arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2111.03032cond-mat.mes-hall
收藏

金属中的电极化与磁化

Electric polarization and magnetization in metals

Perry T. Mahon, J. E. Sipe

AI总结:

本文提出基于指数局域化 Wannier 函数的微观电磁场定义,用于描述金属中的极化与磁化,并与现代磁化理论比较,揭示二者分歧及各自物理哲学。

摘要:

“现代理论”的一个特点是,在金属基态中电极化无法被良好定义。另一种方法则诉诸于一组完备的指数局域化 Wannier 函数的普遍存在,基于这组函数,微观电子极化场、磁化场以及自由电荷密度和电流密度的一般定义始终成立。这些定义不预设晶体的任何特定初始电子态,并且这组微观场满足经典电动力学的通常关系。值得注意的是,当应用于最初处于其 T=0 基态的平凡绝缘体时,由这些不同方法得到的未微扰极化、轨道磁化以及轨道磁电极化率张量的表达式可以一致。然而,“现代磁化理论”已通过热力学论证被推广到包括金属和陈绝缘体。我们在此与该推广进行比较,发现存在分歧;这些表达式产生差异的方式阐明了这些方法在哲学上的不同。我们的方法在长波极限下给出通常的电导率张量;在没有任何散射机制的情况下,该张量的直流发散源于自由电流密度,而反常霍尔贡献的有限频率推广则来自束缚电流密度和自由电流密度的组合。此外,在电子基态为平凡绝缘体基态的极限下,我们的表达式约化为未微扰极化、磁化以及电极化率所期望的结果。

英文摘要:

A feature of the "modern theory" is that electric polarization is not well-defined in a metallic ground state. A different approach invokes the general existence of a complete set of exponentially localized Wannier functions, with respect to which general definitions of microscopic electronic polarization and magnetization fields, and free charge and current densities are always admitted. These definitions assume no particular initial electronic state of the crystal, and the set of microscopic fields satisfy the usual relations of classical electrodynamics. Notably, when applied to a trivial insulator initially occupying its $T=0$ ground state, the expressions for the unperturbed polarization and orbital magnetization, and for the orbital magnetoelectric polarizability tensor obtained from these different approaches can agree. However, the "modern theory of magnetization" has been extended via thermodynamic arguments to include metals and Chern insulators. We here compare with that generalization and find disagreement; the manner in which the expressions differ elucidates the distinct philosophies of these approaches. Our approach leads to the usual electrical conductivity tensor in the long-wavelength limit; in the absence of any scattering mechanisms, the dc divergence of that tensor is due to the free current density and the finite-frequency generalization of the anomalous Hall contribution arises from a combination of bound and free current densities. As well, in the limit that the electronic ground state is that of a trivial insulator, our expressions reduce to those expected for the unperturbed polarization and magnetization, and the electric susceptibility.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑