Klein Paradox in Spatial and Temporal Resolution

Krekora, P.; Su, Q.; Grobe, R.

doi:10.1103/physrevlett.92.040406

Cited by 171 publications

(144 citation statements)

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“…This relativistic effect can be attributed to the fact that a sufficiently strong potential, being repulsive for electrons, is attractive for positrons and results in positron states inside the barrier, which align in energy with the electron continuum outside 4,5,6 . Matching between electron and positron wavefunctions across the barrier leads to the high-probability tunneling described by the Klein paradox 7 . The essential feature of QED responsible for the effect is the fact that states at positive and negative energies (electrons and positrons)…”

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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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confidence: 99%

Chiral tunnelling and the Klein paradox in graphene

2006

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“…(1). It is valid for the energy regime c 2 <E<V-c 2 with V>2c 2 , at which a portion of the wave function (modeling an incoming particle) can actually penetrate the potential barrier of total height V. This purely mathematical transmission, however, does not mean that an actual physical electron can pass through this barrier as its energy E is less than the barrier height V. This mathematical property of the Dirac (and also of the Klein-Gordon) equations is related to the famous Klein paradox [25][26][27][28].…”

Section: The Pair Creation Rate and Its Relationship To The Transmissmentioning

confidence: 99%

“…In other words, this initial growth can be viewed as the result of an incoherent process due to each (subcritical) electric field pulse, where the created particles at one force location do not have sufficient time to affect the creation process (via Pauli blocking [27,28,32]) at the other location.…”

Section: Quantum Field Theoretical Simulationsmentioning

confidence: 99%

“…It can provide an alternative approach to the traditional S-matrix approach, which is based on the in-and out-states only and therefore cannot visualize the processes inside the interaction zone. In addition to visualizing the details of the pair creation dynamics, direct time-dependent quantum field theoretical solutions to the Dirac equation have also contributed to the resolution of various conceptual problems related to the negative energy states such as the Zitterbewegung [23], the relativistic localization problem [24] as well as the Klein-paradox [25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

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Electron-positron pair creation induced by quantum-mechanical tunneling

Jiang

et al. 2011

Phys. Rev. A

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We study the creation of electron-positron pairs from the vacuum induced by two spatially displaced static electric fields. The strength and spatial width of each localized field is less than required for pair-creation. If, however, the separation between the fields is less than the quantum mechanical tunneling length associated with the corresponding quantum scattering system, the system produces a steady flux of electron-positron pairs. We compute the time-dependence of the pair-creation probability by solving the Dirac equation numerically for various external field sequences. For the special case of two very narrow fields we provide an analytical expression for the pair-creation rate in the long-time limit.2

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“…It presumes a constructive quantum interference between an incoming electron (e) and a hole (h) moving inside the graphene barrier in a reverse direction and is characterized by the same pseudospin as sketched in Fig. 1(c) (Klein paradox [8,9]). The interference pattern resulting from the chiral tunneling is very sensitive to the phase difference ϕ between the e and h wavefunctions.…”

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confidence: 99%

Reversible heat flow through the carbon tube junction

Shafranjuk¹

2009

Europhys. Lett.

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Microscopic mechanisms of externally controlled reversable heat flow through the carbon nanotube junctions (NJ) are studied theoretically. Our model suggests that the heat is transfered along the tube section T by electrons (e) and holes (h) moving ballistically in either in parallel or in opposite directions and accelerated by the bias source-drain voltage VSD (Peltier effect). We compute the Seebeck coefficient α, electric σ and thermal κ conductivities and find that their magnitudes strongly depend on VSD and VG. The sign reversal of α versus the sign of VG formerly observed experimentally is interpreted in this work in terms of so-called chiral tunneling phenomena (Klein paradox).PACS numbers: 73.23. Hk, 73.63.Kv, 73.40.Gk Physics of the heat transfer determines functionality, precision and effectiveness of solid state nanocoolers [1,2,3,5] which are environment friendly and have a lot of applications in the experimental physics, nanoelectronics, chemistry, industry and medicine. Therefore exploiting of new thermoelectric materials with high figures of merit Z · T (T being the temperature) attracts a lot of attention. Recently such interest arose toward the carbon nanotube and graphene junctions which electronic properties are highly unconventional [5]. The thermoelectric power experiments [5] addressed single wall carbon nanotube junctions. In Ref.[5] a temperature difference ∆T induced a finite bias voltage ∆V p across the junction which sign changed versus the gate voltage V G . A question here is how that unconventional thermoelectric behavior is related to the intrinsic nature of the carbon nanotube and graphene? It is widely accepted that the charge carrier motion in carbon nanotubes and in graphene is essentially phase-correllated. For such a reason the conducting electrons and holes in that materials behave as relativistic massless 'chiral fermions' (CF) characterized by a 'pseudospin' (see review [6] and references thereis).In this Letter we argue that the phase-correlated thermoelectric transport of charge carriers implicates a voltage-controlled and reversable heat flow through the single wall carbon nanotube junctions (Peltier effect). The enhancement of Z · T in those 1D devices where the charge carriers propagate ballistically occurs due to strong van Hove singularities (VHS). The VHS position is tuned by the gate voltage V G in respect to the Fermi level ε F of the electrodes. When an VHS and ε F match each other, it results in a sufficient density of charge carriers which contribute to the electric conductivity despite the Fermi energy itself is relatively small. A finite gate voltage V G = 0 is not just merely supplies either the electrons or holes into T , but rather creates a potential barrier (U 0 > 0) or well (U 0 < 0) for chiral fermions transmitted across the junction as illustarted in Figs across the junction tilts the chiral barrier and causes the electric charge carriers to accelerate. This means that the energy of the charge carriers changes by δ = eV SD , which inflicts a local...

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Klein Paradox in Spatial and Temporal Resolution

Cited by 171 publications

References 10 publications

Chiral tunnelling and the Klein paradox in graphene

Chiral tunnelling and the Klein paradox in graphene

Electron-positron pair creation induced by quantum-mechanical tunneling

Reversible heat flow through the carbon tube junction

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