Wave packet dynamics in various two-dimensional systems: A unified description

Singh, Ashutosh Kumar; Biswas, Tutul; Ghosh, Tarun Kanti; Agarwal, Amit

doi:10.1016/j.aop.2014.12.019

Cited by 6 publications

(3 citation statements)

References 58 publications

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“…However, a ray of hope was shown in 2005 when Zawadki [2] argued that a narrow gap semiconductor not only can host the intriguing phenomenon ZB but also the associated length scale can be enhanced up to five orders higher than that in vacuum. As a result, subsequent years witnessed immense interest in ZB in numerous systems [3] including spin-orbit coupled two dimensional (2D) electron/hole gases [4][5][6][7][8][9][10][11], superconductors [12], sonic crystal [13], photonic crystal [14,15], carbon nanotube [16], graphene [17][18][19][20][21], other Dirac materials [22][23][24] and ultra-cold atomic gases [25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a quasiparticle in theα-T₃model: role of pseudospin polarization and transverse magnetic field onzitterbewegung

Biswas

Ghosh

2018

J. Phys.: Condens. Matter

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We consider the $\alpha$-$T_3$ model which provides a smooth crossover between the honeycomb lattice with pseudospin $1/2$ and the dice lattice with pseudospin $1$ through the variation of a parameter $\alpha$. We study the dynamics of a wave packet representing a quasiparticle in the $\alpha$-T$_3$ model with zero and finite transverse magnetic field. For zero field, it is shown that the wave packet undergoes a transient $zitterbewegung$ (ZB). Various features of ZB depending on the initial pseudospin polarization of the wave packet have been revealed. For an intermediate value of the parameter $\alpha$ i.e. for $0<\alpha<1$ the resulting ZB consists of two distinct frequencies when the wave packet was located initially in $rim$ site. However, the wave packet exhibits single frequency ZB for $\alpha=0$ and $\alpha=1$. It is also unveiled that the frequency of ZB corresponding to $\alpha=1$ gets exactly half of that corresponding to the $\alpha=0$ case. On the other hand, when the initial wave packet was in $hub$ site, the ZB consists of only one frequency for all values of $\alpha$. Using stationary phase approximation we find analytical expression of velocity average which can be used to extract the associated timescale over which the transient nature of ZB persists. On the contrary the wave packet undergoes permanent ZB in presence of a transverse magnetic field. Due to the presence of large number of Landau energy levels the oscillations in ZB appear to be much more complicated. The oscillation pattern depends significantly on the initial pseudospin polarization of the wave packet. Furthermore, it is revealed that the number of the frequency components involved in ZB depends on the parameter $\alpha$.

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Section: Introductionmentioning

confidence: 99%

Dynamics of a quasiparticle in theα-T₃model: role of pseudospin polarization and transverse magnetic field onzitterbewegung

Biswas

Ghosh

2018

J. Phys.: Condens. Matter

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“…(We note that the KaneMele and Rashba SO couplings are respectively referred to as intrinsic and extrinsic SO couplings in the literature; however, in this paper we will refer to them as Kane-Mele and Rashba couplings for convenience). The dynamics of wave packets in graphene has been studied in a number of papers using both the microscopic lattice model of graphene 38 and a continuum theory which is valid close to the Dirac points [39][40][41] .…”

Section: Introductionmentioning

confidence: 99%

Electron dynamics in graphene with spin–orbit couplings and periodic potentials

Seshadri¹,

Sen²

2017

J. Phys.: Condens. Matter

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We use both continuum and lattice models to study the energy-momentum dispersion and the dynamics of a wave packet for an electron moving in graphene in the presence of spin-orbit couplings and either a single potential barrier or a periodic array of potential barriers. Both Kane-Mele and Rashba spin-orbit couplings are considered. A number of special things occur when the Kane-Mele and Rashba couplings are equal in magnitude. In the absence of a potential, the dispersion then consists of both massless Dirac and massive Dirac states. A periodic potential is known to generate additional Dirac points; we show that spin-orbit couplings generally open gaps at all those points, but if the two spin-orbit couplings are equal, some of the Dirac points remain gapless. We show that the massless and massive states respond differently to a potential barrier; the massless states transmit perfectly through the barrier at normal incidence while the massive states reflect from it. In the presence of a single potential barrier, we show that there are states localized along the barrier. Finally, we study the time evolution of a wave packet in the presence of a periodic potential. We discover special points in momentum space where there is almost no spreading of a wave packet; there are six such points in graphene when the spin-orbit couplings are absent.

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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

2015

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We study the zitterbewegung of a heavy hole in presence of both cubic Rashba and cubic Dresselhaus spin-orbit interactions. On contrary to the electronic case, zitterbewegung does not vanish for equal strength of Rashba and Dresselhaus spin-orbit interaction. This non-vanishing of zitterbewegung is associated with the Berry phase. Due to the presence of the spin-orbit coupling the spin associated with the heavy hole precesses about an effective magnetic field. This spin precession produces a transverse spin-orbit force which also generates an electric voltage associated with zitterbewegung. We have estimated the magnitude of this voltage for a possible experimental detection of zitterbewegung.

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Wave packet dynamics in various two-dimensional systems: A unified description

Cited by 6 publications

References 58 publications

Dynamics of a quasiparticle in theα-T₃model: role of pseudospin polarization and transverse magnetic field onzitterbewegung

Dynamics of a quasiparticle in theα-T₃model: role of pseudospin polarization and transverse magnetic field onzitterbewegung

Electron dynamics in graphene with spin–orbit couplings and periodic potentials

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

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Wave packet dynamics in various two-dimensional systems: A unified description

Cited by 6 publications

References 58 publications

Dynamics of a quasiparticle in theα-T3model: role of pseudospin polarization and transverse magnetic field onzitterbewegung

Dynamics of a quasiparticle in theα-T3model: role of pseudospin polarization and transverse magnetic field onzitterbewegung

Electron dynamics in graphene with spin–orbit couplings and periodic potentials

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

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Dynamics of a quasiparticle in theα-T₃model: role of pseudospin polarization and transverse magnetic field onzitterbewegung

Dynamics of a quasiparticle in theα-T₃model: role of pseudospin polarization and transverse magnetic field onzitterbewegung