Multidimensional Bosonization

Bosonization of degenerate fermions yields insight both into Landau Fermi liquids, and into non-Fermi liquids. We begin our review with a pedagogical introduction to bosonization, emphasizing its applicability in spatial dimensions greater than one. After a brief historical overview, we present the essentials of the method. Well known results of Landau theory are recovered, demonstrating that this new tool of many-body theory is robust. Limits of multidimensional bosonization are tested by considering several examples of non-Fermi liquids, in particular the composite fermion theory of the half-filled Landau level. Nested Fermi surfaces present a different challenge, and these may be relevant in the cuprate superconductors. We conclude by discussing the future of multidimensional bosonization.Comment: 91 pages, 15 eps figures, LaTeX. Minor changes to match the published versio

Electronic Structures of Antiperovskite Superconductor MgCNi3_3 and Related Compounds

Electronic structure of a newly discovered antiperovskite superconductor MgCNi$_3$ is investigated by using the LMTO band method. The main contribution to the density of states (DOS) at the Fermi energy $E_{\rm F}$ comes from Ni 3$d$ states which are hybridized with C 2$p$ states. The DOS at $E_{\rm F}$ is varied substantially by the hole or electron doping due to the very high and narrow DOS peak located just below $E_{\rm F}$. We have also explored electronic structures of C-site and Mg-site doped MgCNi$_3$ systems, and described the superconductivity in terms of the conventional phonon mechanism.Comment: 3 pages, presented at ORBITAL2001 September 11-14, 2001 (Sendai, JAPAN

Electronic structures of antiperovskite superconductors: MgXNi3_3 (X=B,C,N)

We have investigated electronic structures of a newly discovered antiperovskite superconductor MgCNi$_3$ and related compounds MgBNi$_3$ and MgNNi$_3$. In MgCNi$_3$, a peak of very narrow and high density of states is located just below $\rm E_F$, which corresponds to the $\pi^*$ antibonding state of Ni-3d and C-$2p$ but with the predominant Ni-3d character. The prominent nesting feature is observed in the $\Gamma$-centered electron Fermi surface of an octahedron-cage-like shape that originates from the 19th band. The estimated superconducting parameters based on the simple rigid-ion approximation are in reasonable agreement with experiment, suggesting that the superconductivity in MgCNi$_3$ is described well by the conventional phonon mechanism.Comment: 5 pages, 5 figure