ARQH Workshop Questions

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Names of speakers
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• Carlo Beenakker
• Önder Gül
• Gleb Finkelstein
• Javad Shabani
• Antonio Manesco
• Ivan Kulesh
• Vladislav D. Kurilovich

Questions for the discussion

Technical Experimental Details

• For Gleb Finkelstein regarding the measurement of supercurrent in these QH devices – you explained that there are non-chiral states that carry the supercurrent independently at both edges, generating the squid like pattern of the critical current.. but why is it that the 'chiral' mechanism involving the entire perimeter of the Hall bar is absent?? I would expect both mechanisms to be present, generating a beating pattern as a function of flux with both h/e and h/2e periodicities. From Lucila Peralta Gavensky.
  A: This is essentially related to how to engineer two pairs of CAES together for establishing superconducting phase coherence across. It’s probably very hard before establishing e/h coherence along vacuum edge. From Lingfei Zhao.
  A: The chiral contribution has a much smaller size, the perimeter is much larger, so at finite temperature it will be strongly suppressed. From Carlo Beenakker.
• For Javad – Do you know the chemical potential or electron density of the InAs 2DEG directly underneath the NbN? From Valla.
• Assuming negligible effects on the 2DEG quality, what pros and cons do the panel see for making the contact through a surface superconductor instead [see Fig b) below]? (Current experimental publications make the 2DEG-superconductor contact from the side of the heterostructure [see Fig a) below].)
  
• For Onder Gul – what is the expected or measured Fermi level mismatch between NbN and Au with respect to graphene? From Valla Fatemi.
• For Onder Gul – in the measurement of
  $R_{xx}$ vs CAR it seems like
  $R_{xx}$ is about to turn negative at 2K, is that correct? Do you have lower temperature dependence data? From Anton Akhmerov.
  
• For Javad Shabani – In working with InAs with epitaxial coupling to Al, has there been any issues obtaining the interference pattern (Fraunhofer Oscillations) in 2-terminal Josephson junctions? In working with this material we are able to reproduce all the published characteristics except for the interference pattern. Understandably there can be many reasons for this but any insights will be helpful. From Mohit Gupta.
• For Javad Shabani – why do you see a more complex pattern of plateaus in the
  $B$ vs
  $V_g$ diagram than the usual Landau fan? From Anton Akhmerov.
  
• For Javad Shabani – InAs is known to have accumalation of charge near the end of the 2DEG. did you try making similar JJ in the QHE to the one Gleb showed? Maybe there is SC currents also between the diffrent SC contacts in the experiment you showed? (Yuval Ronen)
• For Javad Shabani – the SC contact of the NbTiN is on top of the Al or not? Are you etching with ion milling in-situ? and sputter NbTiN? how do you know when to stop, effect of disorder? From Yuval Ronen
• For Javad Shabani – in the new QPC devices, why was the use of boron nitride necessary for the gate dielectric? From Valla Fatemi.
• For Javad Shabani – For the bias dependence you showed, roughly what values of voltage would the currents correspond to? And how do these voltages compare to the superconducting gap? From Srijit Goswami. (Regarding the plot showing resistance as a function of current bias and magnetic field)
  A: The integer gaps are 5-10K and while dc current tilts the modes at the end it corresponds to the heating of the edges with same energy scales. I like to say 100uv-1meV.
• For Javad Shabani – What will be the role of the vortices formed near the large interface area in this structure? From Saurabh Srivastav.
  A: In all these systems vortices are present since they are all type II. Our measurement does not distinguish vortices but in the simplest form you can think of those vortices cause normal reflection (I assume).
• For Gleb Finkelstein – How reliable ("yield") are the edge contacts made to graphene? Is it relatively easy to fabricate?
  A: 70-80% for obtaining transparent contact at zero field with contact length above 300-400 nm.
• For Javad Shabani – Does the thickness of InAs influence the quality of the proximity effect? From Elsa Prada.
  A: Not that we have seen. We optimize for QH quality and coupling to superconductor.
  R: Thank you Javad. And what is exactly the thickness that you use? – Elsa.
  A: It is a 4nm-7nm-10nm (InGaAs-InAs-InGaAs), see Fig 2c .
• For Gleb Finkelstein regarding the measurement of supercurrent in these QH devices: you explained that there are non-chiral states that carry the supercurrent independently at both edges, generating the squid like pattern of the critical current.. but why is it that the 'chiral' mechanism involving the entire perimeter of the Hall bar is absent?? I would expect both mechanisms to be present, generating a beating pattern as a function of flux with both h/e and h/2e periodicities. From Lucia Peralta.
  A: From Carlo Beenakker: the chiral contribution has a much smaller size, the perimeter is much larger, so at finite temperature it will be strongly suppressed.

Data Interpretation

• For Javad Shabani – The Harvard experiment observes negative downstream current that grows with dropping filling fraction. Does this also apply to your experiment?
• For Onder Gul – in the magnetic field dependence, does the raw CAR resistance also fluctuate more at lower magnetic field (as opposed to the
  $p_{CAR}$)? From Valla Fatemi.
• For Javad Shabani – In the subtrated RU-RD data, there seems to be a systematic deviation between the blue and red curves as a function of gate voltage in the transition between plateaus. Blue is higher to the left and lower to the right of the transition. Is this understood? From Valla Fatemi.
• For Onder Gul – Do I understand correctly that you normalize by the 4-terminal
  $R_{xx}$ and not
  $\nu \times G_0$? If yes, why? From Anton Akhmerov.
  A:
  $p_{CAR}$ is obtained by normalizing
  $R_{CAR}$ with
  $R_{xy}=\nu \times G_0$.
  $R_{xx}$ is very closed to 0. Answered by Philip Kim in chat.

Confounding phenomena

• Can the out of equilibrium charge density and the bulk current distribution in the quantum Hall regime influence the observations?
• Can nonchiral edge states play a role in systematically enabling negative current by enabling local Andreev reflection? How can an experiment rule them out? From Anton Akhmerov.
  • By Valla: clarification, meaning nonchiral states in addition to chiral ones or simply edges with only nonchiral edges (like QSHE)? Has the latter been checked theoretically?

Theoretical model questions

• A general question: different quantum Hall states in symmetry broken graphene belongs to different flavour polarisation, either spin/ valley. What will be the effect of these flavoured degree of freedom in these experiments? It seems to me from these experimental data, it is not affecting drastically. Is it true? From Saurabh Srivastav.
• How high should the Andreev reflection probability be at the superconductor-QH interface for realizing non-Abelian anyonic zero modes?
• How is this Andreev reflection probability expected to evolve as a function of the large perpendicular magnetic fields required for IQH and FQH?
• Following Vladislav's talk: how does the conductance correlations (
  $⟨G(V_G),G(V_G+\delta V)⟩$) evolve with disorder? At small disorder, I expect the correlations to be large, and that is also the case when disorder is too large. So what happens in between? From Antonio Manesco.
  A: Good question, thanks. Yes, that's right, the conductances at
  $V_G$ and
  $V_G+\delta V_G$ are close to each other both in the low-disorer and in the high-disorder limits, but the reasons why are different. For low disorder, it is just that both conductances are close to the ballistic value and fluctuate only weakly. For high disorder, the reason is this motional narrowing business I was talking about. In between the two limits, the dependence in not monotonous. We can discuss more in depth in personal communication.
• How to distinguish Majorana edge mode from Chiral Andreev mode?
• For Gleb Flinkenstein – Regarding the simulations of graphene and SC shown. Is there a way to control the period of oscillation between electrons and holes? From Juan Torres.
  A: Yes, in the clean case, it's purely determined by the
  $\delta k$ in dispersion which depends on B, bias and other parameters. So by simply looking at the dispersion you know the period in length.
• For Carlo Beenakker – Referring to slide 3 of Carlo's talk: in the bottom left picture, it really depends on the deatils of the lattice because the boundary. Could one deform the top in the bottom picture? Is there any intermediate point? From Benjamin Hunt. (extend discussion later)
• For Carlo Beenakker – In these experiments how do we consider spins? From Yoichi Ando.
• Where should one think of the Andreev reflection taking place? At the interface of the normal part - proximitized part, or the at the physical interface of the normal metal to superconductor? (Essentially does one need an order parameter to be defined or the quasiparticle gap is enough?)

Ideas for further experiments

• For Gleb Finkelstein – Is it possible to obtain pristine oscillations in CAES using a type-II superconductor having a high Hc1, before magnetic fields when vortices start developing? From Rajarshi Bhattacharyya.

• For experimentalists – Do you imagine a way to minimize effects of vortices? From Antonio Manesco.

• A possible control experiment that simulates low and inhomogenous normal DOS (like due to vortices) but without AR: use a contact of the material in question tuned by a gate to near a transition to an insulator, where resistance is high and puddles probably dominate to keep things inhomogeneous.

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Unstructured questions

(Questions that don't fit into categories above)

• For Carlo Beenakker – It is a historial question: From review I have learned about a paper that looked at the same thing, skipping orbits along the edge. It was a metal in the 80's. From Leonid Glazman. (no question asked)
  • Leonid: could you link this paper? -Valla
• For panelists – A general question to the panelist, what is the pathway forward for utilizing Andreev edge states for functional devices? From Zhihui Cheng.

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to be classified

• For panelists – different quantum Hall states in symmetry broken graphene belongs to different flavour polarisation, either spin/ valley. What will be the effect of these flavoured degree of freedom in these experiments? It seems to me from these experimental data, it is not affecting drastically. Is it true? From Saurabh Srivastav.