Angle-resolved photoemission spectroscopy (ARPES): probing electronic structure and many-body interactions

Zhi-Xun Shen

doi:10.61109/cs.202405.130

Complex phenomenon in quantum materials is a major theme of physics today. As better controlled model systems, a sophisticated understanding of the universality and diversity of these solids may lead to revelations well beyond themselves. Angle-resolved photoemission spectroscopy (ARPES), formulated after Einstein’s photoelectric effect, has been a key tool to uncover the microscopic processes of the electrons that give rise to the rich physics in these solids. Over the last three decades, the improved resolution and carefully matched experiments have been the keys to turn this technique into a leading experimental probe of electronic structures and many-body effects.

Drawing upon examples spanning from novel superconductors and topological materials to magnetic and one-dimensional materials, we illustrate ARPES's pivotal role in testing ideas, benchmarking theoretical frameworks, uncovering unexpected phenomena, and elucidating the fingerprints of many-body interactions. Moreover, we demonstrate how the integration of modern ultrafast UV lasers and spin polarimetry has empowered photoemission spectroscopy to capture essential microscopic quantities of electrons—energy, momentum, spin, and temporal dynamics—yielding invaluable insights from a wealth of rich and precise information.

Keywords:

band structure

electron correlation

unconventional superconductors

topological insulators

The works are supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under Contract No. DE-AC02-76SF00515.

1. J.R. Chelikowsky and M.L. Cohen, Electronic structure of silicon, Phys. Rev. B 10, 5095 (1974).

2. A. Damascelli, Z. Hussain, and Z.-X. Shen, Angle-resolved photoemission studies of the cuprate superconductors, Rev. Mod. Phys. 75, 473 (2003).

3. J.A. Sobota, Y. He, and Z.-X. Shen, Angle-resolved photoemission studies of quantum materials, Rev. Mod. Phys. 93, 025006 (2021).

4. Z.-X. Shen, D.S. Dessau, B.O. Wells, D.M. King, W.E. Spicer, A.J. Arko, D. Marshall, L.W. Lombardo, A. Kapitulnik, P. Dickinson, S. Doniach, J. DiCarlo, T. Loeser, and C.H. Park, Anomalously large gap anisotropy in the a-b plane of Bi₂Sr₂CaCu₂O_8+δ, Phys. Rev. Lett. 70, 1553 (1993).

5. Y.L. Chen, J.G. Analytis, J.H. Chu, Z.K. Liu, S.K. Mo, X.L. Qi, H.J. Zhang, D.H. Lu, X. Dai, Z. Fang, S.C. Zhang, I.R. Fisher, Z. Hussain, and Z.-X. Shen, Experimental realization of a three-dimensional topological insulator, Bi₂Te₃, Science 325, 178 (2009).

6. B.O. Wells, Z.-X. Shen, A. Matsuura, D.M. King, M.A. Kastner, M. Greven, and R.J. Birgeneau, E versus k relations and many body effects in the model insulating copper oxide Sr₂CuO₂Cl₂, Phys. Rev. Lett. 74, 964 (1995).

7. Z.Y. Chen, Y. Wang, S.N. Rebec, T. Jia, M. Hashimoto, D.H. Lu, B. Moritz, R.G. Moore, T.P. Devereaux, and Z.-X. Shen, Anomalously strong near-neighbor attraction in doped 1D cuprate chains, Science 373, 1235 (2021).

8. D.M. King, D.S. Dessau, A.G. Loeser, Z.-X. Shen, and B.O. Wells, Electronic structure evolution from mott insulator to superconductor — an angle-resolved photoemission investigation, J. Phys. Chem. Solids 56, 1865 (1995).

9. A.G. Loeser, Z.-X. Shen, D.S. Dessau, D.S. Marshall, C.H. Park, P. Fournier, and A. Kapitulnik, Excitation gap in the normal state of underdoped Bi₂Sr₂CaCu₂O_8+δ, Science 273, 325 (1996).

10. D.S. Marshall, D.S. Dessau, A.G. Loeser, C.H. Park, A.Y. Matsuura, J.N. Eckstein, I. Bozovic, P. Fournier, A. Kapitulnik, W.E. Spicer, and Z.-X. Shen, Unconventional electronic structure evolution with hole doping in Bi₂Sr₂CaCu₂O_8+δ: angle-resolved photoemission results, Phys. Rev. Lett. 76, 4841 (1996).

11. K. Tanaka, W.S. Lee, D.H. Lu, A. Fujimori, T. Fujii, Risdiana, I. Terasaki, D.J. Scalapino, T.P. Devereaux, Z. Hussain, and Z.-X. Shen, Distinct Fermi-momentum-dependent energy gaps in deeply underdoped Bi2212, Science 314, 1910 (2006).

12. S.D. Chen, M. Hashimoto, Y. He, D.J. Song, K.J. Xu, J.F. He, T.P. Devereaux, H. Eisaki, D.H. Lu, J. Zaanen, and Z.-X. Shen, Incoherent strange metal sharply bounded by a critical doping in Bi2212, Science 366, 1099 (2019).

13. S.D. Chen, M. Hashimoto, Y. He, D.J. Song, J.F. He, Y.F. Li, S. Ishida, H. Eisaki, J. Zaanen, T.P. Devereaux, D.H. Lee, D.H. Lu, and Z.-X. Shen, Unconventional spectral signature of T_c in a pure d-wave superconductor, Nature 601, 562 (2022).

14. A. Lanzara, P.V. Bogdanov, X.J. Zhou, S.A. Kellar, D.L. Feng, E.D. Lu, T. Yoshida, H. Eisaki, A. Fujimori, K. Kishio, J.I. Shimoyama, T. Noda, S. Uchida, Z. Hussain, and Z.-X. Shen, Evidence for ubiquitous strong electron–phonon coupling in high-temperature superconductors, Nature 412, 510 (2001).

15. T. Cuk, F. Baumberger, D.H. Lu, N. Ingle, X.J. Zhou, H. Eisaki, N. Kaneko, Z. Hussain, T.P. Devereaux, N. Nagaosa, and Z.-X. Shen, Coupling of the B_1g phonon to the antinodal electronic states of Bi₂Sr₂Ca_0.92Y_0.08Cu₂O_8+δ, Phys. Rev. Lett. 93, 117003 (2004).

16. J.J. Lee, F.T. Schmitt, R.G. Moore, S. Johnston, Y.T. Cui, W. Li, M. Yi, Z.K. Liu, M. Hashimoto, Y. Zhang, D.H. Lu, T.P. Devereaux, D.H. Lee, and Z.-X. Shen, Interfacial mode coupling as the origin of the enhancement of T_c in FeSe films on SrTiO₃, Nature 515, 245 (2014).

17. S. Gerber, S.L. Yang, D. Zhu, H. Soifer, J.A. Sobota, S. Rebec, J.J. Lee, T. Jia, B. Moritz, C. Jia, A. Gauthier, Y. Li, D. Leuenberger, Y. Zhang, L. Chaix, W. Li, H. Jang, J.S. Lee, M. Yi, G.L. Dakovski, S. Song, J.M. Glownia, S. Nelson, K.W. Kim, Y.D. Chuang, Z. Hussain, R.G. Moore, T.P. Devereaux, W.S. Lee, P.S. Kirchmann, and Z.-X. Shen, Femtosecond electron-phonon lock-in by photoemission and x-ray free-electron laser, Science 357, 71 (2017).

18. P.V. Bogdanov, Study of high temperature superconductors with angle-resolved photoemission spectroscopy (Doctoral dissertation, Stanford University, 2002).

19. M. Hashimoto, I.M. Vishik, R.H. He, T.P. Devereaux, and Z.-X. Shen, Energy gaps in high-transition-temperature cuprate superconductors, Nat. Phys. 10, 483 (2014).

20. I.M. Vishik, M. Hashimoto, R.H. He, W.S. Lee, F. Schmitt, D.H. Lu, R.G. Moore, C. Zhang, W. Meevasana, T. Sasagawa, S. Uchida, K. Fujita, S. Ishida, M. Ishikado, Y. Yoshida, H. Eisaki, Z. Hussain, T.P. Devereaux, and Z.-X. Shen, Phase competition in trisected superconducting dome, Proc. Natl. Acad. Sci. 109, 18332 (2012).

21. K.M. Shen, F. Ronning, D.H. Lu, F. Baumberger, N.J.C. Ingle, W.S. Lee, W. Meevasana, Y. Kohsaka, M. Azuma, M. Takano, H. Takagi, and Z.-X. Shen, Nodal quasiparticles and antinodal charge ordering in Ca_2-xNa_xCuO₂Cl₂, Science 307, 901 (2005).

22. D.S. Dessau, B.O. Wells, Z.-X. Shen, W.E. Spicer, A.J. Arko, R.S. List, D.B. Mitzi, and A. Kapitulnik, Anomalous spectral weight transfer at the superconducting transition of Bi₂Sr₂CaCu₂O_8+δ, Phys. Rev. Lett. 66, 2160 (1991).

23. Z.-X. Shen, W.E. Spicer, D.M. King, D.S. Dessau, and B.O. Wells, Photoemission studies of high-T_c superconductors: the superconducting gap, Science 267, 343 (1995).

24. N.P. Armitage, D.H. Lu, C. Kim, A. Damascelli, K.M. Shen, F. Ronning, D.L. Feng, P.V. Bogdanov, Z.-X. Shen, Y. Onose, Y. Taguchi, Y. Tokura, P.K. Mang, N. Kaneko, and M. Greven, Anomalous electronic structure and pseudogap effects in Nd_1.85Ce_0.15CuO₄, Phys. Rev. Lett. 87, 147003 (2001).

25. W.S. Lee, I.M. Vishik, K. Tanaka, D.H. Lu, T. Sasagawa, N. Nagaosa, T.P. Devereaux, Z. Hussain, and Z.-X. Shen, Abrupt onset of a second energy gap at the superconducting transition of underdoped Bi2212, Nature 450, 81 (2007).

26. Z.K. Liu, B. Zhou, Y. Zhang, Z.J. Wang, H.M. Weng, D. Prabhakaran, S.K. Mo, Z.-X. Shen, Z. Fang, X. Dai, Z. Hussain, and Y.L. Chen, Discovery of a three-dimensional topological Dirac semimetal, Na₃Bi, Science 343, 864 (2014).

27. Y. Zhang, T.R. Chang, B. Zhou, Y.T. Cui, H. Yan, Z.K Liu, F. Schmitt, J. Lee, R. Moore, Y.L. Chen, H. Lin, H.T. Jeng, S.K. Mo, Z. Hussain, A. Bansil, and Z.-X. Shen, Direct observation of the transition from indirect to direct bandgap in atomically thin epitaxial MoSe₂, Nat. Nanotechnol. 9, 111 (2014).

28. S.J. Tang, C.F. Zhang, D. Wong, Z. Pedramrazi, H.Z. Tsai, C.J Jia, B. Moritz, M. Claassen, H. Ryu, S. Kahn, J. Jiang, H. Yan, M. Hashimoto, D.H Lu, R.G. Moore, C.C. Hwang, C. Hwang, Z. Hussain, Y.L. Chen, M.M. Ugeda, Z. Liu, X.M. Xie, T.P. Devereaux, M.F. Crommie, S.K. Mo, and Z.-X. Shen, Quantum spin Hall state in monolayer 1T'-WTe₂, Nat. Phys. 13, 683 (2017).

29. Y. He, M. Hashimoto, D. Song, S.D. Chen, J. He, I.M. Vishik, B. Moritz, D.H. Lee, N. Nagaosa, J. Zaanen, T.P. Devereaux, Y. Yoshida, H. Eisaki, D.H. Lu, and Z.-X. Shen, Rapid change of superconductivity and electron-phonon coupling through critical doping in Bi-2212, Science 362, 62 (2018).

30. H.J. Zhang, C.X. Liu, X.L. Qi, X. Dai, Z. Fang, and S.C. Zhang, Topological insulators in Bi₂Se₃, Bi₂Te₃ and Sb₂Te₃ with a single Dirac cone on the surface, Nat. Phys. 5, 438 (2009).

31. C.L. Kane and E.J. Mele, Z₂ topological order and the quantum spin Hall effect, Phys. Rev. Lett. 95, 146802 (2005).

32. B.A. Bernevig, T.L. Hughes, and S.C. Zhang, Quantum spin Hall effect and topological phase transition in HgTe quantum wells, Science 314, 1757 (2006).

33. L. Fu and C.L. Kane, Topological insulators with inversion symmetry, Phys. Rev. B 76, 045302 (2007).

34. J.E. Moore and L. Balents, Topological invariants of time-reversal-invariant band structures, Phys. Rev. B 75, 121306(R) (2007).

35. X.L. Qi and S.C. Zhang, Spin-charge separation in the quantum spin Hall state, Phys. Rev. Lett. 101, 086802 (2008).

36. M.Z. Hasan and C.L. Kane, Colloquium: topological insulators, Rev. Mod. Phys. 82, 3045 (2010).

37. D. Hsieh, D. Qian, L. Wray, Y. Xia, Y.S. Hor, R.J. Cava, and M.Z. Hasan, A topological Dirac insulator in a quantum spin Hall phase, Nature 452, 970 (2008).

38. Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y.S. Hor, R.J. Cava, and M.Z. Hasan, Observation of a large-gap topological-insulator class with a single Dirac cone on the surface, Nat. Phys. 5, 398 (2009).

39. N. Nagaosa, A new state of quantum matter, Science 318, 758 (2007).

40. C. Day, Quantum spin Hall effect shows up in a quantum well insulator, just as predicted, Phys. Today 61(1), 19 (2008).

41. Y.M. Shi, J. Kahn, B. Niu, Z.Y. Fei, B.S. Sun, X.H. Cai, B.A. Francisco, D. Wu, Z.-X. Shen, X.D. Xu, D.H. Cobden, and Y.T. Cui, Imaging quantum spin Hall edges in monolayer WTe₂, Sci. Adv. 5 : eaat8799 (2019).

42. X.F. Qian, J.W. Liu, L. Fu, and J. Li, Quantum spin Hall effect in two-dimensional transition metal dichalcogenides, Science 346, 1344 (2014).

43. M.M. Ugeda, A. Pulkin, S.J. Tang, H. Ryu, Q.S. Wu, Y. Zhang, D. Wong, Z. Pedramrazi, A.M. Recio, Y. Chen, F. Wang, Z.-X. Shen, S.K. Mo, O.V. Yazyev, and M.F. Crommie, Observation of topologically protected states at crystalline phase boundaries in single-layer WSe₂, Nat. Commun. 9, 3401 (2018).

44. P. Zhang, K. Yaji, T. Hashimoto, Y. Ota, T. Kondo, K. Okazaki, Z.J. Wang, J.S. Wen, G.D. Gu, H. Ding, and S. Shin, Observation of topological superconductivity on the surface of an iron-based superconductor, Science 360, 182 (2018).

45. Y.F. Li, S.D. Chen, M. Garcia-Diez, M.I. Iraola, H. Pfau, Y.L. Zhu, Z.Q. Mao, T. Chen, M. Yi, P.C. Dai, J.A. Sobota, M. Hashimoto, M.G. Vergniory, D.H. Lu, and Z.-X. Shen, Spectroscopic evidence for topological band structure in FeTe_0.55Se_0.45, arXiv:2307.03861v2 (2023).

46. C. Kim, A.Y. Matsuura, Z.-X. Shen, N. Motoyama, H. Eisaki, S. Uchida, T. Tohyama, and S. Maekawa, Observation of spin-charge separation in one-dimensional SrCuO₂, Phys. Rev. Lett. 77, 4054 (1996).

47. B.J. Kim, H. Koh, E. Rotenberg, S.J. Oh, H. Eisaki, N. Motoyama, S. Uchida, T. Tohyama, S. Maekawa, Z.-X. Shen, and C. Kim, Distinct spinon and holon dispersions in photoemission spectral functions from one-dimensional SrCuO₂, Nat. Phys. 2, 397 (2006).

48. H.M. Hill, Augmented model captures behavior in one-dimensional cuprates, Phys. Today (2021).

49. H. Ding, T. Yokoya, J.C. Campuzano, T. Takahashi, M. Randeria, M.R. Norman, T. Mochiku, K. Kadowaki, and J. Giapintzakis, Spectroscopic evidence for a pseudogap in the normal state of underdoped high-T_c superconductors, Nature 382, 51 (1996).

50. M. Hashimoto, R.H. He, K. Tanaka, J.P. Testaud, W. Meevasana, R.G. Moore, D.H. Lu, H. Yao, Y. Yoshida, H. Eisaki, T.P. Devereaux, Z. Hussain, and Z.-X. Shen, Particle–hole symmetry breaking in the pseudogap state of Bi2201, Nat. Phys. 6, 414 (2010).

51. R.H. He , M. Hashimoto , H. Karapetyan, J.D. Koralek, J.P. Hinton, J.P. Testaud, V. Nathan, Y. Yoshida, H. Yao, K. Tanaka, W. Meevasana, R.G. Moore, D.H. Lu, S.K. Mo, M. Ishikado, H. Eisaki, Z. Hussain, T.P. Devereaux, S.A. Kivelson, J. Orenstein, A. Kapitulnik, and Z.-X. Shen, From a single-band metal to a high-temperature superconductor via two thermal phase transitions, Science 331, 1579 (2011).

52. M. Hashimoto, E.A. Nowadnick, R.H. He, I.M. Vishik, B. Moritz, Y. He, K. Tanaka, R.G. Moore, D.H. Lu, Y. Yoshida, M. Ishikado, T. Sasagawa, K. Fujita, S. Ishida, S. Uchida, H. Eisaki, Z. Hussain, T.P. Devereaux, and Z.-X. Shen, Direct spectroscopic evidence for phase competition between the pseudogap and superconductivity in Bi₂Sr₂CaCu₂O_8+δ, Nat. Mater. 14, 37 (2015).

53. K.J. Xu, Q.D. Guo, M. Hashimoto, Z.X. Li, S.D. Chen, J.F. He, Y. He, C. Li, M.H. Berntsen, C.R. Rotundu, Y.S. Lee, T.P. Devereaux, A. Rydh, D.H. Lu, D.H. Lee, O. Tjernberg, and Z.-X. Shen, Bogoliubov quasiparticle on the gossamer Fermi surface in electron-doped cuprates, Nat. Phys. 19, 1834 (2023).

54. K.J. Xu et al., Science, accepted (2024).

55. Q.Y. Wang, Z. Li, W.H. Zhang, Z.C. Zhang, J.S. Zhang, W. Li, H. Ding, Y.B. Ou, P. Deng, K. Chang, J. Wen, C.L. Song, K. He, J.F. Jia, S.H. Ji, Y.Y. Wang, L.L. Wang, X. Chen, X.C. Ma, and Q.K. Xue, Interface-induced high-temperature superconductivity in single unit-cell FeSe films on SrTiO₃, Chin. Phys. Lett. 29, 037402 (2012).

56. N. Choudhury, E.J. Walter, A.I. Kolesnikov, and C.K. Loong, Large phonon band gap in SrTiO3 and the vibrational signatures of ferroelectricity in ATiO₃ perovskites: first-principles lattice dynamics and inelastic neutron scattering, Phys. Rev. B 77, 134111 (2008).

57. J. Qu, X. Han, S. Sakamoto, C.J. Jia, J. Liu, H. Li, D. Guan, Y.J. Zeng, M. Schüler, P.S. Kirchmann, B. Moritz, Z. Hussain, T.P. Devereaux, Z.-X. Shen, and J.A. Sobota, Reversal of spin-polarization near the Fermi level of the Rashba semiconductor BiTeCl, npj Quantum Mater. 8, 13 (2023).

58. X. Han, J. Qu, S. Sakamoto, D.Y. Liu, D.D. Guan, J. Liu, H. Li, C.R. Rotundu, N. Andresen, C. Jozwiak, Z. Hussain, Z.-X. Shen, and J.A. Sobota, Development of deflector mode for spin-resolved time-of-flight photoemission spectroscopy, Rev. Sci. Instrum. 94, 103906 (2023).

59. J.A. Sobota, S. Yang, J.G. Analytis, Y.L. Chen, I.R. Fisher, P.S. Kirchmann, and Z.-X. Shen, Ultrafast optical excitation of a persistent surface-state population in the topological insulator Bi₂Se₃, Phys. Rev. Lett. 108, 117403 (2012).

60. Y. Mizuguchi, Y. Hara, K. Deguchi, S. Tsuda, T. Yamaguchi, K. Takeda, H. Kotegawa, H. Tou, and Y. Takano, Anion height dependence of T_c for the Fe-based superconductor, Supercond. Sci. Technol. 23, 054013 (2010).

61. S. Medvedev, T.M. McQueen, I.A. Troyan, T. Palasyuk, M.I. Eremets, R.J. Cava, S. Naghavi, F. Casper, V. Ksenofontov, G. Wortmann, and C. Felser, Electronic and magnetic phase diagram of β-Fe_1.01Se with superconductivity at 36.7 K under pressure, Nat. Mater. 8, 630 (2009).

62. S. Mandal, R.E. Cohen, and K. Haule, Strong pressure-dependent electron-phonon coupling in FeSe, Phys. Rev. B 89, 220502(R) (2014).

63. P.W. Anderson, More is different: broken symmetry and the nature of the hierarchical structure of science, Science 177, 393 (1972).