Annihilation of Colliding Bogoliubov Quasiparticles Reveals their Majorana Nature

The single-particle excitations of a superconductor are coherent superpositions of electrons and holes near the Fermi level, called Bogoliubov quasiparticles. They are Majorana fermions, meaning that pairs of quasiparticles can annihilate. We calculate the annihilation probability at a beam splitter for chiral quantum Hall edge states, obtaining a $1\pm \cos \varphi$ dependence on the phase difference $\varphi$ of the superconductors from which the excitations originated (with the $\pm$ sign distinguishing singlet and triplet pairing). This provides for a nonlocal measurement of the superconducting phase in the absence of any supercurrent.

Figure 1

Two-particle interferometer for Bogoliubov quasiparticles. Shown is a two-dimensional electron gas in a perpendicular magnetic field (light blue), with chiral edge channels at the edges (arrows indicate the direction of motion and $a$, $b$, $c_p$ denote the quasiparticle operators). A constriction at the center forms a beam splitter. Current is injected at the two ends (red), biased at voltages $V_1$ and $V_2$. Upon passing along a superconducting electrode (grey, labeled $S$), repeated Andreev reflection converts the electrons into a coherent superposition of electrons and holes. The collision and pairwise annihilation of these Bogoliubov quasiparticles is detected by correlating the ac currents $I_1$ and $I_2$.

Figure 2

Noise correlator as a function of frequency (a) and as a function of superconducting phase difference (b). Panel a shows both the collision term $P_{\text{coll}}=2P_{12}$ and the full correlator $P_{\text{full}}=P_{\text{coll}}+P_{11}+P_{22}$, while panel b shows only $P_{\text{coll}}$ (the full correlator differs by a phase-independent offset, such that $P_{\text{full}}=0$ at ${\varphi }_{12}=0$). The curves are calculated from the general result (23) for spin-singlet pairing, with parameters ${\overline{\alpha }}_1={\overline{\alpha }}_2=\pi /4$.