带隙近藤效应的拓扑结构与量子自旋-经典自旋交叉
Topology and Quantum-Spin-Classical-Spin Crossover of the Gapped Kondo Effect
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中文总结 AI 辅助
该研究结合Lanczos变换与自洽组态相互作用方案，数值探究带隙近藤效应的局域相图，利用三类拓扑不变量表征不同相，分析量子与经典杂质自旋间的交叉及相关近藤效应的特征。
中文摘要 AI 辅助
带隙近藤效应描述的是，一个S=1/2的杂质自旋，通过反铁磁交换相互作用，与具有有限硬带隙的传导电子系统发生局域耦合，从而被屏蔽的现象。我们结合Lanczos变换与自洽组态相互作用方案，对该体系的局域相图开展数值研究。此外，我们证明不同相可由若干拓扑不变量表征：对应基础二维宿主体系的常规动量空间陈数（即陈绝缘体）；B空间陈数，其定义为当B→0时，将杂质自旋与虚构局域磁场B耦合；以及S空间陈数，其针对经典杂质自旋（即固定长度的矢量）定义，经典自旋极限在B→∞时获得。通过改变磁场强度，我们可在量子杂质自旋与经典杂质自旋哈密顿量之间连续插值，探究对应的相图是否也连续关联。我们还针对S>1/2的杂质自旋，以及通过B→∞或S→∞趋近的经典自旋极限，研究了带隙欠屏蔽近藤效应，采用不同变体的散射理论对所得相进行解释。最后，我们证实，由量子杂质自旋与单胞内两个轨道的局域电子自旋等耦合实现的带隙双通道过屏蔽近藤效应，具有自发粒子-空穴对称性破缺的特征，这会产生高度非平凡的量子-经典相图。
英文摘要
The gapped Kondo effect describes the screening of an $S=\frac12$ impurity spin locally coupled via an antiferromagnetic exchange interaction to a conduction-electron system exhibiting a finite hard gap. Using a combination of a Lanczos transformation and a self-consistent configuration-interaction scheme, we numerically investigate the local phase diagram. Furthermore, we show that the different phases can be characterized by several topological invariants: the conventional momentum-space Chern number of the underlying two-dimensional host system, corresponding to a Chern insulator; the B-space Chern number, defined by coupling the impurity spin to a fictitious local magnetic field $\boldsymbol B$, in the limit $B \to 0$; and the S-space Chern number, defined for a classical impurity spin, i.e., a vector of fixed length. The classical-spin limit is obtained for $B \to \infty$. By varying the field strength, we can therefore continuously interpolate between quantum-impurity-spin and classical-impurity-spin Hamiltonians and investigate whether the corresponding phase diagrams are likewise continuously connected. The gapped underscreened Kondo effect is studied for an impurity spin $S>\frac12$ as well as in the classical-spin limit approached via $B \to \infty$ or $S \to \infty$. Different variants of scattering theory are employed to interpret the resulting phases. Finally, the gapped two-channel overscreened Kondo effect, realized by coupling a quantum impurity spin equally to the local electron spins of both orbitals within a unit cell, is shown to be characterized by spontaneous particle-hole symmetry breaking. This leads to a highly nontrivial quantum-classical phase diagram.
