固体物理学中的贝里曲率  

Berry curvature in solid state physics

作　　者：袁喆 周仕明[2] YUAN Zhe;ZHOU Shi-ming(Institute for Nanoelectronic Devices and Quantum Computing,Fudan University,Shanghai 200433,China;School of Physics Science and Engineering,Tongji University,Shanghai 200092,China)

机构地区：[1]复旦大学微纳电子器件与量子计算机研究院,上海200433 [2]同济大学物理科学与工程学院,上海200090

出　　处：《大学物理》2024年第5期1-5,18,共6页College Physics

摘　　要：固体中周期性势场和布洛赫定理赋予贝里曲率新的内涵,对于布里渊区k点处第n个能带,其布洛赫函数的调幅因子为u_(nk)(r),则相应贝里曲率Ω_(nk)=▽×A_(nk),其中贝里联络A_(nk)=〈u_(nk)|i▽_(k)|u_(nk)〉.如果晶体同时存在中心反演和时间反演对称性,贝里曲率在倒空间处处为零.若上述对称性被打破,或者存在自旋轨道耦合,或者存在能带交叉,则存在非零的贝里曲率.贝里曲率的存在使布洛赫电子产生与外电场垂直方向的反常速度,由此产生本征反常霍尔效应和自旋霍尔效应以及非线性霍尔效应.本文有助于加深对布洛赫波函数以及玻尔兹曼输运方程的理解.Periodic potential and Bloch's theorem in solid makes Berry curvature different from that in continuous media.The Bloch wave function of the n-th energy band at k point in Brillouin zone has its modulation factor u n k(r),and the corresponding Berry curvature is given by Ω_(nk)=▽×A_(nk) with Berry connection A_(nk)=〈u_(nk)|i▽_(k)|u_(nk)〉.In the presence of inversion and time reversal symmetries,Berry curvature vanishes at in any k point of Brillouin zone.With broken inversion and time reversal symmetries,or with spin-orbit coupling,or the band degeneracy,Berry curvature can be nonzero.Berry curvature induces an anomalous velocity perpendicular to external electric field,which in turn leads to the intrinsic anomalous Hall effect,the intrinsic spin Hall effect and the nonlinear Hall effect.This work is helpful for a better understanding of Bloch wave function and Boltzmann transport equation.

关 键 词：贝里相位 贝里曲率 布洛赫波函数 反常速度 

分 类 号：O481[理学—固体物理]