Relativistic materials from an alternative viewpoint

Electrons in materials containing heavy elements are fundamentally relativistic and should in principle be described using the Dirac equation. However, the current standard for treatment of electrons in such materials involves density functional theory methods originally formulated from the Schr\"{o}dinger equation. While some extensions of the Schr\"{o}dinger-based formulation have been explored, such as the scalar relativistic approximation with or without spin-orbit coupling, these solutions do not provide a way to fully account for all relativistic effects of electrons, and the language used to describe such solutions are still based in the language of the Schr\"{o}dinger equation. In this article, we provide a different method for translating between the Dirac and Schr\"{o}dinger viewpoints in the context of a Coulomb potential. By retaining the Dirac four-vector notation and terminology in taking the non-relativistic limit, we see a much deeper connection between the Dirac and Schr\"{o}dinger equation solutions that allow us to more directly compare the effects of relativity in the angular and radial functions. Through this viewpoint, we introduce the concepts of densitals and Dirac spherical harmonics that allow us to translate more easily between the Dirac and Schr\"{o}dinger solutions. These concepts allow us to establish a useful language for discussing relativistic effects in materials containing elements throughout the full periodic table and thereby enable a more fundamental understanding of the effects of relativity on electronic structure

Edge Electron Gas

The uniform electron gas, the traditional starting point for density-based many-body theories of inhomogeneous systems, is inappropriate near electronic edges. In its place we put forward the appropriate concept of the edge electron gas.Comment: 4 pages RevTex with 7 ps-figures included. Minor changes in title,text and figure

Boundary Effects on Spectral Properties of Interacting Electrons in One Dimension

The single electron Green's function of the one-dimensional Tomonaga-Luttinger model in the presence of open boundaries is calculated with bosonization methods. We show that the critical exponents of the local spectral density and of the momentum distribution change in the presence of a boundary. The well understood universal bulk behavior always crosses over to a boundary dominated regime for small energies or small momenta. We show this crossover explicitly for the large-U Hubbard model in the low-temperature limit. Consequences for photoemission experiments are discussed.Comment: revised and reformatted paper to appear in Phys. Rev. Lett. (Feb. 1996). 5 pages (revtex) and 3 embedded figures (macro included). A complete postscript file is available from http://FY.CHALMERS.SE/~eggert/luttinger.ps or by request from [email protected]

Spin Dynamics of the Triangular Heisenberg Antiferromagnet: A Schwinger Boson Approach

We have analyzed the two-dimensional antiferromagnetic Heisenberg model on the triangular lattice using a Schwinger boson mean-field theory. By expanding around a state with local $120^\circ$ order, we obtain, in the limit of infinite spin, results for the excitation spectrum in complete agreement with linear spin wave theory (LSWT). In contrast to LSWT, however, the modes at the ordering wave vectors acquire a mass for finite spin. We discuss the origin of this effect.Comment: 15 pages REVTEX 3.0 preprint, 6 postscript figures ( uuencoded and compressed using the script uufiles ) are submitted separately

Correlation Functions and Coulomb Blockade of Interacting Fermions at Finite Temperature and Size

We present explicit expressions for the correlation functions of interacting fermions in one dimension which are valid for arbitrary system sizes and temperatures. The result applies to a number of very different strongly correlated systems, including mesoscopic quantum wires, quantum Hall edges, spin chains and quasi-one-dimensional metals. It is for example possible to calculate Coulomb blockade oscillations from our expression and determine their dependence on interaction strength and temperature. Numerical simulations show excellent agreement with the analytical results.Comment: 10 pages in revtex format including 2 embedded figures (using epsf). The latest complete postscript file is available from http://fy.chalmers.se/~eggert/papers/corrfcn.ps or by request from [email protected]