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Geometric dependence of Nb-Bi${_2}$Te${_3}$-Nb topological Josephson junction transport parameters

Superconductor-topological insulator-superconductor Josephson junctions have been fabricated in order to study the width dependence of the critical current, normal state resistance and flux periodicity of the critical current modulation in an external field. Previous literature reports suggest anomalous scaling in topological junctions due to the presence of Majorana bound states. However, for most realised devices, one would expect that trivial $2π$-periodic Andreev levels dominate transport. We also observe anomalous scaling behaviour of junction parameters, but the scaling can be well explained by mere geometric effects, such as the parallel bulk conductivity shunt and flux focusing.