Theory of topological spin Josephson junctions

Superconductor/normal-metal/superconductor junction of topological superconductors revisited: Fractional Josephson current, fermion parity, and oscillating wavefunctions

“…Finally, we consider possible applications of our study as future works. Although the model calculated in this paper is non-interacting, it may be possible to discuss a Z 4 fractional Josephson effect if many-body interactions are taken into account [26][27][28][29][30][31]. As a technical aspect, our calculation method may be applicable to the topological physics of multi-terminal Josephson junctions, which has been discussed in recent studies [47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63].…”

“…He showed that the groundstate fermion parity (FP) of a topological Josephson junction switches its sign every 2𝜋 change of the phase difference, resulting in the 4𝜋-periodic Josephson current. More recently, it has been shown that many-body interactions or impurities can induce an 8𝜋-periodic fractional Josephson effect, due to the presence of Z 4 parafermions or fractional MZMs [26][27][28][29][30][31].…”

Tunable Kondo screening length at a Y-junction of three inhomogenous spin chains

“…According to Ref. [43] we describe each quantum spin chain by means of a one-dimensional, inhomogenous lattice quantum spin Hamiltonian H λ SC over an L site lattice with open boundary conditions at the endpoint at j = L. Therefore, denoting with λ the chain index, we set…”

“…Following the drawing code of Ref. [43], each sphere represents a quantum spin. Spheres with the equatorial plane colored in red represent spins interacting with an isotropic magnetic interaction lying within the XY-plane in spin space (the XX-part of the whole chain), while spheres with just one colored segment within the equatorial plane correspond to spins with an Ising interaction directed along the segment.…”

“…An important step in extending this approach to a YSC has recently been provided in Ref. [43], where it has been shown how, when applying the JW transformation to the interface between an XX-chain and a quantum Ising chain with Ising axis rotated with respect to the z-axis (in spin space) of the XX-chain, the interface is mapped onto the interface between a spinless normal 1D conductor and a p-wave superconductor, with the phase of the order parameter equal to twice the tilting angle of the Ising axis. In the low-energy, long-wavelength limit, once the system parameters are pertinently chosen, an interface as such stabilizes perfect Andreev reflection on the normal side, which is the same as connecting a "truly" fermionic system to a bulk superconductor at fixed phase.…”