Topological protection, disorder, and interactions: Survival at the surface of three-dimensional topological superconductors
Topological protection, disorder, and interactions: Survival at the surface of three-dimensional topological superconductors
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DOI：
10.1103/physrevb.89.155140
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发表时间：
2014-03
影响因子：
3.7
通讯作者：
M. Foster;Hong-Yi Xie;Y. Chou
中科院分区：
文献类型：
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作者：
M. Foster;Hong-Yi Xie;Y. Chou
我们考虑 3D 拓扑超导体无间隙表面态上无序和相互作用的相互作用。拓扑和超导顺序的结合反转了时间反转对称性的作用，因此外在时间反转不变的表面扰动仅以“赝磁”场的形式出现（阿贝尔和非阿贝尔矢量势，耦合到自旋和谷电流）。无序的主要影响是在表面态波函数中引起多重分形缩放。这些严重离域但强烈不均匀的状态相对于清洁系统重新规范化了相互作用矩阵元素。我们使用共形场论精确计算由于无序而导致的相互作用尺度维度的增强或抑制。我们确定了在对称类别 AIII 和 DIII 存在无序的情况下相互作用保持不相关的条件。在大拓扑缠绕数（许多表面谷）的限制下，我们证明有效场理论采用 Finkel’stein 非线性 sigma 模型的形式，并通过 Wess-Zumino-Novikov-Witten 项进行增强。西格玛模型结合了所有阶次的相互作用效应，并为受控扰动扩张提供了框架；逆自旋或热导是小参数。对于 DIII 类，我们表明相互作用总是无关紧要的，而在 AIII 类中，存在有限的稳定窗口，由无序控制。在此窗口之外，我们确定了新的交互稳定固定点。
We consider the interplay of disorder and interactions upon the gapless surface states of 3D topological superconductors. The combination of topology and superconducting order inverts the action of time-reversal symmetry, so that extrinsic time-reversal invariant surface perturbations appear only as “pseudomagnetic” fields (Abelian and non-Abelian vector potentials, which couple to spin and valley currents). The main effect of disorder is to induce multifractal scaling in surface state wave functions. These critically delocalized, yet strongly inhomogeneous states renormalize interaction matrix elements relative to the clean system. We compute the enhancement or suppression of interaction scaling dimensions due to the disorder exactly, using conformal field theory. We determine the conditions under which interactions remain irrelevant in the presence of disorder for symmetry classes AIII and DIII. In the limit of large topological winding numbers (many surface valleys), we show that the effective field theory takes the form of a Finkel’stein nonlinear sigma model, augmented by the Wess-Zumino-Novikov-Witten term. The sigma model incorporates interaction effects to all orders and provides a framework for a controlled perturbative expansion; the inverse spin or thermal conductance is the small parameter. For class DIII, we show that interactions are always irrelevant, while in class AIII, there is a finite window of stability, controlled by the disorder. Outside of this window, we identify new interaction-stabilized fixed points.