The dot-wire interaction observed in Fig. 5D
can be understood in terms of leakage of the
MBS into the dot when the dot is on resonance
(41). The energy splitting of a pair of MBSs is
given by dEºjsinðkFLÞe−L=xj (where kF is the
effective Fermi wave vector). In Fig. 5D, this
splitting is initially small, when the dot is off resonance and coupling of the MBSs to the dot states
is suppressed by Coulomb blockade. For a finite-size wire, this implies that sin(k FL) 0 at that
particular tuning. As the dot level comes closer
to the resonant point, the nearby MBS partially
leaks into the dot, which changes the details of
the MBSs wave function [the numerical study
on the wave-function distribution is provided in
(35)]. This can change the effective kFL in dE,
which causes the zero-bias peak to split at resonance. Numerical simulations of the conductance spectrum of the coupled dot-MBS (Fig. 5,
E and F) show good qualitative agreement with
the experimental data, both in the trivial superconducting regime (Fig. 5, C and E) and in the
topological superconducting phase (Fig. 5, D
and F). Similar zero-bias peak splitting in another coupled dot-MBS device (device 4) is shown
in Fig. 5H. To enhance image visibility, conductance values in Fig. 5H are normalized by the
conductance at Vsd = 0.2 mV at the corresponding gate voltage.
Last, we examined the magnetic field evo-
lution of the subgap states in the strong dot-
wire coupling regime, in which dot and wire
states cannot be separated. Shown in Fig. 6 is
the evolution with field of the spectral features
of the dot-wire system measured for device 1,
with two ABSs merging at B = 0.75 T into a
stable zero-bias peak that remains up to B = 2 T.
The effective g*-factor that can be deduced from
the inward ABS branches is ~6. The conduct-
ance at the base of the zero-bias peak is almost
zero even at B = 1 T, indicating a hard super-
conducting gap also after the topological phase
transition. Related measurements are shown
in (35).
The long field range and intensity of the zero-
bias peak in Fig. 6 can be understood as arising
from the hybridization of the MBS with the end-
dot state. In the strong coupling regime, MBS
can partially reside at the end dot, making the
effective length of the wire longer than in
Fig. 3I. The MBS wave function has larger
amplitude at the wire end, where the dot couples,
than either finite-energy ABSs or states in the
Al shell. This leads to a relatively higher con-
ductance peak at zero energy and makes the
excited states and the Al shell superconduct-
ing coherence peaks almost invisible (13). The
long field range of the zero-bias peak in Fig. 6
(also Fig. 3I) may also be enhanced by elec-
trostatic effects that depend on magnetic field
(14, 19).
Our measurements have revealed how the
ABSs in a hybrid superconductor-semiconductor
nanowire evolve into MBSs as a function of field
and gate voltage.
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ACKNOWLEDGMENTS
We thank R. Aguado, S. Albrecht, J. Alicea, L. Glazman,
A. Higginbotham, B. van Heck, T. Sand Jespersen,
F. Kuemmeth, R. Lutchyn, and J. Paaske for valuable
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C. Sørensen, G. Ungaretti, and S. Upadhyay for contributions
to growth, fabrication, and analysis. This research was
supported by Microsoft Research, Project Q, the Danish
National Research Foundation, the Villum Foundation,
and the European Commission. M.L. acknowledges the
Crafoord Foundation and the Swedish Research Council
(VR). P.K., J.N., and C.M.M. are co-inventors on patent
application PCT/EP2015/065110, submitted by the
University of Copenhagen, covering epitaxial semiconductor-superconductor nanowires.
SUPPLEMENTARY MATERIALS
www.sciencemag.org/content/354/6319/1557/suppl/DC1
Supplementary Text
Figs. S1 to S11
References (42–46)
3 February 2016; accepted 16 November 2016
10.1126/science.aaf3961
1562 23 DECEMBER 2016 • VOL 354 ISSUE 6319 sciencemag.org SCIENCE
B (T)
0.3
0.00 0.08
-0.3
0 21
dI/dV (e2/h)
dI/
dV(
e 2/
h)
0 T
1 T
1.5 T
V
Vsd (mV)
-0.3 0 0.3
0.00
0.12
0.5 T
Fig. 6. Tunneling spectrum for resonant dot-wire coupling. (A) B-Vsd sweep at Vbg = –8.5 V, Vg1 =
22 V, and Vg2 = Vg3 = –10 V. (B) Differential conductance line-cut plots taken from (A) at various B
values. At this gate configuration, a pronounced zero-bias conductance peak emerges around B =
0.75 Tand persists above B = 2 T, without splitting. The intensity of the zero-bias peak is higher than
other finite-energy ABSs and even higher than the Al superconducting coherence peaks. The background conductance is almost zero even at B = 1 T, indicating that the induced gap is still a hard gap
after the phase transition.
