The first-principles band theory paradigm has been a key player not only in the process of discovering new classes of topologically interesting materials, but also for identifying salient characteristics of topological states, enabling direct and sharpened confrontation between theory and experiment. We begin this review by discussing underpinnings of the topological band theory, which basically involves a layer of analysis and interpretation for assessing topological properties of band structures beyond the standard band theory construct. Methods for evaluating topological invariants are delineated, including crystals without inversion symmetry and interacting systems. The extent to which theoretically predicted properties and protections of topological states have been verified experimentally is discussed, including work on topological crystalline insulators, disorder/interaction driven topological insulators (TIs), topological superconductors, Weyl semimetal phases, and topological phase transitions. Successful strategies for new materials discovery process are outlined. A comprehensive survey of currently predicted 2D and 3D topological materials is provided. This includes binary, ternary and quaternary compounds, transition metal and f-electron materials, Weyl and 3D Dirac semimetals, complex oxides, organometallics, skutterudites and antiperovskites. Also included is the emerging area of 2D atomically thin films beyond graphene of various elements and their alloys, functional thin films, multilayer systems, and ultra-thin films of 3D TIs, all of which hold exciting promise of wide-ranging applications. We conclude by giving a perspective on research directions where further work will broadly benefit the topological materials field.

Topological insulators (TIs) are a new type of electronic materials in which the nontrivial insulating bulk band topology governs conducting boundary states with embedded spin-momentum locking. Such edge states are more robust in a two-dimensional (2D) TI against scattering by nonmagnetic impurities than in its three-dimensional (3D) variant, because in 2D the two helical edge states are protected from the only possible backscattering. This makes the 2D TI family a better candidate for coherent spin transport and related applications. While several 3D TIs are already synthesized experimentally, physical realization of 2D TI is so far limited to hybrid quantum wells with a tiny bandgap that does not survive temperatures above 10 K. Here, combining first-principles calculations and scanning tunneling microscopy/spectroscopy (STM/STS) experimental studies, we report nontrivial 2D TI phases in 2-monolayer (2-ML) and 4-ML Bi(110) films with large and tunable bandgaps determined by atomic buckling of Bi(110) films. The gapless edge states are experimentally detected within the insulating bulk gap at 77 K. The band topology of ultrathin Bi(110) films is sensitive to atomic buckling. Such buckling is sensitive to charge doping and could be controlled by choosing different substrates on which Bi(110) films are grown.

Both theoretical and experimental studies of topological phases in non-Hermitian systems have made a remarkable progress in the last few years of research. In this article, we review the key concepts pertaining to topological phases in non-Hermitian Hamiltonians with relevant examples and realistic model setups. Discussions are devoted to both the adaptations of topological invariants from Hermitian to non-Hermitian systems, as well as origins of new topological invariants in the latter setup. Unique properties such as exceptional points and complex energy landscapes lead to new topological invariants including winding number/vorticity defined solely in the complex energy plane, and half-integer winding/Chern numbers. New forms of Kramers degeneracy appear here rendering distinct topological invariants. Modifications of adiabatic theory, time-evolution operator, biorthogonal bulk-boundary correspondence lead to unique features such as topological displacement of particles, 'skin-effect', and edge-selective attenuated and amplified topological polarizations without chiral symmetry. Extension and realization of topological ideas in photonic systems are mentioned. We conclude with discussions on relevant future directions, and highlight potential applications of some of these unique topological features of the non-Hermitian Hamiltonians.

We use first-principles electronic structure calculations to predict a new class of two-dimensional (2D) topological insulators (TIs) in binary compositions of group III elements (B, Al, Ga, In, and Tl) and bismuth (Bi) in a buckled honeycomb structure. We identify band inversions in pristine GaBi, InBi, and TlBi bilayers, with gaps as large as 560 meV, making these materials suitable for room-temperature applications. Furthermore, we demonstrate the possibility of strain engineering in that the topological phase transition in BBi and AlBi could be driven at ∼6.6% strain. The buckled structure allows the formation of two different topological edge states in the zigzag and armchair edges. More importantly, isolated Dirac-cone edge states are predicted for armchair edges with the Dirac point lying in the middle of the 2D bulk gap. A room-temperature bulk band gap and an isolated Dirac cone allow these states to reach the long-sought topological spin-transport regime. Our findings suggest that the buckled honeycomb structure is a versatile platform for hosting nontrivial topological states and spin-polarized Dirac fermions with the flexibility of chemical and mechanical tunability.

S2 MethodsReagents. Bismuth nitrate (Bi(NO3)35H2O, Alfa Aesar, 99.9%), selenourea (SeC(NH2)2, Alfa Aesar, 99.9%), potassium hydroxide (KOH, S D Fine-Chem Limited (SDFCL)), sodium hydroxide (NaOH, SDFCL), Disodium EDTA (C10H14O8Na2N2H2O, SDFCL) and ethanol were used without any further purification.Synthesis procedure. 100 mg (0.206 mmol) of Bi(NO3)35H2O, 12.7 mg (0.103 mmol) of SeC(NH2)2 and 306.8 mg (0.824 mmol) of disodium EDTA were sequentially added at a 5 minutes interval into 20 ml water in a glass beaker. The solution was stirred continuously. The addition of Bi(NO3)35H2O into water results in a milky white color solution which turns into an orange color solution after the addition of SeC(NH2)2. The solution becomes clear after the addition of disodium EDTA. Finally, 120 mg (2.14 mmol) of KOH and 320 mg (8 mmol) of NaOH were added into the solution which turns the solution color black. After 10 minutes of stirring, the solution was put to rest which results in precipitation of the dark brown color nanosheets. We observed that nanosheets of similar morphology and thickness can also be obtained without using disodium EDTA, however, in that case, the required amount of water solvent is much higher, 200 ml. These were then washed with alcohol and water and centrifuged to remove disodium EDTA. The purified product was then dried in a vacuum oven at 150 C.Step I: In water, Bi(NO3)3 undergoes hydrolysis to produce BiONO3 and the process of hydrolysis is expedites in alkaline medium:Step II: Selenourea SeC(NH2)2 undergoes decomposition in alkaline medium to generate selenide ions (Se 2-) along with cyanamide (H2NCN): SeC(NH2)2 + OH -→ Se 2-+ H2NCN + H2O

We calculate RPA-BCS-based spin resonance spectra of the newly discovered iron-selenide superconductor by using the two-orbital tight-binding model in a 1-Fe-unit cell. The slightly squarish electron pocket Fermi surfaces at (π,0)/(0,π ) momenta produce leading interpocket nesting instability at incommensurate vector q ∼ (π,0.5π ) in the normal-state static susceptibility, pinning a strong stripe-like spin-density wave or antiferromagnetic order at some critical value of U . The same nesting also induces d x 2 −y 2 pairing in a 1-Fe-unit cell. The superconducting gap is nodeless and isotropic on the Fermi surfaces, as they lie concentric to the fourfold symmetric point of the d-wave gap maxima, in agreement with various experiments. This produces a slightly incommensurate spin resonance with upward dispersion, in close agreement with neutron data on chalcogenides. Finally, we demonstrate the conversion procedure from a 1-Fe-unit cell to a 2-Fe-unit cell in which the gap symmetry transformed simultaneously into a d xy pairing and the resulting resonance spectrum moves from the q (π,π) to the q (2π,0)/(2π,0) region.

We review the intermediate coupling model for treating electronic correlations in the cuprates. Spectral signatures of the intermediate coupling scenario are identified and used to adduce that the cuprates fall in the intermediate rather than the weak or the strong coupling limits. A robust, 'beyond LDA' framework for obtaining wide-ranging properties of the cuprates via a GW-approximation based self-consistent self-energy correction for incorporating correlation effects is delineated. In this way, doping and temperature dependent spectra, from the undoped insulator to the overdoped metal, in the normal as well as the superconducting state, with features of both weak and strong coupling can be modeled in a material-specific manner with very few parameters. Efficacy of the model is shown by considering available spectroscopic data on electron and hole doped cuprates from angle-resolved photoemission (ARPES), scanning tunneling microscopy/spectroscopy (STM/STS), neutron scattering, inelastic light scattering, optical and other experiments. Generalizations to treat systems with multiple correlated bands such as the heavy-fermions, the ruthenates, and the actinides are discussed.

We investigate the doping dependence of the penetration depth versus temperature in electron-doped Pr(2-x)Ce(x)CuO(4-delta) using a model which assumes the uniform coexistence of (mean-field) antiferromagnetism and superconductivity. Despite the presence of a d(x2-y2) pairing gap in the underlying spectrum, we find nodeless behavior of the low-T penetration depth in the underdoped case, in accord with experimental results. As doping increases, a linear-in-T behavior of the penetration depth, characteristic of d-wave pairing, emerges as the lower magnetic band crosses the Fermi level and creates a nodal Fermi surface pocket.