arXiv 1912.021012019-12-02cond-mat.mes-hallcond-mat.supr-conquant-ph

各向异性和低维导体中的塞曼、自旋轨道和量子自旋霍尔相互作用

The Zeeman, Spin-Orbit, and Quantum Spin-Hall Interactions in Anisotropic and Low-Dimensional Conductors

Aiying Zhao, Qiang Gu, Timothy J. Haugan, Richard A. Klemm

备注：: arXiv admin note: text overlap with arXiv:1906.10164
发表信息：: J. Phys.:Condens. Matter vol. 33, art. no. 085802 (2021)
DOI：: 10.1088/1361-648X/20/085802+9

摘要：

当电子或空穴在晶体的导带中时，它可以与2非常不同，这取决于晶体的各向异性和所施加的磁感应${\bf B}$的方向。事实上，它甚至可以是0！为了定量地证明这一点，Dirac方程被扩展到一个相对论性的电子或空穴在正交各向异性导带与有效质量$m_j$为$j=1,2,3$与几何平均$m_g=(m_1m_2m_3)^{1/3}$。适当的Foldy-Wouthuysen变换扩展到$O({\rm m}c^2)^{-4}$，其中${\rm m}c^2$是粒子的爱因斯坦静止能量的非相对论性哈密顿量的评估。对于${\bf B}||\hat{\bf e}_μ$，塞曼$g_μ$因子为$2{\rm m}\sqrt{m_μ}/m_g^{3/2} + O({\rm m}c^2)^{-2}$。当在二维（2D）导带中与$m_3\gg m_1,m_2$、$g_{||}<<2$传播时，与超导单层NbSe $_2$和扭曲双层石墨烯中的平行上临界感应$B_{c2,||}(T)$的温度$T$依赖性的最近测量一致。当一个粒子处于沿$\hat{\bf e}_μ$、$g<<2$的原子级薄的一维金属链的导带中时，对于所有${\bf B}={\bf\nabla}\times{\bf A}$方向，$g<<2$是零，而对于${\bf B}||\hat{\bf e}_μ$是零。含$m_1=m_2=m_{||}$的二维金属的量子自旋霍尔哈密顿量是$K[{\bf E}\times({\bf p}-q{\bf A})]_{\perp}σ_{\perp}+O({\rm m}c^2)^{-4}$，其中${\bf E}$和${\bf p}-q{\bf A}$是平面电场和规范不变动量，$q=\mp|e|$是粒子的电荷，$σ_{\perp}$是垂直于层的泡利矩阵，$K=\pmμ_B/(2m_{||}c^2)$和$μ_B$是玻尔磁子。

英文摘要：

When an electron or hole is in a conduction band of a crystal, it can be very different from 2, depending upon the crystalline anisotropy and the direction of the applied magnetic induction ${\bf B}$. In fact, it can even be 0! To demonstrate this quantitatively, the Dirac equation is extended for a relativistic electron or hole in an orthorhombically-anisotropic conduction band with effective masses $m_j$ for $j=1,2,3$ with geometric mean $m_g=(m_1m_2m_3)^{1/3}$. The appropriate Foldy-Wouthuysen transformations are extended to evaluate the non-relativistic Hamiltonian to $O({\rm m}c^2)^{-4}$, where ${\rm m}c^2$ is the particle's Einstein rest energy. For ${\bf B}||\hat{\bf e}_μ$, the Zeeman $g_μ$ factor is $2{\rm m}\sqrt{m_μ}/m_g^{3/2} + O({\rm m}c^2)^{-2}$. While propagating in a two-dimensional (2D) conduction band with $m_3\gg m_1,m_2$, $g_{||}<<2$, consistent with recent measurements of the temperature $T$ dependence of the parallel upper critical induction $B_{c2,||}(T)$ in superconducting monolayer NbSe$_2$ and in twisted bilayer graphene. While a particle is in its conduction band of an atomically thin one-dimensional metallic chain along $\hat{\bf e}_μ$, $g<<2$ for all ${\bf B}={\bf\nabla}\times{\bf A}$ directions and vanishingly small for ${\bf B}||\hat{\bf e}_μ$. The quantum spin Hall Hamiltonian for 2D metals with $m_1=m_2=m_{||}$ is $K[{\bf E}\times({\bf p}-q{\bf A})]_{\perp}σ_{\perp}+O({\rm m}c^2)^{-4}$, where ${\bf E}$ and ${\bf p}-q{\bf A}$ are the planar electric field and gauge-invariant momentum, $q=\mp|e|$ is the particle's charge, $σ_{\perp}$ is the Pauli matrix normal to the layer, $K=\pmμ_B/(2m_{||}c^2)$, and $μ_B$ is the Bohr magneton.

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。

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英文摘要：

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