Kramers Pairs Research Articles

Spin properties of free electrons and holes in Hg1-xCdxTe/CdTe quantum well

Spin properties of Hg1ixCdxTe / CdTe quantum wells (QW) with inverted energy bands are considered using eight-band k ¢ p Hamiltonian. The spin splitting of doubly degenerate bands (Kramers pairs) was included via either Rashba or external voltage Hamiltonians. The spin surfaces, which describe the average spin as a function of spin direction of a ballistic 2D charge carrier, in general, are shown to be ellipsoidal rather than spherical. In extreme cases the spin surfaces may reduce to disk, line, or Bloch sphere. Characteristic shapes of the spin surfaces at different wave vectors and QW composition x are presented in a form of graphs in the spin space.

Stability of the quantum spin Hall effect: Effects of interactions, disorder, andZ2topology

The stability to interactions and disorder of the quantum spin Hall effect (QSHE) proposed for time-reversal-invariant 2D systems is discussed. The QSHE requires an energy gap in the bulk and gapless edge modes that conduct spin-up and spin-down excitations in opposite directions. When the number of Kramers pairs of edge modes is odd, certain one-particle scattering processes are forbidden due to a topological $\mathbb{Z}_2$ index. We show that in a many-body description, there are other scattering processes that can localize the edge modes and destroy the QSHE: the region of stability for both classes of models (even or odd number of Kramers pairs) is obtained explicitly in the chiral boson theory. For a single Kramers pair the QSHE is stable to weak interactions and disorder, while for two Kramers pairs it is not; however, the two-pair case can be stabilized by {\it either} finite attractive or repulsive interactions. For the simplest case of a single pair of edge modes, it is shown that changing the screening length in an edge with screened Coulomb interactions can be used to drive a phase transition between the QSHE state and the ordinary insulator.

Spinor optimization for a relativistic spin-dependent CASSCF program

Detailed formulae for the implementation of the multi-configuration SCF spinor optimization in a basis of Kramers pair 2-spinors – i.e. exploiting time-reversal symmetry – are presented. Full expressions for the spinor gradient and spinor Hessian elements are given in abstract form as well as within the usual CASSCF subspace division. As far as possible, the resulting terms are grouped to relativistic inactive and active Fock matrices, which have been introduced previously. Approximations for the Hessian are introduced so as to initialize it in an inverse Hessian update algorithm for a diagonal first approximation within the standard quasi-Newton-Raphson procedure. The effects of double group symmetry arising from spin dependence on Fock matrices and therefore gradient and Hessian are discussed and a group scheme for the implementation is proposed.

Nonadiabatic dynamics and electronic energy relaxation of Cl(2P) atoms in solid Ar

The dynamics of Cl(2P) atoms in a solid Ar matrix is studied, with emphasis on electronic energy relaxation of excited states, and on p-orbital reorientation effects. The method used follows Tully’s approach for nonadiabatic molecular dynamics simulations, which treats the electronic degrees of freedom quantum-mechanically, and the atomic motions classically, allowing for ‘‘hopping’’ of the atoms between different potential energy surfaces. We introduce an extended version of this method, to handle ‘‘Berry Phase’’ effects due to the doubly degenerate Kramers pairs of states present in this system. The role of both electrostatic and of spin–orbit interactions between different electronic states is incorporated in the treatment. The simulations yield a time scale of 13 ps for the energy relaxation of the highest excited electronic state of Cl(2P). A time scale of similar magnitude is found for the depolarization of this state. However, the time scale for orbital reorientation at thermal conditions is only 0.7 ps. This is attributed to the fact that at thermal conditions, only the two lowest electronic states are populated. The physical mechanisms of these basic radiationless decay processes are discussed on the basis of the simulations.

Many-body potentials of an open shell atom: Spectroscopy of spin–orbit transitions of iodine in crystalline Xe and Kr

Temperature dependent emission spectra of spin excited iodine in crystalline Xe and Kr are presented and analyzed in terms of nonadditive anisotropic pair interactions. In the octahedral trap site, the atomic 2P states split into E1/2 and G3/2 groups of the double valued representation. The fourfold degenerate G3/2 state is subject to strong Jahn–Teller instability and further splits by coupling to phonons into E1/2 and E3/2 Kramers pairs. Accordingly, the observed emission spectra are composed of two bands: 2E1/2→1E1/2 and 2E1/2→E3/2 transitions. Two pairs of bands are observed each in Xe and Kr. The long-lived pairs (at 15 K, τ=250 μs and 930 μs in Xe and Kr, respectively) are assigned to the isolated atom, while a short lived pair of bands (at 15 K, τ<1 μs in Xe, and τ=2.2 μs in Kr) are assigned to I atoms trapped as nearest neighbor to a localized charge, identified as (HRg)+. The isolated atom spectra are simulated by Monte Carlo methods which assume classical statistics in the heavy atom coordinates, and adiabatic following of the electronic coordinate. Angle dependent, gas phase pair interactions are used as a starting point. Minor modifications to the pair interactions, and a temperature dependent spin–orbit splitting constant, adequately reproduce the experimental spectra. Many-body contributions to the effective pair potentials can be estimated to change pair parameters by less than ∼3%.

On the relativistic theory of nuclear spin-spin coupling constants

Time-reversal symmetry is exploited to halve the computational effort for the calculation of nuclear spin-spin coupling constants in the framework of the relativistic analogue of Ramsey's theory. The derivation is given for quaternionic relativistically parameterized extended Huckel (QATREX) wavefunctions, but the arguments used apply to any quantum-chemical method which generates Kramers pairs. Applications to selected heavy-element fluorides MF n (n = 2, 4, 6) are given based on charge-iterated REX calculations.

Spin-lattice relaxation in magnetic ion pairs

A new theoretical model of spin-lattice relaxation for magnetic "ion pairs" has been developed in which both the "spin-phonon" and "spin-spin" interactions are jointly effective in producing a net relaxation transition. The Raman-type indirect two-phonon relaxation rate for non-Kramers as well as Kramers ion pairs shows ${T}^{7}$ dependence at low temperatures and ${T}^{3}$ dependence at high temperatures. The ${T}^{3}$ dependence is entirely a new result. The ${T}^{7}$ dependence for Kramers pairs is also a new result as it is not possible in the usual Van Vleck mechanism. Even the ${T}^{7}$ dependence for non-Kramers ion pairs is different from a similar standard result for unpaired ions. It appears that the electronic spin relaxation behavior of ion pairs may be quite different from that of unpaired ions.

Time-reversal symmetry, Kramers' degeneracy and the algebraic eigenvalue problem

Abstract A method is presented whereby time-reversal symmetry may be fully exploited in systems exhibiting Kramers' degeneracy. A basis adapted to time-reversal symmetry, i.e. consisting of Kramers pairs, will be transformed into another of the same structure by symplectic unitary or equivalently, by quaternionic unitary transformations. Only one quaternionic hermitean eigenvalue problem of half the original order has to be solved for each Kramers pair. This leads to a significant reduction of the necessary computational effort.

Study of the Anomalous Paramagnetic Relaxation Observed at Low Fields in a Kramers Pair Salt

Measurements of the paramagnetic relaxation rate were made for various concentrations of Fe+++ ions in K3Co(CN)6 (0.2–1.0 at.%) at low-field values (60–650 Oe) and low temperatures (1.24 < T < 1.38 °K) using the direct-observation sampled-recovery technique. The results obtained were found to be concentration dependent and to display at the higher concentrations a double exponential dependence on time. This behavior is at variance with the single-ion Kronig–Van Vleck theory that has been shown to apply at higher fields. It is shown that this behavior can be attributed to the existence of numerous alternate relaxation paths that involve exchange coupled clusters of magnetic complexes.