Cooper-pair splitting in two parallel InAs nanowires

We report on the fabrication and electrical characterization of an InAs double - nanowire (NW) device consisting of two closely placed parallel NWs coupled to a common superconducting electrode on one side and individual normal metal leads on the other. In this new type of device we detect Cooper-pair splitting (CPS) with a sizeable efficiency of correlated currents in both NWs. In contrast to earlier experiments, where CPS was realized in a single NW, demonstrating an intrawire electron pairing mediated by the superconductor (SC), our experiment demonstrates an inter- wire interaction mediated by the common SC. The latter is the key for the realization of zero-magnetic field Majorana bound states, or Parafermions; in NWs and therefore constitutes a milestone towards topological superconductivity. In addition, we observe transport resonances that occur only in the superconducting state, which we tentatively attribute to Andreev Bound states and/or Yu-Shiba resonances that form in the proximitized section of one NW.


I. INTRODUCTION
Topologically protected electronic states in nanostructures have recently attracted wide attention, as they may provide fundamental building blocks for quantum computation. 1,2 Recent advances in material science and device fabrication resulted in considerable progress towards the generation and detection of topologically protected bound states in topologically non-trivial semiconducting nanowires (NWs), so called Majorana Fermions (MF). 3-7 Two MFs can combine together into a regular Fermion that is why MFs are also known as Z 2 Fermions. MFs are predicted to have non-Abelian braid statistics and may provide a platform for topological quantum computation. 8,9 However, one can not implement all required operations for universal quantum computation in quantum bits (qubits) based on MFs by using topologically protected braiding. In this respect, Z 4 Fermions, also known as Parafermions (PFs), are better as they allow for a larger set of operations. 10 Recently, it has theoretically been predicted that PFs can be generated in a system based on two NWs with different spin orbit interaction coupled to a common superconducting electrode. [11][12][13] The SC induces both a pairing interaction within each NW and between the two NWs due to Cooper-pair splitting (CPS). In order to realize PFs, the interwire coupling must dominate. 12 It has been shown that this is possible in systems with strong electron-electron interaction, such as nanoscaled semiconducting wires. [14][15][16] Another advantage of the parallel two-wire approach, even if PFs are not formed, is the fact, that for large interwire pairing an external magnetic field is not required or only a small field is enough to reach the topological phase. 17 A large magnetic field is a limiting factor, because of the critical magnetic field of the SC. It is therefore crucial both for MF-based charge qubits and for the realization of PFs to demonstrate an appreciable magnitude of interwire pairing interaction mediated by a SC. This coupling is also known as crossed-Andreev reflection or CPS. 14,18,19 In the last few years, several CPS experiments have been performed using different platforms, mainly single NWs, [20][21][22][23][24] Carbon Nanotubes 25,26 and graphene. 27,28 Splitting efficiencies close to 100% have been reported, 26 demonstrating that intrawire pairing can exceed local Cooper pair tunneling. Up to now, all NW based CPS devices consisted of a single NW contacted by two normal metal electrodes and one superconducting contact in between. In order to assess the interwire pairing in double NW structures, it is essential to investigate CPS in such a system. In this work we demonstrate CPS in a parallel double NW device, which is an important first step towards topological quantum computation with PFs.

II. SCHEME AND SAMPLE
We investigate a device shown schematically in figure 1(a). Two InAs semiconducting NWs with large spin orbit interaction are placed in parallel (NW 1 green, NW 2 red) and electrically coupled by a common superconducting electrode S (blue). Both NWs are contacted by individual normal metal leads N 1/2 (yellow). Sidegates SG 1/2 (yellow) are located on each side of the NWs, in order to separately tune the chemical potentials of the quantum dots (QDs), which form between N 1/2 and S. We note, that the exact location of the QDs is not known, since we do not use additional barrier gates to terminate the QDs. 29 However, it is clear that both N 1/2 and S induce a potential step from which (partial) electron reflection is possible and QD bound states can form. We also point out already here that the electronic boundary conditions on the S side may change if S is in the normal or superconducting state, due to the proximity effect. Besides local Cooper pair tunneling from S to N 1/2 , 30 Cooper pairs (white circle with red/black dot) can be split, resulting in a non-local current consisting of entangled single electrons. This process is expected to be large if both QDs, QD 1/2 , are in resonance and the electrons can sequentially tunnel from the SC to the two normal metal leads.

A. Fabrication and Characterization
The InAs NWs used in this study are grown by Chemical Beam Epitaxy along the 111 direction. They have a diameter of about 80 nm and possess pure Wurtzite crystal structure.
After transferring NWs from the growth chip to the substrate by standard dry transfer, we use scanning electron microscopy, to select NWs naturally lying next to each other. It is important to note that the NWs are electronically disconnected by their native oxide, which is about 2 nm to 3 nm thick surrounding each NW. Next, we deposit the common superconducting lead S made of Ti/Al (thickness: 3 nm/90 nm) after removing the native oxide at the contact area using a solution of (N H 4 ) 2 S x . 31 Afterwards, the individual normal metal contacts N 1/2 made of Ti/Au (3 nm/130 nm) are deposited at the same time as the local sidegates SG 1/2 . A false color scanning electron microscopy image of the device is shown in figure 1(b). The distance between the source Al contact and the Au drain contacts is about 250 nm.
All measurements were carried out in a dilution refrigerator with a base temperature of about 50 mK. Differential conductance has been measured for the respective NWs simultaneously using synchronized lock-in techniques (see figure 1(b)). Characterization measurements (see figure A1 in appendix) indicate two individual QDs QD 1 and QD 2 in each of the NWs, similar to previous measurements. 32 From Coulomb blockade measurements we extract the following parameters for the two QDs for the charging energy U , single particle level spacing and the life-time broadening of the QD eigenstates Γ to the leads: U 1,2 = 0.5 − 0.7 meV, 3 meV for QD 1 and QD 2 , respectively. Both quantum dots hold similar properties, implying that each QD is formed between the Al contact and individual Au contacts. In addition, we observe a slight suppression of conductance for some regions within the superconducting energy gap δ of about 150 µeV, which is similar to other experiments, see appendix. 22 We note here, that since ∆ < Γ, local pair tunneling should exceed CPS. 26? We also emphasize that we cannot distinguish the individual tunnel coupling strengths of each QD to either S or N. The respective tunnel-rate ratio has an important effect on the magnitude of CPS. In particular, CPS can appear to be suppressed in the experiment if tunneling out of the QD into the drain electrode is the rate-limiting step. 24,26

III. COOPER PAIR SPLITTING IN DOUBLE NW
In figure 2(a) and 2(b) the simultaneously measured differential conductance G 1 through QD 1 and G 2 through QD 2 are shown, both as a function of the side-gate voltages V SG1 and V SG2 . These measurement are done at zero bias and without an external magnetic field.
Varying the sidegate voltage V SG1 tunes QD 1 through several Coulomb blockade resonances, Each resonance signifies a change in charge state of the respective QD. The charge on one QD can be sensed by the other QD, due to the capacitive coupling between QD 1 and QD 2 .
In our experiment, QD 2 acts as a good sensor for the charge on QD 1 , as the Coulomb blockade resonance lines of QD 1 shift whenever the charge on QD 2 changes by one electron, see Fig.2(b). Due to capacitive crosstalk from V SG1 on QD 2 (V SG2 on QD 1 respectively) the resonance positions are slightly tilted in both graphs. At certain gate voltages, when both QDs are in resonance, an increase of conductance can be observed on both sides. This can be seen more clearly in the cross sections indicated by black and white dashed lines Fig.2(a,b). We observe an enhancement of G 1 along the black dashed line in Fig.2(a)  The measurements of type II resonances suggest the existence of sub-gap states which are not located in QD 1 , but rather in the lead connecting to S. Since these states are gate-tunable, they are not fully screened by S. We therefore propose that a proximitized region is formed in NW1 that extends to some distance out from S. QD 1 is coupled to this proximitized lead. Within the lead, bound states can form due to potential fluctuations and residual disorder. There are two kinds of bound states, Andreev bound states (ABS) [33][34][35] or Yu-Shiba Rusinov (YSR) 36 states. These states do not usually occur at zero energy, but can be tuned electrically to zero energy, signaling a ground state transition between the proximitized lead region and the bulk of the SC. This gives in effect rise to a density-of-state peak in the gap of the SC, enhancing the subgap conductance which we measure. In this case the two electrons that are launched by CPS are transmitted in a different way to the respective drain electrodes. The electron that takes the path through QD 2 is transferred by the usual (resonant) sequential tunneling, while the one that takes the path through QD 1 is transferred by co-tunneling. One might expect that this suppresses CPS as the latter process corresponds to a low probability for out-tunneling into the drain contact. However, due to the sub-gap resonance in the proximitized lead, this process is enhanced and one can therefore reach almost similar CPS efficiencies.

IV. CONCLUSION
In summary, we demonstrate the fabrication of an electronic device, consisting of two closely placed parallel InAs NWs, contacted by a common superconducting lead and indi-    Fig.2 in the main text, is now either absent or replaced by a negative correlation. The latter is expected for classical correlations that can be described by a simple resistor network. 20 In (d) a linear background was removed from G 1 , therefore its denoted as ∆G 1 .