Early investigations on vanadium in the cubic 3C-SiC polytype concluded that the luminescence of the center is not possible because the excited state is degenerate with the conduction band. However, later work refuted this notion, demonstrating a doublet in photoluminescence (PL) at ∼ 1493 – 1495 nm , apparently associated with vanadium (V). In this work, we undertake a detailed experimental and theoretical study of the V center in 3C-SiC. We show that the vanadium PL can be seen as a recombination of an exciton bound to V, in contrast to the other two common hexagonal polytypes (4H- and 6H-SiC), where the PL is due to an interatomic transition of the 3 d electron within the V center, according to a well-established model. We also show that the splitting observed in the PL lines is likely not inherent to the center and is due to stress present in the samples. Ideally, in a strain-free 3C-SiC material, the vanadium PL will comprise a single line, which makes the V center in this polytype attractive for applications as a qubit at moderate temperatures. This contrasts with the hexagonal polytypes where the splitting of the zero-phonon line is inherent to the center due to the crystal structure, which has a negative effect on the spin coherence at liquid helium temperature, and millikelvin temperatures are needed to improve the spin coherence.

This Letter presents the theory of planar ballistic superconductor–normal metal–superconductor junctions at T = 0 for any normal layer thickness L taking into account phase gradients in superconducting leads. The current-phase relation was derived in the model of the steplike pairing potential analytically and is exact in the limit of large ratio of the Fermi energy to the superconducting gap. At small L (short junction) the obtained current-phase relation is essentially different from that in the previous theory neglecting phase gradients. It was confirmed by recent numerical calculations and was observed in the experiment on short InAs nanowire Josephson junctions. The analysis resolves the problem with the charge conservation law in the steplike pairing potential model.

We discuss a class of lattice S = 1 2 quantum Hamiltonians with bond-dependent Ising couplings and a mutually “anticommuting” algebra of extensively many local Z 2 conserved charges that was explicated by Pujari []. This mutual algebra is reminiscent of the spin- 1 2 Pauli matrix algebra but encoded in the structure of . These models have finite residual entropy density in the ground state with a simple but nontrivial degeneracy counting and concomitant quantum spin liquidity as proved by Pujari []. The spin liquidity relies on a geometrically site-interlinked character of the local conserved Z 2 charges that is rather natural in the presence of an anticommuting structure. One may contrast this with, for example, the bond-interlinked character of the local conserved Z 2 charges on the hexagonal plaquettes of the Kitaev honeycomb spin- 1 2 model, which leads to a mutually commuting local algebra. In this work, we make several exact statements on the kinds of many-body orders that can be present within the class of anticommuting quantum spin liquids coexisting with extensive residual ground state entropy. We elucidate the differences between the many-body order in these models and that found in some gapped quantum spin liquids whose canonical example is the Kitaev toric code. The toric code belongs to the more general class of Levin-Wen or string net constructions that possess mutually commuting algebras for the local conserved charges. We also point out a mutually commuting algebra with local support that is naturally expressed as multilinear Majorana forms in the Kitaev representation of these quantum spin liquids. They capture quantum resonances spread across the lattice in anticommuting Z 2 quantum spin liquids.