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Dynamical breakdown of parity and time-reversal invariance in the many-body theory of graphene

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Abstract

We show that, at sufficiently large strength of the long-range Coulomb interaction, a mass term breaking parity (so-called Haldane mass) is dynamically generated in the many-body theory of Dirac fermions describing the graphene layer. While the tendency towards chiral symmetry breaking is stronger than for the dynamical breakdown of parity at spatial dimension D > 2, we find that the situation is reversed at D = 2. The need to regularize the many-body theory in a gauge-invariant manner (taking the limit D = 2 − ϵ) is what leads to the dominance of the parity-breaking pattern in graphene. We compute the critical coupling for the generation of a parity-breaking mass from the finite radius of convergence of the ladder series supplemented with electron self-energy corrections, finding a value quite close to the effective interaction strength for graphene in vacuum after including Fermi velocity renormalization and static random-phase approximation (RPA) screening of the Coulomb interaction.

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References

  1. K.S. Novoselov et al., Electric field effect in atomically thin carbon films, Science 306 (2004) 666.

    Article  ADS  Google Scholar 

  2. K.S. Novoselov et al., Two-dimensional gas of massless Dirac fermions in graphene, Nature 438 (2005) 197 [cond-mat/0509330] [INSPIRE].

    Article  ADS  Google Scholar 

  3. Y. Zhang, Y.-W. Tan, H.L. Stormer and P. Kim, Experimental observation of the quantum Hall effect and Berry’s phase in graphene, Nature 438 (2005) 201 [INSPIRE].

    Article  ADS  Google Scholar 

  4. A.H. Castro Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov and A.K. Geim, The electronic properties of graphene, Rev. Mod. Phys. 81 (2009) 109 [INSPIRE].

    Article  ADS  Google Scholar 

  5. H. Suzuura and T. Ando, Crossover from symplectic to orthogonal class in a two-dimensional honeycomb lattice, Phys. Rev. Lett. 89 (2002) 266603.

    Article  ADS  Google Scholar 

  6. M.I. Katsnelson, K.S. Novoselov and A.K. Geim, Chiral tunnelling and the Klein paradox in graphene, Nature Phys. 2 (2006) 620.

    Article  ADS  Google Scholar 

  7. V.M. Pereira, J. Nilsson and A.H. Castro Neto, Coulomb impurity problem in graphene, Phys. Rev. Lett. 99 (2007) 166802.

    Article  ADS  Google Scholar 

  8. M.M. Fogler, D.S. Novikov and B.I. Shklovskii, Screening of a hypercritical charge in graphene, Phys. Rev. B 76 (2007) 233402.

    ADS  Google Scholar 

  9. A.V. Shytov, M.I. Katsnelson and L.S. Levitov, Vacuum polarization and screening of supercritical impurities in graphene, Phys. Rev. Lett. 99 (2007) 236801.

    Article  ADS  Google Scholar 

  10. I.S. Terekhov et al., Screening of Coulomb impurities in graphene, Phys. Rev. Lett. 100 (2008) 076803.

    Article  ADS  Google Scholar 

  11. J. González, F. Guinea and M.A.H. Vozmediano, Unconventional quasiparticle lifetime in graphite, Phys. Rev. Lett. 77 (1996) 3589.

    Article  ADS  Google Scholar 

  12. S. Yu et al., Energy dependence of electron lifetime in graphite observed with femtosecond photoemission spectroscopy, Phys. Rev. Lett. 76 (1996) 483.

    Article  ADS  Google Scholar 

  13. D.V. Khveshchenko, Ghost excitonic insulator transition in layered graphite, Phys. Rev. Lett. 87 (2001) 246802 [INSPIRE].

    Article  ADS  Google Scholar 

  14. E.V. Gorbar, V.P. Gusynin, V.A. Miransky and I.A. Shovkovy, Magnetic field driven metal insulator phase transition in planar systems, Phys. Rev. B 66 (2002) 045108 [cond-mat/0202422] [INSPIRE].

    ADS  Google Scholar 

  15. O. Vafek and M.J. Case, Renormalization group approach to two-dimensional Coulomb interacting Dirac fermions with random gauge potential, Phys. Rev. B 77 (2008) 033410.

    ADS  Google Scholar 

  16. D.V. Khveshchenko, Massive Dirac fermions in single-layer graphene, J. Phys. Condens. Mat. 21 (2009) 075303.

    Article  ADS  Google Scholar 

  17. I.F. Herbut, V. Juričić and O. Vafek, Relativistic Mott criticality in graphene, Phys. Rev. B 80 (2009) 075432 [arXiv:0904.1019] [INSPIRE].

    ADS  Google Scholar 

  18. V. Juričić, I.F. Herbut and G.W. Semenoff, Coulomb interaction at the metal-insulator critical point in graphene, Phys. Rev. B 80 (2009) 081405 [arXiv:0906.3513] [INSPIRE].

    ADS  Google Scholar 

  19. J.E. Drut and T.A. Lähde, Is graphene in vacuum an insulator?, Phys. Rev. Lett. 102 (2009) 026802 [arXiv:0807.0834] [INSPIRE].

    Article  ADS  Google Scholar 

  20. J.E. Drut and T.A. Lähde, Critical exponents of the semimetal-insulator transition in graphene: A Monte Carlo study, Phys. Rev. B 79 (2009) 241405 [arXiv:0905.1320] [INSPIRE].

    ADS  Google Scholar 

  21. S.J. Hands and C.G. Strouthos, Quantum critical behaviour in a graphene-like model, Phys. Rev. B 78 (2008) 165423 [arXiv:0806.4877] [INSPIRE].

    ADS  Google Scholar 

  22. W. Armour, S. Hands and C. Strouthos, Monte Carlo simulation of the semimetal-insulator phase transition in monolayer graphene, Phys. Rev. B 81 (2010) 125105 [arXiv:0910.5646] [INSPIRE].

    ADS  Google Scholar 

  23. O.V. Gamayun, E.V. Gorbar and V.P. Gusynin, Supercritical Coulomb center and excitonic instability in graphene, Phys. Rev. B 80 (2009) 165429.

    ADS  Google Scholar 

  24. J. Wang, H.A. Fertig and G. Murthy, Critical behavior in graphene with Coulomb interactions, Phys. Rev. Lett. 104 (2010) 186401.

    Article  ADS  Google Scholar 

  25. O.V. Gamayun, E.V. Gorbar and V.P. Gusynin, Gap generation and semimetal-insulator phase transition in graphene, Phys. Rev. B 81 (2010) 075429 [arXiv:0911.4878] [INSPIRE].

    ADS  Google Scholar 

  26. J. González, Renormalization group approach to chiral symmetry breaking in graphene, Phys. Rev. B 82 (2010) 155404 [arXiv:1007.3705] [INSPIRE].

    ADS  Google Scholar 

  27. J. González, Electron self-energy effects on chiral symmetry breaking in graphene, Phys. Rev. B 85 (2012) 085420 [arXiv:1103.3650] [INSPIRE].

    ADS  Google Scholar 

  28. D.C. Elias et al., Dirac cones reshaped by interaction effects in suspended graphene, Nature Phys. 7 (2011) 701.

    Article  ADS  Google Scholar 

  29. J. González, F. Guinea and M.A.H. Vozmediano, Non-Fermi liquid behavior of electrons in the half-filled honeycomb lattice (a renormalization group approach), Nucl. Phys. B 424 (1994) 595 [hep-th/9311105] [INSPIRE].

    Article  ADS  Google Scholar 

  30. J. González, F. Guinea and M.A.H. Vozmediano, Marginal-Fermi-liquid behavior from two-dimensional Coulomb interaction, Phys. Rev. B 59 (1999) R2474.

    ADS  Google Scholar 

  31. J. Sabio, F. Sols and F. Guinea, Variational approach to the excitonic phase transition in graphene, Phys. Rev. B 82 (2010) 121413 [arXiv:1007.3471] [INSPIRE].

    ADS  Google Scholar 

  32. S. Raghu, X.L. Qi, C. Honerkamp and S.C. Zhang, Topological Mott insulators, Phys. Rev. Lett. 100 (2008) 156401.

    Article  ADS  Google Scholar 

  33. I.F. Herbut, Pseudomagnetic catalysis of the time-reversal symmetry breaking in graphene, Phys. Rev. B 78 (2008) 205433.

    ADS  Google Scholar 

  34. R.D. Pisarski, Chiral symmetry breaking in three-dimensional electrodynamics, Phys. Rev. D 29 (1984) 2423 [INSPIRE].

    ADS  Google Scholar 

  35. T. Appelquist, D. Nash and L.C.R. Wijewardhana, Critical behavior in (2 + 1)-dimensional QED, Phys. Rev. Lett. 60 (1988) 2575 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  36. E. Dagotto, J.B. Kogut and A. Kocić, A computer simulation of chiral symmetry breaking in (2 + 1)-dimensional QED with N flavors, Phys. Rev. Lett. 62 (1989) 1083 [INSPIRE].

    Article  ADS  Google Scholar 

  37. T. Appelquist, M.J. Bowick, D. Karabali and L. Wijewardhana, Spontaneous breaking of parity in (2 + 1)-dimensional QED, Phys. Rev. D 33 (1986) 3774 [INSPIRE].

    ADS  Google Scholar 

  38. G.W. Semenoff and L.C.R. Wijewardhana, Dynamical mass generation in 3D four fermion theory, Phys. Rev. Lett. 63 (1989) 2633 [INSPIRE].

    Article  ADS  Google Scholar 

  39. S. Ryu, C. Mudry, C.-Y. Hou and C. Chamon, Masses in graphenelike two-dimensional electronic systems: Topological defects in order parameters and their fractional exchange statistics, Phys. Rev. B 80 (2009) 205319.

    ADS  Google Scholar 

  40. A. Giuliani, V. Mastropietro and M. Porta, Lattice quantum electrodynamics for graphene, Annals Phys. 327 (2012) 461 [arXiv:1107.4741] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  41. G.W. Semenoff, Condensed matter simulation of a three-dimensional anomaly, Phys. Rev. Lett. 53 (1984) 2449 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  42. F.D.M. Haldane, Model for a quantum Hall effect without Landau levels: condensed-matter realization of the ’parity anomaly’, Phys. Rev. Lett. 61 (1988) 2015 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  43. S. Gangadharaiah, A.M. Farid and E.G. Mishchenko, Charge response function and a novel plasmon mode in graphene, Phys. Rev. Lett. 100 (2008) 166802.

    Article  ADS  Google Scholar 

  44. V. Juričić, O. Vafek and I.F. Herbut, Conductivity of interacting massless Dirac particles in graphene: collisionless regime, Phys. Rev. B 82 (2010) 235402 [arXiv:1009.3269] [INSPIRE].

    ADS  Google Scholar 

  45. J. González, Higher-order renormalization of graphene many-body theory, JHEP 08 (2012) 027 [arXiv:1204.4673] [INSPIRE].

    Article  ADS  Google Scholar 

  46. B. Rosenstein, M. Lewkowicz and T. Maniv, Chiral anomaly and strength of the electron-electron interaction in graphene, Phys. Rev. Lett. 110 (2013) 066602 [arXiv:1210.3345] [INSPIRE].

    Article  ADS  Google Scholar 

  47. D.J. Amit and V. Martín-Mayor, Field theory, the renormalization group, and critical phenomena, World Scientific, Singapore (2005).

    Book  Google Scholar 

  48. I.L. Aleiner, D.E. Kharzeev and A.M. Tsvelik, Spontaneous symmetry breakings in graphene subjected to in-plane magnetic field, Phys. Rev. B 76 (2007) 195415 [arXiv:0708.0394] [INSPIRE].

    ADS  Google Scholar 

  49. J.E. Drut and D.T. Son, Renormalization group flow of quartic perturbations in graphene: Strong coupling and large-N limits, Phys. Rev. B 77 (2008) 075115 [arXiv:0710.1315] [INSPIRE].

    ADS  Google Scholar 

  50. P. Ramond, Field theory: a modern primer, Benjamin/Cummings, Reading U.K. (1981).

    Google Scholar 

  51. J.G. Checkelsky, L. Li and N.P. Ong, Zero-energy state in graphene in a high magnetic field, Phys. Rev. Lett. 100 (2008) 206801.

    Article  ADS  Google Scholar 

  52. L. Zhang et al., Metal to insulator transition on the N = 0 Landau level in graphene, Phys. Rev. Lett. 105 (2010) 046804.

    Article  ADS  Google Scholar 

  53. C. Vafa and E. Witten, Parity conservation in QCD, Phys. Rev. Lett. 53 (1984) 535 [INSPIRE].

    Article  ADS  Google Scholar 

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  1. Instituto de Estructura de la Materia, Consejo Superior de Investigaciones Científicas, Serrano 123, 28006, Madrid, Spain

    J. González

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ArXiv ePrint: 1211.3905

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González, J. Dynamical breakdown of parity and time-reversal invariance in the many-body theory of graphene. J. High Energ. Phys. 2013, 175 (2013). https://doi.org/10.1007/JHEP07(2013)175

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  • DOI: https://doi.org/10.1007/JHEP07(2013)175

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