Zhu Zengwei, Fauqué Benoît, Behnia Kamran, Fuseya Yuki
Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, People's Republic of China.
J Phys Condens Matter. 2018 Aug 8;30(31):313001. doi: 10.1088/1361-648X/aaced7. Epub 2018 Jun 25.
In this paper, we first review fundamental aspects of magnetoresistance in multi-valley systems based on the semiclassical theory. Then we will review experimental evidence and theoretical understanding of magnetoresistance in an archetypal multi-valley system, where the electric conductivity is set by the sum of the contributions of different valleys. Bulk bismuth has three valleys with an extremely anisotropic effective mass. As a consequence the magnetoconductivity in each valley is extremely sensitive to the orientation of the magnetic field. Therefore, a rotating magnetic field plays the role of a valley valve tuning the contribution of each valley to the total conductivity. In addition to this simple semiclassical effect, other phenomena arise in the high-field limit as a consequence of an intricate Landau spectrum. In the vicinity of the quantum limit, the orientation of magnetic field significantly affects the distribution of carriers in each valley, namely, the valley polarization is induced by the magnetic field. Moreover, experiment has found that well beyond the quantum limit, one or two valleys become totally empty. This is the only case in condensed matter physics where a Fermi sea is completely dried up by a magnetic field without a metal-insulator transition. There have been two long-standing problems on bismuth near the quantum limit: the large anisotropic Zeeman splitting of holes, and the extra peaks in quantum oscillations, which cannot be assigned to any known Landau levels. These problems are solved by taking into account the interband effect due to the spin-orbit couplings for the former, and the contributions from the twinned crystal for the latter. Up to here, the whole spectrum can be interpreted within the one-particle theory. Finally, we will discuss transport and thermodynamic signatures of breaking of the valley symmetry in this system. By this term, we refer to the observed spontaneous loss of threefold symmetry at high magnetic field and low temperature. Its theoretical understanding is still missing. We will discuss possible explanations.
在本文中，我们首先基于半经典理论回顾多谷系统中磁阻的基本方面。然后我们将回顾一个典型多谷系统中磁阻的实验证据和理论理解，在该系统中，电导率由不同谷的贡献之和决定。体铋有三个谷，其有效质量具有极强的各向异性。因此，每个谷中的磁导率对磁场方向极为敏感。所以，旋转磁场起到了谷阀的作用，调节每个谷对总电导率的贡献。除了这种简单的半经典效应外，由于复杂的朗道谱，在高场极限下还会出现其他现象。在量子极限附近，磁场方向会显著影响每个谷中载流子的分布，即磁场会诱导谷极化。此外，实验发现，在远超量子极限的情况下，一个或两个谷会完全变空。这是凝聚态物理中唯一一种费米海被磁场完全排空而不发生金属 - 绝缘体转变的情况。在量子极限附近的铋存在两个长期问题：空穴的大各向异性塞曼分裂以及量子振荡中的额外峰，这些峰无法归因于任何已知的朗道能级。对于前者，通过考虑自旋 - 轨道耦合引起的带间效应来解决；对于后者，则通过孪晶的贡献来解决。至此，整个谱可以在单粒子理论内得到解释。最后，我们将讨论该系统中谷对称性破缺的输运和热力学特征。通过这个术语，我们指的是在高磁场和低温下观察到的三重对称性的自发丧失。其理论理解仍然缺失。我们将讨论可能的解释。
