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The Van Hove singularity (VHS) provides a paradigm for the study of the role of peaks in the density of states (dos) on electronic properties. More importantly, it appears to play a major role in the physics of the high-Tc superconductors, particularly since recent photoemission studies have found that the VHS is close to the Fermi level in most of the high-Tc cuprates near the composition of optimum Tc. This paper offers a comprehensive survey of the VHS model, describing both theoretical properties and experimental evidence for the picture. Special topics discussed include a survey of the Fermi surfaces of the cuprates and related compounds, and an analysis of the reliability of the slave boson approach to correlation effects. While many properties of the cuprates can be qualitatively understood by a simple rigid-band-filling model, this is inadequate for more quantitative results, since correlation effects tend to pin the Fermi level near the VHS over an extended doping range, and can lead to a nanoscale phase separation. Furthermore, the peaks in the dos lead to competition from other instabilities, both magnetic and structural (related to charge density waves). A novel form of dynamic structural instability, involving dynamic VHS-Jahn-Teller effects has been predicted. Scattered through the literature, there is considerable experimental evidence for both nanoscale phase separation of holes, and for local, possibly dynamic, structural disorder. This review attempts to gather these results into a comprehensive database, to sort the results, and to see how they fit into the Van Hove scenario. Recent experiments on underdoped cuprates are found to provide a strong confirmation that the pseudogap is driven by a splitting of the VHS degeneracy.

We have investigated band structures of a series of 28 ternary half-Heusler compounds MMЈX of MgAgAs type, where M = ͑Lu, La, Sc, Y͒ and MЈX = ͑PtBi, AuPb, PdBi, PtSb, AuSn, NiBi, PdSb͒. Our results show that the Z 2 topological order is due to a single band inversion at the ⌫ point. In native states, these half-Heusler compounds are identified as being topologically nontrivial semimetals, or nontrivial metals, or trivial insulators, which can be turned into insulating thin films on suitable substrates. Our analysis reveals a straightforward relationship which connects the band inversion strength ͑extent of deviation from the critical point͒ to the atomic charge of constituents and the lattice parameter. Our findings suggest a general method for identifying Z 2 topological insulators in nonmagnetic ternary compounds.

We discuss the effects of interlayer hopping and the resulting kz-dispersion in the cuprates within the framework of the one-band tight binding (TB) model Hamiltonian. Specific forms of the dispersion relations in terms of the in-plane hopping parameters t, t ′ , t ′′ and t ′′′ and the effective interlayer hopping tz in La2−xSrxCuO4 (LSCO) and Nd2−xCexCuO4 (NCCO) and the added intracell hopping t bi between the CuO2 bilayers in Bi2Sr2CaCu2O8 (Bi2212) are presented. The values of the 'bare' parameters are obtained via fits with the first principles LDA-based band structures in LSCO, NCCO and Bi2212. The corresponding 'dressed' parameter sets which account for correlation effects beyond the LDA are derived by fitting experimental FS maps and dispersions near the Fermi energy in optimally doped and overdoped systems. The interlayer couplings tz and t bi are found generally to be a substantial fraction of the in-plane hopping t, although the value of tz in NCCO is anomalously small, reflecting absence of apical O atoms in the crystal structure. Our results provide some insight into the issues of the determination of doping from experimental FS maps in Bi2212, the role of intercell coupling in c-axis transport, and the possible correlations between the doping dependencies of the binding energies of the Van Hove singularities (VHSs) and various prominent features observed in the angle-resolved photoemission (ARPES) and tunneling spectra of the cuprates.

We have investigated several strong spin-orbit coupling ternary chalcogenides related to the (Pb,Sn)Te series of compounds. Our first-principles calculations predict the low temperature rhombohedral ordered phase in TlBiTe2, TlBiSe2, and TlSbX2 (X=Te, Se, S) to be topologically Z2 = -1 nontrivial. We identify the specific surface termination that realizes the single Dirac cone through first-principles surface state computations. This termination minimizes effects of dangling bonds making it favorable for photoemission (ARPES) experiments. Our analysis predicts that thin films of these materials would harbor novel 2D quantum spin Hall states, and support odd-parity topological superconductivity. For a related work also see arXiv:1003.2615v1. Experimental ARPES results will be published elsewhere. PACS numbers:Topological insulators are a recently discovered new phase of quantum matter [1][2][3]. The search for topological insulators in real materials has benefitted from the fruitful interplay between topological band theory of Kane and Mele (2005) and realistic band structure calculations [4][5][6][7][8][9][10][11][12]. As a result, Bi x Sb 1−x , Bi 2 Se 3 and Bi 2 Te 3 have been experimentally realized as three-dimensional topological insulators [6-9, 11, 12]. Recently, this search has been extended to ternary compounds [13,14]. Here, we report first-principles band calculations of Tl-based III-V-VI 2 ternary chalcogenide series, and compare the results to those of the related (Pb,Sn)Te series studied previously in connection with Dirac fermion physics in the 1980s [15]. The low temperature rhombohedral ordered phase in TlBiTe 2 , TlBiSe 2 , and TlSbX 2 (X=Te, Se, S) is predicted to be topologically nontrivial. Moreover, we have carried out first-principles slab computations in order to identify the specific surface termination which gives rise to the simple Dirac-cone surface band for ARPES measurements. An analysis of the symmetry of states indicates that thin films of the present materials would support 2D-quantum spin Hall states.Designing new topological insulators involves modifying atomic structure or doping to shift band orders out of the natural sequence. Consider, for example, the wellknown case of (Pb,Sn)Te with rocksalt structure. The end phase PbTe with face-centered cubic (FCC) lattice is topologically trivial. In contrast, SnTe has band inversions at four equivalent L-points where parities of conduction and valence bands are switched (Fig. 2E). Since this inversion occurs at an even number of points in the Brillouin zone, SnTe is also a topologically trivial band insulator. Fu and Kane [5] proposed that a rhombohedral distortion along a particular 111 direction can induce (Pb,Sn)Te into a strong topological phase because then the band inversion occurs only at the L-point along the 111 direction which is distinguished from the other three L-points (Fig. 1B).The Tl-based III-V-VI 2 ternary chalcogenides M M ′ X 2 are, or can be, approximately viewed as a rhombohedral structure with space group R3m[...