Discrete Caroli-de Gennes-Matricon vortex bound states induced by the incipient and shallow bands in iron based superconductors

Due to the spatial confinement to the quasiparticles within a vortex, it was predicted in 1964 by Caroli, de Gennes and Matricon (CdGM) that bound states with energies of (m=±1/2, 3/2, 5/2,,,) should exist within the vortex core. In conventional superconductors, because , these discrete CdGM states are too close to be discernable because the spacing between these energy levers is very small. By doing STM measurements on the surface of FeTe_0.55Se_0.45, we observed the long sought discrete CdGM bound states^[1] which roughly satisfy the theoretically predicted ratio 1:3:5. Furthermore we have observed the discrete CdGM vortex bound states in another iron based superconductor KCa₂Fe₄As₄F₂, now they deviate from the widely believed 1:3:5, but more close to 1:2:3. Meanwhile we observed clear Friedel oscillations of the vortex bound states in this system^[2]. By solving the BdG equations self-consistently, we found that the order parameter should exhibit a Friedel oscillation on top of a smooth function in the extreme quantum limit T/T_c<<, a natural consequence is that the bound state energies deviate from the ratio of 1:3:5 and Friedel oscillations of the bound states should show up^[3]. Our results indicate a quite general feature of shallow and incipient bands in iron based superconductors, and shed new light in understanding the underline superconductivity mechanism. Finally, some bamboo like vortices are observed at the domain walls, showing intriguing physics induced by the shallow band effect.



[1] Mingyang Chen, Xiaoyu Chen, Huan Yang, Zengyi Du, Xiyu Zhu, Enyu Wang, Hai-Hu Wen. Nature Communications 9, 970 (2018).

[2] Xiaoyu Chen, Wen Duan, Xinwei Fan, Wenshan Hong, Kailun Chen, Huan Yang, Shiliang Li, Huiqian Luo, Hai-Hu Wen. Phys. Rev. Letts.126, 257002(2021).

[3] Xinwei Fan, Xiaoyu Chen, Huan Yang and Hai-Hu Wen. Europhys. Lett. 136 46002 (2021).