Theory of topological spin Josephson junctions

Abstract

We study the spin transport through a 1D quantum Ising-XY-Ising spin link that emulates a topological superconducting-normal-superconducting structure via Jordan-Wigner (JW) transformation. We calculate, both analytically and numerically, the spectrum of spin Andreev bound states and the resulting ${\mathbb{Z}}_2$ fractional spin Josephson effect (JE) pertaining to the emerging Majorana JW fermions. Deep in the topological regime, we identify an effective time-reversal symmetry that leads to ${\mathbb{Z}}_4$ fractional spin JE in the $\text{presence}$ of interactions within the junction. Moreover, we uncover a hidden inversion time-reversal symmetry that protects the ${\mathbb{Z}}_4$ periodicity in chains with an odd number of spins, even in the $\text{absence}$ of interactions. We also analyze the entanglement between pairs of spins by evaluating the concurrence in the presence of spin current and highlight the effects of the JW Majorana states. We propose to use a microwave cavity setup for detecting the aforementioned JEs by dispersive readout methods and show that, surprisingly, the ${\mathbb{Z}}_2$ periodicity is immune to $\text{any}$ local magnetic perturbations. Our results are relevant for a plethora of spin systems, such as trapped ions, photonic lattices, electron spins in quantum dots, or magnetic impurities on surfaces.

arXiv comment11+6 pages, 7 figures, the final published version

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Cited by in corpus (6)

• Non-Hermitian Fermi-Dirac Distribution in Persistent Current Transport
• Tunable Kondo screening length at a Y-junction of three inhomogenous spin chains
• Quantum spin helices more stable than the ground state: onset of helical protection
• Majorana-magnon interactions in topological Shiba chains
• Superconductor/normal-metal/superconductor junction of topological superconductors revisited: Fractional Josephson current, fermion parity, and oscillating wavefunctions
• Generalized Josephson effect with arbitrary periodicity in quantum magnets