Spin-glass behavior in the antiperovskite manganese nitride Mn3CuN codoped with Ge and Si

Antiperovskite manganese nitrides ${\mathrm{Mn}}_3\left({\mathrm{Cu}}_{0.6}{\mathrm{Si}}_x{\mathrm{Ge}}_{0.4?x}\right)N$ ($x=0.05$, 0.1, 0.15) were prepared and their negative thermal expansion, magnetic and specific heat properties were investigated. A frozen state with a freezing temperature was found at ～207 K in ${\mathrm{Mn}}_3\left({\mathrm{Cu}}_{0.6}{\mathrm{Si}}_{0.15}{\mathrm{Ge}}_{0.25}\right)N$. This indicates that ${\mathrm{Mn}}_3\left({\mathrm{Cu}}_{0.6}{\mathrm{Si}}_{0.15}{\mathrm{Ge}}_{0.25}\right)N$ exhibits a spin glass state at low temperatures. We discussed the cause of spin glass behavior and correlated this spin glass behavior with broadening of the negative thermal expansion operation-temperature window of the manganese nitrides ${\mathrm{Mn}}_3\left({\mathrm{Cu}}_{0.6}{\mathrm{Si}}_{0.15}{\mathrm{Ge}}_{0.25}\right)N$.     

On Mpc-structures and symplectic Dirac operators

We prove that the kernels of the restrictions of the symplectic Dirac operator and one of the two symplectic Dirac–Dolbeault operators on natural sub-bundles of polynomial valued spinor fields are finite dimensional on a compact symplectic manifold. We compute these kernels explicitly for complex projective spaces and show that the remaining Dirac–Dolbeault operator has infinite dimensional kernels on these finite rank sub-bundles. We construct injections of subgroups of the symplectic group (the pseudo-unitary group and the stabiliser of a Lagrangian subspace) in the $M{p}^c$ group and classify $G$-invariant $M{p}^c$-structures on symplectic manifolds with a $G$-action. We prove a variant of Parthasarathy’s formula for the commutator of two symplectic Dirac-type operators on general symmetric symplectic spaces.     

Chern–Simons formulation of three-dimensional gravity with torsion and nonmetricity

We consider various models of three-dimensional gravity with torsion or nonmetricity (metric affine gravity), and show that they can be written as Chern–Simons theories with suitable gauge groups. Using the groups $\mathrm{ISO}(2,1)$, $\mathrm{SL}(2,\mathbb{C})$ and $\mathrm{SL}(2,\mathbb{R})\times \mathrm{SL}(2,\mathbb{R})$, and the fact that they admit two independent coupling constants, we obtain the Mielke–Baekler model for zero, positive and negative effective cosmological constant respectively. Choosing $\mathrm{SO}(3,2)$ as the gauge group, one gets a generalization of conformal gravity that has zero torsion and only the trace part of the nonmetricity. This characterizes a Weyl structure. Finally, we present a new topological model of metric affine gravity in three dimensions arising from an $\mathrm{SL}(4,\mathbb{R})$ Chern–Simons theory.     

Quantum point contact conductance in normal metal/insulator/ metal/dx2−y2+idxy mixed wave superconductor junctions

The tunneling conductance in a normal metal/insulator/metal/$d_{x^2?y^2}+i{d}_{xy}$ mixed wave superconductor (N/I/N/$d_{x^2?y^2}+i{d}_{xy}$) junction is calculated, where the N/I/N region is a quantum wire. It is found in the single-mode case that the magnitude of the tunneling conductance near zero voltage is enhanced due to the Andreev bound state by quasiparticles with perpendicular and horizontal injection, and the zero-bias conductance varies with $L$ ($L$ is the distance from insulating layer to the interface of N/$d_{x^2?y^2}+i{d}_{xy}$ mixed wave superconductor). Splitting of the zero-bias conductance peak appears in the quantum point contact tunneling spectra for an N/I/N/$d_{x^2?y^2}+i{d}_{xy}$ junction, and several subgap peaks can split at the same time. On increasing both $L$ and the magnitude ratio of the two components for the $d_{x^2?y^2}+i{d}_{xy}$ mixed wave, the subgap resonances exhibit an alternately high and low behavior inside the energy gap. These results are different from those in d-wave and p-wave superconductor junctions.     

Diamagnetic susceptibility of a hydrogenic donor in low lying excited states in a Quantum Well

We present the ${\chi }_{\mathrm{dia}}$ of a hydrogenic donor in low lying excited states like 2s, 2p_± and 2p₀ in a GaAs/ Al_xGa_1−xAs Quantum Well for various Al compositions $x$ both in the parabolic and non-parabolic conduction band model using the variational method. To our knowledge there has been no such reports both theoretically and experimentally in the literature. It was observed that ${\chi }_{\mathrm{dia}}$ increases with increase of $x$ for both the parabolic and non-parabolic cases. The effect of non-parabolicity on ${\chi }_{\mathrm{dia}}$ is larger for the lower well width region for 2s and 2p_± states. Interestingly, we observe a “turn over” in the variation of ${\chi }_{\mathrm{dia}}$ against well widths in the lower well width region, a trend which is similar to the one observed in the variation of binding energy of donors in low lying excited states.     

Invariant surfaces of a three-dimensional manifold with constant Gauss curvature

We give a reduction procedure to determine (locally) the surfaces with constant Gauss curvature in a three-dimensional manifold which are invariant under the action of a one-parameter subgroup of the isometry group of the ambient space. We apply this procedure to describe the invariant surfaces with constant Gauss curvature in $H^2\times R$ and in $H_3$.