Snake trajectories in ultraclean graphene p–n junctions

Rickhaus, Peter; Makk, Péter; Liu, Ming‐Hao; Tóvári, Endre; Weiß, Markus; Maurand, Romain; Richter, Klaus; Schönenberger, Christian

doi:10.1038/ncomms7470

Cited by 114 publications

(179 citation statements)

References 34 publications

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“…For a typical junction potential V 0 = 1 eV [40] and two substitutional manganese spins separated by 16 nm, their RKKY J ∼ 16 µeV (amplified by a factor η ≈ 13) is measurable by spin-polarized scanning tunneling spectroscopy [36]. When the distance increases up to the ballistic length ∼ 1 µm [41], the RKKY interaction J ∼ 0.3 µeV (amplified by a factor η ≈ 780) may be detected by an ultrasensitive magnetic sensor based on nitrogen-vacancy center in nanodiamonds [47,48], which has demonstrated nanoscale spatial resolution and the capability to determine weak magnetic dipolar interaction ∼ 10 −5 µeV between two nuclear spins [49,50]. In summary, we have proposed a robust, hidden quantum mirage that could dramatically enhance the non-local responses of electrons as well as the carriermediated interaction.…”

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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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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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“…Owing to the zero energy gap and the relativistic nature of the carriers graphene p-n junctions exhibit new and exciting physical features, unobserved in semiconducting electronics, e.g. Klein tunnelling [3,4], valley-valve effect [5], and snake states [6][7][8][9], to name a few. Recently, encapsulating graphene in h-BN [10][11][12][13] has become a popular technique for the realization of high-quality graphene devices.…”

Section: Introductionmentioning

confidence: 99%

“…Unfortunately, this is often not practical or in the case of suspended devices almost impossible. However, at a p-n interface such e-h puddles have a large impact on electrical transport [7][8][9] that occurs predominantly through snake states. In order to quantify such e-h puddles we investigate the influence of these scatterers on the transport due to snake states along the p-n interface in the bipolar regime.…”

Section: Introductionmentioning

confidence: 99%

Characterization of the size and position of electron–hole puddles at a graphene p–n junction

Milovanović¹,

Peeters²

2016

Nanotechnology

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The effect of an electron-hole puddle on the electrical transport when governed by snake states in a bipolar graphene structure is investigated. Using numerical simulations we show that information on the size and position of the electron-hole puddle can be obtained using the dependence of the conductance on magnetic field and electron density of the gated region. The presence of the scatterer disrupts snake state transport which alters the conduction pattern. We obtain a simple analytical formula that connects the position of the electron-hole puddle with features observed in the conductance. Size of the electron-hole puddle is estimated from the magnetic field and gate potential that maximizes the effect of the puddle on the electrical transport.

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“…The n-p junctions in graphene can be induced by electrostatic potential which moves the Dirac point above or below the Fermi level [3]. In the quantum Hall conditions these junctions form waveguides that confine currents [27][28][29][30][31][32][33][34]. The confinement in the classical terms can be understood as a result of the Lorentz force pushing the electrons to the n-p junction at both its sides.…”

Section: Introductionmentioning

confidence: 99%

“…The confinement in the classical terms can be understood as a result of the Lorentz force pushing the electrons to the n-p junction at both its sides. The opposite orientation of the Lorentz force for the carriers of the conduction and valence band in classical terms produces snake-orbits [32][33][34][35][36][37][38][39][40] winding along the junction. The magnetic confinement of the current along the junction is supported for a single direction of the current only.…”

Section: Introductionmentioning

confidence: 99%

Electron spin inversion in fluorinated graphene nanoribbons

2017

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We consider a dilute fluorinated graphene nanoribbon as a spin-active element. The fluorine adatoms introduce a local spin-orbit Rashba interaction that induces spin-precession for electron passing by. The spin precession involving a single adatom is infinitesimal and accumulation of the spin precession events with many electron passages under adatoms is necessary to accomplish a spin flip. In order to arrange for this accumulation a circular n-p junction can be introduced to the ribbon by e.g. potential of the tip of an atomic force microscope. Alternatively a fluorinated quantum ring can be attached to the ribbon. We demonstrate that the spin-flip probability can be increased in this manner by as much as three orders of magnitude. The Zeeman interaction introduces spin-dependence of the Fermi wave vectors which changes the electron paths within the disordered system depending on the spin orientation. The effect destroys the accumulation of the spin precession events in the n-p junction. For side attached quantum rings however -for which the electron path is determined by the confinement within the channel -the accumulation of the spin precession is robust against the Zeeman spin splitting.

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Snake trajectories in ultraclean graphene p–n junctions

Cited by 114 publications

References 34 publications

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

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

Characterization of the size and position of electron–hole puddles at a graphene p–n junction

Electron spin inversion in fluorinated graphene nanoribbons

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