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AIP conference proceedings

Properties of a correlated nanoscopic chain close to the metal-insulator transition

Adam Rycerz

Published Jan 1, 2003• 1 citation
Publisher

Abstract

We review our recent results concerning the electronic properties of a nanoscopic system with inclusion of long‐range Coulomb interactions that are obtained by combining exact diagonalization in the Fock space with an ab initio method (EDABI). The system evolution is discussed as a function of lattice parameter R. A transformation from a nanometal to localized spin system is observed. With the help of a finite‐size scaling we determine the discontinuity of the momentum distribution at the Fermi points. Our results imply Fermi‐liquid‐like behavior for R ≲ 3a0 (a0 is the Bohr radius). The quasiparticle mass is almost divergent at the localization threshold, where the particle distribution of the Fermi‐Dirac type gets smeared out. The charge‐gap evolution is compared with that of the Slater gap. Also, the single‐particle spectral function and the corresponding density of states are presented. The analysis is performed using 1s‐like Gaussian‐type STO‐3G basis.

DOI
10.1063/1.1612399

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We review our recent results concerning the electronic properties of a nanoscopic system with inclusion of long‐range Coulomb interactions that are obtained by combining exact diagonalization in the Fock space with an ab initio method (EDABI). The system evolution is discussed as a function of lattice parameter R. A transformation from a nanometal to localized spin system is observed. With the help of a finite‐size scaling we determine the discontinuity of the momentum distribution at the Fermi points. Our results imply Fermi‐liquid‐like behavior for R ≲ 3a0 (a0 is the Bohr radius). The quasiparticle mass is almost divergent at the localization threshold, where the particle distribution of the Fermi‐Dirac type gets smeared out. The charge‐gap evolution is compared with that of the Slater gap. Also, the single‐particle spectral function and the corresponding density of states are presented. The analysis is performed using 1s‐like Gaussian‐type STO‐3G basis.
We implement the recently proposed approach combining Exact Diagonalization in the Fock space with an Ab Initio method (EDABI) to obtain a fairly complete description of correlated nanochains. In particular, the microscopic parameters are determined and the evolution of the system properties is traced in a systematic manner as a function of the interatomic distance. Both ground‐state and dynamical correlation functions are discussed within a single scheme. The principal physical results are: (i) the appearance of mixed metallic and insulating features for a one‐dimensional nanochain in the half‐filled band case, and (ii) the transformation from a highly‐conducting nanometal to the charge‐ordered nanoinsulator away from the half‐filling. The analysis is performed using the Gaussian 1s‐like basis and includes long‐range Coulomb interactions.
We have applied our novel numerical scheme combining Lanczos diagonalization in the Fock space with an ab initio renormalization of the single-particle (Wannier) functions, to study the ground state properties of the Extended Hubbard Model. Through the finite-size scaling we determine the discontinuity of the momentum distribution Fermi surface. Our results imply Fermi-liquid behavior for lattice parameter a ≲\lesssim≲ 3a0_{0}0​ (a0_{0}0​ is the Bohr radius) and zero-temperature transition to the localized spin system for larger . Possible further applications of the method are listed at the end.
Abstract We provide a brief overview of the results for correlated nanoscopic systems obtained from the Exact‐Diagonalization Ab Initio (EDABI) method. Explicitly, after a brief summary of the method and its testing for the atomic and crystal‐field states, we summarize the fundamental properties of nanochains modeling a simple‐metal quantum nanowire. All the results are analyzed as a function of interatomic distance and characterize an evolution of electronic states from the Fermi‐liquid‐like state to a localized state via an intermediate Luttinger‐liquid‐like regime. The renormalized electronic (band) structure and the concept of statistical distribution function are shown to be applicable for N = 8 ÷ 16 atoms arranged in chain or ring configurations. The role of boundary conditions involving a ficticious flux representing the Berry phase is also briefly discussed. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
We overview the EDABI method developed recently and combining the exact diagonalization and ab initio aspects of electron states in correlated systems and apply it to nanoscopic systems. In particular, we discuss the localization-delocalization transition for the electrons that corresponds to the Mott-Hubbard transition in bulk systems. We show, that, the statistical distribution function for electrons in a nanochain evolves from the Fermi-Dirac-like to the Luttinger-liquid-like with the increasing interatomic distance. The concept of Hubbard subbands is introduced to nanoclusters, and corresponds to the HOMO-LUMO splitting in the molecular and organic solid states. Also, the nanochains exhibit magnetic splitting (Slater-like), even without the symmetry breaking, since the spin-spin correlations extend over the whole system. Thus, the correlated nanoscopic systems exhibit unique and universal features, which differ from those of molecular and infinite systems. These features define unique properties reflecting "the Mott physics" on the nanoscale. We also employ the EDABI method to the transport properties in nanoscopic systems. For example, we show that the particle-hole symmetry is broken when the tunneling conduction through H2 molecule is calculated.
We briefly summarize the fundamental properties of correlated nanoscopic systems obtained within the EDABI method combining an exact diagonalization in the Fock space with an ab initio readjustment of the single‐particle wave functions in the resultant ground state. Explicitly, we address the following questions: evolution of various systems from a nanometal to a nanoinsulator of the Mott‐Hubbard type, the appearance of the Mott‐Hubbard gap in molecular and cluster (Hn) systems, as well as the stability of those clusters.
We discuss the physical properties of strongly correlated electron states for a linear chain obtained with the help of a recently proposed method combining an exact diagonalization in Fock space with an ab initio readjustment of single-particle orbitals in the correlated state. The method extends the current discussion of correlated states, since the properties are obtained with varying lattice spacings. The finite system of N atoms evolves with the increasing interatomic distance from a Fermi-liquid-like state into the Mott insulator. The criteria of the localization are discussed in detail, since the results are already convergent for N> 8.N>~8.N> 8. During this process the Fermi-Dirac distribution is smeared out, the effective band mass increases by \ensuremath{\sim}50%, and the spin-spin correlation functions reduce to those for a Heisenberg antiferromagnet. Values of microscopic parameters such as the hopping and the kinetic-exchange integrals, as well as the magnitude of both intraatomic and interatomic Coulomb and exchange interactions are calculated. We also determine the values of various local electron-lattice couplings, and show that they are comparable to the kinetic exchange contribution in the strong-correlation limit. The magnitudes of the dimerization and the zero-point motion are also discussed. Our results provide a canonical example of a tractable strongly correlated system with a precise, first-principles description as a function of interatomic distance of a model system involving all hopping integrals, all pair-site interactions, and exact one-band Wannier functions.