Current flow paths in deformed graphene: from quantum transport to classical trajectories in curved space

Recent experimental advances in the reconstruction of the Wigner function (WF) in electronic systems have led us to consider the possibility of employing this theoretical tool in the analysis of electron dynamics of uniaxially strained graphene. In this work, we study the effect of strain on the WF of electrons in graphene under the interaction of a uniform magnetic field. This mechanical deformation modifies drastically the shape of the Wigner and Husimi function of Landau and coherent states. The WF has a different behavior straining the material along the zigzag direction in comparison with the armchair one and favors the obtention of electron coherent states. The time evolution of the WF for electron coherent states shows fluctuations between classical and quantum behavior with a local maximum value moving in a closed path. The phase-space representation shows more clearly the effect of non-equidistant of relative Landau levels in the time evolution of electron coherent states than other approaches. Our findings may be useful in establishing protocols for the realization of electron coherent states in graphene as well as a bridge between condensed matter and quantum optics.

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“…(A.10) and using the variables ξ and s defined in (43), we can obtain the following pair of Hamiltonians:…”

Section: A Wigner Function: Moyal -Productmentioning

confidence: 99%

Phase-space representation of Landau and electron coherent states for uniaxially strained graphene

Díaz-Bautista

Betancur-Ocampo

2020

Phys. Rev. B

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“…From Figs. 2(b) and 2(c) it is also clear that the deformation enhances the current in the region directly behind it, acting as a lens that focuses the current at this electron energy [56].…”

mentioning

confidence: 95%

Graphene Nanobubbles as Valley Filters and Beam Splitters

et al. 2016

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The low energy band structure of graphene has two inequivalent valleys at K and K points of the Brillouin zone. The possibility to manipulate this valley degree of freedom defines the field of valleytronics, the valley analogue of spintronics. A key requirement for valleytronic devices is the ability to break the valley degeneracy by filtering and spatially splitting valleys to generate valley polarized currents. Here we suggest a way to obtain valley polarization using strain-induced inhomogeneous pseudomagnetic fields (PMF) which act differently on the two valleys. Notably, the suggested method does not involve external magnetic fields, or magnetic materials, as in previous proposals. In our proposal the strain is due to experimentally feasible nanobubbles, whose associated PMFs lead to different real space trajectories for K and K electrons, thus allowing the two valleys to be addressed individually. In this way, graphene nanobubbles can be exploited in both valley filtering and valley splitting devices, and our simulations reveal that a number of different functionalities are possible depending on the deformation field.

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“…At low energies and for large-scale deformations, which fulfill the hierarchy lattice constant wavelength deformation scale, the continuum and geometric optics approximations can be applied to the tight-binding Hamiltonian (1). In our previous work [29], we have shown that in that case the current flow in deformed graphene can be predicted by trajectories of relativistic massless fermions which move in a curved space in the presence of a pseudo-magnetic field…”

Section: B Current Flow Lines In the Geometric Optics Approximationmentioning

confidence: 98%

“…1. The finite curvature expressed by the local frame e a (x) also affects significantly the transport [29]. However, it acts equivalently on the two valleys and hence has no effect on the valley polarization.…”

Section: A the Effective Dirac Equation In Curved Spacementioning

confidence: 99%

Current splitting and valley polarization in elastically deformed graphene

Stegmann¹,

Szpak²

2018

2D Mater.

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Elastic deformations of graphene can significantly change the flow paths and valley polarization of the electric currents. We investigate these phenomena in graphene nanoribbons with localized outof-plane deformations by means of tight-binding transport calculations. Such deformations can split the current into two beams of almost completely valley polarized electrons and give rise to a valley voltage. These properties are observed for a fairly wide set of experimentally accessible parameters. We propose a valleytronic nanodevice in which a high polarization of the electrons comes along with a high transmission making the device very efficient. In order to gain a better understanding of these effects, we also treat the system in the continuum limit in which the electronic excitations can be described by the Dirac equation coupled to curvature and a pseudo-magnetic field. Semiclassical trajectories offer then an additional insight into the balance of forces acting on the electrons and provide a convenient tool for predicting the behavior of the current flow paths. The proposed device can also be used for a sensitive measurement of graphene deformations. arXiv:1806.09576v2 [cond-mat.mes-hall]

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Current flow paths in deformed graphene: from quantum transport to classical trajectories in curved space

Cited by 86 publications

References 72 publications

Phase-space representation of Landau and electron coherent states for uniaxially strained graphene

Phase-space representation of Landau and electron coherent states for uniaxially strained graphene

Graphene Nanobubbles as Valley Filters and Beam Splitters

Current splitting and valley polarization in elastically deformed graphene

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