Impurity-induced excitations in a topological two-dimensional ferromagnet/superconductor van der Waals moiré heterostructure

Abstract

The emergence of a topological superconducting state in van der Waals heterostructures provides a new platform for exploring novel strategies to control topological superconductors. In particular, impurities in van der Waals heterostructures, generically featuring a moiré pattern, can potentially lead to the unique interplay between atomic and moiré length scales, a feature absent in generic topological superconductors. Here we address the impact of nonmagnetic impurities on a topological moiré superconductor, both in the weak and strong regime, considering both periodic arrays and single impurities in otherwise pristine infinite moiré systems. We demonstrate a fine interplay between impurity-induced modes and the moiré length, leading to radically different spectral and topological properties depending on the relative impurity location and moiré lengths. Our results highlight the key role of impurities in van der Waals heterostructures featuring moiré patterns, revealing the key interplay between length and energy scales in artificial moiré systems.

Ferroelectric valley valves with graphene/MoTe2 van der Waals heterostructures

“…4g) the interface modes show a modulation in real space following the moiré potential. 27,60 It is worth noting that such a moire modulation does not lead to intervalley scattering, as demonstrated by the gapless nature of the spectral function of Fig. 4d.…”

Hamiltonian learning with real-space impurity tomography in topological moiré superconductors

“…This stems from the fact that the local exchange coupling creates in-gap Yu-Shiba-Rusinov modes inside the original superconducting gap ∆ [32,34,[88][89][90][91][92][93][94], and these modes form the low energy electronic structure leading to a topological superconducting state. As a result, low energy bands reflect the periodicity of the exchange modulation, and their associated in-gap modes in the presence of impurities inherit the same dependence [34,55].…”

“…The appearance of in-gap modes alone is not enough to assess the topological invariant of a superconductor, as in-gap states can appear in both trivial and topological superconductors [87]. Interestingly, the inclusion of a moiré pattern leads to subtle changes in the spatial distribution of in-gap states [55]. As we will show below, the fine structure of the in-gap modes allows for extracting the topological invariant of the underlying state.…”

“…We finally elaborate on the computational procedure to solve this model in the limit of a single impurity in an otherwise pristine system. For this purpose, we will use Green's function embedding method [55,75,76]. The embedding method relies on extracting the Green's function from the Dyson equation of the defective system…”

“…However, extracting the values of these modulations in moiré system is an open problem, as their effect on the electronic structure is greatly challenging to disentangle. Interestingly, the coexistence of a moiré pattern and local impurities opens up a new strategy to infer electronic parameters due to their non-trivial interplay [55][56][57][58][59].…”