Small Level Splitting Research Articles

Linear polarization of x-rays emitted in the decay of highly-charged ions via overlapping resonances

The linear polarization of x-rays, emitted from highly-charged ions, has been studied within the framework of the density matrix theory and the multiconfiguration Dirac-Fock method. Emphasis was placed especially on two-photon cascades that proceed via intermediate overlapping resonances. For such two-step cascades, we here explore how the level-splitting of the resonances affects the linear polarization of the x-rays, and whether modifications in the degree of polarization may help determine small level-splittings in multiply- and highly-charged ions, if carefully analyzed along isoelectronic sequences. Detailed calculations are carried out for the 1s2p2 Ji = 3/2 → 1s2s2p J = 1/2, 3/2 + γ1 → 1s22s Jf = 1/2 + γ1 + γ2 radiative cascade of lithium-like W71+ ions. For this cascade, a quite remarkable increase of the (degree of) linear polarization is found for the second-step γ2 photons, if the level-splitting becomes smaller than Δω ≲ 0.2 a.u. ≈ 5.4 eV. Accurate polarization measurements of x-rays may therefore be also utilized in the future to ascertain small level-splittings in multiply- and highly-charged ions.

Can angle-resolved x-ray measurements help determine small level splittings in highly charged ions?

SynopsisThe angular distribution and photon-photon angular correlation have been studied for x-ray emissions from two-step radiative cascades that proceed via two or more overlapping intermediate resonances. From this study, we suggest that accurate angle-resolved measurements of the x-ray emissions may serve as a tool for determining small level splittings in excited highly-charged ions.

Determination of small level splittings in highly charged ions via angle-resolved measurements of characteristic x rays

It is shown that small energy-level splittings of resonance states in highly charged ions can be extracted from the angular correlations of characteristic x rays emitted in radiative cascades, which may ultimately be used for new tests of QED in highly charged ions.

Orbital-Selective Mott Transition in Multiorbital Hubbard Model with Orbital Degeneracy Lifting

We study the Mott transition in the three-orbital Hubbard model with orbital level splitting. To investigate how the orbital level splitting affects the Mott transition in the case of two electrons per site, we use the dynamical mean field theory combined with continuous-time quantum Monte Carlo simulations. By calculating the double occupancy, we reveal that a small level splitting suppresses the metallic region. On the other hand, the system is smoothly connected to a band insulator in the limit of large level splitting. It is found that in the intermediate region of level splitting, the competition between the two states stabilizes a metallic phase near the Mott transition, which results in the nonmonotonic behavior in the critical interaction strength as a function of the level splitting.

Boris Peter Stoicheff

Boris Peter Stoicheff

Design of a d1-analogueof cuprates: Sr2VO4 and Ba2VO4 under pressure

By means of a combination of the local density approximation and dynamical mean field theory (LDA+ DMFT), we study the possibility of making ad1 analogue ofd9 cuprates on the basisof Sr2VO4. We calculate theelectronic structure of Sr2VO4 under pressure, and show that while the material is a1/6-filled three-band system at ambient pressure with a small level splitting between thedxy- anddyz/zx-bands, an orbital polarization occurs under sufficiently high uniaxial pressure in thec-direction. While all energy scales are relatively small, the electronic structure ofSr2VO4 under pressure issimilar to that of La2CuO4; it is a two-dimensional half-filled single-band system which has, relative to the nearestneighbour hopping, a similar Coulomb repulsion and next-nearest neighbour hopping. Wealso study the effect of substituting Sr by Ba, i.e., chemical pressure, and showthat the pressure needed for the orbital polarization is considerably reduced.

Sr2VO4andBa2VO4under pressure: An orbital switch and potentiald1superconductor

We study Sr$_2$(Ba$_2$)VO$_4$ under high pressure by means of the local density approximation + dynamical mean field theory method. While Sr$_2$VO$_4$ is a 1/6-filling three-band system at ambient pressure with a small level splitting between the $d_{xy}$- and $d_{yz/zx}$-bands, we show that an orbital polarization occurs under uniaxial pressure, resulting in dramatic changes of the magnetic, optical, and transport properties. When pressure is applied in the $c$-direction, a $d^1$ analog of $d^9$ cuprates is realized, making Sr$_2$(Ba$_2$)VO$_4$ a possible candidate for a $d^1$ superconductor. Experimentally, this uniaxial pressure can be realized by growing Ba$_2$VO$_4$ on a substrate with lattice constant 4.1-4.2 \AA.

Quantum localization and dynamical tunneling of quasiseparatrix wave functions for molecular vibration

We report a new kind of “dynamical tunneling” that can be observed in chaotic molecular vibration. The present phenomenon has been found in eigenfunctions quantized in a thin quasiseparatrix (chaotic zone) in phase space. On the classical Poincaré section corresponding to this situation, two or more unstable (hyperbolic) fixed points coexist and are connected through the so-called heteroclinic crossings, whereby the entire quasiseparatrix is generated. When the quasiseparatrix is thin enough, each of the hyperbolic fixed points is surrounded by the relatively “wide lake” of chaos due to the infinite and violent crossings between the stable and unstable manifolds, and these lakes are in turn connected by “narrow canals.” Our finding is, in spite of the fact that the narrow canals are classically allowed for the trajectories to pass through fast, wave packets can be quantized predominantly as “quasistanding-waves” in each lake area and hence can be mostly localized to remain there for much longer time than the corresponding classical trajectories do. In other words, the wave packets are localized in the vicinity of the classically unstable fixed points due to the quantum effect. However, a pair of these “localized” wave packets are eventually delocalized into the other lakes, and thereby form a pair of eigenfunctions (purely standing waves) with a small level splitting. Thus the present phenomenon can be characterized as a tunneling between the states of quantum localization in an oscillator problem.