Spin-orbit coupling has proven indispensable in realizing topological materials and more recently Ising pairing in two-dimensional superconductors. This pairing mechanism relies on inversion symmetry breaking and sustains anomalously large in-plane polarizing magnetic fields whose upper limit is expected to diverge at low temperatures, although experimental demonstration of this has remained elusive due to the required fields. In this work, the recently discovered superconductor few-layer stanene, i.e. epitaxially strained -Sn, is shown to exhibit a new type of Ising pairing between carriers residing in bands with different orbital indices near the Γ-point. The bands are split as a result of spin-orbit locking without the participation of inversion symmetry breaking. The in-plane upper critical field is strongly enhanced at ultra-low temperature and reveals the sought for upturn.

The motion of electrons in a solid has a profound effect on its topological properties and may result in a nonzero Berry's phase, a geometric quantum phase encoded in the system's electronic wave function. Despite its ubiquity, there are few experimental observations of Berry's phase of bulk states. Here, we report detection of a nontrivial π Berry's phase in the bulk Rashba semiconductor BiTeI via analysis of the Shubnikov-de Haas (SdH) effect. The extremely large Rashba splitting in this material enables the separation of SdH oscillations, stemming from the spin-split inner and outer Fermi surfaces. For both Fermi surfaces, we observe a systematic π-phase shift in SdH oscillations, consistent with the theoretically predicted nontrivial π Berry's phase in Rashba systems.

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 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 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 c topological superconductivity.High-T c iron-based superconductors feature multiple bands near E F , which enhances the difficulty in understanding the details of unconventional pairing 1-3 . It, however, also allows for a wealth of, possibly topologically non-trivial, electronic bands, of which a recent example is the TI states discovered in the ironbased superconductor Fe(Te,Se) 4 , hinting at a promising direction to realize topological superconductivity and MBSs 5-9 . In view of Fe(Te,Se), a pressing subsequent question is to which extent this marks a generic phe-nomenon in different classes of iron-based high-T c superconductors. In this work, we find that the emergence of non-trivial topological bands near the Fermi level is indeed a common feature of various iron-based superconductors. Our first-principles calculations reveal that BaFe 2 As 2 , LiFeAs and Fe(Te,Se) all exhibit band inversions along k z . To confirm these calculations, the band structures of Li(Fe,Co)As and Fe(Te,Se) were investigated by laser-based high-resolution ARPES. Firstly, we observe that TI bands reminiscent of Fe(Te,Se) exist in Li(Fe,Co)As as well, supporting the generic existence of non-trivial topology in iron-based superconductors. Secondly and more interestingly, we predict and observe TDS bands in Li(Fe,Co)As and Fe(Te,Se), which we investigate via high-resolution ARPES, spin-resolved ARPES (SARPES), and magnetoresistance (MR) measurements. Finally, we discuss the phase diagram of these topological high-T c compounds as a function of Fermi level (doping). The combination of topological states and superconductivity may produce not only surface topological superconductivity deriving from the TI edge states, but also bulk topological superconductivity from the TDS bands.Normal insulator (NI), TI, and TDS constitute topologically disti...

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