Josephson Effect in a Few‐Hole Quantum Dot

Abstract

A Ge-Si core-shell nanowire is used to realize a Josephson field-effect transistor with highly transparent contacts to superconducting leads. By changing the electric field, access to two distinct regimes, not combined before in a single device, is gained: in the accumulation mode the device is highly transparent and the supercurrent is carried by multiple subbands, while near depletion, the supercurrent is carried by single-particle levels of a strongly coupled quantum dot operating in the few-hole regime. These results establish Ge-Si nanowires as an important platform for hybrid superconductor-semiconductor physics and Majorana fermions.

Multiple Andreev reflections and Shapiro steps in a Ge-Si nanowire Josephson junction

“…For the experimentally measured I c , this would correspond to about 7 modes in the junction, consistent with our estimate of the number of modes based on the normal transport data. We furthermore obtain an average transparency of ∼ 50 %, lower than the previously obtained transparency of ∼ 80 % [44] using the BTK model [71], averaged over a large gate voltage. This difference could be explained by the fact that I SW (T) was only determined at a single value of V BG and that I SW is likely to be suppressed with respect to the actual critical current of the junction.…”

“…For the first subband this gives E 1,1 ≈ 15 meV, corresponding to a Fermi velocity v F ≈ 1 · 10 5 m/s and an estimated elastic scattering length of l e ≈ 100 nm. Using a gate lever arm α = 0.02 and the fact that the nanowire is depleted at V BG ≈ 5 V [44], we find that in the regime V BG = [−7.6, −15] V we operate at 6 (E 6,1 ≈ 256 meV) to 8 (E 8,1 ≈ 388 meV) subbands, increasing l e to ∼ 400 nm.…”

“…As described in extensive detail in Ref. [44], the device is tunable from full depletion (with I SW = 0) to highly transparent where I SW > 40 nA on which this work is focused.…”

“…For a ballistic nanowire and completely transparent interfaces, one expects the normalstate conductance to appear in multiples of the conductance quantum G 0 = 2e 2 /h, and the critical current in multiples of the maximum critical current for a single subband I C,MAX = e∆ Al /h = 51 nA [2]. In our case, the finite interface transparency [44] leads to lower observed values of both the conductance G and the switch-ing current I SW , where I SW is suppressed by additional mechanisms such as electromagnetic coupling with the environment [9], premature switching and heating effects [2,62]. From experiments it is therefore not trivial to conclude whether our nanowire is diffusive or ballistic and we therefore make a quantitative estimation based on calculations.…”

“…c) Same data as b) plotted versus n, only positive V SD is shown. The vertical dashed gray lines show integers of n which can be matched with the MAR peaks up to n = 6. semiconducting island can be host to a single few-hole quantum dot [44] and that highly-tunable normal-state devices can be host to dots of length l > 400 nm [38]. By increasing the Al-nanowire interface transparencies, fully ballistic junctions could therefore be realised with lengths up to a few hundred nanometer.…”