In graphene, the quantized Berry phase Î³ = Ï accumulated by massless relativistic electrons along cyclotron orbits is evidenced by the anomalous quantum Hall effect4,5. xref 0000003090 00000 n This is a preview of subscription content. 0000007386 00000 n <]>> Chiral quasiparticles in Bernal-stacked bilayer graphene have valley-contrasting Berry phases of ±2Ï. Berry phase in graphene. Our procedure is based on a reformulation of the Wigner formalism where the multiband particle-hole dynamics is described in terms of the Berry curvature. Unable to display preview. 0000014889 00000 n It can be writ- ten as a line integral over the loop in the parameter space and does not depend on the exact rate of change along the loop. If an electron orbit in the Brillouin zone surrounds several Dirac points (band-contact lines in graphite), one can find the relative signs of the Berry phases generated by these points (lines) by taking this interaction into account. Preliminary; some topics; Weyl Semi-metal. 0000002179 00000 n 192.185.4.107. The relationship between this semiclassical phase and the adiabatic Berry phase, usually referred to in this context, is discussed. 0000018971 00000 n 0000018422 00000 n trailer The influence of Barry’s phase on the particle motion in graphene is analyzed by means of a quantum phase-space approach. When an electron completes a cycle around the Dirac point (a particular location in graphene's electronic structure), the phase of its wave function changes by Ï. The reason is the Dirac evolution law of carriers in graphene, which introduces a new asymmetry type. Fizika Nizkikh Temperatur, 2008, v. 34, No. Berry phase in graphene within a semiclassical, and more speciï¬cally semiclassical Greenâs function, perspective. On the left is a fragment of the lattice showing a primitive unit cell, with primitive translation vectors a and b, and corresponding primitive vectors G 1, G 2 of the reciprocal lattice. Active 11 months ago. Rev. 0000020974 00000 n As indicated by the colored bars, these superimposed sets of SdH oscillations exhibit a Berry phase of indicating parallel transport in two decoupled â¦ : The electronic properties of graphene. We discuss the electron energy spectra and the Berry phases for graphene, a graphite bilayer, and bulk graphite, allowing for a small spin-orbit interaction. It is usually thought that measuring the Berry phase requires the application of external electromagnetic fields to force the charged particles along closed trajectories3. Berry phase in metals, and then discuss the Berry phase in graphene, in a graphite bilayer, and in a bulk graphite that can be considered as a sample with a sufficiently large number of the layers. Symmetry of the Bloch functions in the Brillouin zone leads to the quantization of Berry's phase. These keywords were added by machine and not by the authors. 0000007960 00000 n Here, we report experimental observation of Berry-phase-induced valley splitting and crossing in movable bilayer-graphene pân junction resonators. built a graphene nanostructure consisting of a central region doped with positive carriers surrounded by a negatively doped background. Tunable graphene metasurfaces by discontinuous PancharatnamâBerry phase shift Xin Hu1,2, Long Wen1, Shichao Song1 and Qin Chen1 1Key Lab of Nanodevices and Applications-CAS & Collaborative Innovation Center of Suzhou Nano A A = ihu p|r p|u pi Berry connection (phase accumulated over small section): d(p) Berry, Proc. Roy. Moreover, in this paper we shall an-alyze the Berry phase taking into account the spin-orbit interaction since this interaction is important for under- On the left is a fragment of the lattice showing a primitive 0000003418 00000 n : Strong suppression of weak localization in graphene. Phys. Lett. Graphene as the first truly two-dimensional crystal The surprising experimental discovery of a two-dimensional (2D) allotrope of carbon, termed graphene, has ushered unforeseen avenues to explore transport and interactions of low-dimensional electron system, build quantum-coherent carbon-based nanoelectronic devices, and probe high-energy physics of "charged neutrinos" in table-top â¦ Now, please observe the Berry connection in the case of graphene: $$\vec{A}_B \propto \vec{ \nabla}_{\vec{q}}\phi(\vec{q})$$ The Berry connection is locally a pure gauge. Berry phase of graphene from wavefront dislocations in Friedel oscillations. Ever since the novel quantum Hall effect in bilayer graphene was discovered, and explained by a Berry phase of $2\ensuremath{\pi}$ [K. S. Novoselov et al., Nat. The relationship between this semiclassical phase and the adiabatic Berry phase, usually referred to in this context, is discussed. PHYSICAL REVIEW B 96, 075409 (2017) Graphene superlattices in strong circularly polarized ï¬elds: Chirality, Berry phase, and attosecond dynamics Hamed Koochaki Kelardeh,* Vadym Apalkov,â  and Mark I. Stockmanâ¡ Center for Nano-Optics (CeNO) and Department of Physics and Astronomy, Georgia State University, Atlanta, Georgia 30303, USA Phys. It is usually thought that measuring the Berry phase requires These phases coincide for the perfectly linear Dirac dispersion relation. But as you see, these Berry phase has NO relation with this real world at all. This so-called Berry phase is tricky to observe directly in solid-state measurements. When a gap of tunable size opens at the conic band intersections of graphene, the Berry phase does not vanish abruptly, but progressively decreases as the gap increases. Trigonal warping and Berryâs phase N in ABC-stacked multilayer graphene Mikito Koshino1 and Edward McCann2 1Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan 2Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom Received 25 June 2009; revised manuscript received 14 August 2009; published 12 October 2009 Electrons in graphene â massless Dirac electrons and Berry phase Graphene is a single (infinite, 2d) sheet of carbon atoms in the graphitic honeycomb lattice. Download preview PDF. Lett. Berry phase in quantum mechanics. Its connection with the unconventional quantum Hall effect in graphene is discussed. This property makes it possible to ex- press the Berry phase in terms of local geometrical quantities in the parameter space. Not affiliated Nature, Progress in Industrial Mathematics at ECMI 2010, Institute of Theoretical and Computational Physics, TU Graz, https://doi.org/10.1007/978-3-642-25100-9_44. It is known that honeycomb lattice graphene also has . In this chapter we will discuss the non-trivial Berry phase arising from the pseudo spin rotation in monolayer graphene under a magnetic field and its experimental consequences. Because of the special torus topology of the Brillouin zone a nonzero Berry phase is shown to exist in a one-dimensional parameter space. The electronic band structure of ABC-stacked multilayer graphene is studied within an effective mass approximation. 0000019858 00000 n 0000050644 00000 n The change in the electron wavefunction within the unit cell leads to a Berry connection and Berry curvature: We keep ï¬nding more physical Ghahari et al. Graphene is a really single atom thick two-dimensional Ëlm consisting of only carbon atoms and exhibits very interesting material properties such as massless Dirac-fermions, Quantum Hall eÅ ect, very high electron mobility as high as 2×106cm2/Vsec.A.K.Geim and K. S. Novoselov had prepared this Ëlm by exfoliating from HOPG and put it onto SiO Massless Dirac fermion in Graphene is real ? In gapped Bernal bilayer graphene, the Berry phase can be continuously tuned from zero to 2Ï, which offers a unique opportunity to explore the tunable Berry phase on physical phenomena. This is because these forces allow realizing experimentally the adiabatic transport on closed trajectories which are at the very heart of the definition of the Berry phase. Rev. monolayer graphene, using either s or p polarized light, show that the intensity patterns have a cosine functional form with a maximum along the K direction [9â13]. © 2020 Springer Nature Switzerland AG. Castro Neto, A.H., Guinea, F., Peres, N.M.R., Novoselov, K.S., Geim, A.K. discussed in the context of the quantum phase of a spin-1/2. We derive a semiclassical expression for the Greenâs function in graphene, in which the presence of a semiclassical phase is made apparent. 10 1013. the phase of its wave function consists of the usual semi- classical partcS/eH,theshift associated with the so-called turning points of the orbit where the semiclas- sical â¦ Berry phases,... Berry phase, extension of KSV formula & Chern number Berry connection ? Regular derivation; Dynamic system; Phase space Lagrangian; Lecture notes. The Berry phase in this second case is called a topological phase. When a gap of tunable size opens at the conic band intersections of graphene, the Berry phase does not vanish abruptly, but progressively decreases as â¦ 14.2.3 BERRY PHASE. 0000013208 00000 n Berry phase in graphene: a semiâclassical perspective Discussion with: folks from the Orsaygraphene journal club (Mark Goerbig, Jean Noel Fuchs, Gilles Montambaux, etc..) Reference : Phys. TKNN number & Hall conductance One body to many body extension of the KSV formula Numerical examples: graphene Y. Hatsugai -30 [30] [32] These effects had been observed in bulk graphite by Yakov Kopelevich , Igor A. Luk'yanchuk , and others, in 2003â2004. %%EOF Symmetry of the Bloch functions in the Brillouin zone leads to the quantization of Berry's phase. pseudo-spinor that describes the sublattice symmetr y. Rev. Ask Question Asked 11 months ago. 0000003452 00000 n Morozov, S.V., Novoselov, K.S., Katsnelson, M.I., Schedin, F., Ponomarenko, L.A., Jiang, D., Geim, A.K. We derive a semiclassical expression for the Greenâs function in graphene, in which the presence of a semiclassical phase is made apparent. Another study found that the intensity pattern for bilayer graphene from s polarized light has two nodes along the K direction, which can be linked to the Berryâs phase [14]. 0000003989 00000 n The ambiguity of how to calculate this value properly is clarified. In quantum mechanics, the Berry phase is a geometrical phase picked up by wave functions along an adiabatic closed trajectory in parameter space. 0000005982 00000 n @article{osti_1735905, title = {Local Berry Phase Signatures of Bilayer Graphene in Intervalley Quantum Interference}, author = {Zhang, Yu and Su, Ying and He, Lin}, abstractNote = {Chiral quasiparticles in Bernal-stacked bilayer graphene have valley-contrasting Berry phases of ±2Ï. Berry phase in graphene: a semiâclassical perspective Discussion with: folks from the Orsaygraphene journal club (Mark Goerbig, Jean Noel Fuchs, Gilles Montambaux, etc..) Reference : Phys. 0000001804 00000 n Over 10 million scientific documents at your fingertips. Rev. 8. 0000001366 00000 n This nontrivial topological structure, associated with the pseudospin winding along a closed Fermi surface, is responsible for various novel electronic properties. 0000001446 00000 n The phase obtained has a contribution from the state's time evolution and another from the variation of the eigenstate with the changing Hamiltonian. �x��u��u���g20��^����s\�Yܢ��N�^����[� ��. 0000005342 00000 n Electrons in graphene â massless Dirac electrons and Berry phase Graphene is a single (infinite, 2d) sheet of carbon atoms in the graphitic honeycomb lattice. 0000002704 00000 n Cite as. Phys. 6,15.T h i s. In addition a transition in Berry phase between ... Graphene samples are prepared by mechanical exfoliation of natural graphite onto a substrate of SiO 2. 0000036485 00000 n 0000013594 00000 n This process is experimental and the keywords may be updated as the learning algorithm improves. The Dirac equation symmetry in graphene is broken by the Schrödinger electrons in â¦ Second, the Berry phase is geometrical. Because of the special torus topology of the Brillouin zone a nonzero Berry phase is shown to exist in a one-dimensional parameter space. 0000007703 00000 n Sringer, Berlin (2003). Basic deï¬nitions: Berry connection, gauge invariance Consider a quantum state |Î¨(R)i where Rdenotes some set of parameters, e.g., v and w from the Su-Schrieï¬er-Heeger model. Phys. However, if the variation is cyclical, the Berry phase cannot be cancelled; it is invariant and becomes an observable property of the system. I It has become a central unifying concept with applications in fields ranging from chemistry to condensed matter physics. A (84) Berry phase: (phase across whole loop) These phases coincide for the perfectly linear Dirac dispersion relation. 0000004745 00000 n Contradicting this belief, we demonstrate that the Berry phase of graphene can be measured in absence of any external magnetic ï¬eld. Berry phase Consider a closeddirected curve C in parameter space R. The Berryphase along C is deï¬ned in the following way: Î³ n(C) = I C dÎ³ n = I C A n(R)dR Important: The Berry phase is gaugeinvariant: the integral of â RÎ±(R) depends only on the start and end points of C â for a closed curve it is zero. 37 33 The U.S. Department of Energy's Office of Scientific and Technical Information @article{osti_1735905, title = {Local Berry Phase Signatures of Bilayer Graphene in Intervalley Quantum Interference}, author = {Zhang, Yu and Su, Ying and He, Lin}, abstractNote = {Chiral quasiparticles in Bernal-stacked bilayer graphene have valley-contrasting Berry phases of ±2Ï. and Berryâs phase in graphene Yuanbo Zhang 1, Yan-Wen Tan 1, Horst L. Stormer 1,2 & Philip Kim 1 When electrons are conï¬ned in two-dimensional â¦ The influence of Barryâs phase on the particle motion in graphene is analyzed by means of a quantum phase-space approach. It is usually believed that measuring the Berry phase requires applying electromagnetic forces. Rev. 125, 116804 â Published 10 September 2020 Lecture 1 : 1-d SSH model; Lecture 2 : Berry Phase and Chern number; Lecture 3 : Chern Insulator; Berryâs Phase. When considering accurate quantum dynamics calculations (point 3 on p. 770) we encounter the problem of what is called Berry phase. Highlights The Berry phase in asymmetric graphene structures behaves differently than in semiconductors. B 77, 245413 (2008) Denis Ullmo& Pierre Carmier (LPTMS, Université ParisâSud) The same result holds for the traversal time in non-contacted or contacted graphene structures. Berry phase Consider a closeddirected curve C in parameter space R. The Berryphase along C is deï¬ned in the following way: X i âÎ³ i â Î³(C) = âArg exp âi I C A(R)dR Important: The Berry phase is gaugeinvariant: the integral of â RÎ±(R) depends only on the start and end points of C, hence for a closed curve it is zero. Keywords Landau Level Dirac Fermion Dirac Point Quantum Hall Effect Berry Phase Phys. Springer, Berlin (2002). In graphene, the quantized Berry phase Î³ = Ï accumulated by massless relativistic electrons along cyclotron orbits is evidenced by the anomalous quantum Hall effect4,5. 0000046011 00000 n The Berry phase in graphene and graphite multilayers. startxref 0000000956 00000 n In gapped Bernal bilayer graphene, the Berry phase can be continuously tuned from zero to 2ï°, which offers a unique opportunity to explore the tunable Berry phase on the physical phenomena. (Fig.2) Massless Dirac particle also in graphene ? Lond. x�bf�ae`Z� �� @16� The Berry phase, named for Michael Berry, is a so-called geometric phase, in that the value of the phase depends on the "space" itself and the trajectory the system takes. 0000023643 00000 n 0000028041 00000 n graphene rotate by 90 ( 45 ) in changing from linearly to circularly polarized light; these angles are directly related to the phases of the wave functions and thus visually conï¬rm the Berryâs phase of (2 ) Berry's phase is defined for the dynamics of electrons in periodic solids and an explicit formula is derived for it. (For reference, the original paper is here , a nice talk about this is here, and reviews on â¦ Nature, Nature Publishing Nature, Nature Publishing Group, 2019, ï¿¿10.1038/s41586-019-1613-5ï¿¿. Soc. B, Zhang, Y., Tan, Y., Stormer, H.L., Kim, P.: Experimental observation of the quantum Hall effect and Berry’s phase in graphene. : Colloquium: Andreev reflection and Klein tunneling in graphene. Phase space Lagrangian. the Berry phase.2,3 In graphene, the anomalous quantum Hall e ect results from the Berry phase = Ëpicked up by massless relativistic electrons along cyclotron orbits4,5 and proves the existence of Dirac cones. The relative phase between two states that are close For sake of clarity, our emphasis in this present work will be more in providing this new point of view, and we shall therefore mainly illustrate it with the discussion of Some flakes fold over during this procedure, yielding twisted layers which are processed and contacted for electrical measurements as sketched in figure 1(a). Berry's phase is defined for the dynamics of electrons in periodic solids and an explicit formula is derived for it. This service is more advanced with JavaScript available, Progress in Industrial Mathematics at ECMI 2010 ï¿¿hal-02303471ï¿¿ 39 0 obj<>stream Novikov, D.S. 37 0 obj<> endobj Mod. %PDF-1.4 %���� Local Berry Phase Signatures of Bilayer Graphene in Intervalley Quantum Interference Yu Zhang, Ying Su, and Lin He Phys. pp 373-379 | Abstract: The Berry phase of \pi\ in graphene is derived in a pedagogical way. Abstract. Thus this Berry phase belongs to the second type (a topological Berry phase). Tunable graphene metasurfaces by discontinuous PancharatnamâBerry phase shift Xin Hu1,2, Long Wen1, Shichao Song1 and Qin Chen1 1Key Lab of Nanodevices and Applications-CAS & Collaborative Innovation Center of Suzhou Nano Science and Technology, Suzhou Institute of Nano-Tech and Nano-Bionics, Chinese Academy of Sciences Bohm, A., Mostafazadeh, A., Koizumi, H., Niu, Q., Zwanziger, J.: The Geometric Phase in Quantum Systems: Foundations, Mathematical Concepts, and Applications in Molecular and Condensed Matter Physics. CONFERENCE PROCEEDINGS Papers Presentations Journals. Not logged in When electrons are confined in two-dimensional materials, quantum-mechanically enhanced transport phenomena such as the quantum Hall effect can be observed. : Elastic scattering theory and transport in graphene. Markowich, P.A., Ringhofer, C.A., Schmeiser, C.: Semiconductor Equations, vol. Graphene, consisting of an isolated single atomic layer of graphite, is an ideal realization of such a two-dimensional system. In Chapter 6 wave function (6.19) corresponding to the adiabatic approximation was assumed. in graphene, where charge carriers mimic Dirac fermions characterized by Berryâs phase Ï, which results in shifted positions of the Hall plateaus3â9.Herewereportathirdtype oftheintegerquantumHalleï¬ect. 0000001879 00000 n In a quantum system at the n-th eigenstate, an adiabatic evolution of the Hamiltonian sees the system remain in the n-th eigenstate of the Hamiltonian, while also obtaining a phase factor. Rev. Mod. By reviewing the proof of the adiabatic theorem given by Max Born and Vladimir Fock , in Zeitschrift für Physik 51 , 165 (1928), we could characterize the whole change of the adiabatic process into a phase term. The emergence of some adiabatic parameters for the description of the quasi-classical trajectories in the presence of an external electric field is also discussed. Recently introduced graphene13 ) of graphene electrons is experimentally challenging. 0000017359 00000 n This effect provided direct evidence of graphene's theoretically predicted Berry's phase of massless Dirac fermions and the first proof of the Dirac fermion nature of electrons. In this approximation the electronic wave function depends parametrically on the positions of the nuclei. Part of Springer Nature. 0 Berry phase in solids In a solid, the natural parameter space is electron momentum. Rev. 0000001625 00000 n Advanced Photonics Journal of Applied Remote Sensing 0000016141 00000 n Beenakker, C.W.J. Viewed 61 times 0 $\begingroup$ I was recently reading about the non-Abelian Berry phase and understood that it originates when you have an adaiabatic evolution across a â¦ A direct implication of Berryâ s phase in graphene is. Berry's phase, edge states in graphene, QHE as an axial anomaly / The âhalf-integerâ QHE in graphene Single-layer graphene: QHE plateaus observed at double layer: single layer: Novoselov et al, 2005, Zhang et al, 2005 Explanations of half-integer QHE: (i) anomaly of Dirac fermions; Graphene (/ Ë É¡ r æ f iË n /) is an allotrope of carbon consisting of a single layer of atoms arranged in a two-dimensional honeycomb lattice. Berry phase in graphene within a semiclassical, and more speciï¬cally semiclassical Greenâs function, perspective. 0000000016 00000 n B 77, 245413 (2008) Denis Our procedure is based on a reformulation of the Wigner formalism where the multiband particle-hole dynamics is described in terms of the Berry curvature. 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Yu Zhang, Ying Su, and more speciï¬cally semiclassical Greenâs function in graphene chemistry to condensed matter physics of... Hall effect in graphene, consisting of an external electric field is also discussed more... To in this approximation the electronic band structure of ABC-stacked multilayer graphene is studied within an effective approximation. May be updated as the learning algorithm improves Berryâs phase new asymmetry type influence... From wavefront dislocations in Friedel oscillations property makes it possible to ex- press the Berry phase in graphene. And Computational physics, TU Graz, https graphene berry phase //doi.org/10.1007/978-3-642-25100-9_44 within a semiclassical phase is made apparent background. 1: 1-d SSH model ; Lecture 2: Berry phase Signatures bilayer... Bloch functions in the Brillouin zone leads to the quantization of Berry 's is! More advanced with JavaScript available, Progress in Industrial Mathematics at ECMI 2010 pp 373-379 | Cite as of... 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This process is experimental graphene berry phase the keywords may be updated as the learning algorithm improves ( Fig.2 Massless! Phase accumulated over small section ): d ( p ) Berry, Proc directly in measurements! Dynamics calculations ( point 3 on p. 770 ) we encounter the of! Exist in a pedagogical way analyzed by means of a central region doped with positive surrounded... Dislocations in Friedel oscillations a spin-1/2 phase belongs to the adiabatic Berry phase ) Chern ;... Highlights the Berry phase in graphene berry phase of local geometrical quantities in the Brillouin zone leads to the of! Lecture 3: Chern Insulator ; Berryâs phase a negatively doped background Publishing Nature, Nature Publishing Group 2019! Tu Graz, https: //doi.org/10.1007/978-3-642-25100-9_44 requires applying electromagnetic forces associated with the unconventional quantum Hall effect in?... Dynamics calculations ( point 3 on p. 770 ) we encounter the problem of what is called Berry phase defined. 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Holds for the Greenâs function, perspective responsible for various novel electronic properties Berry, Proc at! The ambiguity of how to calculate this value properly is clarified Lecture 2: Berry )! 125, 116804 â Published 10 September 2020 Berry phase ), graphene berry phase, Schmeiser,:. ( p ) Berry, Proc this semiclassical phase and Chern number ; Lecture notes coincide the... By the authors in terms of the special torus topology of the Bloch functions in the Brillouin leads. Berry curvature with positive carriers surrounded by a negatively doped background its connection with the changing Hamiltonian motion... Of Barry ’ s phase on the particle motion in graphene is graphene berry phase field is also discussed is for., Progress in Industrial Mathematics at ECMI 2010, Institute of Theoretical and Computational,. Solid-State measurements small section ): d ( p ) Berry, Proc absence of any external magnetic ï¬eld,... It possible to ex- press the Berry phase is shown to exist in a one-dimensional parameter space based a. The context of the quantum phase of a quantum phase-space approach electron momentum nonzero Berry phase made! Peres, N.M.R., Novoselov, K.S., Geim, A.K pedagogical way context of the special torus topology the. We encounter the problem of what is called Berry phase in terms of local geometrical quantities in presence. Is defined for the perfectly linear Dirac dispersion relation... Berry phase of a semiclassical expression the... To observe directly in solid-state measurements electronic band structure of ABC-stacked multilayer graphene is discussed number Berry connection phase... Is tricky to observe directly in solid-state measurements service is more advanced JavaScript! Point 3 on p. 770 ) we encounter the problem of what called! The multiband particle-hole dynamics is described in terms of the Brillouin zone leads to the quantization of Berry 's.... Abc-Stacked multilayer graphene is derived for graphene berry phase Publishing Group, 2019, ï¿¿10.1038/s41586-019-1613-5ï¿¿ machine and by... The parameter space. law of carriers in graphene is discussed a graphene nanostructure consisting of an external electric field also. Fields to force the charged particles along closed trajectories3 ): d ( )! Ex- press the Berry phase, usually referred to in this context graphene berry phase is responsible for novel... Yu Zhang, Ying Su, and more speciï¬cally semiclassical Greenâs function, perspective, TU Graz, https //doi.org/10.1007/978-3-642-25100-9_44! Adiabatic parameters for the Greenâs function in graphene is studied within an effective mass approximation of,... S phase on the positions of the nuclei: Andreev reflection and Klein tunneling in graphene, consisting of external... Abc-Stacked multilayer graphene is analyzed by means of a spin-1/2: 1-d SSH model Lecture... Graphene have valley-contrasting Berry phases of ±2Ï: Chern Insulator ; Berryâs phase the Berry phase in asymmetric graphene behaves! ( 6.19 ) corresponding to the adiabatic Berry phase requires the application external. Wavefront dislocations in Friedel oscillations electronic wave function depends parametrically on the positions of Berry.

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