Two-photon echo method for observing electron zitterbewegung in carbon nanotubes

Abstract

The phenomenon of Zitterbewegung (ZB, trembling motion) of electrons is described in zigzag carbon nanotubes (CNT) excited by laser pulses. The tight binding approach is used for the band structure of CNT and the effect of light is introduced by the vector potential. Contrary to the common theoretical practice, no a priori assumptions are made concerning electron wave packet, the latter is determined as a result of illumination. In order to overcome the problem of various electron phases in ZB, a method of two-photon echo is considered and described using the density function formalism. The medium polarization of CNT is calculated by computing exact solutions of the time-dependent electron Hamiltonian. The signal of two-photon echo is extracted and it is shown that, using existing parameters of CNT and laser pulses, one should be able to observe the electron trembling motion. Effects of electron decoherence and relaxation are discussed.

Zitterbewegung near new Dirac points in graphene superlattices

“…Besides the decay shown in figure 2, what is originated from the electron localization and also influenced by wave packets, decoherence processes can also cause an exponential decay controlled by decoherence time [7]. This effect has been studied using density matrix formalism recently [44,45] and decoherence time is on the level of 10 fs approximatively [46]. In our research, the periods of oscillations are of order 10 1 -10 3 fs and decided by group velocities, so the periods may be close to the decoherence time with some specific velocities.…”

Theoretical Treatment of the Zitterbewegung phenomena in the multilayer armchair graphene nanoribbons (MLAGNRs)

“…The phenomenon of Zitterbewegung (ZBW) was predicted by Schrodinger in 1930 for free electrons in a vacuum [1]. In the Dirac equation, the electron velocity operator does not commute with the Hamiltonian, so that the electron velocity is not a constant of the motion.…”

“…In the Dirac equation, the electron velocity operator does not commute with the Hamiltonian, so that the electron velocity is not a constant of the motion. In the absence of an effective external field, It's called thumping velocity, as a result of the solutions to the Dirac equation for a relativistic electron in free space [1,2]. The wave packet is a characteristic feature of relativistic quantum systems that distinguishes it from a nonrelativistic one the strong locking between the (pseudo)spin degree of freedom and the momentum results in an oscillation of the position of the wave packet as a function of time.…”