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.

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.

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.

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.

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.

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.

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.

Attosecond spectroscopy in condensed matter.

Comprehensive knowledge of the dynamic behaviour of electrons in condensed-matter systems is pertinent to the development of many modern technologies, such as semiconductor and molecular electronics, optoelectronics, information processing and photovoltaics. Yet it remains challenging to probe electronic processes, many of which take place in the attosecond (1 as = 10(-18) s) regime. In contrast, atomic motion occurs on the femtosecond (1 fs = 10(-15) s) timescale and has been mapped in solids in real time using femtosecond X-ray sources. Here we extend the attosecond techniques previously used to study isolated atoms in the gas phase to observe electron motion in condensed-matter systems and on surfaces in real time. We demonstrate our ability to obtain direct time-domain access to charge dynamics with attosecond resolution by probing photoelectron emission from single-crystal tungsten. Our data reveal a delay of approximately 100 attoseconds between the emission of photoelectrons that originate from localized core states of the metal, and those that are freed from delocalized conduction-band states. These results illustrate that attosecond metrology constitutes a powerful tool for exploring not only gas-phase systems, but also fundamental electronic processes occurring on the attosecond timescale in condensed-matter systems and on surfaces.

Long-lived spin waves in a metallic antiferromagnet.

Collective spin excitations in magnetically ordered crystals, called magnons or spin waves, can serve as carriers in novel spintronic devices with ultralow energy consumption. The generation of well-detectable spin flows requires long lifetimes of high-frequency magnons. In general, the lifetime of spin waves in a metal is substantially reduced due to a strong coupling of magnons to the Stoner continuum. This makes metals unattractive for use as components for magnonic devices. Here, we present the metallic antiferromagnet CeCo2P2, which exhibits long-living magnons even in the terahertz (THz) regime. For CeCo2P2, our first-principle calculations predict a suppression of low-energy spin-flip Stoner excitations, which is verified by resonant inelastic X-ray scattering measurements. By comparison to the isostructural compound LaCo2P2, we show how small structural changes can dramatically alter the electronic structure around the Fermi level leading to the classical picture of the strongly damped magnons intrinsic to metallic systems. Our results not only demonstrate that long-lived magnons in the THz regime can exist in bulk metallic systems, but they also open a path for an efficient search for metallic magnetic systems in which undamped THz magnons can be excited.

Ideal two-dimensional electron systems with a giant Rashba-type spin splitting in real materials: surfaces of bismuth tellurohalides.

Spintronics is aimed at actively controlling and manipulating the spin degrees of freedom in semiconductor devices. A promising way to achieve this goal is to make use of the tunable Rashba effect that relies on the spin-orbit interaction in a two-dimensional electron system immersed in an inversion-asymmetric environment. The spin-orbit-induced spin splitting of the two-dimensional electron state provides a basis for many theoretically proposed spintronic devices. However, the lack of semiconductors with large Rashba effect hinders realization of these devices in actual practice. Here we report on a giant Rashba-type spin splitting in two-dimensional electron systems that reside at tellurium-terminated surfaces of bismuth tellurohalides. Among these semiconductors, BiTeCl stands out for its isotropic metallic surface-state band with the Γ-point energy lying deep inside the bulk band gap. The giant spin splitting of this band ensures a substantial spin asymmetry of the inelastic mean free path of quasiparticles with different spin orientations.

Plasmonic nanobilliards: controlling nanoparticle movement using forces induced by swift electrons.

Manipulation of nanoscale objects to build useful structures requires a detailed understanding and control of forces that guide nanoscale motion. We report here observation of electromagnetic forces in groups of nanoscale metal particles, derived from the plasmonic response to the passage of a swift electron beam. At moderate impact parameters, the forces are attractive, toward the electron beam, in agreement with simple image charge arguments. For smaller impact parameters, however, the forces are repulsive, driving the nanoparticle away from the passing electron. Particle pairs are most often pulled together by coupled plasmon modes having bonding symmetry. However, placement of the electron beam between a particle pair pushes the two particles apart by exciting antibonding plasmonic modes. We suggest how the repulsive force could be used to create a nanometer-sized trap for moving and orienting molecular-sized objects.

Mode-selected electron-phonon coupling in superconducting Pb nanofilms determined from He atom scattering.

The electron-phonon coupling (EPC) strength for each phonon mode in superconducting Pb films is measured by inelastic helium atom scattering (IHAS). This surprising ability of IHAS relies on two facts: (a) In ultrathin metal films, the EPC range exceeds the film thickness, thus enabling IHAS to detect most film phonons, even 1 nm below the surface; (b) IHAS scattering amplitudes from single phonons are shown, by first-principle arguments, to be proportional to the respective EPC strengths. Thus IHAS is the first experiment providing mode-selected EPC strengths (mode-lambda spectroscopy).

The effect of spin-orbit coupling on the surface dynamical properties and electron-phonon interaction of Tl(0001).

We present an ab initio study of the effect of spin-orbit coupling on the dynamical properties of the Tl(0001) surface as well as on the electron-phonon interaction at the surface. The calculations based on density-functional theory were carried out using a linear response approach and a mixed-basis pseudopotential method. It is shown that the spin-orbit effects on the phonon spectrum and the electron-phonon interaction at the Fermi level of the surface are weak but conspire to a reduction in the electron-phonon coupling strength by 16%.

Direct observation of electron dynamics in the attosecond domain.

Dynamical processes are commonly investigated using laser pump-probe experiments, with a pump pulse exciting the system of interest and a second probe pulse tracking its temporal evolution as a function of the delay between the pulses. Because the time resolution attainable in such experiments depends on the temporal definition of the laser pulses, pulse compression to 200 attoseconds (1 as = 10(-18) s) is a promising recent development. These ultrafast pulses have been fully characterized, and used to directly measure light waves and electronic relaxation in free atoms. But attosecond pulses can only be realized in the extreme ultraviolet and X-ray regime; in contrast, the optical laser pulses typically used for experiments on complex systems last several femtoseconds (1 fs = 10(-15) s). Here we monitor the dynamics of ultrafast electron transfer--a process important in photo- and electrochemistry and used in solid-state solar cells, molecular electronics and single-electron devices--on attosecond timescales using core-hole spectroscopy. We push the method, which uses the lifetime of a core electron hole as an internal reference clock for following dynamic processes, into the attosecond regime by focusing on short-lived holes with initial and final states in the same electronic shell. This allows us to show that electron transfer from an adsorbed sulphur atom to a ruthenium surface proceeds in about 320 as.

Prominence of Terahertz Acoustic Surface Plasmon Excitation in Gas-Surface Interaction with Metals.

The current understanding of the dynamics of gas-surface interactions is that all of the energy lost in the collision is transferred to vibrations of the target. Electronic excitations were shown to play a marginal role except for cases in which the impinging particles have energies of several electronvolts. Here we show that this picture does not hold for metal surfaces supporting acoustic surface plasmons. Such loss, dressed with a vibronic structure, is shown to make up a prominent energy transfer route down to the terahertz region for Ne atoms scattering off Cu(111) and is expected to dominate for most metals. This mechanism determines, e.g., the drag force acting on telecommunication satellites, which are typically gold-plated to reduce overheating by sunshine. The electronic excitations can be unambiguously discerned from the vibrational ones under mild hyperthermal impact conditions.

Topological Magnetic Materials of the (MnSb2Te4)·(Sb2Te3)n van der Waals Compounds Family.

Using density functional theory, we propose the (MnSb2Te4)·(Sb2Te3)n family of stoichiometric van der Waals compounds that harbor multiple topologically nontrivial magnetic phases. In the ground state, the first three members of the family (n = 0, 1, 2) are 3D antiferromagnetic topological insulators, while for n ≥ 3 a special phase is formed, in which a nontrivial topological order coexists with a partial magnetic disorder in the system of the decoupled 2D ferromagnets, whose magnetizations point randomly along the third direction. Furthermore, due to a weak interlayer exchange coupling, these materials can be field-driven into the FM Weyl semimetal (n = 0) or FM axion insulator states (n ≥ 1). Finally, in two dimensions, we reveal these systems to show intrinsic quantum anomalous Hall and AFM axion insulator states, as well as quantum Hall state, achieved under external magnetic field. Our results demonstrate that MnSb2Te4 is not topologically trivial as was previously believed that opens possibilities of realization of a wealth of topologically nontrivial states in the (MnSb2Te4)·(Sb2Te3)n family.

Evidence for a spin acoustic surface plasmon from inelastic atom scattering.

Closed-shell atoms scattered from a metal surface exchange energy and momentum with surface phonons mostly via the interposed surface valence electrons, i.e., via the creation of virtual electron-hole pairs. The latter can then decay into surface phonons via electron-phonon interaction, as well as into acoustic surface plasmons (ASPs). While the first channel is the basis of the current inelastic atom scattering (IAS) surface-phonon spectroscopy, no attempt to observe ASPs with IAS has been made so far. In this study we provide evidence of ASP in Ni(111) with both Ne atom scattering and He atom scattering. While the former measurements confirm and extend so far unexplained data, the latter illustrate the coupling of ASP with phonons inside the surface-projected phonon continuum, leading to a substantial reduction of the ASP velocity and possibly to avoided crossing with the optical surface phonon branches. The analysis is substantiated by a self-consistent calculation of the surface response function to atom collisions and of the first-principle surface-phonon dynamics of Ni(111). It is shown that in Ni(111) ASP originate from the majority-spin Shockley surface state and are therefore collective oscillation of surface electrons with the same spin, i.e. it represents a new kind of collective quasiparticle: a Spin Acoustic Surface Plasmon (SASP).

Quantum-well-induced giant spin-orbit splitting.

We report on the observation of a giant spin-orbit splitting of quantum-well states in the unoccupied electronic structure of a Bi monolayer on Cu(111). Up to now, Rashba-type splittings of this size have been reported exclusively for surface states in a partial band gap. With these quantum-well states we have experimentally identified a second class of states that show a huge spin-orbit splitting. First-principles electronic structure calculations show that the origin of the spin-orbit splitting is due to the perpendicular potential at the surface and interface of the ultrathin Bi film. This finding allows for the direct possibility to tailor spin-orbit splitting by means of thin-film nanofabrication.

Potential energy landscape for hot electrons in periodically nanostructured graphene.

We explore the spatial variations of the unoccupied electronic states of graphene epitaxially grown on Ru(0001) and observed three unexpected features: the first graphene image state is split in energy; unlike all other image states, the split state does not follow the local work function modulation, and a new interfacial state at +3 eV appears on some areas of the surface. First-principles calculations explain the observations and permit us to conclude that the system behaves as a self-organized periodic array of quantum dots.