Effect of Zeeman coupling on the Majorana vortex modes in iron-based topological superconductors

Abstract

In the superconducting regime of FeTe (1−x) Sex, there exist two types of vortices which are distinct by the presence or absence of zero energy states in their core. To understand their origin, we examine the interplay of Zeeman coupling and superconducting pairings in three-dimensional metals with band inversion. Weak Zeeman fields are found to suppress the intra-orbital spin-singlet pairing, known to localize the states at the ends of the vortices on the surface. On the other hand, an orbital-triplet pairing is shown to be stable against Zeeman interactions, but leads to delocalized zero-energy Majorana modes which extend through the vortex. In contrast, the finite-energy vortex modes remain localized at the vortex ends even when the pairing is of orbital-triplet form. Phenomenologically, this manifests as an observed disappearance of zero-bias peaks within the cores of topological vortices upon increase of the applied magnetic field. The presence of magnetic impurities in FeTe (1−x) Sex, which are attracted to the vortices, would lead to such Zeeman-induced delocalization of Majorana modes in a fraction of vortices that capture a large enough number of magnetic impurities. Our results provide an explanation to the dichotomy between topological and non-topological vortices recently observed in FeTe (1−x) Sex.Introduction: To date, one of the major impediments in the search for Majorana fermions (MFs) is that a requisite topological superconductivity, either intrinsic [1,2] or induced in a host material via a proximity coupling to a standard s-wave superconductor [3-6]. Of the available materials that possess topology, superconductivity and magnetism, iron-based superconductors are of recent interest [7][8][9][10][11][12][13][14][15]. In particular, the iron-based superconductor FeTe 0.55 Se 0.45 (FTS) has recently been shown to have strong spin-orbit interactions and band inversion that result in a helical, topologically-protected, Dirac cone on the surface [16][17][18][19]. The phenomenology of vortices, proliferated in the presence of magnetic fields, is also noteworthy in FTS [20][21][22][23]. The low charge density in the superconducting phase of this system is experimentally advantageous as it results in large Caroli-de Gennes-Matricon (CDM) vortex mode gaps [24] which facilitates the spectral detection of zero-energy vortex modes via scanning tunneling microscopy (STM). Intriguingly, vortices in FTS show two distinct types of behavior: topological, carrying zero energy states consistent with the presence of MF, and trivial vortices that lack the zero energy state but carry finite energy CDMs.

Time-reversal symmetry breaking in the Fe-chalcogenide superconductors

“…Through spin-orbit coupling, the complex order parameter can induce spin magnetization as described in SI Appendix and explained in detail elsewhere (6). We note that alternative theories that may explain the appearance of the gap at the Dirac point have also been suggested (18,19). The presence of ferromagnetism in the surface region associated with strong spin-orbit coupling would potentially make this system an ideal platform for supporting a range of unique topological phenomena.…”

On the Remarkable Superconductivity of FeSe and Its Close Cousins

“…This scenario offers a prediction of chiral Majorana modes located at the domain wall between these two spatially distinct phases. Another theoretical study suggested that Zeeman coupling from clustering of magnetic impurities may locally induce a superconducting orbital-triplet spin-singlet state near some vortices, thereby rendering those vortices non-topological and hence unable to support zero-energy MZMs [421]. [409].…”

Emergent vortex Majorana zero mode in iron-based superconductors

“…Recently, the threedimensional model has been extended to more specific circumstances, including 1) the vortex phase transitions in Fe(Te,Se) single crystals [198]; 2) the vortex phase transitions when the topological bands are coupled with trivial bands. In this case, the topological regime deforms, but still includes the Dirac points [199]; 3) the topological vortex phase transitions induced by Zeeman coupling [200]; 4) the topological vortex phase transitions of the weak topological insulator [201] and the Dirac semimetal [202,203].…”