We investigate the propagation of wave-packets on graphene in a perpendicular magnetic field and the appearance of collapses and revivals in the time-evolution of an initially localised wave-packet. The wave-packet evolution in graphene differs drastically from the one in an electron gas and shows a rich revival structure similar to the dynamics of highly excited Rydberg states.
We present a novel numerical wave-packet propagation scheme in order to solve the effective single-particle Dirac-Hamiltonian of graphene and show how the collapse and revival dynamics is affected by the presence of disorder. Our effective numerical method is of general interest for the solution of the Dirac equation in the presence of potentials and magnetic fields.
Quantum revival is described as the time-periodic reconstruction of a wave packet initially localized in space and time. This effect is expected in finite-size systems which exhibits commensurable discrete spectrum such as the infinite quantum well. Here, we report on the experimental observation of full and fractional quantum revival for classical waves in a two dimensional cavity. We consider flexural waves propagating in thin plates, as their quadratic dispersion at low frequencies mimics the dispersion relation of quantum systems governed by Schrödinger equation. Time-dependent excitation …
The time evolution of a low-energy two-dimensional Gaussian wave packet in ABC-stacked $n$-layer graphene (ABC-NLG) is investigated. Expectation values of the position $(x,y)$ of center-of-mass and the total probability densities of the wave packet are calculated analytically using the Green's function method. These results are confirmed using an alternative numerical method based on the split-operator technique within the Dirac approach for ABC-NLG, which additionally allows to include external fields and potentials. The main features of the zitterbewegung (trembling motion) of wave packets i…
We study the effects of $δ$-function periodic kicks on the Floquet energy-momentum dispersion in graphene. We find that a rich variety of dispersions can appear depending on the parameters of the kicking: at certain points in the Brillouin zone, the dispersion can become linear but anisotropic, linear in one direction and quadratic in the perpendicular direction, gapped with a quadratic dispersion, or completely flat (called dynamical localization). We show all these results analytically and demonstrate them numerically through the dynamics of wave packets propagating in graphene. We propose e…
We have investigated the role of pseudospin polarization in electron wave packet dynamics in pristine graphene and in a graphene antidot lattice subject to an external magnetic field. Employing a Green's function formalism, we show that the electron dynamics can be controlled by tuning pseudospin polarization. We find that in Landau quantized pristine graphene both the propagation of an electron wave packet and Zitterbewegung oscillations strongly depend on pseudospin polarization. The electron wave packet is found to propagate in the direction of initial pseudospin polarization. We also show …
Twisted bilayer graphene near the magic angle exhibits remarkably rich electron correlation physics, displaying insulating, magnetic, and superconducting phases. Here, using measurements of the local electronic compressibility, we reveal that these phases originate from a high-energy state with an unusual sequence of band populations. As carriers are added to the system, rather than filling all the four spin and valley flavors equally, we find that the population occurs through a sequence of sharp phase transitions, which appear as strong asymmetric jumps of the electronic compressibility near…
The wave equation describing the interaction of two electrons in graphene at arbitrary value of the Fermi energy $E_F$ is derived. For the solutions of this equation, we have found the explicit forms of the density and the current which obey the continuity equation. We have traced the evolution of the wave packet during a scattering process. It is shown that the long-leaving localized quasi-stationary peak may appear at $E_F<0$ . Then this peak decays into a set of wave packets following each other. At $t\rightarrow\infty$ a total norm of all outgoing wave packets equals to that of incoming wa…
Graphene deposited on top of a Copper(111) substrate may develop a Y-shaped Kekulé bond texture (Kekulé-Y), locking the momentum of its Dirac fermions with its valley degree of freedom. As a consequence, the valley degeneracy of its band structure is broken, generating an energy dispersion with two nested Dirac cones with different Fermi velocities. In this work, we investigate the dynamics of electronic wave packets in the Kekulé-Y superlattice. We show that, as a result of the valley-momentum coupling, a valley-driven oscillatory motion of the wave packets ({\it Zitterbewegung}) could appear…
A wave-packet time evolution method, based on the split-operator technique, is developed to investigate the scattering of quasi-particles at a normal-superconductor interface of arbitrary profile and shape. As a practical application, we consider a system where low energy electrons can be described as Dirac particles, which is the case for most two-dimensional materials, such as graphene and transition metal dichalcogenides. However the method is easily adapted for other cases such as electrons in few layer black phosphorus, or any Schrödinger quasi-particles within the effective mass approxim…
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 p…
We study the electron scattering produced by local out-of-plane strain deformations in the form of Gaussian bumps in graphene. Of special interest is to take into account the scalar field associated with the redistribution of charge due to deformations, and in the same footing as the pseudomagnetic field. Working with the Born approximation approach we show analytically that even when a relatively small scalar field is considered, a rather strong valley asymmetric scattering could arise as a function of the energy and angle of incidence. In addition, we find that the valley polarization can re…
Quantum phenomena are relevant to the transport of light atoms and molecules through nanoporous two-dimensional (2D) membranes. Indeed, confinement provided by (sub-)nanometer pores enhances quantum effects such as tunneling and zero point energy (ZPE), even leading to quantum sieving of different isotopes of a given element. However, these features are not always taken into account in approaches where classical theories or approximate quantum models are preferred. In this work we present an exact three-dimensional wave packet propagation treatment for simulating the passage of atoms through p…
We consider systems described by the two-dimensional Dirac equation where the Fermi velocity is inhomogeneous as a consequence of mechanical deformations. We show that the mechanical deformations can lead to deflection and focusing of the wave packets. The analogy with known reflectionless quantum systems is pointed out. Furthermore, with the use of the qualitative spectral analysis, we discuss how inhomogeneous strains can be used to create waveguides for valley polarized transport of partially dispersionless wave packets.
The Zitterbewegung (ZB) effect is investigated in graphene with spacially modulated potential near the original Dirac point (ODP) and extra Dirac points (EDPs). Our calculations show that to get the large ZB oscillations, the wave packet center must be at the angle $θ_0=0$ for EDPs located at zero-energy, or $θ_0=π/2$ for both ODP and EDPs at finite energy $\varepsilon=mπ$ ($m$ integer). By varying the parameters ($q_2, \mathbb{V}$) of the periodic potential and the initial momentum ($κ_0, θ_0$) of Gaussian wave packet, it is found that the frequency of the ZB oscillations is in the range $[10…
We describe a method for measuring the Berry curvature from the wave-packet dynamics in perturbed arrays of evanescently coupled optical waveguides with honeycomb lattice structure. To disentangle the effects of the Berry curvature and the energy dispersion we utilize a difference measurement by propagating the wave packet under the influence of a constant external force back and forth. In this way a non-vanishing Berry curvature is obtained for photonic graphene with small sublattice bias or strain, where the relative error between the exact Berry curvature and the one derived from the semicl…
Much having learned about Floquet dynamics of pseudospin-$1/2$ system namely, graphene, we here address the stroboscopic properties of a periodically kicked {three-band fermionic system such as $α$-T$_3$ lattice. This particular model provides an interpolation between graphene and dice lattice via the continuous tuning of the parameter $α$ from 0 to 1.} In the case of dice lattice ($α=1$), we reveal that one can, in principle, engineer various types of low energy dispersions around some specific points in the Brillouin zone by tuning the kicking parameter in the Hamiltonian along a particular …
