¦ van der Waals gap Septuple layer J § J || T 1/2 J 0,1 || J 0,2 || J 0,3 || J 0,4 ||

A topological insulator is a state of quantum matter that, while being an insulator in the bulk, hosts topologically protected electronic states at the surface. These states open the opportunity to realize a number of new applications in spintronics and quantum computing. To take advantage of their peculiar properties, topological insulators should be tuned in such a way that ideal and isolated Dirac cones are located within the topological transport regime without any scattering channels. Here we report ab-initio calculations, spin-resolved photoemission and scanning tunnelling microscopy experiments that demonstrate that the conducting states can effectively tuned within the concept of a homologous series that is formed by the binary chalcogenides (Bi 2 Te 3 , Bi 2 se 3 and sb 2 Te 3 ), with the addition of a third element of the group IV.

BiTeI has a layered and noncentrosymmetric structure where strong spin-orbit interaction leads to a giant Rashba spin splitting in the bulk bands. We present direct measurements of the bulk band structure obtained with soft x-ray angle-resolved photoemission (ARPES), revealing the three-dimensional Fermi surface. The observed spindle torus shape bears the potential for a topological transition in the bulk by hole doping. Moreover, the bulk electronic structure is clearly disentangled from the two-dimensional surface electronic structure by means of high-resolution and spin-resolved ARPES measurements in the ultraviolet regime. All findings are supported by ab initio calculations.

Feasibility of many emergent phenomena that intrinsic magnetic topological insulators (TIs) may host depends crucially on our ability to engineer and efficiently tune their electronic and magnetic structures. Here we report on a large family of intrinsic magnetic TIs in the homologous series of the van der Waals compounds (MnBi2Te4)(Bi2Te3)m with m = 0, ⋯, 6. Magnetic, electronic and, consequently, topological properties of these materials depend strongly on the m value and are thus highly tunable. The antiferromagnetic (AFM) coupling between the neighboring Mn layers strongly weakens on moving from MnBi2Te4 (m = 0) to MnBi4Te7 (m = 1) and MnBi6Te10 (m = 2). Further increase in m leads to change of the overall magnetic behavior to ferromagnetic (FM) one for (m = 3), while the interlayer coupling almost disappears. In this way, the AFM and FM TI states are, respectively, realized in the m = 0, 1, 2 and m = 3 cases. For large m numbers a hitherto-unknown topologically nontrivial phase can be created, in which below the corresponding critical temperature the magnetizations of the non-interacting 2D ferromagnets, formed by the MnBi2Te4 building blocks, are disordered along the third direction. The variety of intrinsic magnetic TI phases in (MnBi2Te4)(Bi2Te3)m allows efficient engineering of functional van der Waals heterostructures for topological quantum computation, as well as antiferromagnetic and 2D spintronics.

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