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Evidence for Majorana bound states in an iron-based superconductor

The search for Majorana bound states (MBSs) has been fueled by the prospect of using their non-Abelian statistics for robust quantum computation. Two-dimensional superconducting topological materials have been predicted to host MBSs as zero-energy modes in vortex cores. By using scanning tunneling spectroscopy on the superconducting Dirac surface state of the iron-based superconductor FeTe0.55Se0.45, we observed a sharp zero-bias peak inside a vortex core that does not split when moving away from the vortex center. The evolution of the peak under varying magnetic field, temperature, and tunneling barrier is consistent with the tunneling to a nearly pure MBS, separated from nontopological bound states. This observation offers a potential platform for realizing and manipulating MBSs at a relatively high temperature.

M ajorana bound states (MBSs) in condensedmatter systems have attracted tremendous interest owing to their non-Abelian statistics and potential applications in topological quantum computation (1,2). A MBS is theoretically predicted to emerge as a spatially localized zero-energy mode in certain p-wave topological superconductors in one and two dimensions (3,4). Although the material realization of such p-wave superconductors has remained elusive, other platforms for MBSs have recently been proposed, using heterostructures between conventional s-wave superconductors and topological insulators (5), nanowires (6)(7)(8), quantum anomalous Hall insulators (9), or atomic chains (10), where the proximity effect on a spinnondegenerate band creates a superconducting (SC) topological state. Various experimental signatures of MBSs (11)(12)(13)(14) or Majorana chiral modes (15) have been observed in these heterostructures, but clear detection and manipulation of MBSs are often hindered by the contribution of nontopological bound states and complications of material interface.
Very recently, using high-resolution angleresolved photoemission spectroscopy (ARPES), a potential platform for MBSs was discovered in the bulk superconductor FeTe 0.55 Se 0.45 , with a SC transition temperature T c = 14.5 K and a simple crystal structure (Fig. 1A). Because of the topological band inversion between the p z and d xz /d yz bands around the G point (16,17) and the multiband nature (Fig. 1B), this single material naturally has a spin-helical Dirac surface state, with an induced full SC gap and a small Fermi energy ( Fig. 1C) (18); these properties would create favorable conditions for observing a pure MBS (5) that is isolated from other nontopological Caroli-de Gennes-Matricon bound states (CBSs) (19,20). The combination of high-T c superconductivity and Dirac surface states in a single material removes the challenging interface problems in previous proposals and offers clear advantages for the detection and manipulation of MBSs.
Motivated by the above considerations, we carried out a high-resolution scanning tunneling microscopy/spectroscopy (STM/S) experiment on the surface of FeTe 0.55 Se 0.45 , which has a good atomic resolution that reveals the lattice formed by Te/Se atoms on the surface (Fig. 1D). We started with a relatively low magnetic field of 0.5 T along the c axis at a low temperature of 0.55 K, with a clear observation of vortex cores in Fig. 1E. At the vortex center, we observed a strong zero-bias peak (ZBP) with a full width at half maximum (FWHM) of 0.3 meV and an amplitude of 2 relative to the intensity just outside the gapped region. Outside of the vortex core, we clearly observed a SC spectrum with multiple gap features, similar to the ones observed in previous STM studies on the same material (21,22). These different SC gaps correspond well with the SC gaps on different Fermi surfaces of this material observed in previous ARPES studies (table S1) (23,24). A similar ZBP was reported previously (22). We next demonstrate in Fig. 2 and fig. S4 (24) that across a large range of magnetic fields, the observed ZBP does not split when moving away from a vortex center. It can be clearly seen from Fig. 2, A to D, that the ZBP remains at the zero energy, while its intensity fades away when moving away from the vortex center. The nonsplit ZBP contrasts sharply with the split ZBP originating from CBS observed in conventional superconductors  (19,20) and is consistent with tunneling into an isolated MBS in a vortex core of a SC topological material (5,(25)(26)(27). We then extracted the position-dependent values of the ZBP height and width using simple Gaussian fits of the data in Fig. 2C and obtained the spatial profile shown in Fig. 2E; the decaying profile has a nearly constant line width of~0.3 meV in the center, which is close to the total width (~0.28 meV) contributed from the STM energy resolution [~0.23 meV as shown in part I of (24)] and the thermal broadening [3.5k B T at 0.55 K~0.17 meV, where k B is the Boltzmann constant]. We further compared the observed ZBP height with a theoretical MBS spatial profile obtained by solving the Bogoliubov-de Gennes equation analytically (5,25) or numerically (26,27). By using the parameters of E F = 4.4 meV, D sc = 1.8 meV, and x 0 = v F /D sc = 12 nm, which are obtained directly from the topological surface state by our scanning tunneling spectroscopy (STS) and ARPES results (Fig. 2F) (18), the theoretical MBS profile matches well the experimental one (Fig. 2G).
The observation of a nonsplit ZBP, which is different from the split ZBP observed in a vortex of the Bi 2 Te 3 /NbSe 2 heterostructure (13,28,29), indicates that the MBS peak in our system is much less contaminated by nontopological CBS peaks, which is made possible by the large D sc /E F ratio in this system. In a usual topological insulator/ superconductor heterostructure, this ratio is tiny, on the order of 10 −3 to 10 −2 (28). This has been shown to induce, in addition to the MBS at the zero energy, many CBSs, whose level spacing is proportional to D sc 2 /E F . As a result, these CBSs were crowded together very close to the zero energy, making difficult a clean detection of MBS from the dI/dV spectra (29). However, on the surface of FeTe 0.55 Se 0.45 , the value of D sc 2 /E F is~0.74 meV, which is sufficiently large to push most CBSs away from the zero energy (24), leaving the MBS largely isolated and unspoiled. A large energy separation (0.7 meV) between the ZBP and the CBS was observed in fig. S3, E to H, which is in agreement with D sc 2 /E F of the topological surface states [(24), part IV]. Also, all the bulk bands in this multiband material have fairly small values of E F owing to large correlation-induced mass renormalization, ranging from a few to a few tens of millielectron volts; thus, their values of D sc 2 /E F are also quite large (>0.2 meV) (table S1) (24). These large bulk ratios enlarge the energy-level spacing of CBSs inside the bulk vortex line, which helps reduce quasiparticle poisoning of the MBS at low temperature [(24), part II].
It has been predicted (30) that the width of the ZBP from tunneling into a single isolated MBS is determined by thermal smearing (3.5k B T), tunneling broadening, and STM instrumentation resolution. We measured the tunneling barrier evolution of the ZBP (Fig. 3A). Robust ZBPs can be observed over two orders of magnitude in tunneling barrier conductance, with the width barely changing (Fig. 3B). Also, the line width of ZBPs is almost completely limited by the combined broadening of energy resolution and STM thermal effect, suggesting that the intrinsic width of the MBS is much smaller, and our measurements are within the weak tunneling regime.
However, we did observe some other ZBPs with a larger broadening (Fig. 3C). A larger ZBP broadening is usually accompanied with a softer SC gap, or the FWHM of ZBP increases with increasing subgap background conductance. The subgap background conductance, which is determined by factors such as the strength of scattering from disorder and quasiparticle interactions (31)(32)(33), introduces a gapless fermion bath that can poison the MBS, as explained previously (34). The effect of quasiparticle poisoning is to reduce the MBS amplitude and increase its width. This scenario is likely the origin of a larger broadening of ZBP accompanied by a softer gap.
It has been pointed out by previous theoretical studies ( [35][36][37] that the condition of a bulk vortex line, such as its chemical potential, has substantial influences on the Majorana mode on the surface by the vortex phase transition. In order to further characterize the effects of bulk vortex lines, we have monitored the temperature evolution of a ZBP. As shown in Fig. 3D, the ZBP intensity measured at a vortex center decreases with increasing temperature and becomes extremely weak at 4.2 K and totally invisible at 6.0 K. A peak associated with a CBS would persist to higher temperatures and exhibit simple Fermi-Dirac broadening up to about T c /2 (~8 K), below which the SC gap amplitude is almost constant, as observed in our previous ARPES measurement (18). Our observation (Fig. 3D) contradicts this expectation and indicates an additional suppression mechanism that is likely related to the poisoning of MBS by thermally excited quasiparticles. From the extraction of ZBP amplitude measured on several different vortices (three cases are shown in Fig. 3E), we found that most of the observed ZBPs vanish around 3 K, which is higher than the temperature in many previous Majorana platforms (11,38). This vanishing temperature is comparable with the energy level spacing of the bulk vortex line as discussed above; thus, the temperature dependence we found is consistent with a case of a MBS poisoned by thermally induced quasiparticles inside the bulk vortex line (24).
Our observations provide strong evidence for tunneling to an isolated MBS; many alternative trivial explanations [(24), part III] cannot account for all the observed features. It is technically possible to move a vortex by a STM tip, which in principle can be used to exchange MBSs inside vortices (Fig. 3F), consequently demonstrating non-Abelian statistics under a sufficiently low (k B T ≪ D sc 2 =E F ) temperature (2). The high transition temperature and large SC gaps in this superconductor offer a promising platform to fabricate robust devices for topological quantum computation.