Manipulation of electronic and magnetic properties of M2_2C (M=Hf, Nb, Sc, Ta, Ti, V, Zr) monolayer by applying mechanical strains

Tuning the electronic and magnetic properties of a material through strain engineering is an effective strategy to enhance the performance of electronic and spintronic devices. Recently synthesized two-dimensional transition metal carbides M$_2$C (M=Hf, Nb, Sc, Ta, Ti, V, Zr), known as MXenes, has aroused increasingly attentions in nanoelectronic technology due to their unusual properties. In this paper, first-principles calculations based on density functional theory are carried out to investigate the electronic and magnetic properties of M$_2$C subjected to biaxial symmetric mechanical strains. At the strain-free state, all these MXenes exhibit no spontaneous magnetism except for Ti$_2$C and Zr$_2$C which show a magnetic moment of 1.92 and 1.25 $\mu_B$/unit, respectively. As the tensile strain increases, the magnetic moments of MXenes are greatly enhanced and a transition from nonmagnetism to ferromagnetism is observed for those nonmagnetic MXenes at zero strains. The most distinct transition is found in Hf$_2$C, in which the magnetic moment is elevated to 1.5 $\mu_B$/unit at a strain of 15%. We further show that the magnetic properties of Hf$_2$C are attributed to the band shift mainly composed of Hf(5$d$) states. This strain-tunable magnetism can be utilized to design future spintronics based on MXenes

The Happer's puzzle degeneracies and Yangian

We find operators distinguishing the degenerate states for the Hamiltonian $H= x(K+{1/2})S_z +{\bf K}\cdot {\bf S}$ at $x=\pm 1$ that was given by Happer et al$^{[1,2]}$ to interpret the curious degeneracies of the Zeeman effect for condensed vapor of $^{87}$Rb. The operators obey Yangian commutation relations. We show that the curious degeneracies seem to verify the Yangian algebraic structure for quantum tensor space and are consistent with the representation theory of $Y(sl(2))$.Comment: 8 pages, Latex fil

A study on the relations between the topological parameter and entanglement

In this paper, some relations between the topological parameter $d$ and concurrences of the projective entangled states have been presented. It is shown that for the case with $d=n$, all the projective entangled states of two $n$-dimensional quantum systems are the maximally entangled states (i.e. $C=1$). And for another case with $d\neq n$, $C$ both approach $0$ when $d\rightarrow +\infty$ for $n=2$ and $3$. Then we study the thermal entanglement and the entanglement sudden death (ESD) for a kind of Yang-Baxter Hamiltonian. It is found that the parameter $d$ not only influences the critical temperature $T_{c}$, but also can influence the maximum entanglement value at which the system can arrive at. And we also find that the parameter $d$ has a great influence on the ESD.Comment: 8 pages, 5 figure