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 wavefunctions. 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 non-linear 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.
Disorder-enhanced topological protection and universal quantum criticality in a spin-3/2 topological superconductor
Texas Center for Superconductivity and Department of Physics, University of Houston（休斯顿大学物理系超导电性中心）；Department of Physics and Astronomy, Rice University（莱斯大学物理与天文学系）；Rice Center for Quantum Materials, Rice University（莱斯大学量子材料中心）
Many-body-localization induced protection of symmetry-protected topological order in a XXZ spin model
Huse { \it et al} [Phys. Rev. B { \bf 88}，014206（2013）]和Elisran { \it et al} [Phys. Rev. B 89，144201（2014）]提出了一种反直觉的预期：即使在高激发本征态中，局域化也保护基态的量子顺序。在这项工作中，我们数值研究的本地化保护的拓扑（SPT）秩序考虑修改后的XXZ自旋模型，相关的相互作用的Su-Schrieffer-Heeger（SSH）模型。我们系统地研究了多体局域化（MBL）如何保护SPT对不同类型的疾病和不同形式的相互作用。一定的无序度导致各激发多体本征态的低纠缠谱明显简并。这一事实表明，存在的边缘模式，这是一个标志的SPT秩序，是由MBL在激发多体本征态的保护。此外，我们还报告了如何MBL保护边缘模式在激发多体本征态消失的对角型无序。
Coexistence of topologically nontrivial and trivial insulating states in topological Anderson Chern insulator
Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）
