Zitterbewegung of electrons in quantum wells and dots in the presence of an in-plane magnetic field

Abstract

We study the effect of an in-plane magnetic field on the zitterbewegung (ZB) of electrons in a semiconductor quantum well (QW) and in a quantum dot (QD) with the Rashba and Dresselhaus spin-orbit interactions (SOIs). We obtain a general expression of the time-evolution of the position vector and current of the electron in a semiconductor QW. The amplitude of the oscillatory motion is directly related to the Berry connection in momentum space. We find that in presence of the magnetic field the ZB in a QW does not vanish when the strengths of the Rashba and Dresselhaus SOIs are equal. The in-plane magnetic field helps to sustain the ZB in QWs even at a low value of k(0)d (where d is the width of the Gaussian wavepacket and k(0) is the initial wavevector). The trembling motion of an electron in a semiconductor QW with high Landé g-factor (e.g. InSb) is sustained over a long time, even at a low value of k(0)d. Further, we study the ZB of an electron in QDs within the two sub-band model numerically. The trembling motion persists in time even when the magnetic field is absent as well as when the strengths of the SOI are equal. The ZB in QDs is due to the superposition of oscillatory motions corresponding to all possible differences of the energy eigenvalues of the system. This is an another example of multi-frequency ZB phenomenon.

Zitterbewegung of a heavy hole in presence of spin-orbit interactions

“…By observing Eqs. (8), (11), and (23), we conclude that our results are consistent with that prediction.…”

“…(8), (11), and (14) can not be done exactly and hence numerical treatment has to be implemented to see the explicit time dependence of |A(t)| 2 , x(t) , and v x (t) . From Fig.…”

“…In principle, ZB is not a pure relativistic phenomenon. In recent years, it has been shown that ZB could exist in a plethora of nonrelativistic physical systems [2] including narrow-gap semiconductors [3], spin-orbit coupled low-dimensional systems [4][5][6][7][8][9][10], graphene [11][12][13][14][15], carbon nanotube [16], topological insulator [17], superconductors [18], sonic crystal [19], photonic crystal [20], optical superlattice [21], Bose-Einstein condensates [22][23][24][25], dichalcogenide materials like MoS 2 [26,27] etc.…”

Wave packet dynamics in monolayer MoS2 with and without a magnetic field

“…The relation between amplitude of ZB oscillations and Berry connection was explicitly shown in Refs. [38][39][40]. Recently experimental observations of ZB phenomenon has been reported in trapped ion systems 41 as well as in 87 Rb Bose Einstein condensates 42,43 .…”

Resonant longitudinalZitterbewegungin zigzag graphene nanoribbons

“…One way to overcome this damping is to use discretized weight which can be achieved by applying a perpendicular magnetic field [26,31] or pseudomagnetic field induced by strain [32]. The same remedy also works for an asymmetric quantum well [33].…”