2026-04-30T17:37:22Zhttps://www.radar-service.eu/oai/OAIHandler

10.58160/e9470w3nu2w18n452026-04-24T07:50:07Z

10.58160/e9470w3nu2w18n45 Odobesko, Artem Artem Odobesko 0000-0003-3414-067X University of Würzburg University of Würzburg 2024 2025 Physics chiral symmetry topological defects topological crystalline insulators Landau levels Dirac fermions STM and STS raw measurements data Open Access Creative Commons Attribution 4.0 International Odobesko, Artem 0000-0003-3414-067X Bode, Matthias 0000-0001-7514-5560 Bode, Matthias 0000-0001-7514-5560 University of Würzburg Thomale, Ronny 0000-0002-3979-8836 University of Würzburg 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. We acknowledges funding supported by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through SFB 1170 Project No. 258499086 (project C02) and the Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter – ct.qmat (EXC 2147, Project No. 390858490). T.N. acknowledges support from the Swiss National Science Foundation through a consolidator grant (iTQC, TMCG-2-213805). R.T. and T.N. acknowledge support from the FOR 5249 (QUAST) led by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), in Switzerland funded by the Swiss National Science Foundation (Project 200021E-198011). G.W. acknowledges funding from the University of Zurich postdoc grant FK-23-134. The work of J.K. and T.S. was supported by the Foundation for Polish Science project “MagTop” no. FENG.02.01-IP.05-0028/23, co-financed by the European Union from the funds of Priority 2 of the European Funds for a Smart Economy Program 2021–2027 (FENG). STM The raw data was obtained and plotted in the same manner as presented in the paper, with minimal averaging applied to smooth the noise. The second derivative, d²I/dU², shown in the paper was calculated from the acquired dI/dU spectra using the Lock-In technique (see main text for details), averaged over an 8×Ubias window to improve the signal-to-noise ratio without losing key spectral features. All data was analyzed using a Python script, which is also included in the archive. en 10.1016/j.newton.2025.100009 GERMANY Deutsche Forschungsgemeinschaft https://ror.org/018mejw64 390858490 Komplexität und Topologie in Quantenmaterialien (CT.QMAT) Deutsche Forschungsgemeinschaft https://ror.org/018mejw64 258499086 Ultrahochauflösende Oberflächenstudien an topologischen Supraleitern application/x-tar