Helical Andreev bound states in topological insulator f-wave Josephson junction

• We study effect of ff-wave superconductivity on the surface states of a three-dimensional topological insulator.
• The magnetization of ferromagnetic section is perpendicular to the surface of junction.
• We carry out our goal by introducing relevant form of Dirac spinors for helical gapless excitations.
• It is shown the results are completely different from those in conventional singlet superconductivity.
• Strongly suppressed Andreev reflection is demonstrated.

We study the effect of f  -wave triplet superconductivity induced by proximity effect on the surface states of a three-dimensional topological insulator (3DTI). In fact, the gapless surface state for excitation spectrum of a triplet superconductor topological insulator gives rise to formation of helical Andreev bound states (ABSs) and, necessarily, suppression of Andreev reflection at the interface of a superconductor/ferromagnetic structure. By calculating the relevant form of Dirac spinors for two-dimensional time-reversal symmetric Hamiltonian, the normal and Andreev reflection coefficients and ABSs corresponding to tunneling and Josephson junctions, respectively, are obtained. It is shown, that the Andreev process vanishing occurs strongly, so that, the evanescent waves will be permissible in tunneling process. It is found that the dispersion of ABSs is an even function of electron incident angle θθ for f1f1-wave and odd for f2f2-wave. In f1f1-order, for module of incident angle, |θ|>0.167πθ>0.167π, the ABSs are independent of superconducting phase difference, ϕϕ, so that the Josephson current may vanish for this region. Effect of magnetization on flattening of ABSs occurs in f2f2 order faster than f1f1.