arXiv subjects

S. Kudla

Publications and source records attributed to S. Kudla.

6 recordsLinked to original sources

arXiv2018

Charge and spin conductivity of a two-dimensional electron gas with random Rashba interaction

We calculate the transport relaxation time $τ_{\rm tr}$ and spin transport relaxation time $τ_{s,{\rm tr}}$ for a two-dimensional electron gas with spatially fluctuating Rashba spin-orbit interaction. These relaxation times determine the electrical and spin conductivity of the two-dimensional system, respectively. It is shown that the transport relaxation time $τ_{\rm tr}$ is a nonmonotonic function of electron energy $\varepsilon $, whereas the spin transport relaxation time $τ_{s,{\rm tr}}$ decreases with increasing $\varepsilon $, similarly to the conventional electron relaxation time $τ$ that characterizes the decay of an electron state corresponding to certain values of the momentum and spin. Such a behavior of the relaxation times leads to unusual temperature dependence of the electrical and spin conductivity.

cond-mat.mes-hall↗

arXiv2017

Transmission of charge and spin in a topological-insulator-based magnetic structure

We discuss the effect of a magnetic thin-film ribbon at the surface of a topological insulator on the charge and spin transport due to surface electrons.\\ If the magnetization in the magnetic ribbon is perpendicular to the surface of a topological insulator, it leads to a gap in the energy spectrum of surface electrons. As a result, the ribbon is a barrier for electrons, which leads to electrical resistance.\\ We have calculated conductance of such a structure. The conductance reveal some oscillations with the length of the magnetized region due to the interference of transmitted and reflected waves. We have also calculated the Seebeck coefficient when electron flux is due to a temperature gradient.

cond-mat.mes-hall↗

arXiv2001

Derivatives of Eisenstein series and Faltings heights

We prove a relation between a generating series for the heights of Heegner cycles on the arithmetic surface associated to a Shimura curve and the second term in the Laurent expansion at s=1/2 of an Eisenstein series of weight 3/2 for SL(2). On the geometric side, a typical coefficient of the generating series involves the Faltings heights of abelian surfaces isogenous to a product of CM elliptic curves, an archimedean contribution, and contributions from vertical components in the fibers of bad reduction. On the analytic side, these terms arise via the derivatives of local Whittaker functions. It should be noted that s=1/2 is not the central point for the functional equation of the Eisenstein series in question. Moreover, the first term of the Laurent expansion at s=1/2 coincides with the generating function for the degrees of the Heegner cycles on the generic fiber, and, in particular, does not vanish.

math.NT↗

arXiv1999

Arithmetic Hirzebruch Zagier cycles

We define special cycles on arithmetic models of twisted Hilbert-Blumenthal surfaces at primes of good reduction. These are arithmetic versions of these cycles. In particular, we characterize the non-degenerate intersections and partially determine the generating series formed from the intersection numbers of them relating it to the value at the center of symmetry of the derivative of a certain metaplectic Eisenstein series in 6 variables. These results are analogous to those obtained by us in the case of Siegel threefolds (alg-geom/9711025). We also study the case of degenerate intersections and show that in this case the intersection locus is a configuration of projective lines whose dual graph is described in terms of subcomplexes of the Bruhat-Tits building of PGL(2,F), where F is an unramified quadratic extension of Q_p.

math.AG↗

arXiv1998

Height pairings on Shimura curves and p-adic uniformization

We establish a relation between intersection numbers of special cycles on a Shimura curve and special values of derivatives of metaplectic Eisenstein series at a place of bad reduction where p-adic uniformization in the sense of Cherednik and Drinfeld holds. The result extends the one established by one of us (S. Kudla: Ann. of Math. 146 (1997)) for the archimedean place and for the non-archimedean places of good reduction. The bulk of the paper is concerned with the corresponding problem on the Drinfeld upper half plane (the formal scheme version).

math.AG↗

arXiv1997

Cycles on Siegel 3-folds and derivatives of Eisenstein series

We consider the Siegel modular variety of genus 2 and a p-integral model of it for a good prime p>2, which parametrizes principally polarized abelian varieties of dimension two with a level structure. We consider cycles on this model which are characterized by the existence of certain special endomorphisms, and their intersections. We characterize that part of the intersection which consists of isolated points in characteristic p only. Furthermore, we relate the (naive) intersection multiplicities of the cycles at isolated points to special values of derivatives of certain Eisenstein series on the metaplectic group in 8 variables.

alg-geom↗