Peer review of: Transmission phase read-out of a large quantum dot in a nanowire interferometer (2020)

Reviewers' comments: 

Reviewer #1 (Remarks to the Author): 

This paper studies the Aharonov-Bohm effect in semiconducting-nanowire-based interferometers. In 
particular, the focus of the paper is on detection of the transmission phase through a network of 
interconnected InSb nanowires when one of the arms contains a quantum dot. In my opinion, the 
reading is somewhat intricate, and the presentation is rather technical. While the presented results 
might be of interest for the mesoscopic physics community, I find that the manuscript lacks the 
character of generality and clarity that is necessary for the readership of Nature Communications. I 
understand that these results are motivated by the prospect of using interferometry for read-out of 
topological qubits (through the dependence of the transmission phase on electron parity), but, as it is 
now, this manuscript just presents a detailed analysis of how two distinct quantum dot regimes (few-
electron and many electron) affect the transmission phase through the interferometer. Concerning 
novelty, there are various previous papers reporting on this kind of experiments (Refs. 14-17), 
although not using nanowire networks. One could argue that showing interference effects and 
quantum coherence through such networks is already an important achievement (which is true), but 
this has been already reported by the same group in Ref. 23. In what follows, I explain this overall 
assessment by asking/pointing out specific questions/points that should be addressed: 

1) Having in mind that this is an experimental paper, I find it very strange that the authors stress the 
importance of their tight-binding model (even at the abstract level) in order to understand their 
results. As it is clear when reading the manuscript, the physics described here is just that of Fano 
interference between discrete resonances (the Coulomb blockade peak) and the contribution from the 
continuum. In this respect, the phenomenon is general and not limited to the specific modeling (here 
tight binding) of the transmission (Eqs. 2 and 3). In my opinion, the manuscript would have benefited 
from a more general explanation in terms of Fano interference. 

2) As I mentioned in my general assessment, the paper is rather technical. This happens right from 
the start, where the authors talk about read-out of topological states to motivate their experiments. 
Why parity read out is such a big deal? (this is a rethorical question: I know why parity read out is a 
big deal but not the readers necessarily...). This is also a bit confusing since, as far as I can see, they 
don't clearly demonstrate parity-dependent readout in a mesoscopic regime in their device. More 
technicalities can be found at the beginning of the paper (the distinction between two- and four-
terminal configurations, the breakdown of Onsager relations, phase rigidity, etc) with almost no 
context/explanation. This continues in the next paragraph which is plagued with technicalities: spin-
orbit and its relation with topological qubits, cotunneling regime, tight-binding model... 

3) When discussing the results (section II), I would suggest to use an image of the actual sample (the 
one shown in Fig 6) together with the illustration. Also, it would be very useful at this level of the 
paper to find a minimal explanation of what a Coulomb blockade peak/valley is and why cotunneling 
measurements are important. 

4) Related to the previous point: their model is just a tight-binding chain coupled to N resonances. Is 
Coulomb blockade irrelevant to understand the main mechanism of Fano interference? If yes, the 
authors should try to present their results/explanation in a more general language, avoiding jargon as 
much as possible. 

5) The universal behaviour through phase lapses is clearly demonstrated in these experiments (and, 
as claimed by the authors, this is probably the first time that this regime has been studied in detail). 
Unfortunately, this is not the relevant regime towards read out of topological qubits (since in the 
universal regime, phase lapses are not linked to the electron number). Here, some numbers are 
mentioned (like the full width half max, the level spacing, etc), but it would be nice to see a short 
explanation of what these parameters are (even at a pictorial level) when these numbers are first 
mentioned in the previous paragraph (i.e the paragraph describing how they are extracted when the 
reference arm is pinched off). 

6) Section D aims at understanding the quasi-1D limit (relevant for Majorana wires). Here the effect of 
complicated multi path trajectories is elucidated which results in a phase behaviour somewhat in 
between mesoscopic and universal. In my view, this is probably the more relevant section of the paper 
since this is probably the first experiments where the role of topologically-trivial modes on the so-
called Majorana teleportation (and their specific contribution to transmission phase lapses) is 
discussed. In this context, I like also section III (Discussion) since the implications of this data set are 
discussed in a more general (and relevant) context. 

Given the above arguments, I do not recommend the paper for publication in Nature Communications. 
Some parts of the paper, see my point 6 above, might be considered of enough relevance but, as it is 
now, the manuscript does not stress enough the novelty and/or relevance of the experiments 
presented here (even at the abstract level this last part about multiple trajectories is not highlighted 
enough). My recommendation would thus be to considerably rewrite the manuscript given my above 
criticism. Importantly, the sentence in the discussion part "Nevertheless, we conclude by remarking 
that, despite the presence of phase lapses, the transmission phase remains parity-sensitive in the 
vicinity of the transmission resonances." should be carefully explained (and demonstrated by 
measurements). A detailed and convincing explanation of experimental data demonstrating deviations 
from the simplistic theory presented in Refs. 11-12 could be reconsidered for publication in Nature 
Communications. 



Reviewer #2 (Remarks to the Author): 

The authors demonstrate an electron interferometer integrating a quantum dot in one of its arms. The 
study is performed on devices built starting from crossed-wire InSb nanostructures [23] and can be 
relevant in view of phase-resolved tunnel spectroscopy of Majorana states. The work specifically 
focuses on the evolution of tunneling phase as a function of the electron filling in the quantum dot, 
depending on a variety of parameters. Part of the results can be framed within the so-called "universal 
behavior", which was demonstrated at Weitzmann in 2005. The main novelties of the paper are: 

(i) the physical system used to implement the interferometer. Crossed InSb nanowires are used here; 
this is a rather unique system, and one of the election systems for the creation of Majorana states for 
topological quantum computation. 

(ii) the devices work in a multi-level regime, which is unusual. Results in the literature have been 
typically reported in the single-level regime, i.e. in the quantum Coulomb blockade limit. Here we are 
apparently in a cross-over towards the classical Coulomb blockade limit. 

I believe the manuscript is interesting and related to a timely research subject. Devices and 
measurements are at the state of the art. Some of the interpretations are a bit speculative but in my 
view the paper is innovative enough to be suitable for Nature Comm. I believe some points should be 
clarified/fixed before publication: 

1. I have few comments on the presentation. One concerns figure 3a and the DoS sketched therein. 
First question: the authors report markedly different lineshapes, which suggest - I guess - that 
different orbitals have markedly different hopping parameters. Is this an evidence, an expectation, or? 
I think this might be better clarified. Second question: the authors use a 1D TB model, but I see here 
a 3D-like DoS. I would expect the true DoS of the InSb conductor to be indeed close to 3D, but a 
clarification is maybe needed. Also, I wonder if the functional form of the DoS is really relevant here. I 
would guess that the InSb conductor has an almost "metallic" DoS with mesoscopic fluctuations on top? 
I also note that in other experimens 1D indeed appeared to be a more appropriate description. Since 
the existence of multiple areas and trajectories in the ring is relevant at the end of the paper, I would 
maybe spend few words on the issue, in the initial part of the paper. 

A second (really minor) comment concerns "N" after equation (3). I would clarify that N is the number 
of levels relevant to the tunneling process. I think an average reader might not expect that many 
levels participate to the transport. The authors mention that cotunneling is important in the 
experiment, but I think this does not necessarily imply that \Gamma > \delta. 

2. Concerning the phase evolution shown in Fig.4d, I see there are some missing points due - I guess 
- to the difficulty/impossibility in performing a reasonable fit of the data. I am sure that this is not an 
on/off problem... can the authors maybe add some error bars so that the transition from a well-
defined phase to an unknown phase is better quantified? I also notice that the 4kBT scale bar is a not 
very easy to understand, possibly because of its low aspect ratio it does not look like a scale bar. 

Moving to the physics, I notice that the "smooth" phase transition from 0 to \pi actually occurs on an 
energy scale on the order of \Gamma. Is this just a coincidence? I am wondering if it is reasonable to 
expect a transition width \propto kBT in the regime studied by the authors, or if rather \Gamma is the 
important scale. I am not aware of any theoretical prediction, my observation comes from a naive 
analogy with what happens to the CP linewidth (\propto kBT in the single-level regime, \propto 
\Gamma when lifetime broadening dominates). The discussion about the breakdown of time-reversal 
is interesting but its connection with the effect remains a bit vague. Also, are lower magnetic field 
data avaliable maybe? 

3. The different phenomenology presented in D is intriguing, but also puzzling. I appreciate the fact 
that the authors were able to reproduce the effect by adding some complexity to their model . 
However, in the present version of the paper the transition from evidences in C to those in D remains 
a bit obscure to me and one has the impression that fine adjustment has been introduced in the 
modelling. I don't want to be negative, I think the evidence is interesting and deserves publication. I 
would at least report the fit parameters somewhere and try and give some intuitive explanation of the 
mechanism leading to the change in the phase pattern. 

4. Datasets in C and D refer to VBG=+1.5V and -1.5V, respectively. I thus expect to have less 
electrons in D? Why is area less well-defined in the D configuration? Since there is less carrier density, 
I would expect the ring area to be MORE well-defined in configuration D than in C. 




Reviewer #3 (Remarks to the Author): 

Review report - NCOMMS-19-40640 
In this manuscript, the authors study the transmission phase of a quantum dot (QD) in the many-
electron regime via interferometry. The experimental system consists of a network of four InSb 
nanowires arranged in a hashtag shape during epitaxial growth, acting as a two terminal Aharonov-
Bohm (AB) interferometer, where the gate defined QD is incorporated in one of the arms. Several 
gates are employed to tune the carrier concentration in both the QD and the nanowire leads. The 
authors show that phase coherent transport is conserved through the QD in the Coulomb blockade 
regime as indicated by the observation of AB oscillations in the differential conductance (G) [Fig. 2]. A 
tight-binding model, using an expression for the total transmission from ref. [25], is used to fit the 
resonant peaks (dips) in G [Fig.3]. Furthermore, by tuning the gates, two regimes are identified: one 
with universal phase behavior (rapid phase changes of pi close to the resonance follows by a phase 
laps in the Coulomb blocked region) [Fig.4]. The second regime, exhibit phase behavior in between 
the universal and the mesoscopic regime [Fig. 5]. This behavior is attributed to transport channels in 
the arms with different loop areas coupling to the different QD states. 
This appears to be the first AB interferometry study on the InSb hashtag material system when a QD 
is included in one of the arms. Owing to the strong spin-orbit interaction and large g-factor, InSb is a 
promising material system to realize topological quantum computing. AB interferometry including a 
large “topological QD” has been suggested as a mean for read-out of topological qubits, but also for 
distinguishing between trivial and topological states in semiconductor-superconductor hybrid devices 
which is an important step towards topological quantum computing. 
The manuscript is well-organized and easy to follow. I appreciate the clear experimental data and the 
close resembles between experimental and model results. Thus, overall I recommend this paper for 
publication in Nature communications given that the comments below are addressed: 

(1) The authors point out the particular regime studied where multiple orbitals on the QD contribute to 
the transport has never been studied before. Can the authors comment on why this is an interesting 
regime to study? How would the effect of multiple lead channels masking the intrinsic transmission 
phase affect read out of topological qubits? Is this effect robust when lowering the back gate further? 
Can the authors comment on electron density in the studied regime vs the electron density needed for 
entering topological regime in a semiconductor-superconductor hybrid device? 

(2) Fig. 2 caption: Define “G”. 

(3) Regarding the definition of the “QD electrochemical potential”: E_QD = \alpha V_PG. Strictly 
speaking, this is only the gate contribution to the electrochemical potential. Is there an elementary 
charge missing or how do you define \alpha? Not C_gate/C_total? 

(4) Regarding Fig. 3c caption: E_c and \delta are not defined in the caption. To me it looks like the bar 
indicating \delta is shifted slightly too far down (I assume it is supposed to indicate the distance 
between the conductance line of the border of the diamond and the first parallel line). In addition, the 
indicated distance is 2 times the orbital spacing whereas in in main text \delta is referred to as the 
orbital spacing. How has the orbital spacing been extracted? Furthermore, the dashed line indicating 
the diamond seems to be slightly off, overestimating the E_c. 

(5) Regarding estimation of electron population on the dot: For more transparency declare the 
estimated volume of the dot. 

(6) Fig. 4: Add information on the DC bias in the caption. “magnetic flux” should be magnetic flux 
density of B-field. Expand the description of panel d (top) in the caption. From the caption, it is not 
clear why the 4k_BT marker is there. 

(7) “In order to convert between the evolving phase of JL = jL exp(i2 B 0 ) and the magnetic field we 
use the area of the loop.” Can you be more specific here and insert the full relation? Furthermore, can 
you include a more detailed description how you extract the transmission phase in Fig. 4d (or refer to 
the SI)? 
(8) Regarding the SI: I suggest to refer to the SI in the main text to highlight how the SI is supporting 
the main text? 

(9) Can you tune the QD into the few electron regime or have you a device with smaller distance 
between the defining gates? If so, can you see mesoscopic phase behavior or is the multiple channel 
effect hindering to see the mesoscopic phase behavior? 

(10) Regarding the last sentence in the conclusion: “Nevertheless, we conclude by remarking that, 
despite the presence of phase lapses, the transmission phase remains parity-sensitive in the vicinity of 
the transmission resonances. What do you mean with parity sensitive? That you see a pi-shift at the 
resonance (change of parity)? But you cannot extract the absolute parity of the dot from the transition 
phase?