First-principles band theory, properly augmented by topological considerations, has provided a remarkably successful framework for predicting new classes of topological materials. This Colloquium discusses the underpinnings of the topological band theory and its materials applications.

Colloquium : Topological band theory

A modern, graduate-level introduction to many-body physics in condensed matter, this textbook explains the tools and concepts needed for a research-level understanding of the correlated behavior of quantum fluids. Starting with an operator-based introduction to the quantum field theory of many-body physics, this textbook presents the Feynman diagram approach, Green's functions and finite-temperature many-body physics before developing the path integral approach to interacting systems. Special chapters are devoted to the concepts of Fermi liquid theory, broken symmetry, conduction in disordered systems, superconductivity and the physics of local-moment metals. A strong emphasis on concepts and numerous exercises make this an invaluable course book for graduate students in condensed matter physics. It will also interest students in nuclear, atomic and particle physics.

Introduction to Many-Body Physics

The Kondo insulator SmB6 has long been known to exhibit low-temperature transport anomalies whose origin is of great interest. Here we uniquely access the surface electronic structure of the anomalous transport regime by combining state-of-the-art laser and synchrotron-based angle-resolved photoemission techniques. We observe clear in-gap states (up to ~4 meV), whose temperature dependence is contingent on the Kondo gap formation. In addition, our observed in-gap Fermi surface oddness tied with the Kramers' point topology, their coexistence with the two-dimensional transport anomaly in the Kondo hybridization regime, as well as their robustness against thermal recycling, taken together, collectively provide strong evidence for protected surface metallicity with a Fermi surface whose topology is consistent with the theoretically predicted topological Fermi surface. Our observations of systematic surface electronic structure provide the fundamental electronic parameters for the anomalous Kondo ground state of correlated electron material SmB6.

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Surface electronic structure of the topological Kondo-insulator candidate correlated electron system SmB6.

A topological insulator (TI) is an unusual quantum state in which the insulating bulk is topologically distinct from vacuum, resulting in a unique metallic surface that is robust against time-reversal invariant perturbations. The surface transport, however, remains difficult to isolate from the bulk conduction in most existing TI crystals (particularly Bi2Se3, Bi2Te3 and Sb2Te3) due to impurity caused bulk conduction. We report in large crystals of topological Kondo insulator (TKI) candidate material SmB6 the thickness-independent surface Hall effects and non-local transport, which persist after various surface perturbations. These results serve as proof that at low temperatures SmB6 has a metallic surface that surrounds an insulating bulk, paving the way for transport studies of the surface state in this proposed TKI material.

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Surface Hall Effect and Nonlocal Transport in SmB6: Evidence for Surface Conduction

In the Kondo insulator samarium hexaboride (SmB6), strong correlation and band hybridization lead to an insulating gap and a diverging resistance at low temperature. The resistance divergence ends at about 3 kelvin, a behavior that may arise from surface conductance. We used torque magnetometry to resolve the Fermi surface topology in this material. The observed oscillation patterns reveal two Fermi surfaces on the (100) surface plane and one Fermi surface on the (101) surface plane. The measured Fermi surface cross sections scale as the inverse cosine function of the magnetic field tilt angles, which demonstrates the two-dimensional nature of the conducting electronic states of SmB6.

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Two-dimensional Fermi surfaces in Kondo insulator SmB6

Recent theoretical calculations and experimental results suggest that the strongly correlated material SmB6 may be a realization of a topological Kondo insulator. We have performed an angle-resolved photoemission spectroscopy study on SmB6 in order to elucidate elements of the electronic structure relevant to the possible occurrence of a topological Kondo insulator state. The obtained electronic structure in the whole three-dimensional momentum space reveals one electron-like 5d bulk band centered at the X point of the bulk Brillouin zone that is hybridized with strongly correlated f electrons, as well as the opening of a Kondo band gap (Delta(B) similar to 20 meV) at low temperature. In addition, we observe electron-like bands forming three Fermi surfaces at the center Gamma point and boundary (X) over bar point of the surface Brillouin zone. These bands are not expected from calculations of the bulk electronic structure, and their observed dispersion characteristics are consistent with surface states. Our results suggest that the unusual low-temperature transport behavior of SmB6 is likely to be related to the pronounced surface states sitting inside the band hybridization gap and/or the presence of a topological Kondo insulating state.

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Surface and bulk electronic structure of the strongly correlated system SmB 6 and implications for a topological Kondo insulator

We report angle-resolved photoemission spectroscopy on two families of high-temperature superconductors (${\mathrm{Ca}}_{x}{\mathrm{La}}_{1\ensuremath{-}x}){\mathrm{(Ba}}_{1.75\ensuremath{-}x}$ La ${}_{0.25+x}{\mathrm{)Cu}}_{3}{\mathrm{O}}_{y}$ with $x=0.1$ (${T}_{c}^{\mathrm{max}}=56$ K) and $x=0.4$ (${T}_{c}^{\mathrm{max}}=82$ K). The Fermi surface (FS) is found to be independent of $x$ or $y$, and its size indicates extreme sample-surface overdoping. This universal FS allows the comparison of dynamical properties between superconductors of similar structure and identical doping, but different ${T}_{c}^{\mathrm{max}}$. We find that the high-energy ($|E|g50$ meV) nodal velocity in the $x=0.4$ family is higher than in the $x=0.1$ family. The implied correlation between ${T}_{c}^{\mathrm{max}}$ and the hopping rate $t$ supports the notion of kinetic energy driven superconductivity in the cuprates. We also find that the antinodal gap is higher for the $x=0.4$ family.

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Linking dynamic and thermodynamic properties of cuprates: An angle-resolved photoemission study of ( Ca x La 1 − x ) (Ba 1.75 − x La 0.25 + x )Cu 3 O y ( x = 0.1 and 0.4)

R. S. Dhaka

Papers

Surface and bulk electronic structure of the strongly correlated system SmB 6 and implications for a topological Kondo insulator

Linking dynamic and thermodynamic properties of cuprates: An angle-resolved photoemission study of ( Ca x La 1 − x ) (Ba 1.75 − x La 0.25 + x )Cu 3 O y ( x = 0.1 and 0.4)