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Optimal choice of spin polarization enables electron injection into the helical edge state at a precise position, despite the uncertainty principle, permitting access to specific nonlocal Green's functions. We show, within 1D effective description, that this fact facilitates a direct identification of odd-frequency pairing through parity measurement (under frequency reversal) of the nonlocal differential conductance in a setup comprising the Josephson junction on the helical edge state of a 2D topological insulator with two spin-polarized probes tunnel-coupled to the junction region. A 2D numerical simulation has also been conducted to confirm theoretical predictions as well as to demonstrate the experimental feasibility of the proposal., Comment: 11 pages, 3 figures

Existence of distinctive correlation between the thermal conductance and the Josephson current across a 1-D topological Josephson junction (T-JJ) is established and an expression connecting the two is derived in the short junction limit. It is shown that the three terminal T-JJ provides us with an ideal set-up for exploiting the distinctive correlations which aid in identifying hallmarks of Majorana bound state localized at the junction. Our approach combines information form sub-gap Cooper pair transport and transport of above-gap thermally excited quasiparticle which is complementary to the existing studies., Comment: 19 pages, 8 figures

We theoretically investigate the transport properties of a quasi one dimensional ferromagnet-superconductor junction where the superconductor consists of mixed singlet and triplet pairings. We show that the relative orientation of the stoner field ($\bf{\tilde{h}}$) in the ferromagnetic lead and the $\bf{d}$ vector of the superconductor acts like a on-off switch for the zero bias conductance of the device. In the regime, where triplet pairing amplitude dominates over the singlet counterpart (topological phase), a pair of Majorana zero modes appear at each end of the superconducting part of the nanowire. When $\bf{\tilde{h}}$ is parallel or anti-parallel to the $\bf{d}$ vector, transport gets completely blocked due to blockage in pairing while, when $\bf{\tilde{h}}$ and $\bf{d}$ are perpendicular to each other, the zero energy two terminal differential conductance spectra exhibits sharp transition from $4e^2/h$ to $2e^2/h$ as the magnetization strength in the lead becomes larger than the chemical potential indicating the spin selective coupling of pair of Majorana zero modes to the lead., Comment: This is the published version