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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.

A new kind of magnetically-doped antiferromagnetic (AFM) topological insulators (TIs) with stoichiometry Bi 1.09 Gd 0.06 Sb 0.85 Te 3 has been studied by angle-resolved photoemission spectroscopy (ARPES), superconducting magnetometry (SQUID) and X-ray magnetic circular dichroism (XMCD) with analysis of its electronic structure and surface-derived magnetic properties at different temperatures. This TI is characterized by the location of the Dirac gap at the Fermi level (E F ) and a bulk AFM coupling below the Neel temperature (4–8 K). At temperatures higher than the bulk AFM/PM transition, a surface magnetic layer is proposed to develop, where the coupling between the magnetic moments located at magnetic impurities (Gd) is mediated by the Topological Surface State (TSS) via surface Dirac-fermion-mediated magnetic coupling. This hypothesis is supported by a gap opening at the Dirac point (DP) indicated by the surface-sensitive ARPES, a weak hysteresis loop measured by SQUID at temperatures between 30 and 100 K, XMCD measurements demonstrating a surface magnetic moment at 70 K and a temperature dependence of the electrical resistance exhibiting a mid-gap semiconducting behavior up to temperatures of 100–130 K, which correlates with the temperature dependence of the surface magnetization and confirms the conclusion that only TSS are located at the E F . The increase of the TSS’s spectral weight during resonant ARPES at a photon energy corresponding to the Gd 4 d -4 f edge support the hypothesis of a magnetic coupling between the Gd ions via the TSS and corresponding magnetic moment transfer at elevated temperatures. Finally, the observed out-of-plane and in-plane magnetization induced by synchrotron radiation (SR) due to non-equal depopulation of the TSS with opposite momentum, as seen through change in the Dirac gap value and the k ∥ -shift of the Dirac cone (DC) states, can be an indicator of the modification of the surface magnetic coupling mediated by the TSS.

Polar Rashba-type semiconductor BiTeI doped with magnetic elements constitutes one of the most promising platforms for the future development of spintronics and quantum computing thanks to the combination of strong spin-orbit coupling and internal ferromagnetic ordering. The latter originates from magnetic impurities and is able to open an energy gap at the Kramers point (KP gap) of the Rashba bands. In the current work using angle-resolved photoemission spectroscopy (ARPES) we show that the KP gap depends non-monotonically on the doping level in case of V-doped BiTeI. We observe that the gap increases with V concentration until it reaches 3% and then starts to mitigate. Moreover, we find that the saturation magnetisation of samples under applied magnetic field studied by superconducting quantum interference device (SQUID) magnetometer has a similar behaviour with the doping level. Theoretical analysis shows that the non-monotonic behavior can be explained by the increase of antiferromagnetic coupled atoms of magnetic impurity above a certain doping level. This leads to the reduction of the total magnetic moment in the domains and thus to the mitigation of the KP gap as observed in the experiment. These findings provide further insight in the creation of internal magnetic ordering and consequent KP gap opening in magnetically-doped Rashba-type semiconductors.

Graphene in spintronics is predominantly considered for spin current leads of high performance due to weak intrinsic spin–orbit coupling of the graphene π electrons. Externally induced large spin–orbit coupling opens the possibility of using graphene in active elements of spintronic devices such as the Das-Datta spin field-effect transistor. Here we show that Au intercalation at the graphene–Ni interface creates a giant spin–orbit splitting (~100 meV) of the graphene Dirac cone up to the Fermi energy. Photoelectron spectroscopy reveals the hybridization with Au 5 d states as the source for this giant splitting. An ab initio model of the system shows a Rashba-split spectrum around the Dirac point of graphene. A sharp graphene–Au interface at the equilibrium distance accounts for only ~10 meV spin–orbit splitting and enhancement is due to the Au atoms in the hollow position that get closer to graphene and do not break the sublattice symmetry. The potential use of graphene in spintronic devices is limited by its weak spin–orbit coupling. Marchenko et al. report an enhancement of the spin splitting in graphene due to hybridization with gold 5 d orbitals, showing a very large Rashba spin–orbit splitting of about 100 meV.

Effect of magnetization generated by synchrotron or laser radiation in magnetically-doped and pristine topological insulators (TIs) is presented and analyzed using angle-resolved photoemission spectroscopy. It was found that non-equal photoexcitation of the Dirac cone (DC) states with opposite momenta and spin orientation indicated by the asymmetry in photoemission intensity of the DC states is accompanied by the k || -shift of the DC states relative to the non-spin-polarized conduction band states located at k || = 0. We relate the observed k || -shift to the induced surface in-plane magnetic field and corresponding magnetization due to the spin accumulation. The direction of the DC k || -shift and its value are changed with photon energy in correlation with variation of the sign and magnitude of the DC states intensity asymmetry. The theoretical estimations describe well the effect and predict the DC k || -shift values which corroborate the experimental observations. This finding opens new perspectives for effective local magnetization manipulation.

One of the most promising platforms for spintronics and topological quantum computation is the two-dimensional electron gas (2DEG) with strong spin-orbit interaction and out-of-plane ferromagnetism. In proximity to an s -wave superconductor, such 2DEG may be driven into a topologically non-trivial superconducting phase, predicted to support zero-energy Majorana fermion modes. Using angle-resolved photoemission spectroscopy and ab initio calculations, we study the 2DEG at the surface of the vanadium-doped polar semiconductor with a giant Rashba-type splitting, BiTeI. We show that the vanadium-induced magnetization in the 2DEG breaks time-reversal symmetry, lifting Kramers degeneracy of the Rashba-split surface state at the Brillouin zone center via formation of a huge gap of about 90 meV. As a result, the constant energy contour inside the gap consists of only one circle with spin-momentum locking. These findings reveal a great potential of the magnetically-doped semiconductors with a giant Rashba-type splitting for realization of novel states of matter.

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.

This work aims to study the conditions of topological phase transition (TPT) between the topological and trivial states in the antiferromagnetic topological insulator (AFM TI) MnBi 2 Te 4 and propose some theory about the relationship of this TPT with the possibility of axion-like state realization in this material. Using the density functional approach we have analyzed the changes in the electronic and spin structure of topological surface states (TSSs) and the nearest conduction and valence bands (CB and VB) including the changes in the bulk band gap as well as the Dirac point (DP) gap in TSSs under variation of the spin-orbit coupling strength in the region of the TPT for infinite crystal and slab with a surface both. We have shown that in both cases the TPT occurs with inversion of the contributions of the Bi- p z and Te- p z states of different parity at the gap edges related to change in the gap sign. In the case of surface calculations, the Bi- p z and Te- p z states at the edges of the bulk band gap and their inversion at the TPT point are transformed into the TSSs with an energy gap at the DP. In this case the TPT takes place without closing the band gap, i.e. with a “jump” through zero and the formation of the nonzero gap during such a transition. Our calculations show that the TPT point is also characterized by an inversion of the out-of-plane spin polarization s z at the Γ point for lower and upper parts of the Dirac cone and a significant spatial redistribution of the TSSs between the surface and the bulk. We suppose that the nonzero Dirac gap can have some relationship with the formation of the axion-like state, which presumably couples nonmagnetic spin-orbit and magnetic contributions at the boundary between the topological and trivial phases for a system with parameters close to the TPT conditions. A practically realized system is proposed - the AFM TI with a stoichiometry close to that of MnBi 2 Te 2 Se 2 with partial (about 50%) substitution of Te atoms for Se atoms in MnBi 2 Te 4 which can be an experimental platform for the implementation and experimental analysis of the TPT and the corresponding possibility of the axion-like state realization in Condensed Matter. Besides, such system could serve as a good platform for studying the dynamic axion effect, where the axion field fluctuations are maximised when a small external field is applied to the system which state is close to the TPT.

Using angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT), an experimental and theoretical study of changes in the electronic structure (dispersion dependencies) and corresponding modification of the energy band gap at the Dirac point (DP) for topological insulator (TI) have been carried out with gradual replacement of magnetic Mn atoms by non-magnetic Ge atoms when concentration of the latter was varied from 10% to 75%. It was shown that when Ge concentration increases, the bulk band gap decreases and reaches zero plateau in the concentration range of 45–60% while trivial surface states (TrSS) are present and exhibit an energy splitting of 100 and 70 meV in different types of measurements. It was also shown that TSS disappear from the measured band dispersions at a Ge concentration of about 40%. DFT calculations of band structure were carried out to identify the nature of observed band dispersion features and to analyze the possibility of magnetic Weyl semimetal state formation in this system. These calculations were performed for both antiferromagnetic (AFM) and ferromagnetic (FM) ordering types while the spin-orbit coupling (SOC) strength was varied or a strain (compression or tension) along the c-axis was applied. Calculations show that two different series of topological phase transitions (TPTs) may be implemented in this system, depending on the magnetic ordering. In the case of AFM ordering, the transition between TI and the trivial insulator phase passes through the Dirac semimetal state, whereas for FM phase such route admits three intermediate states instead of one (TI—Dirac semimetal—Weyl semimetal—Dirac semimetal—trivial insulator). Weyl points that form in the FM system along the direction annihilate when either the SOC strength decreases or a sufficient tensile strain is applied, which is accompanied by the corresponding TPTs. Model calculations of the influence of local magnetic ordering in AFM were carried out by alternating Mn layers with Ge-doped layers and showed that the magnetic Weyl semimetal state in this system is reachable at a Ge concentration of approximately 40% without application of any external magnetic fields.

Experimental investigations of antiferromagnetic topological insulator MnBi 2 Te 4 have shown that the energy gap in samples may vary in a wide range. Since the energy gap is a key parameter of this system when used in developing new functional electronic devices, the reason for variation of the MnBi 2 Te 4 energy gap at the Dirac point and its possible interrelation with magnetic interactions are matters of great importance and call for thorough analysis. To elucidate factors influencing the energy gap, we analyzed the variation of the electronic structure of the given topological insulator with surface van der Waals gap. Calculation data have shown that the energy gap at such structure modifications may vary in a wide range from 80–88 meV to 4–5 meV because of an intense spatial redistribution of topological surface states between septuple-layer MnBi 2 Te 4 blocks with oppositely directed Mn magnetic moments. Our results suggest that the spatial localization of topological surface states is a primary factor governing the value of the energy gap, this localization being strongly dependent on structure modifications on the crystal surface.