Repulsive Casimir force from a Majorana zero-mode

Abstract

Fu and Kane have taught us that a Majorana zero-mode appears on the quantum spin Hall edge at the interface with a superconductor. If a magnetic scatterer is placed on the edge, the zero-point energy of massless edge excitations exerts a force on the scatterer. This is the fermionic analogue of the electromagnetic Casimir effect. We show that the Majorana zero-mode produces a repulsive Casimir force, pushing the scatterer away from the superconductor. Unlike some other signatures of Majorana zero-modes, the repulsive Casimir force is directly tied to the topological invariant of the system (the sign of the determinant of the reflection matrix from the superconductor).

6 pages, 3 figures; V2: references added; V3: appendix with derivation of the scattering formula for the Casimir free energy; V4: typo in eq. 11 corrected

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