Zitterbewegung of nearly-free and tightly bound electrons in solids

We show theoretically that nonrelativistic nearly-free electrons in solids should experience a trembling motion (Zitterbewegung, ZB) in absence of external fields, similarly to relativistic electrons in vacuum. The Zitterbewegung is directly related to the influence of periodic potential on the free electron motion. The frequency of ZB is $\omega\approx E_g/\hbar$, where $E_g$ is the energy gap. The amplitude of ZB is determined by the strength of periodic potential and the lattice period and it can be of the order of nanometers. We show that the amplitude of ZB does not depend much on the width of the wave packet representing an electron in real space. An analogue of the Foldy-Wouthuysen transformation, known from relativistic quantum mechanics, is introduced in order to decouple electron states in various bands. We demonstrate that, after the bands are decoupled, electrons should be treated as particles of a finite size. In contrast to nearly-free electrons we consider a two-band model of tightly bound electrons. We show that also in this case the electrons should experience the trembling motion. It is concluded that the phenomenon of Zitterbewegung of electrons in crystalline solids is a rule rather than an exception.Comment: 22 pages, 6 figures Published version, minor changes mad

Self-consistent equilibrium of a two-dimensional electron system with a reservoir in a quantizing magnetic field: Analytical approach

An analytical approach has been developed to describe grand canonical equilibrium between a three dimensional (3D) electron system and a two dimensional (2D) one, an energy of which is determined self-consistently with an electron concentration. Main attention is paid to a Landau level (LL) pinning effect. Pinning means a fixation of the LL on a common Fermi level of the 2D and the 3D systems in a finite range of the magnetic field due to an electron transfer from the 2D to the 3D system. A condition and a start of LL pinning has been found for homogeneously broadened LLs. The electronic transfer from the 3D to the 2D system controls an extremely sharp magnetic dependency of an energy of the upper filled LL at integer filling of the LLs. This can cause a significant increase of inhomogeneous broadening of the upper LL that was observed in recent local probe experiments.Comment: 12 pages, 2 figures, revtex

One-dimensional semirelativity for electrons in carbon nanotubes

It is shown that the band structure of single-wall semiconducting carbon nanotubes (CNT) is analogous to relativistic description of electrons in vacuum, with the maximum velocity $u$= $10^8$cm/s replacing the light velocity. One-dimensional semirelativistic kinematics and dynamics of electrons in CNT is formulated. Two-band k.p Hamiltonian is employed to demonstrate that electrons in CNT experience a Zitterbewegung (trembling motion) in absence of external fields. This Zitterbewegung should be observable much more easily in CNT than its analogue for free relativistic electrons in vacuum.Comment: 4 pages no figure

Volumetric microvascular imaging of human retina using optical coherence tomography with a novel motion contrast technique

Phase variance-based motion contrast imaging is demonstrated using a spectral domain optical coherence tomography system for the in vivo human retina. This contrast technique spatially identifies locations of motion within the retina primarily associated with vasculature. Histogram-based noise analysis of the motion contrast images was used to reduce the motion noise created by transverse eye motion. En face summation images created from the 3D motion contrast data are presented with segmentation of selected retinal layers to provide non-invasive vascular visualization comparable to currently used invasive angiographic imaging. This motion contrast technique has demonstrated the ability to visualize resolution-limited vasculature independent of vessel orientation and flow velocity

Coherent Transport Through a Quadruple Point in a Few Electron Triple Dot

A few electron double electrostatic lateral quantum dot can be transformed into a few electron triple quantum dot by applying a different combination of gate voltages. Quadruple points have been achieved at which all three dots are simultaneously on resonance. At these special points in the stability diagram four occupation configurations are possible. Both charge detection and transport experiments have been performed on this device. In this short paper we present data and confirm that transport is coherent by observing a Pi phase shift in magneto-conductance oscillations as one passes through the quadruple point.Comment: To be published in ICPS Conf. Proceedings 200

Non-locality of Foldy-Wouthuysen and related transformations for the Dirac equation

Non-localities of Foldy-Wouthuysen and related transformations, which are used to separate positive and negative energy states in the Dirac equation, are investigated. Second moments of functional kernels generated by the transformations are calculated, the transformed functions and their variances are computed. It is shown that all the transformed quantities are smeared in the coordinate space by the amount comparable to the Compton wavelength $\lambda_c=\hbar/mc$.Comment: 7 pages, two figure

The Properties of Outer Retinal Band Three Investigated With Adaptive-Optics Optical Coherence Tomography.

PurposeOptical coherence tomography's (OCT) third outer retinal band has been attributed to the zone of interdigitation between RPE cells and cone outer segments. The purpose of this paper is to investigate the structure of this band with adaptive optics (AO)-OCT.MethodsUsing AO-OCT, images were obtained from two subjects. Axial structure was characterized by measuring band 3 thickness and separation between bands 2 and 3 in segmented cones. Lateral structure was characterized by correlation of band 3 with band 2 and comparison of their power spectra. Band thickness and separation were also measured in a clinical OCT image of one subject.ResultsBand 3 thickness ranged from 4.3 to 6.4 μm. Band 2 correlations ranged between 0.35 and 0.41 and power spectra of both bands confirmed peak frequencies that agree with histologic density measurements. In clinical images, band 3 thickness was between 14 and 19 μm. Measurements of AO-OCT of interband distance were lower than our corresponding clinical OCT measurements.ConclusionsBand 3 originates from a structure with axial extent similar to a single surface. Correlation with band 2 suggests an origin within the cone photoreceptor. These two observations indicate that band 3 corresponds predominantly to cone outer segment tips (COST). Conventional OCT may overestimate both the thickness of band 3 and outer segment length