物理中的几何相位(2024春)

主讲老师：牛谦   高阳       邮箱：niuqian@ustc.edu.cn   ygao87@ustc.edu.cn

助教：邓世越   李树       邮箱：dsy2018@mail.ustc.edu.cn   lishu@mail.ustc.edu.cn

上课时间：1-14周周二(8,9,10)   上课地点：2321

往年主页：物理学中的几何相位(2023/春季)

欢迎对课程内容有疑问的同学给老师和助教发邮件提问！

---

• 参考资料
  1. Di Xiao, Ming-Che Chang, and Qian Niu, Berry phase effects on electronic properties, Rev. Mod. Phys. 82, 1959(2010).
  2. Ganesh Sundaram and Qian Niu, Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects, Phys. Rev. B. 59, 14915(1999).
  3. B. Andrei Bernevig, Topological Insulators and Topological Superconductors, 2013.
  4. Michael P. Marder. Condensed Matter Physics, 2010.
  5. Alfred Shapere and Frank Wilczek. Geometric Phases in Physics, 1989.

---

• project
  1. 题目一：Hofstadter Butterfly与Landau Levels
  2. 题目二： 非线性反常Hall效应
  3. 题目三：磁光Kerr效应
  4. 题目四：Klein tunneling in graphene
  5. 题目五：磁振子Hall效应

---

• 本学期内容
  1. 第一周 2024.2.27
     1. 牛谦老师部分：Chern Number and Berry Curvature Lecture 1
     2. 高阳老师部分：拓扑与几何 Lecture 1
     3. 参考阅读：牛谦：初涉电子拓扑 | 纪念索利斯
     4. 参考阅读：电子粒子观的蜕变
     5. 参考文献：
        1. D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Quantized Hall Conductance in a Two-Dimensional Periodic Potential, Phys. Rev. Lett. 49. 405(1982).
        2. F. D. M. Haldane, Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the "Parity Anomaly", Phys. Rev. Lett. 61. 2015(1988).
        3. M. V. Berry, Quantal phase factors accompanying adiabatic changes, Proc. R. Soc. London, Ser. A 392, 45(1984).
  2. 第二周 2024.3.5
     1. 牛谦老师部分：New dynamics of Bloch electrons Lecture 2
     2. 高阳老师部分：拓扑与几何
     3. 第一次作业：homework1   2024年3月19日之前上交。
     4. 参考文献：
        1. Yugui Yao et al, First Principles Calculation of Anomalous Hall Conductivity in Ferromagnetic bcc Fe, Phys. Rev. Lett. 92.037204(2004).
        2. Changgan Zeng, Yugui Yao, Qian Niu, and Hanno H. Weitering, Linear Magnetization Dependence of the Intrinsic Anomalous Hall Effect, Phys. Rev. Lett. 96, 037204 (2006).
        3. Di Xiao, Wang Yao, and Qian Niu, Valley-Contrasting Physics in Graphene: Magnetic Moment and Topological Transport, Phys. Rev. Lett. 99, 236809 (2007).
  3. 第三周 2024.3.12
     1. 牛谦老师部分：Pumping and Polarization Lecture 3
     2. 高阳老师部分：固体中的电子 Lecture 2
     3. 第二次作业：homework2   2024年3月26日之前上交。
     4. 参考文献：
        1. D. J. Thouless, Quantization of particle transport, Phys. Rev. B 27, 6083(1983).
        2. Di Xiao, Junren Shi and Qian Niu, Berry Phase Correction to Electron Density of States in Solids, Phys. Rev. Lett. 95, 137204(2005).
  4. 第四周 2024.3.19
     1. 牛谦老师部分：Magnetic Properties Lecture 4
     2. 高阳老师部分：半经典理论框架 Lecture 3
     3. 第三次作业：homework3   2024年4月2日之前上交。
     4. 参考文献：
        1. Di Xiao, Yugui Yao, Zhong Fang and Qian Niu, Berry-Phase Effect in Anomalous Thermoelectric Transport, Phys. Rev. Lett. 97, 026603(2006).
        2. Dimitrie Culcer, Yugui Yao and Qian Niu, Coherent wave-packet evolution in coupled bands, Phys. Rev. B 72, 085110(2005).
        3. Ryuichi Shindou and Ken-Ichiro Imura, Noncommutative geometry and non-Abelian Berry phase in the wave-packet dynamics of Bloch electrons, Nuclear Physics B 720 [FS] (2005).
        4. Ming-Che Chang and Qian Niu, Berry curvature, orbital moment, and effective quantum theory of electrons in electromagnetic fields, J. Phys. : Condens. Matter 20(2008).
  5. 第五周 2024.3.26
     1. 牛谦老师部分：Magneto-electronic Applications Lecture 5
     2. 高阳老师部分：半经典理论框架
     3. 参考文献：
        1. G E Volovik, Linear momentum in ferromagnets, J. Phys. C: Solid State Phys. 20 L83(1987).
        2. Masamitsu Hayashi et al, Direct observation of the coherent precession of magnetic domain walls propagating along permalloy nanowires, Nature Physics(2007).
        3. Shengyuan A. Yang et al, Universal Electromotive Force Induced by Domain Wall Motion, Phys. Rev. Lett. 102, 067201(2009).
        4. Shengyuan A. Yang et al, Topological electromotive force from domain-wall dynamics in a ferromagnet, Phys. Rev. B 82, 054410(2010).
  6. 第六周 2024.4.2
     1. 牛谦老师部分：Thermo-electronic Applications Lecture 6
     2. 高阳老师部分：量子化电导率与拓扑性 Lecture 4-1 紧束缚近似 Lecture 4-2
     3. 第四次作业：homework4   2024年4月16日之前上交。
     4. 参考文献：
        1. Liang Dong et al, Berry Phase Effects in Dipole Density and the Mott Relation, Phys. Rev. Lett. 124, 066601(2020).
        2. Wei-Li Lee et al, Dissipationless Anomalous Hall Current in the Ferromagnetic Spinel CuCr2Se4–xBrx, Science(2004).
        3. J. M. Luttinger, Theory of Thermal Transport Coefficients, Phys. Rev. 135, A1505(1964).
        4. Ryo Matsumoto and Shuichi Murakami, Theoretical Prediction of a Rotating Magnon Wave Packet in Ferromagnets, Phys. Rev. Lett. 106, 197202(2011).
        5. Tao Qin, Qian Niu and Junren Shi, Energy Magnetization and the Thermal Hall Effect, Phys. Rev. Lett. 107, 236601(2011).
  7. 第七周 2024.4.9
     1. 牛谦老师部分：Electron dynamics in deformed crystals Lecture 7
     2. 高阳老师部分：量子霍尔效应 Lecture 5
     3. 第五次作业：homework5   2024年4月23日之前上交。
     4. 参考文献：
        1. Magnetic Translation Group：
           1. J. Zak, Magnetic Translation Group, Phys. Rev. 134, A1602(1964).
           2. M. C. Chang and Q. Niu, Electron band structure in a two-dimensional periodic magnetic field, Phys. Rev. B, 50, 10483(1994).
           3. M. C. Chang and Q. Niu, Berry phase, hyperorbits, and the Hofstadter spectrum: Semiclassical dynamics in magnetic Bloch bands, Phys. Rev. B, 53, 7010(1996).
        2. Laughlin arugment：
           1. R. B. Laughlin, Quantized Hall conductivity in two dimensions, Phys. Rev. B, 23, 5632(1981).
           2. B. I. Halperin, Quantized Hall conductance, current-carrying edge states, and the existence of extended states in a two-dimensional disordered potential, Phys. Rev. B, 25, 2185(1982).
        3. deformed crystals：
           1. Liang Dong and Qian Niu, Geometrodynamics of electrons in a crystal under position and time-dependent deformation, Phys. Rev. B, 98, 115162(2018).
           2. Qiang Gao and Qian Niu, Floquet-Bloch Oscillations and Intraband Zener Tunneling in an Oblique Spacetime Crystal, Phys. Rev. Lett. 127, 036401(2021).
           3. Anzhuoer Li, Liang Dong and Qian Niu, Geodynamics in spacetime crystal under slow perturbation and deformation.
  8. 第八周 2024.4.16
     1. 牛谦老师部分：Molecular Berry curvature Lecture 8
     2. 高阳老师部分：光学现象中的几何相位 Lecture 6
     3. 第六次作业：homework6   2024年4月30日之前上交。
     4. 参考文献：
        1. Daniyar Saparov et al, Lattice dynamics with molecular Berry curvature: Chiral optical phonons, Phys. Rev. B 105, 064303(2022).
        2. Lifa Zhang and Qian Niu, Angular Momentum of Phonons and the Einstein-de Haas Effect, Phys. Rev. Lett. 112, 085503(2014).
        3. Lifa Zhang and Qian Niu, Chiral Phonons at High-Symmetry Points in Monolayer Hexagonal Lattices, Phys. Rev. Lett. 115, 115502(2015).
  9. 第九周 2024.4.23
     1. 牛谦老师部分：Superconductors Lecture 9
     2. 秦维老师部分：Quantum Geometry and Superconductor Lecture
     3. 参考阅读：布洛赫电子的拓扑与几何
     4. 参考文献：
        1. Zhi Wang et al, Berry Curvature Effects on Quasiparticle Dynamics in Superconductors, Phys. Rev. Lett. 126, 187001(2021).
        2. Junren Shi and Qian Niu, Attractive electron-electron interaction induced by geometric phase in a Bloch band, Sci. China-Phys. Mech. Astron. 63, 227422(2020).
        3. Wei Qin et al, Chiral topological superconductivity arising from the interplay of geometric phase and electron correlation, Nature Physics(2019).
        4. Wei Qin et al, Critical magnetic fields and electron pairing in magic-angle twisted bilayer graphene, Phys. Rev. B 107, 024509(2023).
  10. 第十二周 2024.5.14
      1. 牛谦老师部分：Magnetization Dynamics Lecture 10
      2. 参考文献：
         1. Qian Niu and Leonard Kleinman, Spin-Wave Dynamics in Real Crystals, Phys. Rev. Lett. 80, 2205(1998).
         2. Qian Niu et al, Adiabatic Dynamics of Local Spin Moments in Itinerant Magnets, Phys. Rev. Lett. 83, 207(1999).
         3. Cong Xiao et al, Electric driving of magnetization dynamics in a hybrid insulator, Phys. Rev. B, 104, 064433(2021).