When thin films of the topological insulator Bi2Se3 are grown by molecular beam epitaxy on the d-wave high-temperature cuprate superconductor Bi2Sr2CaCu2O8+δ (Bi2212), angle-resolved photoemission reported a large (up to 15 meV) proximity-induced gap on the topological surface states that is nearly isotropic — hence consistent with predominant s-wave rather than d-wave pairing — while bulk quantum-well states acquired much smaller gaps. This heterostructure was proposed as a high-temperature platform for the Fu–Kane scenario, in which s-wave pairing on a Dirac surface state yields effective spinless p+ip superconductivity with Majorana zero modes in vortex cores. The surviving open problem is threefold and internally linked: (i) the existence and symmetry of the induced gap remain contested, with independent non-replications and reinterpretations of the spectroscopic features; (ii) the interface, growth, and disorder physics controlling any s/d admixture, gap magnitude, and reproducibility is unmapped; and (iii) no experimental regime of this platform has excluded the low-gap bulk quantum-well states, and no Majorana zero mode has been spectroscopically detected or braided in its vortices.

Background

A three-dimensional topological insulator (TI) such as Bi2Se3 is a bulk insulator whose surfaces host gapless Dirac-cone states protected by time-reversal symmetry; the film thickness is counted in quintuple layers (QLs), the five-atom Se–Bi–Se–Bi–Se slabs that stack to form the crystal. Bi2Sr2CaCu2O8+δ (Bi2212) is a cuprate high-temperature superconductor with Tc≈90 KT_c \approx 90\,\mathrm{K} whose order parameter is predominantly d-wave, i.e. it changes sign under a 90° rotation in the CuO2 plane and has nodes along specific in-plane directions. The superconducting proximity effect is the induction of superconducting order in a normal material in contact with a superconductor. Fu and Kane (2008) proposed that an s-wave superconductor proximitizing a TI surface Dirac cone realizes effective spinless chiral p+ipp+ip pairing, so that vortices of the hybrid trap Majorana zero modes (MZMs) — zero-energy quasiparticles that are their own antiparticles and obey non-Abelian exchange statistics, of interest for fault-tolerant quantum computation. Cuprate substrates were pursued to raise the temperature and gap scales of this scenario (Zareapour et al., 2012, mechanically bonded Bi2Se3/Bi2212 junctions). The primary source of the present problem (Wang et al., 2013) grew Bi2Se3 films by molecular beam epitaxy (MBE, a layer-by-layer vacuum growth technique) on Bi2212 and used angle-resolved photoemission spectroscopy (ARPES, which resolves electron energy versus momentum) to report a large, nearly isotropic gap on the topological surface states — attributed to predominant s-wave pairing, attributed plausibly to lattice-orientation mismatch and disorder — together with much smaller gaps on the bulk quantum-well states (QWSs, the discrete size-quantized subbands of an ultrathin film), and presented this as a step toward MZMs. Parallel experimental programs on the s-wave analog Bi2Te3/NbSe2 (Xu et al., 2014; reviewed by Sun and Jia, 2017) pursued vortex-core MZM signatures on a different substrate class.

Problem Statement

The problem, as it arises from Wang et al. (2013) and the subsequent literature, is to establish — or conclusively rule out — that the interface between the topological insulator Bi2Se3 and the d-wave high-temperature superconductor Bi2Sr2CaCu2O8+δ realizes proximity-induced superconductivity on the topological surface states with a well-determined pairing symmetry, in a controllable and reproducible interface, and to demonstrate Majorana zero modes in its vortices. Concretely, the linked open questions are: (1) provide a definitive, phase-sensitive or otherwise conclusive determination of whether the induced gap on the topological surface states exists and whether its symmetry is s-wave, d-wave, or a mixed s/d state — quantifying any anisotropic component rather than inferring symmetry from gap isotropy in ARPES, and resolving the existing conflict between the original isotropic-gap report, the independent ARPES non-replications, the twofold-anisotropic STM spectra on the Bi2Te3/Bi2212 analog, and Coulomb-blockade reinterpretations of the same spectroscopic features; (2) map theoretically and experimentally how interface registry, lattice- and rotational-symmetry mismatch, domain structure, interfacial charge transfer, and disorder strength control the induced gap magnitude, its s/d admixture, and its spatial homogeneity, thereby explaining the reported sample-to-sample variability; (3) demonstrate a preparation regime (by gating, doping, or thickness control) in which the chemical potential avoids the bulk quantum-well states whose small induced gaps would otherwise hybridize with vortex-core states and degrade the non-Abelian Majorana physics; and (4) in such a controlled regime, detect Majorana zero modes spectroscopically in vortices of the heterostructure. Items (1)–(3) are the prerequisites that jointly define the completion boundary for item (4): a qualified expert would consider the problem answered when the induced gap's existence and symmetry are settled by reproducible, phase-sensitive or otherwise conclusive evidence, its interface dependence is quantitatively mapped, and vortex-core spectroscopy in a QWS-free regime either demonstrates Majorana zero modes or excludes them for this platform — or, if the induced gap is conclusively ruled out for this platform, the problem is resolved by that conclusive null result alone and items (2)–(4) need not be pursued.

References

  1. Wang, E., Ding, H., Fedorov, A. V., Yao, W., Li, Z., Lv, Y.-F., Zhao, K., Zhang, L.-G., Xu, Z., Schneeloch, J., Zhong, R., Ji, S.-H., Wang, L., He, K., Ma, X., Gu, G., Yao, H., Xue, Q.-K., Chen, X., Zhou, S. (2013). Fully gapped topological surface states in Bi2Se3 films induced by a d-wave high-temperature superconductor. Nature Physics 9, 621–625. DOI: 10.1038/nphys2744. https://doi.org/10.1038/nphys2744
  2. Fu, L., Kane, C. L. (2008). Superconducting proximity effect and Majorana fermions at the surface of a topological insulator. Physical Review Letters 100, 096407. DOI: 10.1103/PhysRevLett.100.096407. https://doi.org/10.1103/PhysRevLett.100.096407
  3. Zareapour, P., Hayat, A., Zhao, S. Y. F., Kreshchuk, M., Jain, A., Kwok, D. C., Lee, N., Cheong, S.-W., Xu, Z., Yang, A., Gu, G. D., Jia, S., Cava, R. J., Burch, K. S. (2012). Proximity-induced high-temperature superconductivity in the topological insulators Bi2Se3 and Bi2Te3. Nature Communications 3, 1056. DOI: 10.1038/ncomms2042. https://doi.org/10.1038/ncomms2042
  4. Yilmaz, T., Pletikosić, I., Weber, A. P., Sadowski, J. T., Gu, G. D., Caruso, A. N., Sinkovic, B., Valla, T. (2014). Absence of a proximity effect for a thin-films of a Bi2Se3 topological insulator grown on top of a Bi2Sr2CaCu2O8+δ cuprate superconductor. Physical Review Letters 113, 067003. DOI: 10.1103/PhysRevLett.113.067003. https://doi.org/10.1103/PhysRevLett.113.067003
  5. Xu, S.-Y., Liu, C., Richardella, A., Belopolski, I., Alidoust, N., Neupane, M., Bian, G., Samarth, N., Hasan, M. Z. (2014). Fermi-level electronic structure of a topological-insulator/cuprate-superconductor based heterostructure in the superconducting proximity effect regime. Physical Review B 90, 085128. DOI: 10.1103/PhysRevB.90.085128. https://doi.org/10.1103/PhysRevB.90.085128 (preprint arXiv:1403.2109, https://arxiv.org/abs/1403.2109, posted under the title 'Search for superconducting proximity effect in a topological insulator and high temperature superconductor heterostructure Bi2Se3/Bi2Sr2CaCu2O8+δ')
  6. Wan, S., Gu, Q., Li, H., Yang, H., Schneeloch, J., Zhong, R. D., Gu, G. D., Wen, H.-H. (2020). Twofold symmetry of proximity-induced superconductivity in Bi2Te3/Bi2Sr2CaCu2O8+δ heterostructures revealed by scanning tunneling microscopy. Physical Review B 101, 220503(R). DOI: 10.1103/PhysRevB.101.220503. https://doi.org/10.1103/PhysRevB.101.220503
  7. Rachmilowitz, B., Zhao, H., Ren, Z., Li, H., Thomas, K. H., Marangola, J., Gao, S., Schneeloch, J., Zhong, R., Gu, G., Flindt, C., Zeljkovic, I. (2020). Coulomb blockade effects in a topological insulator grown on a high-Tc cuprate superconductor. npj Quantum Materials 5, 72. DOI: 10.1038/s41535-020-00274-6. https://doi.org/10.1038/s41535-020-00274-6
  8. Kundu, A. K., Wu, Z.-B., Drozdov, I., Gu, G., Valla, T. (2020). Origin of suppression of proximity-induced superconductivity in Bi/Bi2Sr2CaCu2O8+δ heterostructures. Advanced Quantum Technologies 3, 2000038. DOI: 10.1002/qute.202000038. https://doi.org/10.1002/qute.202000038
  9. Lu, X., Sénéchal, D. (2020). Proximity effect in a heterostructure of a high-Tc superconductor with a topological insulator from dynamical mean field theory. Physical Review B 101, 054512. DOI: 10.1103/PhysRevB.101.054512. https://doi.org/10.1103/PhysRevB.101.054512
  10. Shimamura, N., Sugawara, K., Sucharitakul, S., Souma, S., Iwaya, K., Nakayama, K., Trang, C. X., Yamauchi, K., Oguchi, T., Kudo, K., Noji, T., Koike, Y., Takahashi, T., Hanaguri, T., Sato, T. (2018). Ultrathin bismuth film on high-temperature cuprate superconductor Bi2Sr2CaCu2O8+δ as a candidate of a topological superconductor. ACS Nano 12, 10977–10983. DOI: 10.1021/acsnano.8b04869. https://doi.org/10.1021/acsnano.8b04869
  11. Flötotto, D., Ota, Y., Bai, Y., Zhang, C., Okazaki, K., Tsuzuki, A., Hashimoto, T., Eckstein, J. N., Shin, S., Chiang, T.-C. (2018). Superconducting pairing of topological surface states in bismuth selenide films on niobium. Science Advances 4, eaar7214. DOI: 10.1126/sciadv.aar7214. https://doi.org/10.1126/sciadv.aar7214
  12. Xu, J.-P., Liu, C., Wang, M.-X., Ge, J., Liu, Z.-L., Yang, X., Chen, Y., Liu, Y., Xu, Z.-A., Gao, C.-L., Qian, D., Zhang, F.-C., Jia, J.-F. (2014). Artificial topological superconductor by the proximity effect. Physical Review Letters 112, 217001. DOI: 10.1103/PhysRevLett.112.217001. https://doi.org/10.1103/PhysRevLett.112.217001
  13. Sun, H.-H., Jia, J.-F. (2017). Majorana zero mode in the vortex of an artificial topological superconductor. Science China Physics, Mechanics & Astronomy 60, 057401. DOI: 10.1007/s11433-017-9011-7. https://doi.org/10.1007/s11433-017-9011-7
  14. Mercado, A., Sahoo, S., Franz, M. (2022). High-temperature Majorana zero modes. Physical Review Letters 128, 137002. DOI: 10.1103/PhysRevLett.128.137002. https://doi.org/10.1103/PhysRevLett.128.137002
  15. Chen, K., Chen, M., Wen, C.-H., Hou, Z., Yang, H., Wen, H.-H. (2023). Superconductivity and vortex structure in Bi2Te3/FeTe0.55Se0.45 heterostructures with varying Bi2Te3 thickness. Physical Review B 108, 184512. DOI: 10.1103/PhysRevB.108.184512. https://doi.org/10.1103/PhysRevB.108.184512
  16. Sato, M., Ando, Y. (2017). Topological superconductors: a review. Reports on Progress in Physics 80, 076501. DOI: 10.1088/1361-6633/aa6ac7. https://doi.org/10.1088/1361-6633/aa6ac7
  17. Mandal, M., Drucker, N. C., Siriviboon, P., Nguyen, T., Boonkird, A., Lamichhane, T. N., Okabe, R., Chotrattanapituk, A., Li, M. (2023). Topological superconductors from a materials perspective. Chemistry of Materials 35, 6184–6200. DOI: 10.1021/acs.chemmater.3c00713. https://doi.org/10.1021/acs.chemmater.3c00713