Single-Particle Excitations under Coexisting Electron Correlation and Disorder: A Numerical Study of the Anderson–Hubbard Model
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概要
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Interplay of electron correlation and randomness is studied using the Anderson–Hubbard model within the Hartree–Fock (HF) approximation. Under the coexistence of short-range interaction and diagonal disorder, we obtain the ground-state phase diagram in three dimensions (3D), which includes an antiferromagnetic insulator, an antiferromagnetic metal, a paramagnetic insulator (Anderson-localized insulator), and a paramagnetic metal. Although only the short-range interaction is present in this model, we find unconventional soft gaps in the insulating phases irrespective of electron filling, spatial dimensions, and long-range order, where the single-particle density of states (DOS) vanishes with a power-law scaling in 1D or even faster in 2D and 3D toward the Fermi energy. We call such a gap a soft Hubbard gap. Moreover, exact-diagonalization results for 1D support the formation of a soft Hubbard gap beyond the mean-field level. The formation of the soft Hubbard gap cannot be attributed to the conventional theory by Efros and Shklovskii (ES) owing the emergence of soft gaps to the long-range Coulomb interaction. Indeed, on the basis of a multivalley energy landscape, we propose a phenomenological scaling theory, which predicts a scaling of the DOS, $A$ in energy $E$ as $A(E)\propto\exp[-(-\gamma\log|E-E_{\text{F}}|)^{d}]$. Here, $d$ is the spatial dimension, $E_{\text{F}}$ is the Fermi energy, and $\gamma$ is a non universal constant. This scaling is in perfect agreement with the numerical results. We further discuss a correction of the scaling of the DOS by the long-range part of the Coulomb interaction, which modifies the ES scaling. Furthermore, explicit formulae for the temperature dependence of the DC resistivity via variable-range hopping under the influence of the soft gaps are derived. Finally, we compare the present theory with experimental results for SrRu1-xTixO3.
- Physical Society of Japanの論文
- 2009-09-15
著者
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Imada Masatoshi
Department Of Applied Physics University Of Tokyo
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Shinaoka Hiroshi
Department Of Applied Physics The University Of Tokyo
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Shinaoka Hiroshi
Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-8656
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Imada Masatoshi
Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-8656
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