Robust topological bound states in the continuum in a quantum Hall bar with an anti-dot

Bound states in the continuum (BICs) are quantum states with normalizable wave functions and energies that lie within the continuous spectrum for which extended or dispersive states are also available. These special states, which have shown great applicability in photonic systems for devices such as lasers and sensors, are also predicted to exist in electronic low-dimensional solid-state systems. The non-trivial topology of materials is within the known mechanisms that prevent the bound states to couple with the extended states. In this work we search for topologically protected BICs in a quantum Hall bar with an anti-dot formed by a pore far from the borders of the bar. The bound state energies and wavefunctions are calculated by means of the Recursive S-Matrix method. The resulting bound state energies coexist with extended states and exhibit a pattern complimentary to the Hofstadter butterfly. A symmetry-breaking diagonal disorder was introduced, showing that the BICs with energies far from the Landau levels remain robust. Moreover, the energy difference between consecutive BICs multiplied by the anti-dot perimeter follows the same curve despite disorder. Finally, a BIC-mediated current switching effect was found in a multi-terminal setup for zero and finite temperature, which might permit their experimental detection.