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Anomalous spatial shifts in interface electronic scattering

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Abstract

The anomalous spatial shifts at interface scattering, first studied in geometric optics, recently found their counterparts in the electronic context. It was shown that both longitudinal and transverse shifts, analogous to the Goos-Hänchen and Imbert-Fedorov effects in optics, can exist when electrons are scattered at a junction interface. More interestingly, the shifts are also discovered in the process of Andreev reflection at a normal/superconductor interface. Particularly, for the case with unconventional superconductors, it was discovered that the transverse shift can arise solely from the superconducting pair potential and exhibit characteristic features depending on the pairing. Here, we briefly review the recent works in this field, with an emphasis on the physical picture and theoretical understanding.

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References

  1. F. Goos and H. Hänchen, Ein neuer und fundamentaler Versuch zur Totalreflexion, Ann. Phys. 436(7–8), 333 (1947)

    Google Scholar 

  2. F. Fornel, Evanescent Waves from Newtonian Optics to Atomic Optics, Berlin: Springer, 2010

    Google Scholar 

  3. F. Fedorov, K teorii polnogo otrazheniya, Dokl. Akad. Nauk SSSR 105, 465 (1955)

    MathSciNet  Google Scholar 

  4. C. Imbert, Calculation and experimental proof of the transverse shift induced by total internal reflection of a circularly polarized light beam, Phys. Rev. D 5(4), 787 (1972)

    ADS  Google Scholar 

  5. M. Onoda, S. Murakami, and N. Nagaosa, Hall effect of light, Phys. Rev. Lett. 93 (8), 083901 (2004)

    ADS  Google Scholar 

  6. M. C. Chang and Q. Niu, Berry phase, hyperorbits, and the Hofstadter spectrum, Phys. Rev. Lett. 75 (7), 1348 (1995)

    ADS  Google Scholar 

  7. M. C. Chang and Q. Niu, Berry phase, hyperorbits, and the Hofstadter spectrum: Semiclassical dynamics in magnetic Bloch bands, Phys. Rev. B 53(11), 7010 (1996)

    ADS  Google Scholar 

  8. G. Sundaram and Q. Niu, Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects, Phys. Rev. B 59(23), 14915 (1999)

    ADS  Google Scholar 

  9. S. Murakami, N. Nagaosa, and S. C. Zhang, Dissipationless quantum spin current at room temperature, Science 301(5638), 1348 (2003)

    ADS  Google Scholar 

  10. J. Sinova, D. Culcer, Q. Niu, N. A. Sinitsyn, T. Jungwirth, and A. H. MacDonald, Universal intrinsic spin Hall effect, Phys. Rev. Lett. 92(12), 126603 (2004)

    ADS  Google Scholar 

  11. K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, Spin-orbit interactions of light, Nat. Photonics 9(12), 796 (2015)

    ADS  Google Scholar 

  12. O. Hosten and P. Kwiat, Observation of the spin Hall effect of light via weak measurements, Science 319(5864), 787 (2008)

    ADS  Google Scholar 

  13. X. Zhou, Z. Xiao, H. Luo, and S. Wen, Experimental observation of the spin Hall effect of light on a nanometal film via weak measurements, Phys. Rev. A 85(4), 043809 (2012)

    ADS  Google Scholar 

  14. X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, Photonic spin Hall effect at metasurfaces, Science 339(6126), 1405 (2013)

    ADS  Google Scholar 

  15. X. Zhou, X. Ling, H. Luo, and S. Wen, Identifying graphene layers via spin Hall effect of light, Appl. Phys. Lett. 101(25), 251602 (2012)

    ADS  Google Scholar 

  16. S. C. Miller and N. Ashby, Shifts of electron beam position due to total reflection at a barrier, Phys. Rev. Lett. 29(11), 740 (1972)

    ADS  Google Scholar 

  17. D. M. Fradkin and R. J. Kashuba, Spatial displacement of electrons due to multiple total reflections, Phys. Rev. D 9(10), 2775 (1974)

    ADS  Google Scholar 

  18. D. M. Fradkin and R. J. Kashuba, Position-operator method for evaluating the shift of a totally reflected electron, Phys. Rev. D 10(4), 1137 (1974)

    ADS  Google Scholar 

  19. N. A. Sinitsyn, Q. Niu, J. Sinova, and K. Nomura, Disorder effects in the anomalous Hall effect induced by Berry curvature, Phys. Rev. B 72(4), 045346 (2005)

    ADS  Google Scholar 

  20. X. Chen, C. F. Li, and Y. Ban, Tunable lateral displacement and spin beam splitter for ballistic electrons in two-dimensional magnetic-electric nanostructures, Phys. Rev. B 77(7), 073307 (2008)

    ADS  Google Scholar 

  21. X. Chen, X. J. Lu, Y. Wang, and C. F. Li, Controllable Goos-Hänchen shifts and spin beam splitter for ballistic electrons in a parabolic quantum well under a uniform magnetic field, Phys. Rev. B 83(19), 195409 (2011)

    ADS  Google Scholar 

  22. C. W. J. Beenakker, R. A. Sepkhanov, A. R. Akhmerov, and J. Tworzydło, Quantum Goos-Hänchen effect in graphene, Phys. Rev. Lett. 102(14), 146804 (2009)

    ADS  Google Scholar 

  23. L. Zhao and S. F. Yelin, Proposal for graphene-based coherent buffers and memories, Phys. Rev. B 81(11), 115441 (2010)

    ADS  Google Scholar 

  24. M. Sharma and S. Ghosh, Electron transport and Goos-Hänchen shift in graphene with electric and magnetic barriers: optical analogy and band structure, J. Phys.: Condens. Matter 23(5), 055501 (2011)

    ADS  Google Scholar 

  25. Z. Wu, F. Zhai, F. M. Peeters, H. Q. Xu, and K. Chang, Valley-dependent brewster angles and Goos-Hänchen effect in strained graphene, Phys. Rev. Lett. 106(17), 176802 (2011)

    ADS  Google Scholar 

  26. X. Chen, J. W. Tao, and Y. Ban, Goos-Hänchen-like shifts for Dirac fermions in monolayer graphene barrier, Eur. Phys. J. B 79(2), 203 (2011)

    ADS  Google Scholar 

  27. X. Chen, P. L. Zhao, and X. J. Lu, Giant negative and positive lateral shifts in graphene superlattices, Eur. Phys. J. B 86(5), 223 (2013)

    ADS  Google Scholar 

  28. S. Chen, Z. Han, M. M. Elahi, K. M. M. Habib, L. Wang, B. Wen, Y. Gao, T. Taniguchi, K. Watanabe, J. Hone, A. W. Ghosh, and C. R. Dean, Electron optics with p-n junctions in ballistic graphene, Science 353(6307), 1522 (2016)

    ADS  Google Scholar 

  29. J. Spector, H. L. Stormer, K. W. Baldwin, L. N. Pfeiffer, and K. W. West, Electron focusing in two-dimensional systems by means of an electrostatic lens, Appl. Phys. Lett. 56(13), 1290 (1990)

    ADS  Google Scholar 

  30. L. W. Molenkamp, A. A. M. Staring, C. W. J. Beenakker, R. Eppenga, C. E. Timmering, J. G. Williamson, C. J. P. M. Harmans, and C. T. Foxon, Electron-beam collimation with a quantum point contact, Phys. Rev. B 41(2), 1274 (1990)

    ADS  Google Scholar 

  31. D. Dragoman and M. Dragoman, Optical analogue structures to mesoscopic devices, Prog. Quantum Electron. 23(4–5), 131 (1999)

    ADS  MATH  Google Scholar 

  32. Q. D. Jiang, H. Jiang, H. Liu, Q. F. Sun, and X. C. Xie, Topological Imbert-Fedorov Shift in Weyl Semimetals, Phys. Rev. Lett. 115(15), 156602 (2015)

    ADS  Google Scholar 

  33. S. A. Yang, H. Pan, and F. Zhang, Chirality-Dependent Hall Effect in Weyl Semimetals, Phys. Rev. Lett. 115(15), 156603 (2015)

    ADS  Google Scholar 

  34. L. Wang and S. K. Jian, Imbert-Fedorov shift in Weyl semimetals: Dependence on monopole charge and intervalley scattering, Phys. Rev. B 96(11), 115448 (2017)

    ADS  Google Scholar 

  35. U. Chattopadhyay, L.K. Shi, B. Zhang, J. C. W. Song, and Y. D. Chong, Fermi arc induced vortex structure in Weyl beam shifts, arXiv: 1809.03159 (2018)

    Google Scholar 

  36. A. F. Andreev, Thermal conductivity of the intermediate state of superconductors, Sov. Phys. JETP 19, 1228 (1964)

    Google Scholar 

  37. P. G. de Gennes, Superconductivity in Metals and Alloys, New York: Benjamin, 1966

    MATH  Google Scholar 

  38. Y. Liu, Z. M. Yu, and S. A. Yang, Transverse shift in Andreev reflection, Phys. Rev. B 96(12), 121101 (2017)

    ADS  Google Scholar 

  39. Y. Liu, Z. M. Yu, H. Jiang, and S. A. Yang, Goos-Hänchen-like shifts at a metal/superconductor interface, Phys. Rev. B 98(7), 075151 (2018)

    ADS  Google Scholar 

  40. Z. M. Yu, Y. Liu, Y. Yao, and S. A. Yang, Unconventional pairing induced anomalous transverse shift in Andreev reflection, Phys. Rev. Lett. 121(17), 176602 (2018)

    ADS  Google Scholar 

  41. Y. Liu, Z. M. Yu, J. Liu, H. Jiang, and S. A. Yang, Transverse shift in crossed Andreev reflection, Phys. Rev. B 98(19), 195141 (2018)

    ADS  Google Scholar 

  42. J. M. Byers and M. E. Flatté, Probing spatial correlations with nanoscale two-contact tunneling, Phys. Rev. Lett. 74(2), 306 (1995)

    ADS  Google Scholar 

  43. G. Deutscher and D. Feinberg, Coupling superconducting-ferromagnetic point contacts by Andreev reflections, Appl. Phys. Lett. 76(4), 487 (2000)

    ADS  Google Scholar 

  44. X. Chen, X. J. Lu, Y. Ban, and C. F. Li, Electronic analogy of the Goos-Hänchen effect: A review, J. Opt. 15(3), 033001 (2013)

    ADS  Google Scholar 

  45. K. Y. Bliokh and A. Aiello, Goos-Hänchen and Imbert-Fedorov beam shifts: An overview, J. Opt. 15(1), 014001 (2013)

    ADS  Google Scholar 

  46. D. Xiao, M. C. Chang, and Q. Niu, Berry phase effects on electronic properties, Rev. Mod. Phys. 82(3), 1959 (2010)

    ADS  MathSciNet  MATH  Google Scholar 

  47. S. A. Yang, G. S. D. Beach, C. Knutson, D. Xiao, Z. Zhang, M. Tsoi, Q. Niu, A. H. MacDonald, and J. L. Erskine, Topological electromotive force from domain-wall dynamics in a ferromagnet, Phys. Rev. B 82(5), 054410 (2010)

    ADS  Google Scholar 

  48. Y. Gao, S. A. Yang, and Q. Niu, Field induced positional shift of Bloch electrons and its dynamical implications, Phys. Rev. Lett. 112(16), 166601 (2014)

    ADS  Google Scholar 

  49. Y. Gao, S. A. Yang, and Q. Niu, Geometrical effects in orbital magnetic susceptibility, Phys. Rev. B 91(21), 214405 (2015)

    ADS  Google Scholar 

  50. Y. Gao, S. A. Yang, and Q. Niu, Intrinsic relative magnetoconductivity of nonmagnetic metals, Phys. Rev. B 95(16), 165135 (2017)

    ADS  Google Scholar 

  51. D. Culcer, Y. Yao, and Q. Niu, Coherent wave-packet evolution in coupled bands, Phys. Rev. B 72(8), 085110 (2005)

    ADS  Google Scholar 

  52. X. Wan, A. M. Turner, A. Vishwanath, and S. Y. Savrasov, Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates, Phys. Rev. B 83(20), 205101 (2011)

    ADS  Google Scholar 

  53. N. P. Armitage, E. J. Mele, and A. Vishwanath, Weyl and Dirac semimetals in three-dimensional solids, Rev. Mod. Phys. 90(1), 015001 (2018)

    ADS  MathSciNet  Google Scholar 

  54. S. A. Yang, Dirac and Weyl materials: Fundamental aspects and some spintronics applications, SPIN 06(02), 1640003 (2016)

    ADS  Google Scholar 

  55. Q. D. Jiang, H. Jiang, H. Liu, Q. F. Sun, and X. C. Xie, Chiral wave-packet scattering in Weyl semimetals, Phys. Rev. B 93 (19), 195165 (2016)

    ADS  Google Scholar 

  56. G. E. Blonder, M. Tinkham, and T. M. Klapwijk, Transition from metallic to tunneling regimes in superconducting microconstrictions: Excess current, charge imbalance, and supercurrent conversion, Phys. Rev. B 25(7), 4515 (1982)

    ADS  Google Scholar 

  57. M. J. M. de Jong and C. W. J. Beenakker, Andreev reflection in ferromagnet-superconductor junctions, Phys. Rev. Lett. 74(9), 1657 (1995)

    ADS  Google Scholar 

  58. S. Kashiwaya and Y. Tanaka, Tunnelling effects on surface bound states in unconventional superconductors, Rep. Prog. Phys. 63(10), 1641 (2000)

    ADS  Google Scholar 

  59. H. Plehn, U. Gunsenheimer, and R. Kümmel, Subgap peak and Tomash-McMillan-Anderson oscillations in the density of states of SNS Bridges., J. Low Temp. Phys. 83(1–2), 71 (1991)

    ADS  Google Scholar 

  60. J. Hara, M. Ashida, and K. Nagai, Pair potential and density of states in proximity-contact superconducting-normal-metal double layers, Phys. Rev. B 47(17), 11263 (1993)

    ADS  Google Scholar 

  61. H. Plehn, O. J. Wacker, and R. Kümmel, Electronic structure of superconducting multilayers, Phys. Rev. B 49(17), 12140 (1994)

    ADS  Google Scholar 

  62. C. W. J. Beenakker, Specular Andreev reflection in graphene, Phys. Rev. Lett. 97(6), 067007 (2006)

    ADS  Google Scholar 

  63. H. Weng, Y. Liang, Q. Xu, R. Yu, Z. Fang, X. Dai, and Y. Kawazoe, Topological node-line semimetal in three-dimensional graphene networks, Phys. Rev. B 92(4), 045108 (2015)

    ADS  Google Scholar 

  64. Y. Chen, Y. Xie, S. A. Yang, H. Pan, F. Zhang, M. L. Cohen, and S. Zhang, Nanostructured carbon allotropes with Weyl-like loops and points, Nano Lett. 15(10), 6974 (2015)

    ADS  Google Scholar 

  65. M. Sigrist, A. Avella, and F. Mancini, Introduction to unconventional superconductivity, AIP Conf. Proc. 789, 165 (2005)

    ADS  Google Scholar 

  66. Y. Tanaka and S. Kashiwaya, Theory of tunneling spectroscopy of d-wave superconductors, Phys. Rev. Lett. 74(17), 3451 (1995)

    ADS  Google Scholar 

  67. C. C. Tsuei and J. R. Kirtley, Pairing symmetry in cuprate superconductors, Rev. Mod. Phys. 72(4), 969 (2000)

    ADS  Google Scholar 

  68. A. P. Mackenzie and Y. Maeno, The superconductivity of Sr2RuO4 and the physics of spin-triplet pairing, Rev. Mod. Phys. 75(2), 657 (2003)

    ADS  Google Scholar 

  69. C. Kallin and J. Berlinsky, Chiral superconductors, Rep. Prog. Phys. 79(5), 054502 (2016)

    ADS  Google Scholar 

  70. D. Beckmann, H. B. Weber, and H. v. Löhneysen, Evidence for Crossed Andreev Reflection in Superconductor-Ferromagnet Hybrid Structures, Phys. Rev. Lett. 93 (19), 197003 (2004)

    ADS  Google Scholar 

  71. S. Russo, M. Kroug, T. M. Klapwijk, and A. F. Morpurgo, Experimental observation of bias-dependent non-local Andreev reflection, Phys. Rev. Lett. 95(2), 027002 (2005)

    ADS  Google Scholar 

  72. P. Cadden-Zimansky, and V. Chandrasekhar, Nonlocal correlations in normal-metal superconducting systems, Phys. Rev. Lett. 97(23), 237003 (2006)

    ADS  Google Scholar 

  73. M. Veldhorst, and A. Brinkman, Nonlocal Cooper pair splitting in a pSn junction, Phys. Rev. Lett. 105(10), 107002 (2010)

    ADS  Google Scholar 

  74. S. Y. Lee, A. Goussev, O. Georgiou, G. Gligorić, and A. Lazarides, Sticky Goos-Hänchen effect at normal/superconductor interface, Europhys. Lett. (EPL) 103(2), 20004 (2013)

    ADS  Google Scholar 

  75. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Electric field effect in atomically thin carbon films, Science 306(5696), 666 (2004)

    ADS  Google Scholar 

  76. 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(1), 109 (2009)

    ADS  Google Scholar 

  77. A. Ohtomo and H. Hwang, A high-mobility electron gas at the LaAlO3/SrTiO3 heterointerface, Nature 427(6973), 423 (2004)

    ADS  Google Scholar 

  78. L. Liu, J. Park, D. A. Siegel, K. F. McCarty, K. W. Clark, W. Deng, L. Basile, J. C. Idrobo, A. P. Li, and G. Gu, Heteroepitaxial growth of two-dimensional hexagonal boron nitride templated by graphene edges, Science 343(6167), 163 (2014)

    ADS  Google Scholar 

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Acknowledgements

We thank Xinxing Zhou and D. L. Deng for valuable discussions. This work was supported by the Singapore Ministry of Education AcRF Tier 2 (MOE2017-T2-2-108).

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Correspondence to Zhi-Ming Yu, Ying Liu or Shengyuan A. Yang.

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Yu, ZM., Liu, Y. & Yang, S.A. Anomalous spatial shifts in interface electronic scattering. Front. Phys. 14, 33402 (2019). https://doi.org/10.1007/s11467-019-0882-7

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