# Archive ouverte HAL – 4 π and 8 π dual Josephson effects induced by symmetry defects

### Corneliu Malciu 1 Leonardo Mazza 2 Christophe Mora 1

#### Corneliu Malciu, Leonardo Mazza, Christophe Mora. 4 π and 8 π dual Josephson effects induced by symmetry defects. Physical Review B : Condensed matter and materials physics, American Physical Society, 2019, 99 (12), ⟨10.1103/PhysRevB.99.125153⟩. ⟨hal-02102139⟩

In topological insulator edges, the duality between the Zeeman field orientation and the proximitized superconducting phase has been recently exploited to predict a magneto-Josephson effect with a 4$\pi$ periodicity. We revisit this latter Josephson effect in the light of this duality and show that the same 4$\pi$ quantum anomaly occurs when bridging two spinless Thouless pumps to a p-wave superconducting region that could be as small as a single and experimentally-relevant superconducting quantum dot - a point-like defect. This interpretation as a dual Josephson effect never requires the presence of Majorana modes but rather builds on the topological properties of adiabatic quantum pumps with Z topological invariants. It allows for the systematic construction of dual Josephson effects of arbitrary periodicity, such as 4$\pi$ and 8$\pi$, by using point-like defects whose symmetry differs from that of the pump, dubbed symmetry defects. Although adiabatic quantum pumps are typically discussed via mappings to two-dimensional geometries, we show that this phenomenology does not have any counterpart in conventional two-dimensional systems.

• 1. LPA - Laboratoire Pierre Aigrain
• 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques