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Andreev bound states trapped in a multi-terminal Josephson junction (JJ) canbe assigned a synthetic band topology owing to their periodic dependence on theJosephson phase bias. We demonstrate that the BdG symmetry adds a twist to thistopological character, i.e., gap closing points may or \textit{may not}correspond to change of Chern number, hence extending the standard paradigm fortopological bands. We further show that the topology of Andreev bands dependsonly on the scattering matrix of the junction and is independent of thetopological nature of superconductors forming the JJ hence indicating auniversal behaviour of multi-terminal JJ. We also show that the chiraljunction, supported by quantum Hall state at the junction region, leads to flatAndreev bands (implying absence of DC Josephson effects) that are devoid ofBerry curvature ( implying absence of AC Josephson effects). Such electricallyinert JJ may be useful for storage of quantum information in future quantumdevices.

Anomalous topology and synthetic flat band in multi-terminal Josephson Junctions