arXiv subjects

R. Johanna Zijderveld

Publications and source records attributed to R. Johanna Zijderveld.

4 recordsLinked to original sources

arXiv2026

ScatterWorks: A Python package for building and solving scattering network models

Network models provide an efficient framework for studying non-interacting transport and wave-propagation phenomena in disordered and topological systems. We introduce ScatterWorks, an open-source Python package for building and solving network models. The package uses a compact network representation with composable transformation operations (tile, cut, relink, and union) to enable flexible construction of periodic and finite networks. Local scattering matrices on nodes can be assigned by node labels or explicit indexing, assembled into global scattering equations, and used to compute quasienergies and transport observables. The package supports sparse scattering matrices, allowing transport observables to be evaluated with Schur-based solvers. We demonstrate the package workflow on a symbolic Fabry-Perot interferometer and a numerical Chalker-Coddington model, recovering analytical expressions and the expected near-critical transport behavior of the quantum Hall transition. Plotting utilities with label-aware rendering are included to streamline debugging and reproducible setup for larger, custom network geometries.

cond-mat.mes-hall↗

arXiv2026

Symmetric approximant formalism for statistical topological matter

The standard approach to characterizing topological matter, computing topological invariants, fails when the symmetry protecting the topological phase is preserved only on average in a disordered system. Because topological invariants rely on enforcing the symmetry exactly, they can overcount phases by incorrectly identifying certain non-robust features as robust. Moreover, in intrinsic statistical topological insulators, enforcing the symmetry exactly is guaranteed to destroy the topological phase. We define a mapping that addresses both issues and provides a unified framework for describing disordered topological matter.

cond-mat.mes-hall↗

arXiv2025

Scattering theory of higher order topological phases

The surface states of intrinsic higher order topological phases are protected by the spatial symmetries of a finite sample. This property makes the existing scattering theory of topological invariants inapplicable because the scattering geometry is either incompatible with the symmetry or does not probe the bulk topology. We resolve this obstacle by using a symmetric scattering geometry that probes transport from the inside to the outside of the sample. We demonstrate that the intrinsic higher order topology is captured by the flux dependence of the reflection matrix. Our finding follows from identifying the spectral flow of a flux line as a signature of higher order topology. We show how this scattering approach applies to several examples of higher order topological insulators and superconductors. Our theory provides an alternative approach for proving bulk--edge correspondence in intrinsic higher order topological phases, especially in presence of disorder.

cond-mat.mes-hall↗

arXiv2024

Quantum Scars and Caustics in Majorana Billiards

We demonstrate that the classical dynamics influence the localization behaviour of Majorana wavefunctions in Majorana billiards. By using a connection between Majorana wavefunctions and eigenfunctions of a normal state Hamiltonian, we show that Majorana wavefunctions in both p-wave and s-wave topological superconductors inherit the properties of the underlying normal state eigenfunctions. As an example, we demonstrate that Majorana wavefunctions in topological superconductors with chaotic shapes feature quantum scarring. Furthermore, we show a way to manipulate a localized Majorana wavefunction by altering the underlying classical dynamics using a local potential away from the localization region. Finally, in the presence of chiral symmetry breaking, we find that the Majorana wavefunction in convex-shaped Majorana billiards exhibits caustics formation, reminiscent of a normal state system with magnetic field.

cond-mat.mes-hall↗