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Register a new userNon-Abelian monopoles in the multiterminal Josephson effect
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We present a detailed theoretical analysis for the spectral properties of Andreev bound states in the multiterminal Josephson junctions by employing a symmetry-constrained scattering matrix approach. We find that in the synthetic five-dimensional space of superconducting phases, crossings of Andreev bands may support the non-Abelian $SU(2)$ monopoles with a topological charge characterized by the second class Chern number. We propose that these topological defects can be detected via nonlinear response measurement of the current autocorrelations. In addition, multiterminal Josephson junction devices can be tested as a hardware platform for realizing holonomic quantum computation.
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We study the Josephson effect in the multiterminal junction of topological superconductors. We use the symmetry-constrained scattering matrix approach to derive band dispersions of emergent sub-gap Andreev bound states in a multidimensional parameter space of superconducting phase differences. We find distinct topologically protected band crossings that serve as monopoles of finite Berry curvature. Particularly, in a four-terminal junction the admixture of $2pi$ and $4pi$ periodic levels leads to the appearance of finite energy Majorana-Weyl nodes. This topological regime in the junction can be characterized by a quantized nonlocal conductance that measures the Chern number of the corresponding bands. In addition, we calculate current-phase relations, variance, and cross-correlations of topological supercurrents in multiterminal contacts and discuss the universality of these transport characteristics. At the technical level these results are obtained by integrating over the group of a circular ensemble that describes the scattering matrix of the junction. We briefly discuss our results in the context of observed fluctuations of the gate dependence of the critical current in topological planar Josephson junctions and comment on the possibility of parity measurements from the switching current distributions in multiterminal Majorana junctions.
Spin superconductor (SSC) is an exciton condensate state where the spin-triplet exciton superfluidity is charge neutral while spin $2(hbar/2)$. In analogy to the Majorana zero mode (MZM) in topological superconductors, the interplay between SSC and band topology will also give rise to a specific kind of topological boundary state obeying non-Abelian braiding statistics. Remarkably, the non-Abelian geometric phase here originates from the Aharonov-Casher effect of the half-charge other than the Aharonov-Bohm effect. Such topological boundary state of SSC is bound with the vortex of electric flux gradient and can be experimentally more distinct than the MZM for being electrically charged. This theoretical proposal provides a new avenue investigating the non-Abelian braiding physics without the assistance of MZM and charge superconductor.
We consider a diffusive S-N-S junction with electrons in the normal layer driven out of equilibrium by external bias. We show that, the non-equilibrium fluctuations of the electron density in the normal layer cause the fluctuations of the phase of the order parameter in the S-layers. As a result, the magnitude of the Josephson current in the non-equilibrium junction is significantly supressed relative to its mean field value.
We consider mesoscopic four-terminal Josephson junctions and study emergent topological properties of the Andreev subgap bands. We use symmetry-constrained analysis for Wigner-Dyson classes of scattering matrices to derive band dispersions. When scattering matrix of the normal region connecting superconducting leads is energy-independent, the determinant formula for Andreev spectrum can be reduced to a palindromic equation that admits a complete analytical solution. Band topology manifests with an appearance of the Weyl nodes which serve as monopoles of finite Berry curvature. The corresponding fluxes are quantified by Chern numbers that translate into a quantized nonlocal conductance that we compute explicitly for the time-reversal-symmetric scattering matrix. The topological regime can be also identified by supercurrents as Josephson current-phase relationships exhibit pronounced nonanalytic behavior and discontinuities near Weyl points that can be controllably accessed in experiments.
Josephson junctions based on three-dimensional topological insulators offer intriguing possibilities to realize unconventional $p$-wave pairing and Majorana modes. Here, we provide a detailed study of the effect of a uniform magnetization in the normal region: We show how the interplay between the spin-momentum locking of the topological insulator and an in-plane magnetization parallel to the direction of phase bias leads to an asymmetry of the Andreev spectrum with respect to transverse momenta. If sufficiently large, this asymmetry induces a transition from a regime of gapless, counterpropagating Majorana modes to a regime with unprotected modes that are unidirectional at small transverse momenta. Intriguingly, the magnetization-induced asymmetry of the Andreev spectrum also gives rise to a Josephson Hall effect, that is, the appearance of a transverse Josephson current. The amplitude and current phase relation of the Josephson Hall current are studied in detail. In particular, we show how magnetic control and gating of the normal region can enable sizable Josephson Hall currents compared to the longitudinal Josephson current. Finally, we also propose in-plane magnetic fields as an alternative to the magnetization in the normal region and discuss how the planar Josephson Hall effect could be observed in experiments.
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