Annihilation of Colliding Bogoliubov Quasiparticles Reveals their Majorana Nature

Abstract

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 AE cos ϕ dependence on the phase difference ϕ of the superconductors from which the excitations originated (with the AE sign distinguishing singlet and triplet pairing). This provides for a nonlocal measurement of the superconducting phase in the absence of any supercurrent. DOI: 10.1103/PhysRevLett.112.070604 PACS numbers: 05.60.Gg, 03.75.Lm, 74.45.+c, 74.78.Na Condensed matter analogies of concepts from particle physics are a source of much inspiration, and many of these involve superconductors or superfluids [1]. Majorana's old idea [2] that a spin-1=2 particle (such as a neutrino) might be its own antiparticle has returned [3] in the context of low-dimensional superconductors, inspiring an intense theoretical and experimental search for condensed matter realizations of Majorana fermions [4]. The search has concentrated on Majorana zero modes [5][6][7]-midgap states (at the Fermi level E ¼ 0) bound to a defect in a superconductor with broken spin-rotation and time-reversal symmetry (a so-called topological superconductor [8,9]). The name Majorana zero mode (or Majorino [10]) is preferred over Majorana fermion, since they are not fermions at all but have a non-Abelian exchange statistics [11].Majorana fermions, in the original sense of the word, do exist in superconductors. In fact they are ubiquitous: the time-dependent four-component Bogoliubov-de Gennes wave equation for quasiparticle excitations (so-called Bogoliubov quasiparticles) can be brought to a real form by a 4 × 4 unitary transformation U [12], in direct analogy to the real Eddington-Majorana wave equation of particle physics [2,13]. A real wave equation implies the linear relation Ψ † ðr; tÞ ¼ UΨðr; tÞ between the particle and antiparticle field operators, which is the hallmark of a Majorana fermion. As argued forcefully by Chamon et al. [14], fermionic statistics plus superconductivity by itself produces Majorana fermions, irrespective of considerations of dimensionality, topology, or broken symmetries.Here we propose an experiment to probe the Majorana nature of Bogoliubov quasiparticles in conventional, nontopological, superconductors. Existing proposals apply to topological superconductors [15][16][17][18][19][20][21][22][23][24][25], where Majorana fermions appear as charge-neutral edge states with a distinct signature in DC transport experiments. In contrast, the Bogoliubov quasiparticles of a nontopological superconductor have charge expectation valueq ≠ 0, so their Majorana nature remains hidden in the energy domain probed by DC transport.It is in the time domain that the wave equation takes on a real form and that particle and antiparticle operators are linearly related. We will show that...

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