Majorana Fermions and Odd-frequency Cooper Pairs in a Nano Wire

We discuss a strong relationship between Majorana fermions and odd-frequency Cooper pairs which appear at a disordered normal (N) nano wire attached to a topologically nontrivial superconducting (S) one. The transport properties in superconducting nano wire junctions show universal behaviors irrespective of the degree of disorder: the quantized zero-bias differential conductance at 2e^{2}/h in NS junction and the fractional current-phase (J-\varphi) relationship of the Josephson effect in SNS junction J\propto \sin(\varphi/2). Such behaviors are exactly the same as those in the anomalous proximity effect of odd-parity spin-triplet superconductors. We show that odd-frequency Cooper pairs support the universal transport properties. The odd-frequency pairs exist wherever the Majorana fermions stay.