SciPost Submission Page
Interaction-induced strong zero modes in short quantum dot chains with time-reversal symmetry
by Ahmet Mert Bozkurt, Sebastian Miles, Sebastiaan Laurens Daniel ten Haaf, Chun-Xiao Liu, Fabian Hassler, Michael Wimmer
Submission summary
| Authors (as registered SciPost users): | A. Mert Bozkurt · Fabian Hassler · Sebastian Miles · Michael Wimmer |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2405.14940v1 (pdf) |
| Code repository: | https://zenodo.org/records/11243862 |
| Date submitted: | 2024-06-06 16:09 |
| Submitted by: | Bozkurt, A. Mert |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We theoretically explore the emergence of strong zero modes in a two-site chain consisting of two quantum dots coupled due to a central dot that mediates electron hopping and singlet superconducting pairing. In the presence of time-reversal symmetry, the on-site Coulomb interaction leads to a three-fold ground-state degeneracy when tuning the system to a sweet spot as a function of the inter-dot couplings. This degeneracy is protected against changes of the dot energies in the same way as "poor man's'' Majorana bound states in short Kitaev chains. In the limit of strong interactions, this protection is maximal and the entire spectrum becomes triply degenerate, indicating the emergence of a ''poor man's'' version of a strong zero mode. We explain the degeneracy and protection by constructing corresponding Majorana Kramers-pair operators and $\mathbb{Z}_3$-parafermion operators. The strong zero modes share many properties of Majorana bound states in short Kitaev chains, including the stability of zero-bias peaks in the conductance and the behavior upon coupling to an additional quantum dot. However, they can be distinguished through finite-bias spectroscopy and the exhibit a different behavior when scaling to longer chains.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Strengths
The paper generalizes the minimal Kitaev chain model to a situation with spin and interactions, and most importantly looks at the time-reversal symmetric case. This is a an interesting study which points out that besides having Kramers degenerated "poor man's" Majorana, the triply degenerate point can be mapping to parafermions.
Weaknesses
The latter part is considered in the limit of infinite U, which of course is a limitation.
Report
One question that arises is how this model compares to true topological Kramers Majorana bound states. The topological case requires two chanels (wires) and a certain relation between the spin-orbit interaction in the two chanels. In the model considered here, there is no spin-orbit interaction. A natural question that arises is if including spin-orbit coupling in the present model changes the physics? Maybe the authors may want to comment on this?
Recommendation
Publish (meets expectations and criteria for this Journal)
Strengths
1. Identification of a potential platform to study the physics of strong zero-modes
2. Explicit constructions of the many-body zero modes operators
Weaknesses
1. It is unclear if the platform can reproduce the physics of zero modes in realistic experimental regimes
2. It is unclear if the transport signatures can be an indicator of many-body zero modes
Report
The authors study the spectrum and transport signatures of a double quantum dot coupled by elastic cotunneling and cross-Andreev reflection processes. The two processes can be controlled via a third proximitized quantum dot.
Similar setups have been proposed previously in the literature as a way to engineer sweet spots with a degenerate ground state so that they effectively reproduce the physics of Poor Man's Majoranas (PPMs) --- see e.g. Ref. 14. In the present work, the authors focus on the case with no magnetic field, so that the system is time-reversal symmetric, and address the role of the interaction.
They find that, for generic on-site interaction, it is possible to obtain a sweet spot by tuning \Delta/t. The sweet spot is correlated with the presence of a conductance peak which persists for a wider range of single energy detuning in the limit of large interactions where the degeneracy is better protected against local energy fluctuations. Finally, in the infinite-interaction limit, they identify an exact degeneracy of the whole spectrum and construct explicitly the associated Majorana and Parafermion zero modes. They show that a straightforward extension to longer chains fails to reproduce the physics of extended Kitaev chains or parafermionic models.
The results are sound and generically correct (modulo a couple of questions outlined below). They are an interesting extension of an idea already proposed in the literature (see e.g. Ref. 14) which provides a platform with the potential to explore the physics of Majorana and parafermions braiding. In this perspective, I find the identification of strong zero modes at infinite U, the most significant result in the manuscript, which could indeed open a new path to explore.
If the authors can better clarify the potential of this setup, given its limitations to extend it to longer chains, and the non-negligible effect of finite U (see below), I think the paper can be suitable for Scipost Physics. I would, otherwise, recommend publication in Scipost Core.
There are a couple of points that I think the authors should address.
- Role of U in the physics of strong zero mode. While for U \to \infty the authors can identify the spectrum degeneracy and explicitly construct the corresponding zero modes operators, it is not clear how finite U will affect this. Tee authors analyze the sweet spot and ground state degeneracy at finite U, but there is no equivalent analysis of how the overall spectral degeneracy is affected by a fine U. The authors should comment on how the lifting of the degeneracy affects the strong zero modes and their physics. Furthermore, while the conductance seems a valid signature of the degeneracy of the ground state, can the authors comment on whether transport properties can give signatures of the many-body zero-mode?
- Conductance computation in the presence of interactions. The authors compute the conductance using a rate equation approach. I do not expect this approach to be valid for the whole range of parameters. For example, for t=\Delta=0 where the setup reduces to a single dot coupled to a lead, the approach would miss Kondo correlations at low temperatures. I would naively expect the rate equation approach to hold for T>>\Gamma for the setup, but the data in Fig. 2 are for T~\Gamma. Can the authors clarify/justify the range of validity of the conductance calculation and ensure it is consistent with the simulations in the figures?
- Minor point. I would suggest clarifying the role of topology in the setup. For example, arguing that the intrinsic "topology" of the charge stability diagram is the basis of the analogy with the Kitaev chain zero energy modes might be misleading. I would suggest clarifying that the system has no zero modes from (symmetry-protected) topology, but it is expected to emulate the physics (braiding properties) of such systems with an analogous degree of protection.
Requested changes
1. Clarify the validity of the platform to observe strong zero-mode physics in an experimentally relevant regime.
2. Address the impact of finite U (see report above)
3. Clarify the validity of the conductance calculations.
Recommendation
Ask for major revision