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Part B:Condensed Matter Physics

Conductivity of disordered 2d binodal Dirac electron gas: effect of internode scattering

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Pages 1799-1822 | Received 26 Oct 2017, Accepted 12 Feb 2018, Published online: 08 Mar 2018

References

  • E. Abrahams, P.W. Anderson, D.C. Licciardello, and T.V. Ramakrishnan, Scaling theory of localization: Absence of quantum diffusion in two dimensions, Phys. Rev. Lett. 42 (1979), pp. 673–676.
  • L.G. Gor’kov, A.I. Larkin, and D.E. Khmel’nitskii, Particle conductivity in a two-dimensional random potential, Pis’ma Zh. Eksp. Teor. Fiz. 30 (1979), pp. 248–252 [JETP Lett. 30 (1979), pp. 228--232].
  • S. Hikami, A. Larkin, and Y. Nagaoka, Spin-orbit interaction and magnetoresistance in the two dimensional random system, Prog. Theor. Phys. 63 (1980), pp. 707–710.
  • D. Vollhardt and P. Wölfle, Diagrammatic, self-consistent treatment of the Anderson localization problem in d ≤ 2 dimensions, Phys. Rev. B 22 (1980), pp. 4666–4679.
  • Y. Hanein, U. Meirav, D. Shahar, C.C. Li, D.C. Tsui, and H. Shtrikman, The metalliclike conductivity of a two-dimensional hole system, Phys. Rev. Lett. 80 (1998), pp. 1288–1291.
  • K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, M.I. Katsnelson, I.V. Grigorieva, S.V. Dubonos, and A.A. Firsov, Two-dimensional gas of massless Dirac fermions in graphene, Nature 438 (2005), pp. 197–200.
  • Y.-W. Tan, Y. Zhang, K. Bolotin, Y. Zhao, S. Adam, E.H. Hwang, and S. Das, Sarma, H.L. Stormer, and P. Kim, It Measurement of scattering rate and minimum conductivity in graphene, Phys. Rev. Lett. 99(246803) (2007), pp. 1–4.
  • D.C. Elias, R.R. Nair, T.M.G. Mohiuddin, S.V. Morozov, P. Blake, M.P. Halsall, A.C. Ferrari, D.W. Boukhvalov, M.I. Katsnelson, A.K. Geim, and K.S. Novoselov, Control of graphene’s properties by reversible hydrogenation: Evidence for graphane, Science 323 (2009), pp. 610–613.
  • M.J. Allen, V.C. Tung, and R.B. Kaner, Honeycomb carbon: A review of graphene, Chem. Rev. 110 (2010), pp. 132–145.
  • L. Chen, Ch-Ch Liu, B. Feng, X. He, P. Cheng, Z. Ding, Sh. Meng, Y. Yao, and K. Wu, Evidence for Dirac fermions in a honeycomb lattice based on silicon, Phys. Rev. Lett. 109(056804) (2012), pp. 1–5.
  • M.Z. Hasan and C.L. Mele, Colloquium: Topological insulators, Rev. Mod. Phys. 82 (2010), pp. 3045–3067.
  • X.-L. Qi and S.-C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83 (2011), pp. 1057–1110.
  • N.H. Shon and T. Ando, Quantum transport in two-dimensional graphite system, J. Phys. Soc. Jap. 67 (1998), pp. 2421–2429.
  • T. Ando, Y. Zheng, and H. Suzuura, Dynamical conductivity and zero-mode anomaly in honeycomb lattices, J. Phys. Soc. Japan 71 (2002), pp. 1318–1324.
  • H. Suzuura and T. Ando, Crossover from symplectic to orthogonal class in a two-dimensional honeycomb lattice, Phys. Rev. Lett. 89(266603) (2002), pp. 1–4.
  • E. McCann, K. Kechedzhi, V.I. Fal’ko, H. Suzuura, T. Ando, and B.L. Altshuler, Weak-localization magnetoresistance and valley symmetry in graphene, Phys. Rev. Lett. 97(146805) (2006), pp. 1–4.
  • D.V. Khveshchenko, Electron localization properties in graphene, Phys. Rev. Lett. 97(036802) (2006), pp. 1–4.
  • B.L. Altshuler, A.G. Aronov, A.I. Larkin, and D.E. Khmel’nitskii, Anomalous magnetoresistance in semiconductors, Th. Eksp. Teor. Fiz. 81 (1981), pp. 768–776 [Sov. Phys. JETP 54 (1981), pp. 411--419].
  • G. Tkachov and E.M. Hankiewicz, Weak antilocalization in HgTe quantum wells and topological surface states: Massive versus massless Dirac fermions, Phys. Rev. B 84(035444) (2011), pp. 1–13.
  • D. Schmeltzer and A. Saxena, Interference effects for T2 = −1 time reversal invariant topological insulators: Surface optical and Raman conductivity, Phys. Rev. B 88(035140) (2013), pp. 1–16.
  • B.L. Altshuler and B.D. Simons, Universalities: From Anderson localization to quantum chaos, in Mesoscopic quantum physics, Les Houches 1994, E. Akkermans, G. Montambaux, J.-L. Pichard, and J. Zinn-Justin, eds., North Holland, Amsterdam, 1995, pp. 1–98.
  • K. Efetov, Supersymmetry in Disorder and Chaos, Cambridge University Press, Cambridge, 1997.
  • L.S. Levitov and A.V. Shytov, Green’s functions. Theory and practice, Fizmatlit-Nauka, Moscow (2002). in Russian. Available at http://www.mit.edu/~levitov/book/.
  • P.A. Lee, Localized states in a d-wave superconductor, Phys. Rev. Lett. 71 (1993), pp. 1887–1890.
  • F.J. Wegner, Disordered system with n orbitals per site: N = ∞ limit, Phys. Rev. B 19 (1979), pp. 783–792.
  • A.J. McKane and M. Stone, Localization as an alternative to Goldstone’s theorem, Ann. Phys. 131 (1981), pp. 36–55.
  • E. Fradkin, Critical behavior of disordered degenerate semiconductors. I. Models, symmetries, and formalism, Phys. Rev. B 33 (1986), pp. 3257–3262.
  • E. Fradkin, Critical behavior of disordered degenerate semiconductors. II. Spectrum and transport properties in mean-field theory, Phys. Rev. B 33 (1986), pp. 3263–3268.
  • K. Ziegler, Scaling behavior and universality near the quantum Hall transition, Phys. Rev. B 55 (1997), pp. 10661–10670.
  • K. Ziegler and G. Jug, Is the peak value of σxx at the quantum Hall transition universal?, Z. Phys. B 104 (1997), pp. 5–6.
  • K. Ziegler, Delocalization of 2D Dirac fermions: The role of a broken supersymmetry, Phys. Rev. Lett. 80 (1998), pp. 3113–3116.
  • F. Wegner, The mobility edge problem: Continuous symmetry and a conjecture, Z. Phys. B 35 (1979), pp. 207–210.
  • L. Schäfer and F. Wegner, Disordered system with n orbitals per site: Lagrange formulation, hyperbolic symmetry, and Goldstone modes, Z. Phys. B 38 (1980), pp. 113–126.
  • S. Hikami, Anderson localization in a nonlinear-σ-model representation, Phys. Rev. B 24 (1981), pp. 2671–2679.
  • K. Ziegler, Random-gap model for graphene and graphene bilayers, Phys. Rev. Lett. 102(126802) (2009), pp. 1–4.
  • K. Ziegler, Diffusion in the random gap model of monolayer and bilayer graphene, Phys. Rev. B 79(195424) (2009), pp. 1–11.
  • K. Ziegler, Quantum diffusion in two-dimensional random systems with particle-hole symmetry, J. Phys. A: Math. Theor. 45(335001) (2012), pp. 1–12.
  • K. Ziegler and A. Sinner, Weak-localization approach to a 2D electron gas with a spectral node, Phys. E 71 (2015), pp. 14–20.
  • A. Sinner and K. Ziegler, Finite-size scaling in a 2D disordered electron gas with spectral nodes, J. Phys.: Cond. Mat. 28 (305701) (2016), pp. 1–7.
  • A. Sinner and K. Ziegler, Perturbative analysis of the conductivity in disordered monolayer and bilayer graphene, Phys. Rev. B 84(233401) (2011), pp. 1–4.
  • A. Sinner and K. Ziegler, Linear response peculiarity of a two-dimensional Dirac electron gas at weak scattering, Phys. Rev. B 89(024201) (2014), pp. 1–13.
  • A. Sinner, A. Sedrakyan, and K. Ziegler, Optical conductivity of graphene in the presence of random lattice deformations, Phys. Rev. B 83(155115) (2011), pp. 1–8.
  • K. Ziegler and A. Sinner, Transport in finite graphene samples with a random gap, Phys. Rev. B 81(241404R) (2010), pp. 1–3.
  • A. Sinner and K. Ziegler, Two-parameter scaling theory of transport near a spectral node, Phys. Rev. B 90(174207) (2014), pp. 1–5.
  • A. Sinner and K. Ziegler, Renormalized transport properties of randomly gapped two-dimensional Dirac fermions, Phys. Rev. B 86(155450) (2012), pp. 1–10.
  • A.W.W. Ludwig, M.P.A. Fisher, R. Shankar, and G. Grinstein, Integer quantum Hall transition: An alternative approach and exact results, Phys. Rev. B 50 (1994), pp. 7526–7552.
  • P.K. Wallace, The band theory of graphite, Phys. Rev. 71 (1947), pp. 622–634.
  • G.W. Semenoff, Condensed-matter simulation of a three-dimensional anomaly, Phys. Rev. Lett. 53 (1984), pp. 2449–2452.
  • A.A. Burkov, Chiral anomaly and transport in Weyl metals, J. Phys.: Condens. Matter 27(113201) (2015), pp. 1–18.
  • K. Huang, Statistical Mechanics, Wiley Inc., New York, 1963.
  • M.R. Zirnbauer, Riemannian symmetric superspaces and their origin in random-matrix theory, J. Math. Phys. 37 (1996), pp. 4986–5018.
  • A. Altland and M. Zirnbauer, Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures, Phys. Rev. B 55 (1997), pp. 1142–1161.
  • D. Bernard and A. LeClair, A classification of 2D random Dirac fermions, J. Phys. A: Math. Gen. 35 (2002), pp. 2555–2567.
  • D. Bernard, E.-A. Kim, and A. LeClair, Edge states for topological insulators in two dimensions and their Luttinger-like liquids, Phys. Rev. B 86(205116) (2012), pp. 1–9.
  • B. Huckestein and A. Altland, Quasi-particle density of states and Thouless conductance of disordered d-wave superconductors, Physica B 329(1461) (2003), pp. 71–72.
  • V.M. Pereira, F. Guinea, J.M.B. Lopes dos Santos, N.M.R. Peres, and A.H. Castro, Neto, Disorder induced localized states in graphene, Phys. Rev. Lett. 96(036801) (2006), pp. 1–4.
  • Sh Wu, L. Jing, Q. Li, Q.W. Shi, J. Chen, H. Su, X. Wang, and J. Yang, Average density of states in disordered graphene systems, Phys. Rev. B 77(195411) (2008), pp. 1–7.
  • I. Aleiner and K. Efetov, Effect of disorder on transport in graphene, Phys. Rev. Lett. 97(236801) (2006), pp. 1–4.
  • R. Oppermann and F. Wegner, Disordered system with n orbitals per site: 1/n expansion, Z. Phys. B 34 (1979), pp. 327–348.
  • K. Ziegler, Scaling relation for the density of states of a disordered n-orbital model, Phys. Lett. A 99 (1983), pp. 19–21.

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