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Fundamentals of Electron Transport

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Electronic Properties of Rhombohedral Graphite

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Abstract

In this chapter a general introduction and overview of electronic transport concepts such as effective mass and mobility will be given where Ohms law will be derived through both from a classical picture as well as a semi-classical picture. Fundamental electron transport phenomena of Shubnikov-de Haas oscillations as well as quantum (anomalous) Hall effect will be introduced. Lastly, quantum transport phenomena of weak (anti)localization will be explained in a pedagogical way.

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References

  1. Hook JR, Hall HE (1990) Solid state physics. Wiley

    Google Scholar 

  2. Kittel C (2004) Introduction to solid state physics. Wiley

    Google Scholar 

  3. Bostwick A, Ohta T, Seyller T, Horn K, Rotenberg E (2007) Quasiparticle dynamics in graphene. Nat Phys 3(1):36–40. https://doi.org/10.1038/nphys477

    Article  Google Scholar 

  4. Drude P (1900) Zur Elektronentheorie der Metalle. Ann Phys 306(3):566–613. https://doi.org/10.1002/andp.19003060312

    Article  MATH  Google Scholar 

  5. Bloch F (1929) Über die Quantenmechanik der Elektronen in Kristallgittern. Zeitschrift für Phys 52(7–8):555–600. https://doi.org/10.1007/BF01339455

    Article  ADS  MATH  Google Scholar 

  6. Datta S (1997) Electronic transport in mesoscopic systems. Cambridge University Press

    Google Scholar 

  7. Hall EH (1879) On a new action of the magnet on electric currents. Am J Math 2(3):287–292

    Article  MathSciNet  Google Scholar 

  8. Prange RE, Girvin SM (1987) The quantum hall effect. Springer, New York

    Book  Google Scholar 

  9. Schubnikow WJ, de Haas L (1930) Neue Erscheinungen bei der Widerstandsänderung von Wismuthkristallen im Magnetfeld bei der Temperatur von flüssigem Wasserstoff (I). Proc R Netherlands Acad Arts Sci 33:363–378

    Google Scholar 

  10. Coleridge PT, Stoner R, Fletcher R (1989) Low-field transport coefficients in GaAs/Ga1-xAlxAs heterostructures. Phys Rev B 39(2):1120–1124. https://doi.org/10.1103/PhysRevB.39.1120

    Article  ADS  Google Scholar 

  11. Kosevich AM, Lifshitz IM (1956) The de Haas-van Alphen effect in thin metal layers. Jetp 2(4):646–649

    Google Scholar 

  12. Klitzing KV, Dorda G, Pepper M (1980) New method for high-accuracy determination of the fine-structure constant based on quantized hall resistance. Phys. Rev. Lett. 45(6):494–497. https://doi.org/10.1103/PhysRevLett.45.494

  13. Klitzing KV (1984) The quantized Hall effect. Physica B 126:242–249. https://doi.org/10.1016/0378-4363(84)90170-0

  14. Chang MC, Niu Q (1995) Berry phase, hyperorbits, and the Hofstadter spectrum. Phys Rev Lett 75(7):1348–1351. https://doi.org/10.1103/PhysRevLett.75.1348

    Article  ADS  Google Scholar 

  15. Hall EH (1881) On the ‘rotational coefficient’ in nickel and cobalt. London Edinburgh Dublin Philos Mag J Sci 12(74):157–172. https://doi.org/10.1080/14786448108627086

    Article  Google Scholar 

  16. Nagaosa N, Sinova J, Onoda S, MacDonald AH, Ong NP (2010) Anomalous Hall effect. Rev Mod Phys 82(2):1539–1592. https://doi.org/10.1103/RevModPhys.82.1539

    Article  ADS  Google Scholar 

  17. Karplus R, Luttinger JM (1954) Hall effect in Ferromagnetics. Phys Rev 95(5):1154–1160. https://doi.org/10.1103/PhysRev.95.1154

    Article  ADS  MATH  Google Scholar 

  18. Berry MV (1984) Quantal phase factors accompanying adiabatic changes. Proc R Soc A Math Phys Eng Sci 392(1802):45–57. https://doi.org/10.1098/rspa.1984.0023

  19. Jungwirth T, Niu Q, MacDonald AH (2002) Anomalous hall effect in ferromagnetic semiconductors. Phys Rev Lett 88(20):4. https://doi.org/10.1103/PhysRevLett.88.207208

    Article  Google Scholar 

  20. Lee WL, Watauchi S, Miller VL, Cava RJ, Ong NP (2004) Dissipationless anomalous hall current in the ferromagnetic spinel CuCr2Se4-xBrx. Science (80-) 303(5664):1647–1649. https://doi.org/10.1126/science.1094383

  21. Smit J (1955) The spontaneous hall effect in ferromagnetics I. Physica 21(6–10):877–887. https://doi.org/10.1016/S0031-8914(55)92596-9

    Article  ADS  Google Scholar 

  22. Thouless DJ, Kohmoto M, Nightingale MP, Den Nijs M (1982) Quantized hall conductance in a two-dimensional periodic potential. Phys Rev Lett 49(6):405–408. https://doi.org/10.1103/PhysRevLett.49.405

    Article  ADS  Google Scholar 

  23. Haldane FDM (1988) Model for a quantum hall effect without landau levels: condensed-matter realization of the ‘parity anomaly.’ Phys Rev Lett 61(18):2015–2018. https://doi.org/10.1103/PhysRevLett.61.2015

    Article  ADS  Google Scholar 

  24. Chang C-Z et al (2013) Experimental observation of the quantum anomalous hall effect in a magnetic topological insulator. Science 340(6129):167–170. https://doi.org/10.1126/science.1234414

    Article  ADS  Google Scholar 

  25. D’yakonov MI, Perel VI (1971) Possibility of orienting electron spins with current. Sov Phys JETP Lett 13(11):467. Available: http://www.jetpletters.ac.ru/ps/1587/article_24366.shtml

  26. Hirsch JE (1999) Spin hall effect. Phys Rev Lett 83(9):1834–1837. https://doi.org/10.1103/PhysRevLett.83.1834

    Article  ADS  Google Scholar 

  27. Sinova J, Culcer D, Niu Q, Sinitsyn NA, Jungwirth T, Macdonald AH (2004) Universal Intrinsic spin hall effect, no March, pp 1–4. https://doi.org/10.1103/PhysRevLett.92.126603

  28. Kato YK, Myers RC, Gossard AC, Awschalom DD (2004) Observation of the spin hall effect in semiconductors. Science 306(5703):1910–1913. https://doi.org/10.1126/science.1105514

    Article  ADS  Google Scholar 

  29. Wunderlich J, Kaestner B, Sinova J, Jungwirth T (2005) Experimental observation of the spin-hall effect in a two-dimensional spin-orbit coupled semiconductor system. Phys Rev Lett 94(4):1–4. https://doi.org/10.1103/PhysRevLett.94.047204

    Article  Google Scholar 

  30. Valenzuela SO, Tinkham M (2006) Direct electronic measurement of the spin Hall effect. Nature 442(7099):176–179. https://doi.org/10.1038/nature04937

    Article  ADS  Google Scholar 

  31. Abanin DA, Shytov AV, Levitov LS, Halperin BI (2009) Nonlocal charge transport mediated by spin diffusion in the spin Hall effect regime. Phys Rev B-Condens Matter Mater Phys 79(3):77–81. https://doi.org/10.1103/PhysRevB.79.035304

  32. Balakrishnan J, Kok Wai Koon G, Jaiswal M, Castro Neto AH, Özyilmaz B (2013) Colossal enhancement of spin-orbit coupling in weakly hydrogenated grapheme. Nat Phys 9(5):284–287. https://doi.org/10.1038/nphys2576

  33. Kane CL, Mele EJ (2005) Quantum Spin hall effect in graphene. Phys Rev Lett 95(22):1–4. https://doi.org/10.1103/PhysRevLett.95.226801

    Article  Google Scholar 

  34. Konig M et al (2007) Quantum spin hall insulator state in HgTe quantum wells. Science 318(5851):766–770. https://doi.org/10.1126/science.1148047

    Article  ADS  Google Scholar 

  35. Zhang F, Jung J, Fiete GA, Niu Q, MacDonald AH (2011) Spontaneous quantum hall states in chirally stacked few-layer graphene systems. Phys Rev Lett 106(15):1–4. https://doi.org/10.1103/PhysRevLett.106.156801

    Article  Google Scholar 

  36. Xiao D, Yao W, Niu Q (2007) Valley-contrasting physics in graphene: magnetic moment and topological transport. Phys Rev Lett 99(23):1–4. https://doi.org/10.1103/PhysRevLett.99.236809

    Article  Google Scholar 

  37. Gunawan O, Shkolnikov YP, Vakili K, Gokmen T, De Poortere EP, Shayegan M (2006) Valley susceptibility of an interacting two-dimensional electron system. Phys Rev Lett 97(18):1–4. https://doi.org/10.1103/PhysRevLett.97.186404

    Article  Google Scholar 

  38. Gunawan O, Habib B, De Poortere EP, Shayegan M (2006) Quantized conductance in an AlAs two-dimensional electron system quantum point contact. Phys Rev B-Condens Matter Mater Phys 74(15):1–8. https://doi.org/10.1103/PhysRevB.74.155436

  39. Rycerz A, Tworzydło J, Beenakker CWJ (2007) Valley filter and valley valve in graphene. Nat Phys 3(3):172–175. https://doi.org/10.1038/nphys547

    Article  Google Scholar 

  40. Morozov SV et al (2006) Strong suppression of weak localization in graphene. Phys Rev Lett 97(1):7–10. https://doi.org/10.1103/PhysRevLett.97.016801

    Article  Google Scholar 

  41. Zhou SY et al (2007) Substrate-induced bandgap opening in epitaxial graphene. Nat Mater 6(10):770–775. https://doi.org/10.1038/nmat2003

    Article  ADS  Google Scholar 

  42. Mak KF, McGill KL, Park J, McEuen PL (2014) The valley hall effect in MoS2 transistors. Science 344(6191):1489–1492. https://doi.org/10.1126/science.1250140

    Article  ADS  Google Scholar 

  43. Gorbachev RV et al (2014) Detecting topological currents in graphene superlattices. Science 346(6208):448–451. https://doi.org/10.1126/science.1254966

    Article  ADS  Google Scholar 

  44. Shimazaki Y, Yamamoto M, Borzenets IV, Watanabe K, Taniguchi T, Tarucha S (2015) Generation and detection of pure valley current by electrically induced Berry curvature in bilayer graphene. Nat Phys 11(12):1032–1036. https://doi.org/10.1038/nphys3551

    Article  Google Scholar 

  45. Hung TYT, Camsari KY, Zhang S, Upadhyaya P, Chen Z (2019) Direct observation of valley-coupled topological current in MoS2. Sci Adv 5(4):1–7. https://doi.org/10.1126/sciadv.aau6478

    Article  ADS  Google Scholar 

  46. Sui M et al (2015) Gate-tunable topological valley transport in bilayer graphene. Nat Phys 11(12):1027–1031. https://doi.org/10.1038/nphys3485

    Article  Google Scholar 

  47. Wu Z et al (2019) Intrinsic valley Hall transport in atomically thin MoS2. Nat Commun 10(1):1–8. https://doi.org/10.1038/s41467-019-08629-9

    Article  ADS  Google Scholar 

  48. Ju L et al (2015) Topological valley transport at bilayer graphene domain walls. Nature 520(7549):650–655. https://doi.org/10.1038/nature14364

    Article  ADS  Google Scholar 

  49. Aivazian G et al (2015) Magnetic control of valley pseudospin in monolayer WSe 2. Nat Phys 11(2):148–152. https://doi.org/10.1038/nphys3201

    Article  Google Scholar 

  50. Srivastava A, Sidler M, Allain AV, Lembke DS, Kis A, Imamoʇlu A (2015) Valley Zeeman effect in elementary optical excitations of monolayer WSe 2. Nat Phys 11(2):141–147. https://doi.org/10.1038/nphys3203

    Article  Google Scholar 

  51. Macneill D et al (2015) Breaking of valley degeneracy by magnetic field in monolayer MoSe2. Phys Rev Lett 114(3):1–5. https://doi.org/10.1103/PhysRevLett.114.037401

    Article  Google Scholar 

  52. Li Y et al (2014) Valley splitting and polarization by the Zeeman effect in monolayer MoSe2. Phys Rev Lett 113(26):1–5. https://doi.org/10.1103/PhysRevLett.113.266804

    Article  Google Scholar 

  53. Duan F, Guojun J (2005) Introduction to condensed matter physics: volume 1, no. v. 1. World Scientific

    Google Scholar 

  54. Anderson PW (1958) Absence of diffusion in certain random lattices. Phys Rev 109(5):1492–1505. https://doi.org/10.1103/PhysRev.109.1492

    Article  ADS  Google Scholar 

  55. Altshuler BL, Khmel’nitzkii D, Larkin AI, Lee PA (1980) Magnetoresistance and Hall effect in a disordered two-dimensional electron gas. Phys Rev B 22(11):5142–5153. https://doi.org/10.1103/PhysRevB.22.5142

  56. Hikami S, Larkin AI, Nagaoka Y (1980) Spin-orbit interaction and magnetoresistance in the two dimensional random system. Prog Theor Phys 63(2):707–710. https://doi.org/10.1143/ptp.63.707

    Article  ADS  Google Scholar 

  57. Kawabata A (1980) Theory of negative magnetoresistance in three-dimensional systems. Solid State Commun 34(6):431–432. https://doi.org/10.1016/0038-1098(80)90644-4

    Article  ADS  Google Scholar 

  58. Al’tshuler BL, Aronov AG, Larkin AI, Khmel’nitskii DE (1981) The anomalous magnetoresistance in semiconductors. Sov Phys JETP 54(2):0411. Available: http://www.jetp.ac.ru/cgi-bin/e/index/e/54/2/p411?a=list

  59. Bergmann G (1982) Weak anti-localization—an experimental proof for the destructive interference of rotated spin. Solid State Commun 42(11):815–817. https://doi.org/10.1016/0038-1098(82)90013-8

    Article  ADS  Google Scholar 

  60. Mccann E, Kechedzhi K, Fala’Ko VI, Suzuura H, Ando T, Altshuler BL (2006) Weak-localization magnetoresistance and valley symmetry in grapheme. Phys Rev Lett 97(14):14–17. https://doi.org/10.1103/PhysRevLett.97.146805

  61. Tikhonenko FV, Kozikov AA, Savchenko AK, Gorbachev RV (2009) Transition between electron localization and antilocalization in graphene. Phys Rev Lett 103(22):1–4. https://doi.org/10.1103/PhysRevLett.103.226801

    Article  Google Scholar 

  62. Kim HJ et al (2013) Dirac versus Weyl fermions in topological insulators: Adler-Bell-Jackiw anomaly in transport phenomena. Phys Rev Lett 111(24):1–5. https://doi.org/10.1103/PhysRevLett.111.246603

    Article  Google Scholar 

  63. Huang X et al (2015) Observation of the chiral-anomaly-induced negative magnetoresistance: In 3D Weyl semimetal TaAs. Phys Rev X 5(3):1–9. https://doi.org/10.1103/PhysRevX.5.031023

    Article  ADS  Google Scholar 

  64. Zhang CL et al (2016) Signatures of the Adler-Bell-Jackiw chiral anomaly in a Weyl fermion semimetal. Nat Commun 7:1–9. https://doi.org/10.1038/ncomms10735

    Article  ADS  Google Scholar 

  65. Li Q et al (2016) Chiral magnetic effect in ZrTe 5. Nat Phys 12(6):550–554. https://doi.org/10.1038/nphys3648

    Article  Google Scholar 

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Authors and Affiliations

  1. Institute of Photonic and Quantum Sciences, Heriot-Watt University, Edinburgh, UK

    Dr. Servet Ozdemir

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Ozdemir, S. (2021). Fundamentals of Electron Transport. In: Electronic Properties of Rhombohedral Graphite. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-88307-2_2

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