SciPost Phys. 18, 146 (2025) ·
published 2 May 2025
|
· pdf
Weyl semimetals have been theoretically predicted to become topological metals with anomalous Hall conductivity in amorphous systems. However, measuring the anomalous Hall conductivity in realistic materials, particularly those with multiple pairs of Weyl points, is a significant challenge. If a system respects time-reversal symmetry, then the anomalous Hall conductivity even vanishes. As such, it remains an open question how to probe the Weyl band like topology in amorphous materials. Here, we theoretically demonstrate that, under magnetic fields, a topological metal slab in amorphous systems exhibits three-dimensional quantum Hall effect, even in time-reversal invariant systems, thereby providing a feasible approach to exploring Weyl band like topology in amorphous materials. We unveil the topological origin of the quantized Hall conductance by calculating the Bott index. The index is carried by broadened Landau levels with bulk states spatially localized except at critical transition energies. The topological property also results in edge states localized at distinct hinges on two opposite surfaces.
SciPost Phys. 15, 193 (2023) ·
published 14 November 2023
|
· pdf
While topological phases have been extensively studied in amorphous systems in recent years, it remains unclear whether the random nature of amorphous materials can give rise to higher-order topological phases that have no crystalline counterparts. Here we theoretically demonstrate the existence of higher-order topological insulators in two-dimensional amorphous systems that can host more than six corner modes, such as eight or twelve corner modes. Although individual sample configuration lacks crystalline symmetry, we find that an ensemble of all configurations exhibits an average crystalline symmetry that provides protection for the new topological phases. To characterize the topological phases, we construct two topological invariants. Even though the bulk energy gap in the topological phase vanishes in the thermodynamic limit, we show that the bulk states near zero energy are localized, as supported by the level-spacing statistics and inverse participation ratio. Our findings open an avenue for exploring average symmetry protected higher-order topological phases in amorphous systems without crystalline counterparts.
Mr Wang: "Please find the detailed reply..."
in Submissions | report on Three-Dimensional Quantum Hall Effect in Topological Amorphous Metals