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Part of the book series: Springer Theses ((Springer Theses))

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Abstract

This chapter forms the introduction to the thesis. It motivates the many questions, revisits some of the fundamental ideas in quantum condensed matter and whets the appetite for what is yet to come.

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Notes

  1. 1.

    Unexpected, since the race included LIGO’s discovery of gravitational waves! [10].

References

  1. Anderson PW (1972) More is different. Science 177(4047):393–396. arXiv:1011.1669v3

    Article  ADS  Google Scholar 

  2. Marx K, Engels F (1987) Karl Marx and Frederick Engels collected works, vol 25. International Publishers

    Google Scholar 

  3. Wilhelm M, Mathison D, Cameron J (2009) Avatar: a confidential report on the biological and social history of Pandora. HarperCollins, UK

    Google Scholar 

  4. Abrahams E, Anderson PW, Licciardello DC, Ramakrishnan TV (1979) Scaling theory of localization: absence of quantum diffusion in two dimensions. Phys Rev Lett 42:673–676

    Article  ADS  Google Scholar 

  5. Kondo J (1964) Resistance minimum in dilute magnetic alloys. Prog Theor Phys 32(1):37–49

    Article  ADS  Google Scholar 

  6. Balian R, Maynard R, Toulouse G (1983) III-condensed matter, vol 31. World Scientific

    Google Scholar 

  7. Wilson KG (1975) The renormalization group: critical phenomena and the kondo problem. Rev Mod Phys 47:773–840

    Article  MathSciNet  ADS  Google Scholar 

  8. 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 45:494–497

    Article  ADS  Google Scholar 

  9. Von Klitzing K (1986) The quantized hall effect. Rev Mod Phys 58(3):519

    Article  ADS  Google Scholar 

  10. Abbott BP, Abbott R et al (2016) Observation of gravitational waves from a binary black hole merger. Phys Rev Lett 116:061102

    Article  MathSciNet  ADS  Google Scholar 

  11. Thouless DJ, Kohmoto M, Nightingale MP, den Nijs M (1982) Quantized hall conductance in a two-dimensional periodic potential. Phys Rev Lett 49:405–408

    Article  ADS  Google Scholar 

  12. Néel L (1971) Magnetism and local molecular field. Science 174(4013):985–992

    Article  ADS  Google Scholar 

  13. Landau L (1930) Diamagnetismus der metalle. Zeitschrift für Physik 64(9–10):629–637

    Article  ADS  Google Scholar 

  14. Su WP, Schrieffer JR, Heeger AJ (1980) Soliton excitations in polyacetylene. Phys Rev B 22:2099–2111

    Article  ADS  Google Scholar 

  15. Haldane FDM (1988) Model for a quantum hall effect without Landau levels: Condensed-matter realization of the “parity anomaly”. Phys Rev Lett 61:2015–2018

    Article  MathSciNet  ADS  Google Scholar 

  16. Kane CL, Mele EJ (2005) \(Z_2\) topological order and the quantum spin hall effect. Phys Rev Lett 95:146802

    Google Scholar 

  17. Kane CL, Mele EJ (2005) Quantum spin hall effect in graphene. Phys Rev Lett 95:226801

    Google Scholar 

  18. Kitaev AY (2001) Unpaired majorana fermions in quantum wires. Physics-Uspekhi 44(10S):131

    Article  ADS  Google Scholar 

  19. Altland A, Zirnbauer MR (1997) Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures. Phys Rev B 55:1142–1161

    Article  ADS  Google Scholar 

  20. Kitaev A (2009) Periodic table for topological insulators and superconductors. AIP Conf Proc 1134:22–30

    Google Scholar 

  21. Schnyder AP, Ryu S, Furusaki A, Ludwig AWW (2008) Classification of topological insulators and superconductors in three spatial dimensions. Phys Rev B 78:195125

    Article  ADS  Google Scholar 

  22. Anderson PW (1958) Absence of diffusion in certain random lattices. Phys Rev 109:1492–1505

    Article  ADS  Google Scholar 

  23. Mott NF, Davis EA (1971) Electronic processes in non-crystalline materials

    Google Scholar 

  24. Thouless DJ (1983) Percolation and localization. In: Balian R et al (eds) III-condensed matter: les houches session XXXI. Published by World Scientific Publishing Co. Pte. Ltd., pp 1–62. ISBN 9789814412728

    Google Scholar 

  25. Lee PA, Ramakrishnan TV (1985) Disordered electronic systems. Rev Mod Phys 57:287–337

    Article  Google Scholar 

  26. Kramer B, MacKinnon A (1993) Localization: theory and experiment. Rep Prog Phys 56(12):1469

    Article  ADS  Google Scholar 

  27. Ramakrishnan T (1987) Electron localization. In: Chance and matter, proceedings of the Les Houches summer school, session XLVI, pp 213–303

    Google Scholar 

  28. Markoš P (2006) Numerical analysis of the Anderson localization. Acta Phys Slovaca 56:561–685

    Google Scholar 

  29. Bulka B, Schreiber M, Kramer B (1987) Localization, quantum interference, and the metal-insulator transition. Zeitschrift fur Physik B Condensed Matter 66(1):21–30

    Article  ADS  Google Scholar 

  30. Anderson PW (1961) Localized magnetic states in metals. Phys Rev 124:41–53

    Article  MathSciNet  ADS  Google Scholar 

  31. Hewson AC (1997) The Kondo problem to heavy fermions, vol 2. Cambridge University Press, Cambridge

    Google Scholar 

  32. Sarachik MP, Corenzwit E, Longinotti LD (1964) Resistivity of Mo-Nb and Mo-Re alloys containing 1% Fe. Phys Rev 135:A1041–A1045

    Article  ADS  Google Scholar 

  33. Yosida K (1966) Bound state due to the \(s\)-\(d\) exchange interaction. Phys Rev 147:223–227

    Article  Google Scholar 

  34. Anderson P (1970) A poor man’s derivation of scaling laws for the kondo problem. J Phys C: Solid State Phys 3(12):2436

    Article  ADS  Google Scholar 

  35. Krishna-murthy HR, Wilkins JW, Wilson KG (1980) Renormalization-group approach to the anderson model of dilute magnetic alloys. i. static properties for the symmetric case. Phys Rev B 21:1003–1043

    Article  ADS  Google Scholar 

  36. Krishna-murthy HR, Wilkins JW, Wilson KG (1980) Renormalization-group approach to the anderson model of dilute magnetic alloys. ii. static properties for the asymmetric case. Phys Rev B 21:1044–1083

    Article  ADS  Google Scholar 

  37. Hirsch JE, Fye RM (1986) Monte carlo method for magnetic impurities in metals. Phys Rev Lett 56:2521–2524

    Article  ADS  Google Scholar 

  38. Sakurai JJ, Tuan S-F, Cummins ED (1995) Modern quantum mechanics, revised edn

    Google Scholar 

  39. Shankar R (2012) Principles of quantum mechanics. Springer Science & Business Media

    Google Scholar 

  40. Bernevig BA, Hughes TL (2013) Topological insulators and topological superconductors. Princeton University Press, Princeton

    Book  Google Scholar 

  41. Shen S-Q (2013) Topological insulators: Dirac equation in condensed matters, vol 174. Springer Science & Business Media

    Google Scholar 

  42. Fradkin E (2013) Field theories of condensed matter physics. Cambridge University Press, Cambridge

    Book  Google Scholar 

  43. Fukui T, Hatsugai Y, Suzuki H (2005) Chern numbers in discretized brillouin zone: efficient method of computing (spin) hall conductances. J Phys Soc Jpn 74(6):1674–1677

    Article  ADS  Google Scholar 

  44. Thouless DJ (1984) Wannier functions for magnetic sub-bands. J Phys C: Solid State Phys 17(12):L325

    Article  MathSciNet  ADS  Google Scholar 

  45. Thonhauser T, Vanderbilt D (2006) Insulator/chern-insulator transition in the haldane model. Phys Rev B 74:235111

    Article  ADS  Google Scholar 

  46. Bernevig BA, Hughes TL, Zhang S-C (2006) Quantum spin hall effect and topological phase transition in HgTe quantum wells. Science 314(5806):1757–1761

    Article  ADS  Google Scholar 

  47. Hasan MZ, Kane CL (2010) Colloquium: topological insulators. Rev Mod Phys 82:3045–3067

    Article  ADS  Google Scholar 

  48. Qi X-L, Zhang S-C (2011) Topological insulators and superconductors. Rev Mod Phys 83:1057–1110

    Article  ADS  Google Scholar 

  49. Qi X-L, Zhang S-C (2010) The quantum spin Hall effect and topological insulators. Phys Today 63:33

    Article  Google Scholar 

  50. Ludwig AWW (2016) Topological phases: classification of topological insulators and superconductors of non-interacting fermions, and beyond. Phys Scr 2016(T168):014001. arXiv:1512.08882

    Article  ADS  Google Scholar 

  51. Chiu CK, Teo JCY, Schnyder AP, Ryu S (2016) Classification of topological quantum matter with symmetries. Rev Mod Phys 88:035005

    Article  ADS  Google Scholar 

  52. Ryu S, Schnyder AP, Furusaki A, Ludwig AWW (2010) Topological insulators and superconductors: tenfold way and dimensional hierarchy. New J Phys 12(6):065010

    Article  ADS  Google Scholar 

  53. Wen X-G (2016) Zoo of quantum-topological phases of matter, pp 1–16. arXiv:1610.03911

  54. Hasan MZ, Kane CL (2010) Colloquium. Rev Mod Phys 82:3045–3067

    Google Scholar 

  55. Ando Y (2013) Topological insulator materials. J Phys Soc Jpn 82(10):102001

    Article  ADS  Google Scholar 

  56. Baskaran G (2016) arXiv:1608.08587. In: Chandra P, Coleman P, Kotliar G, Ong P, Stein DL, Clare Yu (eds) PWA90 A life time of emergence (World Scientific 2016) and Anderson PW, in Modern physics in America—a Michaelson–Morley centennial symposium, Fickinger W, Kuwalski KL (eds) AIP conference proceedings 169 (American Institute of Physics, 1988)

  57. Anderson PW, Baskaran G, Zou Z, Hsu T (1987) Resonating valence-bond theory of phase transitions and superconductivity in La\(_2\)Cuo\(_4\)-based compounds. Phys Rev Lett 58:2790–2793

    Article  Google Scholar 

  58. Manchon A, Koo HC, Nitta J, Frolov SM, Duine RA (2015) New perspectives for rashba spin-orbit coupling. Nat Mater 14:871–882 (review)

    Article  ADS  Google Scholar 

  59. Nandkishore R, Huse DA (2015) Many body localization and thermalization in quantum statistical mechanics. Ann Rev Condens Matter Phys 6(1):15–38

    Article  ADS  Google Scholar 

  60. Kitaev A (2015) A simple model of quantum holography. Talks at KITP

    Google Scholar 

  61. Georges A, Kotliar G, Krauth W, Rozenberg MJ (1996) Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions. Rev Mod Phys 68:13–125

    Article  MathSciNet  ADS  Google Scholar 

  62. Bansil A, Lin H, Das T (2016) Colloquium. Rev Mod Phys 88:021004

    Article  ADS  Google Scholar 

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Correspondence to Adhip Agarwala .

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Agarwala, A. (2019). Introduction. In: Excursions in Ill-Condensed Quantum Matter. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-21511-8_1

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