Quantum confinement effects in Si/Ge heterostructures with spatially ordered arrays of self-assembled quantum dots

Magnetotunneling spectroscopy was employed to probe the confinement in vertical Si/Ge double-barrier resonant tunneling diodes with regularly distributed Ge quantum dots. Their current-voltage characteristics reveal a step-like behavior in the vicinity of zero bias, indicating resonant tunneling of heavy-holes via three-dimensionally confined unoccupied hole states in Ge quantum dots. Assuming parabolic confinement we extract the strength of the confinement potential of quantum dots.Comment: 4 pages, 3 figure

Possibility of local pair existence in optimally doped SmFeAsO(1-x) in pseudogap regime

We report the analysis of pseudogap Delta* derived from resistivity experiments in FeAs-based superconductor SmFeAsO(0.85), having a critical temperature T_c = 55 K. Rather specific dependence Delta*(T) with two representative temperatures followed by a minimum at about 120 K was observed. Below T_s = 147 K, corresponding to the structural transition in SmFeAsO, Delta*(T) decreases linearly down to the temperature T_AFM = 133 K. This last peculiarity can likely be attributed to the antiferromagnetic (AFM) ordering of Fe spins. It is believed that the found behavior can be explained in terms of Machida, Nokura, and Matsubara (MNM) theory developed for the AFM superconductors.Comment: 5 pages, 2 figure

Congruences of lines in P5\mathbb{P}^5, quadratic normality, and completely exceptional Monge-Amp\`ere equations

The existence is proved of two new families of locally Cohen-Macaulay sextic threefolds in $\mathbb{P}^5$, which are not quadratically normal. These threefolds arise naturally in the realm of first order congruences of lines as focal loci and in the study of the completely exceptional Monge-Amp\`ere equations. One of these families comes from a smooth congruence of multidegree $(1,3,3)$ which is a smooth Fano fourfold of index two and genus 9.Comment: 16 page

Nanodiamonds carrying quantum emitters with almost lifetime-limited linewidths

Nanodiamonds (NDs) hosting optically active defects are an important technical material for applications in quantum sensing, biological imaging, and quantum optics. The negatively charged silicon vacancy (SiV) defect is known to fluoresce in molecular sized NDs (1 to 6 nm) and its spectral properties depend on the quality of the surrounding host lattice. This defect is therefore a good probe to investigate the material properties of small NDs. Here we report unprecedented narrow optical transitions for SiV colour centers hosted in nanodiamonds produced using a novel high-pressure high-temperature (HPHT) technique. The SiV zero-phonon lines were measured to have an inhomogeneous distribution of 1.05 nm at 5 K across a sample of numerous NDs. Individual spectral lines as narrow as 354 MHz were measured for SiV centres in nanodiamonds smaller than 200 nm, which is four times narrower than the best SiV line previously reported for nanodiamonds. Correcting for apparent spectral diffusion yielded a homogeneous linewith of about 200 MHz, which is close to the width limit imposed by the radiative lifetime. These results demonstrate that the direct HPHT synthesis technique is capable of producing nanodiamonds with high crystal lattice quality, which are therefore a valuable technical material

Grassmannians Gr(N-1,N+1), closed differential N-1 forms and N-dimensional integrable systems

Integrable flows on the Grassmannians Gr(N-1,N+1) are defined by the requirement of closedness of the differential N-1 forms $\Omega_{N-1}$ of rank N-1 naturally associated with Gr(N-1,N+1). Gauge-invariant parts of these flows, given by the systems of the N-1 quasi-linear differential equations, describe coisotropic deformations of (N-1)-dimensional linear subspaces. For the class of solutions which are Laurent polynomials in one variable these systems coincide with N-dimensional integrable systems such as Liouville equation (N=2), dispersionless Kadomtsev-Petviashvili equation (N=3), dispersionless Toda equation (N=3), Plebanski second heavenly equation (N=4) and others. Gauge invariant part of the forms $\Omega_{N-1}$ provides us with the compact form of the corresponding hierarchies. Dual quasi-linear systems associated with the projectively dual Grassmannians Gr(2,N+1) are defined via the requirement of the closedness of the dual forms $\Omega_{N-1}^{\star}$. It is shown that at N=3 the self-dual quasi-linear system, which is associated with the harmonic (closed and co-closed) form $\Omega_{2}$, coincides with the Maxwell equations for orthogonal electric and magnetic fields.Comment: 26 pages, references adde

Laplace transformations of hydrodynamic type systems in Riemann invariants: periodic sequences

The conserved densities of hydrodynamic type system in Riemann invariants satisfy a system of linear second order partial differential equations. For linear systems of this type Darboux introduced Laplace transformations, generalising the classical transformations in the scalar case. It is demonstrated that Laplace transformations can be pulled back to the transformations of the corresponding hydrodynamic type systems. We discuss periodic Laplace sequences of with the emphasize on the simplest nontrivial case of period 2. For 3-component systems in Riemann invariants a complete discription of closed quadruples is proposed. They turn to be related to a special quadratic reduction of the (2+1)-dimensional 3-wave system which can be reduced to a triple of pairwize commuting Monge-Ampere equations. In terms of the Lame and rotation coefficients Laplace transformations have a natural interpretation as the symmetries of the Dirac operator, associated with the (2+1)-dimensional n-wave system. The 2-component Laplace transformations can be interpreted also as the symmetries of the (2+1)-dimensional integrable equations of Davey-Stewartson type. Laplace transformations of hydrodynamic type systems originate from a canonical geometric correspondence between systems of conservation laws and line congruences in projective space.Comment: 22 pages, Late