The Local Larmor Clock, Partial Densities of States, and Mesoscopic Physics

Abstract

The Larmor clock is one of the most widely discussed approaches to determine the time-scales of tunneling processes. The essential idea [1,2,3] of the Larmor clock is that the motion of the spin polarization in a narrow region of magnetic field can be exploited to provide information on the time carriers spend in this region. It is assumed that incident carriers are spin polarized and that they impinge on a region to which a small magnetic field is applied perpendicular to the spin polarization of the incident carriers (see Fig. 9.1). The spin polarization of the transmitted and reflected carriers can then be compared with the polarization of the incident carriers. Dividing the angle between the polarization of the exciting carriers and that of the incident carrier by the Larmor frequency ωl gives a time. Originally, only spin precession (the movement of the polarization in the plane perpendicular to the magnetic field) was considered. However, [3] pointed out, that especially if we deal with regions in which only evanescent waves exist (tunneling problems) the polarization executes not only a precession but also a rotation into the direction of the magnetic field. In fact in the presence of a tunneling barrier, the spin rotation, is the dominant effect. Reference [3] considered a rectangular barrier and considered a magnetic field of the same spatial extend as the barrier. In the local version of the Larmor clock, introduced by Leavens and Aers [4], we consider an arbitrary region in which the magnetic field is non-vanishing and investigate again the direction of the spin polarization and rotation of the transmitted and reflected carriers.