by a high-intensity 3-J, 60-ns Nd:YAG laser pulse. The strong 13.5 nm emission from this laser-produced plasma is of relevance for next-generation nanolithography machines. Here, we focus on the shorter wavelength features between 7 and 12 nm which have so far remained poorly investigated despite their diagnostic relevance. Using flexible atomic code calculations and local thermodynamic equilibrium arguments, we show that the line features in this region of the spectrum can be explained by transitions from high-lying configurations within the Sn$^{8+}$-Sn$^{15+}$ ions. The dominant transitions for all ions but Sn$^{8+}$ are found to be electric-dipole transitions towards the $n$=4 ground state from the core-excited configuration in which a 4$p$ electron is promoted to the 5$s$ sub-shell. Our results resolve some long-standing spectroscopic issues and provide reliable charge state identification for Sn laser-produced plasma, which could be employed as a useful tool for diagnostic purposes.Comment: 11 pages, 4 figure