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arXiv 1602.02449cond-mat.mtrl-scicond-mat.stat-mech
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Bloch电子的轨道磁性I。通式

Orbital Magnetism of Bloch Electrons I. General Formula

Masao Ogata, Hidetoshi Fukuyama

摘要:

本文从Fukuyama用格林函数表示的精确单线公式出发,导出了用Bloch波函数表示的轨道磁化率的精确公式。得到的公式包含四个贡献:(1)朗道-佩尔斯磁化率,(2)带间贡献,(3)费米面贡献,(4)占据态贡献。除Landau-Peierls磁化率外,其他三个贡献都涉及Bloch波函数的晶体动量导数。每个术语的物理意义被澄清。与Hebborn等人以前得到的公式相比,本公式得到了简化。根据本公式,首先可以看出,在原子极限范围内,芯电子的抗磁性和Van Vleck磁化率是唯一的贡献。然后从原子轨道的线性组合出发,将原子轨道间的重叠积分作为微扰处理,研究了固体中Bloch电子的能带效应,首次系统地阐明了固体中Bloch电子的巡游特性。

英文摘要:

We derive an exact formula of orbital susceptibility expressed in terms of Bloch wave functions, starting from the exact one-line formula by Fukuyama in terms of Green's functions. The obtained formula contains four contributions: (1) Landau-Peierls susceptibility, (2) interband contribution, (3) Fermi surface contribution, and (4) contribution from occupied states. Except for the Landau-Peierls susceptibility, the other three contributions involve the crystal-momentum derivatives of Bloch wave functions. Physical meaning of each term is clarified. The present formula is simplified compared with those obtained previously by Hebborn et al. Based on the formula, it is seen first of all that diamagnetism from core electrons and Van Vleck susceptibility are the only contributions in the atomic limit. The band effects are then studied in terms of linear combination of atomic orbital treating overlap integrals between atomic orbitals as a perturbation and the itinerant feature of Bloch electrons in solids are clarified systematically for the first time.

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