Observation of the 4π-periodic Josephson effect in InAs nanowires Dominique Laroche, 1, * Daniël Bouman, 1, * David J. van Woerkom, 1 Alex Proutski, 1 Chaitanya Murthy, 2 Dmitry I. Pikulin, 3 Chetan Nayak, 2, 3 Ruben J. J. van Gulik, 1 Jesper Nygård, 4 Peter Krogstrup, 4 Leo P. Kouwenhoven, 1, 5 and Attila Geresdi 1, † 1 QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, The Netherlands 2 Department of Physics, University of California, Santa Barbara, CA 93106, USA 3 Station Q, Microsoft Research, Santa Barbara, California 93106-6105, USA 4 Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark 5 Microsoft Station Q Delft, 2600 GA Delft, The Netherlands (Dated: December 25, 2017) Quantum computation by non-Abelian Majo- rana zero modes (MZMs) [1, 2] offers an approach to achieve fault tolerance by encoding quantum information in the non-local charge parity states of semiconductor nanowire networks in the topo- logical superconductor regime [3–5]. Thus far, ex- perimental studies of MZMs chiefly relied on sin- gle electron tunneling measurements [6–11] which leads to decoherence of the quantum information stored in the MZM [4, 12]. As a next step towards topological quantum computation, charge parity conserving experiments based on the Josephson effect [13] are required, which can also help ex- clude suggested non-topological origins [14–18] of the zero bias conductance anomaly. Here we re- port the direct measurement of the Josephson ra- diation frequency [19] in InAs nanowires with epi- taxial aluminium shells [20]. For the first time, we observe the 4π-periodic Josephson effect above a magnetic field of ≈ 200 mT, consistent with the estimated [21, 22] and measured [23] topological phase transition of similar devices. The universal relation between the frequency f J of the oscillating current and an applied DC voltage bias V across a superconducting weak link [13] is determined solely by natural constants: f J V = 2e h =Φ -1 0 = 483.6 MHz/μV, (1) where e is the single electron charge, h is the Planck constant and Φ 0 is the superconducting flux quantum. This relation, describing the conventional, 2π-periodic Josephson effect, can be understood as the tunneling of Cooper pairs with a net charge e ⋆ =2e coupled to pho- tons of energy hf [24]. This coupling, referred to as the AC Josephson effect, has first been measured in super- conducting tunnel junctions [25] and has been shown to persist in metallic weak links [26], carbon nanotubes [27] and semiconductor channels [28, 29], as well as in high critical temperature superconductors [30]. In topological Josephson junctions, the effective tun- neling charge is the single electron charge, e ⋆ = e, which leads to a factor of two increase in the flux periodicity, giving rise to the so-called 4π-periodic Josephson effect [21, 22, 31]. Therefore, in this MZM regime, the fre- quency at a given voltage bias V drops by a factor of two, f MZM (V )= f J (V )/2, providing a robust signature of the topological phase transition in the superconducting leads. In real devices however, the finite size of the topo- logical regions [32], poisoning events [22, 31] and Landau- Zener tunneling to the quasiparticle continuum [33] can effectively restore the 2π-periodic, trivial state. The lat- ter two parity-mixing effects cause the system to relax to its ground state, effectively constraining the system in the lowest topological energy branch (red solid lines in Fig. 1a). Nevertheless, out-of-equilibrium measurements performed at rates faster than these equilibration pro- cesses can still capture the 4π-periodic nature of topo- logical junctions [32–34]. In contrast, finite-size effects can be avoided by biasing the junction at voltages large enough to overcome the Majorana hybridization gap ε M [33]. Here, we report the direct observation of a mag- netic field-induced halving of the Josephson radiation frequency in InAs nanowire (NW) junctions partially covered with an epitaxially grown aluminium shell [20] (Fig. 1d). In this system, previous direct transport ex- periments suggest parity lifetimes above 0.1 μs [35] and hybridization energies ε M  1 μeV for leads longer than 1.5 μm [36]. Thus, a frequency-sensitive measurement in the microwave domain is expected to reveal the 4π- periodic Josephson effect [37, 38]. As a frequency-sensitive microwave detector, we utilize a superconducting tunnel junction with a quasiparticle gap of Δ DET , wherein the photon-assisted electron tun- neling (PAT) current contributes to the DC current above a voltage bias threshold eV DET > 2Δ DET - hf [19, 39] (Fig. 1c). This on-chip detector [40], coupled via capaci- tors C C to the NW junction (see Fig. 1b for the schemat- ics and Fig. 1e for optical image of the device) is engi- neered to result in an overdamped microwave environ- ment characterized by a single f c = (2πRC ) -1 ≈ 28 GHz cutoff frequency with R = 538 Ω and C = 10.4 fF, see Sec. 3 in the Supplementary Information (SI). The re- arXiv:1712.08459v1 [cond-mat.mes-hall] 22 Dec 2017