Prediction and observation of an antiferromagnetic topological insulator.

Magnetic topological insulators are narrow-gap semiconductor materials that combine non-trivial band topology and magnetic order1. 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 spintronics1, such as the quantum anomalous Hall effect2 and chiral Majorana fermions3. So far, magnetic topological insulators have only been created by means of doping nonmagnetic topological insulators with 3d transition-metal elements; however, such an approach leads to strongly inhomogeneous magnetic4 and electronic5 properties of these materials, restricting the observation of important effects to very low temperatures2,3. 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 MnBi2Te4. The antiferromagnetic ordering  that MnBi2Te4  shows makes it invariant with respect to the combination of the time-reversal and primitive-lattice translation symmetries, giving rise to a ℤ2 topological classification; ℤ2 = 1 for MnBi2Te4, confirming its topologically nontrivial nature. Our experiments indicate that the symmetry-breaking (0001) surface of MnBi2Te4 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 coupling6-8 and axion electrodynamics9,10. Other exotic phenomena could become accessible at much higher temperatures than those reached so far, such as the quantum anomalous Hall effect2 and chiral Majorana fermions3.

Dramatic Plasmon Response to the Charge-Density-Wave Gap Development in 1T-TiSe_{2}.

1T-TiSe_{2} is one of the most studied charge density wave (CDW) systems, not only because of its peculiar properties related to the CDW transition, but also due to its status as a promising candidate of exciton insulator signaled by the proposed plasmon softening at the CDW wave vector. Using high-resolution electron energy loss spectroscopy, we report a systematic study of the temperature-dependent plasmon behaviors of 1T-TiSe_{2}. We unambiguously resolve the plasmon from phonon modes, revealing the existence of Landau damping to the plasmon at finite momentums, which does not support the plasmon softening picture for exciton condensation. Moreover, we discover that the plasmon lifetime at zero momentum responds dramatically to the band gap evolution associated with the CDW transition. The interband transitions near the Fermi energy in the normal phase are demonstrated to serve as a strong damping channel of plasmons, while such a channel in the CDW phase is suppressed due to the CDW gap opening, which results in the dramatic tunability of the plasmon in semimetals or small-gap semiconductors.

Surface dynamics on submonolayer Pb/Cu(001) surfaces.

The interplay of the atomic structure and phonon spectra in a variety of two dimensional phases forming during submonolayer Pb adsorption on a Cu(001) surface has been investigated using embedded atom method interatomic interaction potentials. Complementary calculations of the equilibrium atomic structure of these phases were performed using density functional theory. It has been shown that the dynamic stability of the Pb/Cu(001) structures increases with increasing the coverage from 0.375 ML to ultimately 0.6 ML, when a dense Pb layer is formed. The increase of the coverage also results in progressive shift of the Rayleigh mode of the copper surface to higher energy and the appearance of new mixed adsorbate-substrate vibration modes.

Electron-phonon coupling and superconductivity in a 2D Tl-Pb compound on Si(111).

Electron-phonon interaction in a single-layer Tl-Pb compound on Si(111) is investigated within the density-functional theory and linear-response approach in the mixed-basis pseudopotential representation. It is found that phonon-induced scattering of electrons at the Fermi level is primarily determined by surface electronic states responsible for bonding at the interface and by low-energy, predominantly shear-vertical vibrations of adatoms. The contribution of substrate-localized vibrations involved in the electron-phonon scattering turns out to be small. We have also estimated the superconducting transition temperature Tc by solving the linearized gap equation of the Eliashberg theory. An analysis of phonon-mediated transitions for a number of electronic states in the Tl-Pb surface bands showed that the strength of the coupling varies with the binding energy, increasing as it approaches the Fermi level, and significantly depends on the surface band to which the state belongs.

Magnetic and vibrational properties of small chromium clusters on the Cu(111) surface.

The structure and magnetic properties of small Cr clusters, Cr3 and Cr4, adsorbed on the Cu(111) surface have been investigated using density functional theory (DFT) calculations and their vibrational properties have been studied within calculations based on tight-binding second moment approximation interatomic interaction potentials (TBSMA). It has been shown that the magnetic ordering in the Cr clusters significantly affects their crystal structure and symmetry, which influences the vibrational modes of the clusters and nearest neighbor copper atoms. In turn, these modes select potentially possible structures of Cr3 and Cr4, prohibiting the lowest total energy cluster structure as dynamically unstable.

The formation and migration of non-equivalent oxygen vacancies in PrBaCo2-xMxO6-δ, where M = Fe, Co, Ni and Cu.

The ab initio calculated defect formation energies are used for assessment of high-temperature thermodynamic functions that govern the appearance of oxygen vacancies in PrBaCo2-xMxO6-δ, where M = Fe, Co, Ni and Cu. The free energy of oxygen vacancy formation is shown to depend on the dopant and total oxygen content in the cobaltite. The experimentally observed trend for the oxygen vacancy concentration to increase with the atomic number of 3d dopants from Fe to Cu is explained as a result of the decrease of bond strength. The preferable location of oxygen vacancies near impurity atoms is accompanied by an anisotropic redistribution of electronic charge density. The most pronounced development of this effect in the case of iron doping leads to a low probability of tetrahedrally coordinated iron to exist in the layered cobaltites. It is shown that the calculated enthalpies of defect formation satisfactorily explain the experimentally observed changes of oxygen non-stoichiometry in the doped cobaltite. The energy barriers for oxygen jumps are found to vary only weakly at the doping thus suggesting rather insignificant dependence of the oxygen ion conductivity on 3d dopant nature. The earlier findings and results in the present work are indicative of promising properties combination in PrBaCo2-xNixO6-δ for the application as an electrode material in IT-SOFCs.

Publisher's Note: Time-Reversal-Breaking Weyl Fermions in Magnetic Heusler Alloys [Phys. Rev. Lett. 117, 236401 (2016)].

This corrects the article DOI: 10.1103/PhysRevLett.117.236401.

Cubic Rashba Effect in the Surface Spin Structure of Rare-Earth Ternary Materials.

Spin-orbit interaction and structure inversion asymmetry in combination with magnetic ordering is a promising route to novel materials with highly mobile spin-polarized carriers at the surface. Spin-resolved measurements of the photoemission current from the Si-terminated surface of the antiferromagnet TbRh_{2}Si_{2} and their analysis within an ab initio one-step theory unveil an unusual triple winding of the electron spin along the fourfold-symmetric constant energy contours of the surface states. A two-band k·p model is presented that yields the triple winding as a cubic Rashba effect. The curious in-plane spin-momentum locking is remarkably robust and remains intact across a paramagnetic-antiferromagnetic transition in spite of spin-orbit interaction on Rh atoms being considerably weaker than the out-of-plane exchange field due to the Tb 4f moments.

Unique Thickness-Dependent Properties of the van der Waals Interlayer Antiferromagnet MnBi_{2}Te_{4} Films.

Using density functional theory and Monte Carlo calculations, we study the thickness dependence of the magnetic and electronic properties of a van der Waals interlayer antiferromagnet in the two-dimensional limit. Considering MnBi_{2}Te_{4} as a model material, we find it to demonstrate a remarkable set of thickness-dependent magnetic and topological transitions. While a single septuple layer block of MnBi_{2}Te_{4} is a topologically trivial ferromagnet, the thicker films made of an odd (even) number of blocks are uncompensated (compensated) interlayer antiferromagnets, which show wide band gap quantum anomalous Hall (zero plateau quantum anomalous Hall) states. Thus, MnBi_{2}Te_{4} is the first stoichiometric material predicted to realize the zero plateau quantum anomalous Hall state intrinsically. This state has been theoretically shown to host the exotic axion insulator phase.

Evidence of ß-antimonene at the Sb/Bi2Se3 interface.

We report a study of the interface between antimony and the prototypical topological insulator Bi2Se3. Scanning tunnelling microscopy measurements show the presence of ordered domains displaying a perfect lattice match with bismuth selenide. Density functional theory calculations of the most stable atomic configurations demonstrate that the ordered domains can be attributed to stacks of ß-antimonene.

Chemically driven surface effects in polar intermetallic topological insulators A3Bi.

Surface electronic spectra, surface and bulk properties as well as the underlying chemical bonding characteristics in topological insulators with complex bonding patterns are considered for the example of cubic, polar intermetallics KNa2Bi, K3Bi and Rb3Bi (with the general formula A3Bi, A - alkali metal). Chemical bonding in A3Bi has a delocalized, polar character as elucidated by the Bader charge analysis in bulk and at the surface, by real-space bonding indicators and by the maximally localized-Wannier-function technique. We underpin emergent surface features in the electronic spectra that are driven by chemical bonding. The organization of these trivial and topological surface states is juxtaposed with the trends in the Bader charges at the surface and surface contributions to the on-site matrix elements of the ab initio Hamiltonian in the localized basis. The surface states are essentially affected by a large positive or negative on-site contribution induced near the vacuum boundary, where the sign of the contribution depends on the surface termination. Based on our findings, the experimentally observed surface features in the related Na3Bi compound can be correctly interpreted. The listed aspects distinguish the title compounds from the HgX (X - chalcogen) series with the same fingerprint bulk-band dispersion near the Fermi level and similar symmetries, but with covalent bonding character. Surface effects investigated for A3Bi also can be expected for a wide range of compounds of various topological classes with a similar bonding type, and will define their surface reactivity.

Time-Reversal-Breaking Weyl Fermions in Magnetic Heusler Alloys.

Weyl fermions have recently been observed in several time-reversal-invariant semimetals and photonics materials with broken inversion symmetry. These systems are expected to have exotic transport properties such as the chiral anomaly. However, most discovered Weyl materials possess a substantial number of Weyl nodes close to the Fermi level that give rise to complicated transport properties. Here we predict, for the first time, a new family of Weyl systems defined by broken time-reversal symmetry, namely, Co-based magnetic Heusler materials XCo_{2}Z (X=IVB or VB; Z=IVA or IIIA). To search for Weyl fermions in the centrosymmetric magnetic systems, we recall an easy and practical inversion invariant, which has been calculated to be -1, guaranteeing the existence of an odd number of pairs of Weyl fermions. These materials exhibit, when alloyed, only two Weyl nodes at the Fermi level-the minimum number possible in a condensed matter system. The Weyl nodes are protected by the rotational symmetry along the magnetic axis and separated by a large distance (of order 2π) in the Brillouin zone. The corresponding Fermi arcs have been calculated as well. This discovery provides a realistic and promising platform for manipulating and studying the magnetic Weyl physics in experiments.

Interplay of Surface and Dirac Plasmons in Topological Insulators: The Case of Bi_{2}Se_{3}.

We have investigated plasmonic excitations at the surface of Bi_{2}Se_{3}(0001) via high-resolution electron energy loss spectroscopy. For low parallel momentum transfer q_{∥}, the loss spectrum shows a distinctive feature peaked at 104 meV. This mode varies weakly with q_{∥}. The behavior of its intensity as a function of primary energy and scattering angle indicates that it is a surface plasmon. At larger momenta (q_{∥}~0.04 Å^{-1}), an additional peak, attributed to the Dirac plasmon, becomes clearly defined in the loss spectrum. Momentum-resolved loss spectra provide evidence of the mutual interaction between the surface plasmon and the Dirac plasmon of Bi_{2}Se_{3}. The proposed theoretical model accounting for the coexistence of three-dimensional doping electrons and two-dimensional Dirac fermions accurately represents the experimental observations. The results reveal novel routes for engineering plasmonic devices based on topological insulators.

Tuning the Dirac point position in Bi(2)Se(3)(0001) via surface carbon doping.

Angular resolved photoemission spectroscopy in combination with ab initio calculations show that trace amounts of carbon doping of the Bi_{2}Se_{3} surface allows the controlled shift of the Dirac point within the bulk band gap. In contrast to expectation, no Rashba-split two-dimensional electron gas states appear. This unique electronic modification is related to surface structural modification characterized by an expansion of the top Se-Bi spacing of ≈11% as evidenced by surface x-ray diffraction. Our results provide new ways to tune the surface band structure of topological insulators.

Unveiling mode-selected electron-phonon interactions in metal films by helium atom scattering.

The quasi two-dimensional electron gas on a metal film can transmit to the surface even minute mechanical disturbances occurring in the depth, thus allowing the gentlest of all surface probes, helium atoms, to perceive the vibrations of the deepest atoms via the induced surface-charge density oscillations. A density functional perturbation theory (DFPT) and a helium atom scattering study of the phonon dispersion curves in lead films of up to 7 mono-layers on a copper substrate show that: (a) the electron-phonon interaction is responsible for the coupling of He atoms to in-depth phonon modes; and (b) the inelastic HAS intensity from a given phonon mode is proportional to its electron-phonon coupling. The direct determination of mode-selected electron-phonon coupling strengths has great relevance for understanding superconductivity in thin films and two-dimensional systems.

Time-dependent electron phenomena at surfaces.

Femtosecond and subfemtosecond time scales typically rule electron dynamics at metal surfaces. Recent advance in experimental techniques permits now remarkable precision in the description of these processes. In particular, shorter time scales, smaller system sizes, and spin-dependent effects are current targets of interest. In this article, we use state-of-the-art theoretical methods to analyze these refined features of electron dynamics. We show that the screening of localized charges at metal surfaces is created locally in the attosecond time scale, while collective excitations transfer the perturbation to larger distances in longer time scales. We predict that the elastic width of the resonance in excited alkali adsorbates on ferromagnetic surfaces can depend on spin orientation in a counterintuitive way. Finally, we quantitatively evaluate the electron-electron and electron-phonon contributions to the electronic excited states widths in ultrathin metal layers. We conclude that confinement and spin effects are key factors in the behavior of electron dynamics at metal surfaces.

Band structure engineering in topological insulator based heterostructures.

The ability to engineer an electronic band structure of topological insulators would allow the production of topological materials with tailor-made properties. Using ab initio calculations, we show a promising way to control the conducting surface state in topological insulator based heterostructures representing an insulator ultrathin films on the topological insulator substrates. Because of a specific relation between work functions and band gaps of the topological insulator substrate and the insulator ultrathin film overlayer, a sizable shift of the Dirac point occurs resulting in a significant increase in the number of the topological surface state charge carriers as compared to that of the substrate itself. Such an effect can also be realized by applying the external electric field that allows a gradual tuning of the topological surface state. A simultaneous use of both approaches makes it possible to obtain a topological insulator based heterostructure with a highly tunable topological surface state.

Snapshots of Dirac fermions near the Dirac point in topological insulators.

The recent focus on topological insulators is due to the scientific interest in the new state of quantum matter as well as the technology potential for a new generation of THz optoelectronics, spintronics and quantum computations. It is important to elucidate the dynamics of the Dirac fermions in the topologically protected surface state. Hence we utilized a novel ultrafast optical pump mid-infrared probe to explore the dynamics of Dirac fermions near the Dirac point. The femtosecond snapshots of the relaxation process were revealed by the ultrafast optics. Specifically, the Dirac fermion-phonon coupling strength in the Dirac cone was found to increase from 0.08 to 0.19 while Dirac fermions were away from the Dirac point into higher energy states. Further, the energy-resolved transient reflectivity spectra disclosed the energy loss rate of Dirac fermions at room temperature was about 1 meV/ps. These results are crucial to the design of Dirac fermion devices.

Correlated motion of electrons on the Au(111) surface: anomalous acoustic surface-plasmon dispersion and single-particle excitations.

The linear dispersion of the low-dimensional acoustic surface plasmon (ASP) opens perspectives in energy conversion, transport, and confinement far below optical frequencies. Although the ASP exists in a wide class of materials, ranging from metal surfaces and ultrathin films to graphene and topological insulators, its properties are still largely unexplored. Taking Au(111) as a model system, our combined experimental and theoretical study revealed an intriguing interplay between collective and single particle excitations, causing the ASP associated with the Shockley surface state to be embedded within the intraband transitions without losing its sharp character and linear dispersion.

Comment on "Topological insulators in ternary compounds with a honeycomb lattice".

A Comment on the Letter by Zhang et al., Phys. Rev. Lett. 106, 156402 (2011).