Symmetry-protected topological(SPT)phases—such as topological insulators and superconductors—are exotic quantum phases characterized by nontrivial edge states that are stable as long as certain symmetries are preser...Symmetry-protected topological(SPT)phases—such as topological insulators and superconductors—are exotic quantum phases characterized by nontrivial edge states that are stable as long as certain symmetries are preserved[1],[2],[3].Contrary to conventional wisdom,recent studies show that SPT phases can survive even when part of the protecting symmetry is locally broken by quenched disorder,provided that the symmetry is restored after ensemble averaging—a circumstance that defines a new class of topological phases dubbed average symmetry-protected topological(ASPT)phases[4],[5].展开更多
基金the National Key R&D Program of China(2022YFA1403402)the National Natural Science Foundation of China(12174068)+3 种基金the Science and Technology Commission of Shanghai Municipality(24LZ1400100 and 23JC1400600)the Shuguang Program of Shanghai Education Development Foundation and Shanghai Municipal Education CommissionJian-Hao Zhang and Zhen Bi are supported by startup funds from the Pennsylvania State UniversityZhen Bi also acknowledges support from NSF under award number DMR-2339319.
文摘Symmetry-protected topological(SPT)phases—such as topological insulators and superconductors—are exotic quantum phases characterized by nontrivial edge states that are stable as long as certain symmetries are preserved[1],[2],[3].Contrary to conventional wisdom,recent studies show that SPT phases can survive even when part of the protecting symmetry is locally broken by quenched disorder,provided that the symmetry is restored after ensemble averaging—a circumstance that defines a new class of topological phases dubbed average symmetry-protected topological(ASPT)phases[4],[5].
