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Register a new userVortex and Surface Phase Transitions in Superconducting Higher-order Topological Insulators
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Added by
Sayed Ali Akbar Ghorashi
Publication date
2019
fields
Physics
and research's language is
English
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Topological insulators (TIs) having intrinsic or proximity-coupled s-wave superconductivity host Majorana zero modes (MZMs) at the ends of vortex lines. The MZMs survive up to a critical doping of the TI at which there is a vortex phase transition that eliminates the MZMs. In this work, we show that the phenomenology in higher-order topological insulators (HOTIs) can be qualitatively distinct. In particular, we find two distinct features. (i) We find that vortices placed on the gapped (side) surfaces of the HOTI, exhibit a pair of phase transitions as a function of doping. The first transition is a surface phase transition after which MZMs appear. The second transition is the well-known vortex phase transition. We find that the surface transition appears because of the competition between the superconducting gap and the local $mathcal{T}$-breaking gap on the surface. (ii) We present numerical evidence that shows strong variation of the critical doping for the vortex phase transition as the center of the vortex is moved toward or away from the hinges of the sample. We believe our work provides new phenomenology that can help identify HOTIs, as well as illustrating a promising platform for the realization of MZMs.
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Three-dimensional topological (crystalline) insulators are materials with an insulating bulk, but conducting surface states which are topologically protected by time-reversal (or spatial) symmetries. Here, we extend the notion of three-dimensional topological insulators to systems that host no gapless surface states, but exhibit topologically protected gapless hinge states. Their topological character is protected by spatio-temporal symmetries, of which we present two cases: (1) Chiral higher-order topological insulators protected by the combination of time-reversal and a four-fold rotation symmetry. Their hinge states are chiral modes and the bulk topology is $mathbb{Z}_2$-classified. (2) Helical higher-order topological insulators protected by time-reversal and mirror symmetries. Their hinge states come in Kramers pairs and the bulk topology is $mathbb{Z}$-classified. We provide the topological invariants for both cases. Furthermore we show that SnTe as well as surface-modified Bi$_2$TeI, BiSe, and BiTe are helical higher-order topological insulators and propose a realistic experimental setup to detect the hinge states.
We propose a general theoretical framework for both constructing and diagnosing symmetry-protected higher-order topological superconductors using Kitaev building blocks, a higher-dimensional generalization of Kitaevs one-dimensional Majorana model. For a given crystalline symmetry, the Kitaev building blocks serve as a complete basis to construct all possible Kitaev superconductors that satisfy the symmetry requirements. Based on this Kitaev construction, we identify a simple but powerful bulk Majorana counting rule that can unambiguously diagnose the existence of higher-order topology for all Kitaev superconductors. For a systematic construction, we propose two inequivalent stacking strategies using the Kitaev building blocks and provide minimal tight-binding models to explicitly demonstrate each stacking approach. Notably, some of our Kitaev superconductors host higher-order topology that cannot be captured by the existing symmetry indicators in the literature. Nevertheless, our Majorana counting rule does enable a correct diagnosis for these beyond-indicator models. We conjecture that all Wannierizable superconductors should yield a decomposition in terms of our Kitaev building blocks, up to adiabatic deformations. Based on this conjecture, we propose a universal diagnosis of higher-order topology that possibly works for all Wannierizable superconductors. We also present a realistic example of higher-order topological superconductors with fragile Wannier obstruction to verify our conjectured universal diagnosis. Our work paves the way for a complete topological theory for superconductors.
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.
Majorana quasiparticles (MQPs) in condensed matter play an important role in strategies for topological quantum computing but still remain elusive. Vortex cores of topological superconductors may accommodate MQPs that appear as the zero-energy vortex bound state (ZVBS). An iron-based superconductor Fe(Se,Te) possesses a superconducting topological surface state that has been investigated by scanning tunneling microscopies to detect the ZVBS. However, the results are still controversial. Here, we performed spectroscopic-imaging scanning tunneling microscopy with unprecedentedly high energy resolution to clarify the nature of the vortex bound states in Fe(Se,Te). We found the ZVBS at 0 $pm$ 20 $mu$eV suggesting its MQP origin, and revealed that some vortices host the ZVBS while others do not. The fraction of vortices hosting the ZVBS decreases with increasing magnetic field, while chemical and electronic quenched disorders are apparently unrelated to the ZVBS. These observations elucidate the conditions to achieve the ZVBS, and may lead to controlling MQPs.
Topological nodal-line semimetals (TNLSMs) are materials whose conduction and valence bands cross each other, meeting a topologically-protected closed loop rather than discrete points in the Brillouin zone (BZ). The anticipated properties for TNLSMs include drumhead-like nearly flat surface states, unique Landau energy levels, special collective modes, long-range Coulomb interactions, or the possibility of realizing high-temperature superconductivity. Recently, SrAs3 has been theoretically proposed and then experimentally confirmed to be a TNLSM. Here, we report high-pressure experiments on SrAs3, identifying a Lifshitz transition below 1 GPa and a superconducting transition accompanied by a structural phase transition above 20 GPa. A topological crystalline insulator (TCI) state is revealed by means of density functional theory (DFT) calculations on the emergent high-pressure phase. As the counterpart of topological insulators, TCIs possess metallic boundary states protected by crystal symmetry, rather than time reversal. In consideration of topological surface states (TSSs) and helical spin texture observed in the high-pressure state of SrAs3, the superconducting state may be induced in the surface states, and is most likely topologically nontrivial, making pressurized SrAs3 a strong candidate for topological superconductor.
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