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Register a new userQuantized non-Abelian, Berrys flux and higher-order topology of Na$_3$Bi
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Recent theoretical works on effective, four-band models of three-dimensional, Dirac semimetals suggest the generic planes in momentum space, orthogonal to the direction of nodal separation, and lying between two Dirac points are higher-order topological insulators, supporting gapped, edge-states. Furthermore, the second homotopy classification of four-band models shows the higher-order topological insulators support quantized, non-Abelian Berrys flux and the Dirac points are monopoles of $SO(5)$ Berrys connections. Due to the lack of suitable computational scheme, such bulk topological properties are yet to be determined from the emph{ab initio} band structures of Dirac materials. In this work, we report first, comprehensive topological classification of emph{ab initio} band structures of Na$_3$Bi, by computing Wilson loops of non-Abelian, Berrys connections for several, Kramers-degenerate bands. Our work shows the quantized, non-Abelian, Berrys flux can be used as a stable, bulk invariant for describing higher-order topology and topological phase transitions.
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Higher order topological insulators (HOTIs) are a new class of topological materials which host protected states at the corners or hinges of a crystal. HOTIs provide an intriguing alternative platform for helical and chiral edge states and Majorana modes, but there are very few known materials in this class. Recent studies have proposed Bi as a potential HOTI, however, its topological classification is not yet well accepted. In this work, we show that the (110) facets of Bi and BiSb alloys can be used to unequivocally establish the topology of these systems. Bi and Bi$_{0.92}$Sb$_{0.08}$ (110) films were grown on silicon substrates using molecular beam epitaxy and studied by scanning tunneling spectroscopy. The surfaces manifest rectangular islands which show localized hinge states on three out of the four edges, consistent with the theory for the HOTI phase. This establishes Bi and Bi$_{0.92}$Sb$_{0.08}$ as HOTIs, and raises questions about the topological classification of the full family of Bi$_{x}$Sb$_{1-x}$ alloys.
We show that the non-Abelian Berry phase emerges naturally in the s-wave and spin quintet pairing channel of spin-3/2 fermions. The topological structure of this pairing condensate is characterized by the second Chern number. This topological structure can be realized in ultra-cold atomic systems and in solid state systems with at least two Kramers doublets.
The mathematical field of topology has become a framework to describe the low-energy electronic structure of crystalline solids. A typical feature of a bulk insulating three-dimensional topological crystal are conducting two-dimensional surface states. This constitutes the topological bulk-boundary correspondence. Here, we establish that the electronic structure of bismuth, an element consistently described as bulk topologically trivial, is in fact topological and follows a generalized bulk-boundary correspondence of higher-order: not the surfaces of the crystal, but its hinges host topologically protected conducting modes. These hinge modes are protected against localization by time-reversal symmetry locally, and globally by the three-fold rotational symmetry and inversion symmetry of the bismuth crystal. We support our claim theoretically and experimentally. Our theoretical analysis is based on symmetry arguments, topological indices, first-principle calculations, and the recently introduced framework of topological quantum chemistry. We provide supporting evidence from two complementary experimental techniques. With scanning-tunneling spectroscopy, we probe the unique signatures of the rotational symmetry of the one-dimensional states located at step edges of the crystal surface. With Josephson interferometry, we demonstrate their universal topological contribution to the electronic transport. Our work establishes bismuth as a higher-order topological insulator.
Room temperature ferromagnetism was characterized for thin films of SrTi$_{0.6}$Fe$_{0.4}$O$_{3-{delta}}$ grown by pulsed laser deposition on SrTiO$_{3}$ and Si substrates under different oxygen pressures and after annealing under oxygen and vacuum conditions. X-ray magnetic circular dichroism demonstrated that the magnetization originated from Fe$^{2+}$ cations, whereas Fe$^{3+}$ and Ti$^{4+}$ did not contribute. Films with the highest magnetic moment (0.8 {mu}B per Fe) had the highest measured Fe$^{2+}$:Fe${^3+}$ ratio of 0.1 corresponding to the largest concentration of oxygen vacancies ({delta} = 0.19). Post-growth annealing treatments under oxidizing and reducing conditions demonstrated quenching and partial recovery of magnetism respectively, and a change in Fe valence states. The study elucidates the microscopic origin of magnetism in highly Fe-substituted SrTi$_{1-x}$Fe$_x$O$_{3-{delta}}$ perovskite oxides and demonstrates that the magnetic moment, which correlates with the relative content of Fe$^{2+}$ and Fe$^{3+}$, can be controlled via the oxygen content, either during growth or by post-growth annealing.
The simultaneous interplay of strong electron-electron correlations, topological zero-energy states, and disorder is yet an unexplored territory but of immense interest due to their inevitable presence in many materials. Copper oxide high-temperature superconductors (cuprates) with pair breaking edges host a flat band of topological zero-energy states, making them an ideal playground where strong correlations, topology, and disorder are strongly intertwined. Here we show that this interplay in cuprates generates a new phase of matter: a fully gapped phase crystal state that breaks both translational and time reversal invariance, characterized by a modulation of the $d$-wave superconducting phase co-existing with a modulating extended $s$-wave superconducting order. In contrast to conventional wisdom, we find that this phase crystal state is remarkably robust to omnipresent disorder, but only in the presence of strong correlations, thus giving a clear route to its experimental realization.
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