Detecting and leaking a Majorana bound state through proximity to a Kitaev ring

Abstract

We show that the existence of a Majorana bound state at one end of a Kitaev chain is unambiguously signaled by observable quantities in a nearby Kitaev ring. When the Kitaev chain is in the topological phase, the band structure of the Kitaev ring breaks chiral symmetry and the ring-Majoranas' spectral functions are even functions of momentum and energy, the latter wielding time-reversal and particle-hole symmetric occupation numbers and, hence, zero current in the ring. Driving a phase transition in the Kitaev chain (e.g., using a backgate to vary the chemical potential of the chain through its critical value), the replacement of the Majorana bound state by a trivial fermion is manifest by chiral symmetry reappearing in the band structure of the ring and by the ring-Majoranas' spectral functions loss of parity, wielding time-reversal and particle-hole symmetry breaking in the occupation numbers and a spontaneous current in the ring. Energy resonance and maximum spectral weight exactly at the resonance energy concur for a high leakage probability between ring-Majoranas' states and the Majorana bound state, whereas the lack of energy resonance makes unlikely any leakage between ring-Majoranas' states and the trivial fermion states. The proposed setup also invites further investigations in the context of braiding and/or fusion of Majorana states, both as detection mechanisms and for quantum computing purposes.