Robustness of topological order against disorder

Abstract

A universal topological marker has been proposed recently to map the topological invariants of Dirac models in any dimension and symmetry class to lattice sites. Using this topological marker, we examine the conditions under which the global topological order, represented by the spatially averaged topological marker, remains unchanged in the presence of disorder for 1D and 2D systems. We find that if an impurity corresponds to varying a nonzero matrix element of the lattice Hamiltonian, regardless the element represents hopping, chemical potential, pairing, etc, then the average topological marker is conserved. However, if there are many strong impurities and the average distance between them is shorter than a correlation length, then the average marker is no longer conserved. In addition, strong and dense impurities can be used to continuously interpolate between one topological phase and another. A number of prototype lattice models including Su-Schrieffer-Heeger model, Kitaev chain, Chern insulators, Bernevig-Hughes-Zhang model, and chiral p-wave superconductors are used to elaborate the ubiquity of these statements.

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Cited by in corpus (13)

• Phase transitions and scale invariance in topological Anderson insulators
• Dielectric and optical markers originating from quantum geometry
• Topological Phases in Fractals: Local Spin Chern Marker in the Sierpinski carpet Kane-Mele-Rashba Model
• Kibble-Zurek behavior in a topological phase transition with a quadratic band crossing
• Topological characterization of modified Kane-Mele-Rashba models via local spin Chern marker
• Disorder-induced phase transitions in double HgTe quantum wells
• Evaluation of real-space second Chern number using the kernel polynomial method
• Real space quantum metric of solids
• Absorbance marker: Detection of quantum geometry and spread of Wannier function in disordered 2D semiconductors
• Regularized universal topological markers for Dirac systems
• Aharanov-Bohm oscillations and perfectly transmitted mode in amorphous topological insulator nanowires
• Tensor network method for real-space topology in quasicrystal Chern mosaics
• Entanglement as a topological marker in harmonically confined attractive Fermi-Hubbard chains