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We study topological vortex phases in iron-based superconductors. Besides the previously known vortex end Majorana zero modes (MZMs) phase stemming from the existence of a three dimensional (3D) strong topological insulator state, we show that there is another topologically nontrivial phase as iron-based superconductors can be doped superconducting 3D weak topological insulators (WTIs). The vortex bound states in a superconducting 3D WTI exhibit two different types of quantum states, a robust nodal superconducting phase with pairs of bulk MZMs and a full-gap topologically nontrivial superconducting phase which has single vortex end MZM in a certain range of doping level. Moreover, we predict and summarize various topological phases in iron-based superconductors, and find that carrier doping and interlayer coupling can drive systems to have phase transitions between these different topological phases.
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A vortex in an s-wave superconductor with a surface Dirac cone can trap a Majorana bound state with zero energy leading to a zero-bias peak (ZBP) of tunneling conductance. The iron-based superconductor FeTe$_x$Se$_{1-x}$ is one of the material candidates hosting these Majorana vortex modes. It has been observed by recent scanning tunneling spectroscopy measurement that the fraction of vortex cores possessing ZBPs decreases with increasing magnetic field on the surface of this iron-based superconductor. We construct a three-dimensional tight-binding model simulating the physics of over a hundred Majorana vortex modes in FeTe$_x$Se$_{1-x}$ with realistic physical parameters. Our simulation shows that the Majorana hybridization and disordered vortex distribution can explain the decreasing fraction of the ZBPs observed in the experiment. Furthermore, we find the statistics of the energy peaks off zero energy in our simulation with the Majorana physics in agreement with the analyzed peak statistics in the vortex cores from the experiment. This agreement and the explanation of the decreasing ZBP fraction lead to an important indication of scalable Majorana vortex modes in the iron-based superconductor. Thus, FeTe$_x$Se$_{1-x}$ can be one promising platform possessing scalable Majorana qubits for quantum computing. In addition, we further show the interplay of the ZBP presence and the vortex locations qualitatively agrees with our additional experimental observation and predict the universal spin signature of the hybridized multiple Majorana vortex modes.
In iron-based superconductors, band inversion of $d$- and $p$-orbitals yields Dirac semimetallic states. We theoretically investigate their topological properties in normal and superconducting phases, based on the tight-binding model involving full symmetry of the materials. We demonstrate that a Cooper pair between electrons with $d$- and $p$-orbitals relevant to the band structure yields odd-parity superconductivity. Moreover, we present the typical surface states by solving the Bogoliubov-de Gennes equation and characterize them by topological invariants defined with crystal symmetry. It is found that there appear various types of Majorana fermions such as surface flat band, Majorana quartet and M{o}bius twisted surface state. Our theoretical results show that iron-based superconductors are promising platforms to realize rich topological crystalline phases.
Topological insulators and semimetals as well as unconventional iron-based superconductors have attracted major recent attention in condensed matter physics. Previously, however, little overlap has been identified between these two vibrant fields, even though the principal combination of topological bands and superconductivity promises exotic unprecedented avenues of superconducting states and Majorana bound states (MBSs), the central building block for topological quantum computation. Along with progressing laser-based spin-resolved and angle-resolved photoemission spectroscopy (ARPES) towards high energy and momentum resolution, we have resolved topological insulator (TI) and topological Dirac semimetal (TDS) bands near the Fermi level ($E_{text{F}}$) in the iron-based superconductors Li(Fe,Co)As and Fe(Te,Se), respectively. The TI and TDS bands can be individually tuned to locate close to $E_{text{F}}$ by carrier doping, allowing to potentially access a plethora of different superconducting topological states in the same material. Our results reveal the generic coexistence of superconductivity and multiple topological states in iron-based superconductors, rendering these materials a promising platform for high-$T_{text{c}}$ topological superconductivity.
In the superconducting regime of FeTe$_{(1-x)}$Se$_x$, 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$_{(1-x)}$Se$_x$, 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$_{(1-x)}$Se$_x$.
The vortex of iron-based superconductors is emerging as a promising platform for Majorana zero mode, owing to a magic integration among intrinsic vortex winding, non-trivial band topology, strong electron-electron correlations, high-Tc superconductivity and the simplification of single material. It overcomes many difficulties suffered in heterostructure-based Majorana platforms, including small topological gap, interfacial contamination, lattice imperfections, and etc. Isolated zero-bias peaks have been found in vortex of several iron-based superconductors. So far, studies from both experimental and theoretical aspects strongly indicate the realization of vortex Majorana zero mode, with a potential to be applied to topological quantum computation. By taking Fe(Te,Se) superconductor as an example, here we review original idea and research progress of Majorana zero modes in this new platform. After introducing the identifications of topological band structure and real zero modes in vortex, we summarize the physics behaviors of vortex Majorana zero modes systematically. Firstly, relying on the behavior of the zero mode wave function and evidence of quasiparticle poisoning, we analyze the mechanism of emergence of vortex Majorana zero modes. Secondly, assisted with some well-established theories, we elaborate the measurements on Majorana symmetry and topological nature of vortex Majorana zero modes. After that, we switch from quantum physics to quantum engineering, and analyze the performance of vortex Majorana zero mode under real circumstances, which may potentially benefit the exploration of practical applications in the future. This review follows the physics properties of vortex Majorana zero modes, especially emphasizes the link between phenomena and mechanisms. It provides a chance to bridge the gap between the well-established theories and the newly discovered iron home of Majoranas.
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