By Ivan Maggio-Aprile, Tim Gazdić, Christoph Renner, UNIGE
Based on article published in Physical Review X
Magnetic vortices in superconductors are singular objects at the center of which the superconducting order parameter is locally destroyed. As a consequence, the electronic excitations in their cores are expected to be fundamentally different from the ones occurring in the electronic superfluid surrounding the vortices. Scanning tunneling microscopy (STM) is the ideal tool to study these singular states, whose spectroscopic signatures are predicted to carry essential information about the intrinsic nature of the superconducting state.
Numerous STM investigations of “conventional” low-temperature superconductors revealed that the electronic signatures of their vortex cores closely follow the expectations of the BCS theory. In the ultra-clean limit, quasiparticle excitations in the cores form a set of discrete bound states, with a minigap at the Fermi level of the order of Δ2/EF. The more exotic vortex core structure of high-temperature superconductors (HTS) remained a mystery, since the zero-bias anomaly theoretically predicted for d-wave superconductors had never been reported in any STM study. Many arguments were invoked to explain the absence of the expected electronic signature, mainly the normal state itself being far from a conventional Fermi liquid. The observation of enhanced 4a0×4a0 conductance modulations in the vortex halos of HTS compounds was taken as an additional proof that the strong correlations, evidenced by the pseudogap and the persistence of charge or spin orders deep into the superconducting dome, are dominating the quasiparticle excitations.
We have revisited this question focusing on heavily hole-doped Bi2Sr2CaCu2O8+δ single crystals , where a more conventional electronic Fermi liquid is expected in the absence of any pseudogap. We further used an unprecedented low magnetic field of 160 mT for any HTS study by STM to minimize the reciprocal influence of neighbouring flux lines on the quasiparticle DOS. Once we mastered the challenge of identifying the tiny vortex cores at such low densities, we found the vortex core signature predicted by Wang and MacDonald for a superconductor whose Cooper pairs wave functions are anisotropic in momentum space (d-wave symmetry) . This is the first time a HTS vortex reveals the expected conductance peak at zero bias that splits into two conductance peaks which shift away from the Fermi level with increasing distance from the vortex core (Fig. 1B and C). Moreover, we observe that the zero-bias conductance decreases more rapidly along the (110) nodal direction (Fig. 1B) than along the anti-nodal one (Fig. 1C), in perfect agreement with the theoretical predictions. We carefully checked that the low-energy spectroscopic features seen in the core (Fig. 1D) are absent at the exact same location in zero field (Fig. 1E), to make sure they are genuine vortex core features rather than impurity states, for example.
Interestingly, the above Wang-MacDonald d-wave vortex core signature is replaced by the 4a0×4a0 periodic electronic modulation previously observed when increasing the applied magnetic field above 1 Tesla (note the precise threshold field for this change is yet to be established). This clearly indicates the checkerboard vortex core structure is a vortex-enhanced quasiparticle interference (QPI). At the same time, the electronic core structure changes into essentially non-dispersing sets of finite low energy states similar to the ones reported in previous experiments in Bi-based compounds and YBa2Cu3O7‑x. The origin of these features remains unclear, and might be induced by the circulating screening current and the associated Doppler shifts of the electronic levels.
The proper identification of the vortex core states is of prime interest to elucidate the mechanism driving high-temperature superconductivity, which still remains unclear. Whether or not Wang-MacDonald vortex cores also emerge at low magnetic field in low hole-doped Bi2Sr2CaCu2O8+δ remains to be seen.
 Tim Gazdić, Ivan Maggio-Aprile, Genda Gu, and Christoph Renner, “Wang-MacDonald d-Wave Vortex Cores Observed in Heavily Overdoped Bi2Sr2CaCu2O8+δ”, Physical Review X 11, 031040 (2021)
 Y. Wang and A. H. MacDonald, “Mixed-state quasiparticle spectrum for d-wave superconductors”, Physical Review B 52, R3876 (1995).