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Bismuth has been the key element in the discovery and development of topological insulator materials. Previous theoretical studies indicated that Bi is topologically trivial and it can transform into the topological phase by alloying with Sb. However, recent high-resolution angle-resolved photoemission spectroscopy (ARPES) measurements strongly suggested a topological band structure in pure Bi. To address this issue, we study the band structure of Bi and Sb films by ARPES and first-principles calculations. By tuning tight binding parameters, we show that Bi quantum films in topologically trivial and nontrivial phases response differently to surface perturbations. Therefore, we establish an experimental route for detecting the band topology of Bi by spectroscopic methods. In addition, our circular dichroic photoemission illuminates the rich surface states and complex spin texture of the Bi(111) surface.
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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.
The topology of pure Bi is controversial because of its very small ($sim$10 meV) band gap. Here we perform high-resolution angle-resolved photoelectron spectroscopy measurements systematically on 14$-$202 bilayers Bi films. Using high-quality films, we succeed in observing quantized bulk bands with energy separations down to $sim$10 meV. Detailed analyses on the phase shift of the confined wave functions precisely determine the surface and bulk electronic structures, which unambiguously show nontrivial topology. The present results not only prove the fundamental property of Bi but also introduce a capability of the quantum-confinement approach.
Electrides, with their excess electrons distributed in crystal cavities playing the role of anions, exhibit a variety of unique electronic and magnetic properties. In this work, we employ the first-principles crystal structure prediction to identify a new prototype of A$_3$B electride in which both interlayer spacings and intralayer vacancies provide channels to accommodate the excess electrons in the crystal. This A$_3$B type of structure is calculated to be thermodynamically stable for two alkaline metals oxides (Rb$_3$O and K$_3$O). Remarkably, the unique feature of multiple types of cavities makes the spatial arrangement of anionic electrons highly flexible via elastic strain engineering and chemical substitution, in contrast to the previously reported electrides characterized by a single topology of interstitial electrons. More importantly, our first-principles calculations reveal that Rb$_3$O is a topological Dirac nodal line semimetal, which is induced by the Rb-$s$ $rightarrow$ O-$p$ band inversion at the general electronic k momentums in the Brillouin zone associated with the intersitial electric charges. The discovery of flexible electride in combining with topological electronic properties opens an avenue for electride design and shows great promises in electronic device applications.
In this article, we investigate non-trivial topological features in a heterostructure of extreme magnetoresistance (XMR) materials LaAs and LaBi using density functional theory (DFT). The proposed heterostructure is found to be dynamically stable and shows bulk band inversion with non-trivial Z_{2} topological invariant and a Dirac cone at the surface. In addition, its electron and hole carrier densities ratio is also calculated to investigate the possibility to possess XMR effect. Electrons and holes in the heterostructure are found to be nearly compensated, thereby facilitating it to be a suitable candidate for XMR studies.
The study of topology protected electronic properties is a fascinating topic in present day condensed matter physics research. New topological materials are frequently being proposed and explored through various experimental techniques. Ta$_{3}$SiTe$_{6}$ is a newly predicted topological semimetal with fourfold degenerate nodal-line crossing in absence of spin-orbit coupling (SOC) and an hourglass Dirac loop, when SOC is included. Recent angle-resolved photoemission spectroscopy study in this material, has also confirmed Dirac like dispersions and two nodal-lines near the Fermi energy, protected by nonsymmorphic glide mirror symmetry. In this work, we present the detailed magnetotransport properties of single crystalline Ta$_{3}$SiTe$_{6}$. A nonsaturating magnetoresistance has been observed. Hall measurements reveal hole type charge carriers with high carrier density and a moderate value of carrier mobility. Furthermore, we report a robust planar Hall effect, which persists up to high temperatures. These results validate the nontrivial nature of the electronic band structure.
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