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Recently, the search for Majorana fermions (MFs) has become one of the most important and exciting issues in condensed matter physics since such an exotic quasiparticle is expected to potentially give rise to unprecedented quantum phenomena whose functional properties will be used to develop future quantum technology. Theoretically, the MFs may reside in various types of topological superconductor materials that is characterized by the topologically protected gapless surface state which are essentially an Andreev bound state. Superconducting doped topological insulators and topological crystalline insulators are promising candidates to harbor the MFs. In this review, we discuss recent progress and understanding on the research of MFs based on time-reversal-invariant superconducting topological materials to deepen our understanding and have a better outlook on both the search for and realization of MFs in these systems. We also discuss some advantages of these bulk systems to realize MFs including remarkable superconducting robustness against nonmagnetic impurities.
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A nematic topological superconductor has an order parameter symmetry, which spontaneously breaks the crystalline symmetry in its superconducting state. This state can be observed, for example, by thermodynamic or upper critical field experiments in which a magnetic field is rotated with respect to the crystalline axes. The corresponding physical quantity then directly reflects the symmetry of the order parameter. We present a study on the superconducting upper critical field of the Nb-doped topological insulator NbxBi2Se3 for various magnetic field orientations parallel and perpendicular to the basal plane of the Bi2Se3 layers. The data were obtained by two complementary experimental techniques, magnetoresistance and DC magnetization, on three different single crystalline samples of the same batch. Both methods and all samples show with perfect agreement that the in-plane upper critical fields clearly demonstrate a two-fold symmetry that breaks the three-fold crystal symmetry. The two-fold symmetry is also found in the absolute value of the magnetization of the initial zero-field-cooled branch of the hysteresis loop and in the value of the thermodynamic contribution above the irreversibility field, but also in the irreversible properties such as the value of the characteristic irreversibility field and in the width of the hysteresis loop. This provides strong experimental evidence that Nb-doped Bi2Se3 is a nematic topological superconductor similar to the Cu- and Sr-doped Bi2Se3.
Using high-resolution angle-resolved photoemission spectroscopy and scanning tunneling microscopy/spectroscopy, the atomic and low energy electronic structure of the Sr-doped superconducting topological insulators (SrxBi2Se3) was studied. Scanning tunneling microscopy shows that most of the Sr atoms are not in the van der Waals gap. After Sr doping, the Fermi level was found to move further upwards when compared with the parent compound Bi2Se3, which is consistent with the low carrier density in this system. The topological surface state was clearly observed, and the position of the Dirac point was determined in all doped samples. The surface state is well separated from the bulk conduction bands in the momentum space. The persistence of separated topological surface state combined with small Fermi energy makes this superconducting material a very promising candidate for the time reversal invariant topological superconductor
The transport properties of a topological Josephson junction fabricated from a magnetically doped topological insulator (TI) were investigated. The conductance spectra of the Nb/Fe-Bi$_2$Te$_2$Se/Nb junction below 1 K showed an unusual trident-shaped zero-bias conductance peak with a tiny peak width of $sim$ 6 $mu$V. The central peak of the trident peak presents the dc-Josephson current, and the side peaks may reflect an induced unconventional Cooper pairing. Additionally, the critical currents followed inverse to temperature, which may also reflect the presence of an unconventional proximity effect. Furthermore, microwave irradiation derived a drastic change in the conductance spectra from the peak structure into oscillatory ones, a hallmark of the ac-Josephson supercurrent. The current-phase relation of the ac-Josephson effect under high power radiofrequency-irradiation was found to be 4$pi$-periodic. The results suggest that the junction based on magnetically doped 3D TIs may realize an unconventional Cooper pairing, thus enabling access to the basic physics of Majorana bound states and unconventional superconductivity.
Angle resolved photoemission spectroscopy is used to observe changes in the electronic structure of bulk-doped topological insulator Cu$_x$Bi$_2$Se$_3$ as additional copper atoms are deposited onto the cleaved crystal surface. Carrier density and surface-normal electrical field strength near the crystal surface are estimated to consider the effect of chemical surface gating on atypical superconducting properties associated with topological insulator order, such as the dynamics of theoretically predicted Majorana Fermion vortices.
Topological insulators embody a new state of matter characterized entirely by the topological invariants of the bulk electronic structure rather than any form of spontaneously broken symmetry. Unlike the 2D quantum Hall or quantum spin-Hall-like systems, the three dimensional (3D) topological insulators can host magnetism and superconductivity which has generated widespread research activity in condensed-matter and materials-physics communities. Thus there is an explosion of interest in understanding the rich interplay between topological and the broken-symmetry states (such as superconductivity), greatly spurred by proposals that superconductivity introduced into certain band structures will host exotic quasiparticles which are of interest in quantum information science. The observations of superconductivity in doped Bi_2Se_3 (Cu$_x$Bi$_2$Se$_3$) and doped Bi_2Te_3 (Pd$_x$-Bi$_2$Te$_3$ T$_c$ $sim$ 5K) have raised many intriguing questions about the spin-orbit physics of these ternary complexes while any rigorous theory of superconductivity remains elusive. Here we present key measurements of electron dynamics in systematically tunable normal state of Cu$_x$Bi$_2$Se$_3$ (x=0 to 12%) gaining insights into its spin-orbit behavior and the topological nature of the surface where superconductivity takes place at low temperatures. Our data reveal that superconductivity occurs (in sample compositions) with electrons in a bulk relativistic kinematic regime and we identify that an unconventional doping mechanism causes the topological surface character of the undoped compound to be preserved at the Fermi level of the superconducting compound, where Cooper pairing occurs at low temperatures. These experimental observations provide important clues for developing a theory of topological-superconductivity in 3D topological insulators.
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