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Core hole resonance is used in X-ray spectroscopy to incisively probe the local electronic states of many-body systems. Here, resonant inelastic X-ray scattering (RIXS) is studied as a function of incident photon energy on Mott insulators SrCuO2 and NiO to examine how resonance states decay into different excitation symmetries at the transition metal M-, L- and K-edges. Quantum interference patterns characteristic of the two major RIXS mechanisms are identified within the data, and used to distinguish the attosecond scale scattering dynamics by which fundamental excitations of a many-body system are created. A function is proposed to experimentally evaluate whether a particular excitation has constructive or destructive interference in the RIXS cross-section, and corroborates other evidence that an anomalous excitation is present at the leading edge of the Mott gap in quasi-one dimensional SrCuO2., Comment: 12 pages, 7 figures

Topological Surface States (TSS) represent new types of two dimensional electron systems with novel and unprecedented properties distinct from any quantum Hall-like or spin-Hall effects. Their Z$_2$ topological order can be realized at room temperatures without magnetic fields and they can be turned into magnets, exotic superconductors or Kondo insulators leading to worldwide interest and activity in the topic. We review the basic concepts defining such topological matter and the experimental discovery via the key experimental probe that revealed the Z$_2$ topological order in the bulk of these spin-orbit interaction dominated insulators for the first time. This review focuses on the key results that demonstrated the fundamental Z$_2$ topological properties such as spin-momentum locking, non-trivial Berry's phases, mirror Chern number, absence of backscattering, bulk-boundary correspondence (topology), protection by time-reversal and other discrete (mirror) symmetries and their remarkable persistence up to the room temperature elaborating on results first briefly discussed in an early review by M.Z. Hasan and C.L. Kane [Rev. of Mod. Phys., 82, 3045 (2010)]. Additionally, key results on broken symmetry phases such as quantum magnetism and superconductivity induced in topological materials are briefly discussed. Topological insulators beyond the Z$_2$ classification such as Topological Crystalline Insulators (TCI) are discussed based on their spin properties (mirror Chern invariants). The experimental methodologies detailed here have been used in most of the subsequent studies of Z$_2$ topological physics in almost all bulk topological insulator materials to this date., Comment: 18 Figures, 23 pages; Invited Review, Accepted for publication, Related papers at http://arxiv.org/abs/1105.0396 and http://scholar.google.com/citations?user=G1Qpy6MAAAAJ&hl=en

Low-dimensional copper oxide lattices naturally manifest electronic states with strong short range quantum entanglement, which are known to lead to remarkable emergent material properties. However the nanometer scale many-body wavefunction is challenging to measure or manipulate in a simple way. In this study, X-ray induced $dd$ electronic transitions are used to suppress spin entanglement across a single lattice site in the spin-1/2 antiferromagnetic chain compound SrCuO$_2$, revealing a class of cuprate magnetic excitations that result from breaking the spin chain. These measurements are the first to employ two closely spaced X-ray resonances of copper (M$_2$ and M$_3$) as a form of natural 2-slit interferometer to distinguish between different types of electronic transition and resolve how they influence the dynamics of nearby spin-entangled electrons., Comment: 14 pages, 4 figures

Single-Dirac-cone topological insulators (TI) are the first experimentally discovered class of three dimensional topologically ordered electronic systems, and feature robust, massless spin-helical conducting surface states that appear at any interface between a topological insulator and normal matter that lacks the topological insulator ordering. This topologically defined surface environment has been theoretically identified as a promising platform for observing a wide range of new physical phenomena, and possesses ideal properties for advanced electronics such as spin-polarized conductivity and suppressed scattering. A key missing step in enabling these applications is to understand how topologically ordered electrons respond to the interfaces and surface structures that constitute a device. Here we explore this question by using the surface deposition of cathode (Cu/In/Fe) and anode materials (NO$_2$) and control of bulk doping in Bi$_2$Se$_3$ from P-type to N-type charge transport regimes to generate a range of topological insulator interface scenarios that are fundamental to device development. The interplay of conventional semiconductor junction physics and three dimensional topological electronic order is observed to generate novel junction behaviors that go beyond the doped-insulator paradigm of conventional semiconductor devices and greatly alter the known spin-orbit interface phenomenon of Rashba splitting. Our measurements for the first time reveal new classes of diode-like configurations that can create a gap in the interface electron density near a topological Dirac point and systematically modify the topological surface state Dirac velocity, allowing far reaching control of spin-textured helical Dirac electrons inside the interface and creating advantages for TI superconductors as a Majorana fermion platform over spin-orbit semiconductors., Comment: 14 pages, 4 Figures

The three-dimensional topological insulator (originally called "topological insulators") is the first example in nature of a topologically ordered electronic phase existing in three dimensions that cannot be reduced to multiple copies of quantum-Hall-like states. Their topological order can be realized at room temperatures without magnetic fields and they can be turned into magnets and exotic superconductors leading to world-wide interest and activity in topological insulators. One of the major challenges in going from quantum Hall-like 2D states to 3D topological insulators is to develop new experimental approaches/methods to precisely probe this novel form of topological-order since the standard tools and settings that work for IQH-state also work for QSH states. The method to probe 2D topological-order is exclusively with charge transport, which either measures quantized transverse conductance plateaus in IQH systems or longitudinal conductance in quantum spin Hall (QSH) systems. In a 3D topological insulator, the boundary itself supports a two dimensional electron gas (2DEG) and transport is not (Z$_2$) topologically quantized. In this paper, we review the birth of momentum- and spin-resolved spectroscopy as a new experimental approach and as a directly boundary sensitive method to study and prove topological-order in three-dimensions via the direct measurements of the topological invariants {$\nu_o$} that are associated with the Z$_2$ topology of the spin-orbit band structure and opposite parity band inversions, which led to the experimental discovery of the first 3D topological insulators. We also discuss how spectroscopic methods are leading to the identification of spin-orbit superconductors that may work as Majorana platforms and can be used to identify topological superconductors - yet another class of new state of matter., Comment: 31 pages, 26 figures, Review article, Comments welcome

The Bi$_2$Se$_3$ class of topological insulators has recently been shown to undergo a superconducting transition upon hole or electron doping (Cu$_x$-Bi$_2$Se$_3$ with T$_C$=3.8$^o$K and Pd$_x$-Bi$_2$Te$_3$ with T$_C$=5$^o$K), raising the possibilities that these are the first known "topological superconductors" or realizes a superconducting state that can be potentially used as Majorana platforms (L.A. Wray \textit{et.al.}, Nature Phys. \textbf{6}, 855-859 (2010)). We use angle resolved photoemission spectroscopy to examine the full details of the spin-orbital groundstates of these materials including Bi$_2$Te$_3$, observing that the spin-momentum locked topological surface states remain well defined and non-degenerate with respect to bulk electronic states at the Fermi level in the optimally doped superconductor and obtaining their experimental Fermi energies. The implications of this unconventional surface (that undergoes superconducting at lower temperatures) topology are discussed, and we also explore the possibility of realizing the same topology in superconducting variants of Bi$_2$Te$_3$ (with T$_C$ $\sim$ 5$^o$K). Characteristics of the experimentally measured three dimensional bulk states are examined in detail for these materials with respect to the superconducting state and topological properties, showing that a single Majorana fermion zero mode is expected to be bound at each superconducting vortex on the surface. Systematic measurements also reveal intriguing renormalization and charge correlation instabilities of the surface-localized electronic modes., Comment: 13 pages, 13 Figures, Accepted for publication in Physical Review B (2011); High resolution figures at http://www.princeton.edu/physics/people/faculty/zahid-hasan/

Topological insulators embody a new state of matter characterized entirely by the topological invariants of the bulk electronic structure rather than any form of spontaneously broken symmetry. Unlike the 2D quantum Hall or quantum spin-Hall-like systems, the three dimensional (3D) topological insulators can host magnetism and superconductivity which has generated widespread research activity in condensed-matter and materials-physics communities. Thus there is an explosion of interest in understanding the rich interplay between topological and the broken-symmetry states (such as superconductivity), greatly spurred by proposals that superconductivity introduced into certain band structures will host exotic quasiparticles which are of interest in quantum information science. The observations of superconductivity in doped Bi_2Se_3 (Cu$_x$Bi$_2$Se$_3$) and doped Bi_2Te_3 (Pd$_x$-Bi$_2$Te$_3$ T$_c$ $\sim$ 5K) have raised many intriguing questions about the spin-orbit physics of these ternary complexes while any rigorous theory of superconductivity remains elusive. Here we present key measurements of electron dynamics in systematically tunable normal state of Cu$_x$Bi$_2$Se$_3$ (x=0 to 12%) gaining insights into its spin-orbit behavior and the topological nature of the surface where superconductivity takes place at low temperatures. Our data reveal that superconductivity occurs (in sample compositions) with electrons in a bulk relativistic kinematic regime and we identify that an unconventional doping mechanism causes the topological surface character of the undoped compound to be preserved at the Fermi level of the superconducting compound, where Cooper pairing occurs at low temperatures. These experimental observations provide important clues for developing a theory of topological-superconductivity in 3D topological insulators., Comment: 13 pages, 4 Figures, High resolution figures at http://www.princeton.edu/physics/people/faculty/zahid-hasan/

Three dimensional topological insulators embody a newly discovered state of matter characterized by conducting spin-momentum locked surface states that span the bulk band gap as demonstrated via spin-resolved ARPES measurements . This highly unusual surface environment provides a rich ground for the discovery of novel physical phenomena. Here we present the first controlled study of the topological insulator surfaces under strong Coulomb, magnetic and disorder perturbations. We have used interaction of iron, with a large Coulomb state and significant magnetic moment as a probe to \textit{systematically test the robustness} of the topological surface states of the model topological insulator Bi$_2$Se$_3$. We observe that strong perturbation leads to the creation of odd multiples of Dirac fermions and that magnetic interactions break time reversal symmetry in the presence of band hybridization. We also present a theoretical model to account for the altered surface of Bi$_2$Se$_3$. Taken collectively, these results are a critical guide in manipulating topological surfaces for probing fundamental physics or developing device applications., Comment: 14 pages, 4 Figures. arXiv admin note: substantial text overlap with arXiv:1009.6216