Electron focusing in two-dimensional systems by means of an electrostatic lens

Spector, J.; Störmer, H. L.; Baldwin, K. W.; Pfeiffer, L. N.; West, K. W.

doi:10.1063/1.102538

Cited by 157 publications

(82 citation statements)

References 3 publications

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“…The basic principle behind such experiments would be to employ local gates and collimators similar to those used in electron optics in 2D gases 29,30 . One possible experimental setup is shown schematically in Fig.…”

Section: Implications For Experimentsmentioning

confidence: 99%

Chiral tunnelling and the Klein paradox in graphene

2006

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The so-called Klein paradox -unimpeded penetration of relativistic particles through high and wide potential barriers -is one of the most exotic and counterintuitive consequences of quantum electrodynamics (QED). The phenomenon is discussed in many contexts in particle, nuclear and astro-physics but direct tests of the Klein paradox using elementary particles have so far proved impossible. Here we show that the effect can be tested in a conceptually simple condensed-matter experiment by using electrostatic barriers in single-and bi-layer graphene. Due to the chiral nature of their quasiparticles, quantum tunneling in these materials becomes highly anisotropic, qualitatively different from the case of normal, nonrelativistic electrons.Massless Dirac fermions in graphene allow a close realization of Klein's gedanken experiment whereas massive chiral fermions in bilayer graphene offer an interesting complementary system that elucidates the basic physics involved.

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Section: Implications For Experimentsmentioning

confidence: 99%

Chiral tunnelling and the Klein paradox in graphene

2006

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“…This hidden quantum mirage effect has two distinguishing features compared with various conventional quantum mirages, such as electrostatic lens [23], refocusing by an elliptical quantum corral [5], and refocusing by negative refraction [8,9,13]. First, it follows entirely from symmetries (Fermi surface matching and 1D translational invariance).…”

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confidence: 99%

Hidden quantum mirage by negative refraction in semiconductor P-N junctions

Zhang¹,

Zhu²,

Yang³

et al. 2016

Phys. Rev. B

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We predict a novel quantum interference based on the negative refraction across a semiconductor P-N junction: with a local pump on one side of the junction, the response of a local probe on the other side behaves as if the disturbance emanates not from the pump but instead from its mirror image about the junction. This phenomenon is guaranteed by translational invariance of the system and matching of Fermi surfaces of the constituent materials, thus it is robust against other details of the junction (e.g., junction width, potential profile, and even disorder). The recently fabricated P-N junctions in 2D semiconductors provide ideal platforms to explore this phenomenon and its applications to dramatically enhance charge and spin transport as well as carrier-mediated long-range correlation.PACS numbers: 73.40. Lq, 75.30.Hx, 72.80.Vp Half a century ago, Veselago proposed the concept of negative refraction for electromagnetic waves [1][2][3][4]: upon transition from a medium with positive refractive index across a sharp interface into a negative index medium, a diverging pencil of rays is coherently refocused to form a sharp image or "quantum mirage" [5], similar to the bending of light to create mirages in the atmosphere. In the past decade, negative refraction and mirage have been observed for electromagnetic waves of various frequencies (see Ref.[6] for a review) and for cold atoms [7,8]. In 2007, Cheianov et al. [9] proposed the interesting idea that a sharp P-N junction of graphene can exhibit negative refraction and hence focus electrons out of a local pump into a sharp quantum mirage. This effect has been widely used in theoretical proposals to control charge and/or spin transport for massless Dirac fermions in semiconductors (see for a few examples). However, a sharp quantum mirage requires the junction to be sharp compared with the electron wavelength (∼ a few nanometers), otherwise it would disappear due to the path-dependent phase accumulation inside the junction. This makes the observation and application of this effect an experimentally challenging task [13].In this letter, we theoretically demonstrate that in many situations where the quantum mirage is no longer visible, its effect still exists, which could make the response across the P-N junction independent of distance. As a basic observation in physics, the response amplitude in a d-dimensional uniform system decays at least as fast as 1/R (d−1)/2 with distance R, irrespective of the energy dispersion, spin-orbit coupling, etc. This directly leads to rapid decay of many physical properties, such as the charge and spin conductivity [14] As an example, we demonstrate that the P-N junction could dramatically enhance the carriermediated long-range interaction between localized magnetic moments by several orders of magnitudes.For an intuitive physical picture about the hidden quantum mirage, we start from a sharp P-N junction as shown in Fig. 1(a). Here the plane waves excited by a local pump (filled red circle) in the N region is perfectly focuse...

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“…Although electron optics such as lensing 5 and focusing 6 have been demonstrated experimentally, building a collimated electron interferometer in two unconfined dimensions has remained a challenge owing to the difficulty of creating electrostatic barriers that are sharp on the order of the electron wavelength 7 . Here, we report the observation of conductance oscillations in extremely narrow graphene heterostructures where a resonant cavity is formed between two electrostatically created bipolar junctions.…”

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confidence: 99%