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Register a new userDegeneracy-projected polarization formulas for Hall-type conductivities
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Kubo formulas for Hall, transverse thermoelectric and thermal Hall conductivities are simplified into on-shell commutators of degeneracy projected polarizations. The new expressions are computationally economical, and apply to general Hamiltonians without a gap restriction. We show that Hall currents in open boundaries are carried by gapless chiral excitations. Extrapolation of finite lattice calculations to the DC-thermodynamic limit is demonstrated for a disordered metal.
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In previous work, we employed a geometric method of Kazarian to prove Pfaffian formulas for a certain class of degeneracy loci in types B, C, and D. Here we refine that approach to obtain formulas for more general loci, including those coming from all isotropic Grassmannians. In these cases, the formulas recover the remarkable theta- and eta-polynomials of Buch, Kresch, Tamvakis, and Wilson. The streamlined geometric approch yields simple and direct proofs, which proceed in parallel for all four classical types. In an appendix, we develop some foundational algebra and prove several Pfaffian identities. Another appendix establishes a basic formula for classes in quadric bundles.
Controlling charge-spin current conversion by electric fields is crucial in spintronic devices, which can be realized in diatom ferroelectric semiconductor GeTe where it is established that ferroelectricity can change the spin texture. We demonstrated that the spin Hall conductivity (SHC) can be further tuned by ferroelectricity based on the density functional theory calculations. The spin texture variation driven by the electric fields was elucidated from the symmetry point of view, highlighting the interlocked spin and orbital degrees of freedom. We observed that the origin of SHC can be attributed to the Rashba effect and the intrinsic spin-orbit coupling. The magnitude of one component of SHC {sigma}_xy^z can reach as large as 100 {hbar}/e/({Omega}cm) in the vicinity of the band edge, which is promising for engineering spintronic devices. Our work on tunable spin transport properties via the ferroelectric polarization brings novel assets into the field of spintronics.
A system composed of a conducting planar strip with Rashba spin-orbit coupling (RSOC), magnetically coupled to a layer of localized magnetic moments, at equilibrium, is studied within a microscopic Hamiltonian with numerical techniques at zero temperature in the clean limit. In particular, transport properties for the cases of ferromagnetic (FM) and antiferromagnetic (AFM) coupled layers are computed in linear response on strips of varying width. Some behaviors observed for these properties are consistent with the ones observed for the corresponding Rashba helical currents. The case of uncoupled Rashba strips is also studied for comparison. In the case of Rashba strips coupled to an AFM localized order, results for the longitudinal dc conductivity, for small strip widths, suggest the proximity to a metal-insulator transition. More interesting, in the proximity of this transition, and in general at intermediate values of the RSOC, it is observed a large spin-Hall conductivity that is two orders of magnitude larger than the one for the FM order for the same values of the RSOC and strip widths. There are clearly two different regimes for small and for large RSOC, which is also present in the behavior of Rashba helical currents. Different contributions to the optical and the spin-Hall conductivities, according to a new classification of inter- or intra-band origin proposed for planar strips in the clean limit, or coming from the hopping or spin-orbit terms of the Hamiltonian, are examined. Finally, the effects of different orientation of the coupled magnetic moments will be also studied.
Using raising operators and geometric arguments, we establish formulas for the K-theory classes of degeneracy loci in classical types. We also find new determinantal and Pfaffian expressions for classical cases considered by Giambelli: the loci where a generic matrix drops rank, and where a generic symmetric or skew-symmetric matrix drops rank. In an appendix, we construct a K-theoretic Euler class for even-rank vector bundles with quadratic form, refining the Chow-theoretic class introduced by Edidin and Graham. We also establish a relation between top Chern classes of maximal isotropic subbundles, which is used in proving the type D degeneracy locus formulas.
The $10$ GHz microwave conductivity, $sigma(T)$ and high field, $222$ GHz electron spin resonance (HF-ESR) of Li$_4$C$_{60}$ fulleride is measured in a wide temperature range. We suggest that the majority of ESR active sites and at least some of the charge carriers for $sigma(T)$ are electrons bound to a small concentration of surplus or vacancy ions in the polymer phase. Both $sigma(T)$ and the ESR line shape depend on ionic motion. A change of the activation energy of $sigma(T)$ at $125$ K coincides with the onset of the ionic DC conductivity. The ESR line shape is determined mainly by Li ionic motion within octahedral voids below $150$ K. At higher temperatures, fluctuations due to ionic diffusion change the environment of defects from axial to effectively isotropic on the ESR time scale. $sigma(T)$ data up to $700$ K through the depolymerization transition confirm that the monomeric phase of Li$_4$C$_{60}$ is a metal.
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