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Bound states in the continuum (BICs) are quantum states with normalizablewave functions and energies that lie within the continuous spectrum for whichextended or dispersive states are also available. These special states, whichhave shown great applicability in photonic systems for devices such as lasersand sensors, are also predicted to exist in electronic low-dimensionalsolid-state systems. The non-trivial topology of materials is within the knownmechanisms that prevent the bound states to couple with the extended states. Inthis work we search for topologically protected BICs in a quantum Hall bar withan anti-dot formed by a pore far from the borders of the bar. The bound stateenergies and wavefunctions are calculated by means of the Recursive S-Matrixmethod. The resulting bound state energies coexist with extended states andexhibit a pattern complimentary to the Hofstadter butterfly. Asymmetry-breaking diagonal disorder was introduced, showing that the BICs withenergies far from the Landau levels remain robust. Moreover, the energydifference between consecutive BICs multiplied by the anti-dot perimeterfollows the same curve despite disorder. Finally, a BIC-mediated currentswitching effect was found in a multi-terminal setup, which might permit theirexperimental detection.

Robust Topological Bound States in the Continuum in a Quantum Hall Bar with an Anti-dot