Samarium hexaboride crystallizes in a simple cubic structure (space group #221, Pm-3m), but its properties are far from being straightforward. Initially classified as a Kondo insulator born out of its intriguing intermediate valence ground state, SmB6 has been recently predicted to be a strongly correlated topological insulator. The subsequent experimental discovery of surface states has revived the interest in SmB6, and our purpose here is to review the extensive and in many aspects perplexing experimental record of this material. We will discuss both surface and bulk properties of SmB6 with an emphasis on the role of crystal growth and sample preparation. We will also highlight the remaining mysteries and open questions in the field.
Recent photoemission spectra of the perovskite series Sr$_x$Ca$_{1-x}$VO$_3$ revealed strong modifications associated with surface contributions. To study the effect of Coulomb correlations in the bulk and at the surface the quasi-particle spectra are evaluated using the dynamical mean field theory. It is shown that as a result of the reduced coordination number of surface atoms correlation effects are stronger at the surface than in the bulk, in agreement with experiment.
The Mott insulator LaVO$_3$ is known to become metallic if La is replaced by small concentrations of Ca. Since surface quasi-particle spectra of various perovskites are more strongly correlated than their bulk spectra, the coexistence of a metallic bulk and an insulating surface layer might be feasible. To investigate this possibility the dynamical mean field theory is used to evaluate the quasi-particle spectra in the bulk and at the surface of Ca$_x$La$_{1-x}$VO$_3$ for various Ca concentrations.
Shubnikov-de Haas (SdH) oscillations in metallic Bi2Se2.1Te0.9 are studied in magnetic fields up to 35 Tesla. It is demonstrated that two characteristic frequencies determine the quantum oscillations of the conductivity. Angle dependent measurements and calculations of the Berry phase show that the two frequencies F1 and F2 describe oscillations from surface and bulk carriers, respectively. At low magnetic fields, only SdH oscillation from topological surface states can be detected whereas at high magnetic field the bulk oscillations dominate. The origin of the separation of bulk and surface S…
The criteria for strong correlations on surfaces of three-dimensional topological insulators are discussed. Usually, the Coulomb repulsion at such surfaces is too weak for driving a phase transition to a strongly correlated regime. I discuss a mechanism and possibilities of its experimental implementation by which the strength of the Coulomb interaction can be tuned over a wide range. In the strongly interacting regime, the surface states are gapped, even though the topological classification of the bulk band structure predicts gapless surface states.
To investigate valence imbalance phenomena between the surface and bulk in layered manganites, we analyze an eg-orbital degenerate double-exchange model with surfaces for two types of t2g spin structures. We reconfirm that the surface-induced Friedel oscillations occur in the charged structure and that the number of Mn4+ ions on the surface is larger than that in the bulk. This tendency is found to be more significant, when the eg-electron system has Fermi-surface structures with better nesting properties. The behavior of the Friedel oscillations depends on the nesting properties of the Fermi-…
The topology and spin-orbital polarization of two-dimensional (2D) surface electronic states have been extensively studied in this decade. One major interest in them is their close relationship with the parities of the bulk (3D) electronic states. In this context, the surface is often regarded as a simple truncation of the bulk crystal. Here we show breakdown of the bulk-related in-plane rotation symmetry in the topological surface states (TSSs) of the Kondo insulator SmB$_6$. Angle-resolved photoelectron spectroscopy (ARPES) performed on the vicinal SmB$_6$(001)-$p$(2$\times$2) surface showed…
We report bulk Rashba spin splitting (RSS) and associated Dirac surface state in (Bi$_{0.9}$Sb$_{0.1})_2$Se$_3$, exhibiting dominant $p$-type conductivity. We argue from the synchrotron diffraction studies that origin of the bulk RSS is due to a structural transition to a non-centrosymmetric $R3m$ phase below $\sim$ 30 K. The Shubnikov-de Haas Van (SdH) oscillations observed in the magnetoresistance curves at low temperature and the Landau level fan diagram, as obtained from these oscillations, confirm the presence of nontrivial Dirac surface state. The magnetization data at low temperature ex…
In this article, we propose a simple but general scaling relation between interactions in a gapped bulk topological matter and gapless interacting surface states. We explicitly illustrate such a generic bulk-boundary relation (BBR) for a few specific interactions in a topological quantum matter, where we can perform dimensional reduction of a microscopic bulk theory to project out interacting surfaces. We have examined renormalization effects of the gapped bulk fermions on the interacting topological surface fermions. As simple applications, we utilize effective interacting quantum fields impl…
We study the evolution of the spectral function with progressive hole doping in a Mott insulator, $La_{1-x}Ca_xVO_3$ with $x$ = 0.0 - 0.5. The spectral features indicate a bulk-to-surface metal-insulator transition in this system. Doping dependent changes in the bulk electronic structure are shown to be incompatible with existing theoretical predictions. An empirical description based on the single parameter, $U/W$, is shown to describe consistently the spectral evolution.
A hallmark of Weyl semimetal is the existence of surface Fermi arcs connecting two surface-projected Weyl nodes with opposite chiralities. An intriguing question is what determines the connectivity of surface Fermi arcs, when multiple pairs of Weyl nodes are present. To answer this question, we first show that the locations of surface Fermi arcs are predominantly determined by the condition that the Zak phase integrated along the normal direction to the surface is $π$. More importantly, the Zak phase can reveal the peculiar topological structure of Weyl semimetal directly in the bulk. Here, we…
We derive a bulk-boundary correspondence for three-dimensional (3D) symmetry-protected topological (SPT) phases with unitary symmetries. The correspondence consists of three equations that relate bulk properties of these phases to properties of their gapped, symmetry-preserving surfaces. Both the bulk and surface data appearing in our correspondence are defined via a procedure in which we gauge the symmetries of the system of interest and then study the braiding statistics of excitations of the resulting gauge theory. The bulk data is defined in terms of the statistics of bulk excitations, whi…
We investigate the possibility that the surface of a strongly coupled electron-phonon system behaves differently from the bulk when the relevant parameters are inhomogeneous due to the presence of the interface. We consider parameter variations which make the surface either more metallic or more insulating than the bulk. While it appears impossible to stabilize a truly insulating surface when the bulk is metallic, the opposite situation can be realized. A metallic surface can indeed be decoupled from a bipolaronic insulator realized in the bulk.
Whereas bulk bismuth supports very-high mobility, light, Dirac electrons and holes in its interior, its boundaries support a layer of heavy electrons in surface states formed by spin orbit interaction in the presence of the surface electric field. Small diameter d trigonal Bi nanowires (30 nm < d < 200 nm) were studied via magnetotransport at low temperatures and for fields up to 14 T in order to investigate the role of surfaces in electronic transport. A two-dimensional behavior was expected for surface charges; however we found instead a three-dimensional behavior, with a rich spectrum of La…
Some magnetoelectric multiferroics have a canted spin structure that can be described by a Dzyaloshinkii-Moriya coupling. We calculate properties and features expected for surface and bulk magnon polaritons in such media with a linear magnetoelectric interaction for the case of transverse electric polarisation. The dielectric polarisation and magnetisation of weak ferromagnetism are constrained to lie in the plane parallel to the surface. We examine a geometry with the polarisation oriented in the film plane and present numerical results for the transverse electric polarisation. Particular att…
We present atomic scale images of a V_2O_3 (0001)-surface, which show that the surface is susceptible to reconstruction by dimerization of vanadium ions. The atomic order of the surface depends sensitively on the surface preparation. Scanning tunneling spectroscopy proves a dimerized surface has a gap in the electronic density of states at the Fermi energy, while a surface prepared by sputtering and successive annealing shows no dimerization and no gap. Photoemission spectra depend sensitively on the surface structure and are consistent with scanning tunneling spectroscopy data. The measuremen…
Establishing the relation between the ubiquitous antiferromagnetism in the non-superconducting parent compounds of unconventional superconductors and their superconducting phase is believed to be important for the understanding of the complex physics in these materials. Going from the bulk systems to thin films strongly affects the phase diagram of unconventional superconductors. For Fe$_{1+y}$Te, the parent compound of the Fe$_{1+y}$Se$_{1-x}$Te$_x$ superconductors, bulk sensitive neutron diffraction has revealed an in-plane oriented bicollinear antiferromagnetic structure. Here, we show by s…
In the flurry of experiments looking for topological insulator materials, it has been recently discovered that some bulk metals very close to topological insulator electronic states, support the same topological surface states that are the defining characteristic of the topological insulator. First observed in spin-polarized ARPES in Sb (D. Hsieh et al. Science 323, 919 (2009)), the helical surface states in the metallic systems appear to be robust to at least mild disorder. We present here a theoretical investigation of the nature of these "helical metals" - bulk metals with helical surface s…
The role of "Fermi arc" surface-quasiparticle states in "topological metals" (where some Fermi surface sheets have non-zero Chern number) is examined. They act as "Fermi-level plumbing" conduits that transfer quasiparticles among groups of apparently-disconnected Fermi sheets with non-zero Chern numbers to maintain equality of their chemical potentials, which is required by gauge invariance. Fermi arcs have a chiral tangential attachment to the surface projections of sheets of the bulk Fermi Surface: the total Chern number of each projection equals the net chirality of arc-attachments to it. I…
Identifying the effects of surface-bulk coupling is a key challenge towards exploiting the topological nature of the surface states in many available three-dimensional topological `metals'. Here we combine an effective-model calculation and an ab-initio slab calculation to study the effects of the lowest order surface-bulk interaction: the hybridization. In the effective-model study, we discretize an established low-energy effective four-band model and introduce the hybridization between the surface bands and bulk bands in the spirit of the Fano model. We find that the hybridization enhances t…
We present a quantitative microscopic theory of the disorder- and phonon-induced coupling between surface and bulk states in topological insulator (TI) films. We find a simple structure for the surface-to-bulk scattering matrix elements and confirm the importance of bulk-surface coupling in transport and photoemission experiments, assessing its dependence on temperature, carrier density, film thickness and particle-hole asymmetry.
Recent studies suggest that an exemplary Kondo insulator SmB6 belongs to a new class of topological insulators (TIs), in which non-trivial spin-polarized metallic states emerge on surface upon the formation of Kondo hybridization gap in the bulk. Remarkably, the bulk resistivity reaches more than 20 Ohm cm at 4 K, making SmB6 a candidate for a so-called bulk-insulating TI. We here investigate optical-pulse responses of SmB6 by pump-and-probe photoemission spectroscopy. Surface photovoltage effect is observed below ~90 K. This indicates that an optically-active band bending region develops bene…
BiTeI has a layered and non-centrosymmetric structure where strong spin-orbit interaction leads to a giant spin splitting in the bulk bands. Here we present high-resolution angle-resolved photoemission (ARPES) data in the UV and soft x-ray regime that clearly disentangle the surface from the bulk electronic structure. Spin-resolved UV-ARPES measurements on opposite, non-equivalent surfaces show identical spin structures, thus clarifying the surface state character. Soft x-ray ARPES data clearly reveal the spindle-torus shape of the bulk Fermi surface, induced by the spin-orbit interaction.
The surface states of a 3D topological insulator (TI) exhibit topological protection against backscattering. However, the contribution of bulk electrons to the transport data is an impediment to the topological protection of surface. We report the tuning of the chemical potential in the bulk of Bi2Se2Te TI thin films, pinning it near the center of the bulk band gap, thereby suppressing the bulk carriers. The temperature dependent resistance of these films shows activated behavior down to 50K, followed by a metallic transition at lower temperatures, a hallmark of the robustness of TI surface st…
We performed a comprehensive angle-resolved photoemission spectroscopy study of the electronic band structure of LaOFeAs single crystals. We found that samples cleaved at low temperature show an unstable and highly complicated band structure, whereas samples cleaved at high temperature exhibit a stable and clearer electronic structure. Using \emph{in-situ} surface doping with K and supported by first-principles calculations, we identify both surface and bulk bands. Our assignments are confirmed by the difference in the temperature dependence of the bulk and surface states.
We use circular dichroism (CD) in time- and angle-resolved photoemission spectroscopy (trARPES) to measure the femtosecond charge dynamics in the topological insulator (TI) Bi$_{2}$Te$_{3}$. We detect clear CD signatures from topological surface states (TSS) and surface resonance (SR) states. In time-resolved measurements, independently from the pump polarization or intensity, the CD shows a dynamics which provides access to the unexplored electronic evolution in unoccupied states of Bi$_{2}$Te$_{3}$. In particular, we are able to disentangle the unpolarized electron dynamics in the bulk state…
High-resolution scanning tunneling microscopy (STM) measurements on BaFe2As2-one of the parent compounds of the iron-based superconductors-reveals a (1x1) As-terminated unit cell on the (001) surface. However, there are significant differences of the surface unit cell compared to the bulk: only one of the two As atoms in the unit cell is imaged and domain walls between different (1x1) regions display a C2 symmetry at the surface. It should have been C2v if the STM image reflected the geometric structure of the surface or the orthorhombic bulk. The inequivalent As atoms and the bias dependence …
The archetypical 3D topological insulators Bi2Se3, Bi2Te3 and Sb2Te3 commonly exhibit high bulk conductivities, hindering the characterization of the surface state charge transport. The optimally doped topological insulators Bi2Te2Se and Bi2-xSbxTe2S, however, allow for such characterizations to be made. Here we report the first experimental comparison of the topological surface states and bulk conductances of Bi2Te2Se and Bi1.1Sb0.9Te2S, based on temperature-dependent high-pressure measurements. We find that the surface state conductance at low temperatures remains constant in the face of ord…
We present an angle resolved photoemission study of the surface and bulk electronic structure of the single layer ruthenate Sr$_2$RuO$_4$. As the early studies of its electronic structure by photoemission and scanning tunneling microscopy were confronted with a problem of surface reconstruction, surface aging was previously proposed as a possible remedy to access the bulk states. Here we suggest an alternative way by demonstrating that, in the case of Sr$_2$RuO$_4$, circularly polarised light can be used to disentangle the signals from the bulk and surface layers, thus opening the possibility …
We show that in the angle resolved photoemission spectroscopy (ARPES) near-surface induced fields can be useful for disentangling the surface and bulk related emission. The jump of the dielectric function at the interface results in a nonzero term $\operatorname{div}\textbf{A}$ in the photoemission matrix element. The term happens to be significant approximately within the first unit cell and leads to the circular dichroism for the states localized therein. As an example we use ARPES spectra of an YBa$_2$Cu$_3$O$_{7-δ}$ crystal to distinguish between the overdoped surface related component and…
Disentangling bulk and surface states in the electronic structure of PtBi$_2$(0001)
Norwegian University of Science and Technology（挪威科技大学）；University of Amsterdam（阿姆斯特丹大学）；Instituto Balseiro, Univ. Nacional de Cuyo（昆多国立大学巴尔塞罗研究所）；MAX IV Laboratory, Lund University（隆德大学MAX IV实验室）
Bulk and surface state contributions to the electrical resistance of single-crystal samples of the topological Kondo insulator compound SmB6 are investigated as a function of crystal thickness and surface charge density, the latter tuned by ionic liquid gating with electrodes patterned in a Corbino disk geometry on a single surface. By separately tuning bulk and surface conduction channels, we show conclusive evidence for a model with an insulating bulk and metallic surface states, with a crossover temperature that depends solely on the relative contributions of each conduction channel. The su…
We explore the temperature dependent magnetoresistance of bulk insulating topological insulator thin films. Thin films of Bi2Se2Te and BiSbTeSe1.6 were grown using Pulsed Laser Deposition technique and subjected to transport measurements. Magnetotransport measurements indicate a non-saturating linear magnetoresistance (LMR) behavior at high magnetic field values. We present a careful analysis to explain the origin of LMR taking into consideration all the existing models of LMR. Here we consider that the bulk insulating states and the metallic surface states constitute two parallel conduction c…
Unconventional surface states protected by non-trivial bulk orders are sources of various exotic quantum transport in topological materials. One prominent example is the unique magnetic orbit, so-called Weyl orbit, in topological semimetals where two spatially separated surface Fermi-arcs are interconnected across the bulk. The recent observation of quantum Hall states in Dirac semimetal Cd3As2 bulks have drawn attention to the novel quantization phenomena possibly evolving from the Weyl orbit. Here we report surface quantum oscillation and its evolution into quantum Hall states in Cd3As2 thin…
We report temperature and thermal-cycling dependence of surface and bulk structures of double-layered perovskite Sr3Ru2O7 single crystals. The surface and bulk structures were investigated using low-energy electron diffraction (LEED) and single-crystal X-ray diffraction (XRD) techniques, respectively. Single-crystal XRD data is in good agreement with previous reports for the bulk structure with RuO6 octahedral rotation, which increases with decreasing temperature (~ 6.7(6)degrees at 300 K and ~ 8.1(2) degrees at 90 K). LEED results reveal that the octahedra at the surface are much more distort…
We present the Fermi-surface map of the spin-chiral bulk states for the non-centrosymmetric semiconductor BiTeI using de Haas-van Alphen and Shubnikov-de Haas oscillations. We identify two distinct Fermi surfaces with a unique spindle-torus-type topology and the non-trivial Berry phases, confirming the spin chirality with oppositely circulating spin-texture. Near the quantum limit at high magnetic fields, we find a substantial Zeeman effect with an effective g-factor of ~ 60 for the Rashba-split Fermi surfaces. These findings provide clear evidence of strong Rashba and Zeeman coupling in the b…
We investigate the bulk band structures and the surface states of Bi2Se3 and Bi2Te3 topological insulators using first-principles many-body perturbation theory based on the GW approximation. The quasiparticle self-energy corrections introduce significant changes to the bulk band structures, while their effect on the band gaps is opposite in the band-inversion regime compared to the usual situation without band inversion. Parametrized "scissors operators" derived from the bulk studies are then used to investigate the electronic structure of slab models which exhibit topologically protected surf…
The hydrodynamic description of the Fermi arc surface states is proposed. In view of the strong suppression of scattering on impurities, the hydrodynamic regime for Fermi arc states should be, in principle, plausible. By using the kinetic theory, the Fermi arc hydrodynamics is derived and the corresponding effects on the bulk flow and surface collective modes are studied. For the bulk flow, the key effect of the proposed Fermi arc hydrodynamics is the modification of the corresponding boundary conditions. In a slab geometry, it is shown that, depending on the transfer rates between the surface…
Surface of quantum materials often exhibits significantly different behavior than the bulk due to changed topologies and symmetry protections. The outstanding problem is to find out if the exoticity of a material is linked to the changed topology at the surface or it is a bulk property. Hard x-ray photoemission spectroscopy (HAXPES) is a significantly bulk sensitive technique (escape depth of valence electrons is about 40 Å for 6 keV photon energy) and the probing depth can be tuned by changing the electron emission angle. Therefore, HAXPES is often used to reveal the surface-bulk differences …
