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We study the surface crystalline and electronic structures of the antiferromagnetic topological insulator MnBi2Te4 using scanning tunneling microscopy/spectroscopy (STM/S), micro(μ)-laser angle-resolved photoemission spectroscopy (ARPES), and density functional theory calculations. Our STM images reveal native point defects at the surface that we identify as BiTe antisites and MnBi substitutions. Bulk X-ray diffraction further evidences the presence of the Mn-Bi intermixing. Overall, our characterizations suggest that the defects concentration is nonuniform within crystals and differs from sample to sample. Consistently, the ARPES and STS experiments reveal that the Dirac point gap of the topological surface state is different for different samples and sample cleavages, respectively. Our calculations show that the antiparallel alignment of the MnBi moments with respect to those of the Mn layer can indeed cause a strong reduction of the Dirac point gap size. The present study provides important insights into a highly debated issue of the MnBi2Te4 Dirac point gap.

Modification of the gap at the Dirac point (DP) in axion antiferromagnetic topological insulator MnBi 2 Te 4 and its electronic and spin structure have been studied by angle- and spin-resolved photoemission spectroscopy (ARPES) under laser excitation at various temperatures (9–35 K), light polarizations and photon energies. We have distinguished both large (60–70 meV) and reduced ( < 20 meV ) gaps at the DP in the ARPES dispersions, which remain open above the Neél temperature ( T N = 24.5 K ). We propose that the gap above T N remains open due to a short-range magnetic field generated by chiral spin fluctuations. Spin-resolved ARPES, XMCD and circular dichroism ARPES measurements show a surface ferromagnetic ordering for the “large gap” sample and apparently significantly reduced effective magnetic moment for the “reduced gap” sample. These observations can be explained by a shift of the Dirac cone (DC) state localization towards the second Mn layer due to structural disturbance and surface relaxation effects, where DC state is influenced by compensated opposite magnetic moments. As we have shown by means of ab-initio calculations surface structural modification can result in a significant modulation of the DP gap.

Topological surface states usually emerge at the boundary between a topological and a conventional insulator. Their precise physical character and spatial localization depend on the complex interplay between the chemical, structural and electronic properties of the two insulators in contact. Using a lattice-matched heterointerface of single and double bilayers of β-antimonene and bismuth selenide, we perform a comprehensive experimental and theoretical study of the chiral surface states by means of microscopy and spectroscopic measurements complemented by first-principles calculations. We demonstrate that, although β-antimonene is a trivial insulator in its free-standing form, it inherits the unique symmetry-protected spin texture from the substrate via a proximity effect that induces outward migration of the topological state. This “topologization” of β-antimonene is found to be driven by the hybridization of the bands from either side of the interface.

We consider a Sturm–Liouville problem with spectral parameter in the boundary conditions. We give a general characteristic of the arrangement of eigenvalues on the real axis (the complex plane), study the structure of root subspaces and the oscillation properties of eigenfunctions, and analyze the basis properties of systems of root functions of this problem in the space L p (0, 1), 1 < p < ∞.

(ProQuest: Abstract omitted; see image)[PUBLICATION ABSTRACT]

Magnetic topological insulators are narrow-gap semiconductor materials that combine non-trivial band topology and magnetic order 1 . Unlike their nonmagnetic counterparts, magnetic topological insulators may have some of the surfaces gapped, which enables a number of exotic phenomena that have potential applications in spintronics 1 , such as the quantum anomalous Hall effect 2 and chiral Majorana fermions 3 . So far, magnetic topological insulators have only been created by means of doping nonmagnetic topological insulators with 3 d transition-metal elements; however, such an approach leads to strongly inhomogeneous magnetic 4 and electronic 5 properties of these materials, restricting the observation of important effects to very low temperatures 2 , 3 . An intrinsic magnetic topological insulator—a stoichiometric well ordered magnetic compound—could be an ideal solution to these problems, but no such material has been observed so far. Here we predict by ab initio calculations and further confirm using various experimental techniques the realization of an antiferromagnetic topological insulator in the layered van der Waals compound MnBi 2 Te 4 . The antiferromagnetic ordering  that MnBi 2 Te 4  shows makes it invariant with respect to the combination of the time-reversal and primitive-lattice translation symmetries, giving rise to a ℤ 2 topological classification; ℤ 2  = 1 for MnBi 2 Te 4 , confirming its topologically nontrivial nature. Our experiments indicate that the symmetry-breaking (0001) surface of MnBi 2 Te 4 exhibits a large bandgap in the topological surface state. We expect this property to eventually enable the observation of a number of fundamental phenomena, among them quantized magnetoelectric coupling 6 – 8 and axion electrodynamics 9 , 10 . Other exotic phenomena could become accessible at much higher temperatures than those reached so far, such as the quantum anomalous Hall effect 2 and chiral Majorana fermions 3 . An intrinsic antiferromagnetic topological insulator, MnBi 2 Te 4 , is theoretically predicted and then realized experimentally, with implications for the study of exotic quantum phenomena.

We consider a spectral problem for a fourth-order ordinary differential equation with spectral parameter in a boundary condition. We study the structure of root spaces and analyze the basis properties in the space L p (0, l ), 1 < p < ∞, of systems of root functions of that problem.

Further to the structure of the intrinsic magnetic topological insulators MnBi2Te4 n(Bi2Te3) with n<4, where index n is the number of quintuple Te-Bi-Te-Bi-Te building blocks inserted between the neighboring septuple Te-Bi-Te-Mn-Te-Bi-Te building blocks, the structure of the members with n=4, 5 and 6 was studied using X-ray powder diffraction. The unit cell parameters and atomic positions were calculated. The obtained and available structural data were summarized to show that the crystal structure of all members of MnBi2Te4 n(Bi2Te3) follows the cubic close packing principle, independently of the space group of the given member. Confocal Raman spectroscopy was then applied. Comparative analysis of the number, frequency, symmetry, and broadening of the vibration modes responsible for the lines in the Raman spectra of the systems with n=1,. . . ,6, as well as MnBi2Te4 (n=0) and Bi2Te3 (n=infinity) has shown that lattice dynamics of MnBi2Te4 n(Bi2Te3) with n>0 overwhelmingly dominates by the cooperative atomic displacements in the quintuple building blocks.

Modification of the gap at the Dirac point (DP) in axion antiferromagnetic topological insulator$${\\hbox {MnBi}}_2 {\\hbox {Te}}_4$$MnBi 2 Te 4 and its electronic and spin structure have been studied by angle- and spin-resolved photoemission spectroscopy (ARPES) under laser excitation at various temperatures (9–35 K), light polarizations and photon energies. We have distinguished both large (60–70 meV) and reduced ($$<20~ \\hbox {meV}$$< 20 meV ) gaps at the DP in the ARPES dispersions, which remain open above the Neél temperature ($$T_{\\mathrm{N}} = 24.5~ \\hbox {K}$$T N = 24.5 K ). We propose that the gap above$$T_{\\mathrm{N}}$$T N remains open due to a short-range magnetic field generated by chiral spin fluctuations. Spin-resolved ARPES, XMCD and circular dichroism ARPES measurements show a surface ferromagnetic ordering for the “large gap” sample and apparently significantly reduced effective magnetic moment for the “reduced gap” sample. These observations can be explained by a shift of the Dirac cone (DC) state localization towards the second Mn layer due to structural disturbance and surface relaxation effects, where DC state is influenced by compensated opposite magnetic moments. As we have shown by means of ab-initio calculations surface structural modification can result in a significant modulation of the DP gap.