Probing chiral symmetry with a topological domain wall sensor

Chiral symmetry is a fundamental property with profound implications for the characteristics of elementary particles, that implies a spectral symmetry (i.e. E -> -E ) in their dispersion relation. In condensed matter physics, chiral symmetry is often associated with superconductors or materials hosting Dirac fermions, such as graphene or topological insulators. In these contexts, chiral symmetry is an emergent low-energy property, accompanied by an emergent spectral symmetry. However, since the presence of spectral symmetry does not necessarily imply chiral symmetry, a key question arises: how can these two properties be experimentally differentiated? In this study, we demonstrate that a system with preserved spectral symmetry can reveal underlying broken chiral symmetry through the presence of topological defects. Our findings shows that these defects induce a spectral imbalance in the Landau level spectrum, providing direct evidence of symmetry alteration at topological domain walls. Using high-resolution scanning tunneling microscopy and spectroscopy, we demonstrate the intricate interplay between chiral and translational symmetry, which is broken at step edges in topological crystalline insulator Pb$_{1-x}$Sn$_x$Se. The chiral symmetry breaking leads to a shift in the guiding center coordinates of the Landau orbitals near the step edge, thus resulting in a distinct chiral flow of the spectral density of Landau levels. This study underscores the pivotal role of topological defects as sensitive probes for detecting hidden symmetries, offering insights into emergent phenomena with implications for fundamental physics.