Gate-defined Kondo lattices with valley-helical quantum dot arrays

The author proposes a novel approach to realizing electrically tunable Kondo lattices using gate-defined superlattices in Bernal bilayer graphene.

- In contrast to traditional Kondo lattices found in heavy fermion materials—which necessitate complex material synthesis to vary coupling strengths and fillings—this system offers the ability to electrostatically tune interactions, offering a good control over the phase diagram.

-The proposed system circumvents the fabrication challenges associated with moiré systems, such as twist-angle disorder and strain effects, making it more experimentally accessible.

-Although gate-defined potentials are more controllable than moiré systems, the presence of electronic inhomogeneity and disorder can still disrupt the ideal scenario. The stability of valley-helical channels in the face of disorder and interactions is critical for experimental realization.
For example, the author notes "possible challenges on fabricating the multi-gated layout shown in Fig. 1(a)."
It seems unclear how experimentally feasible this setup is. This point is not discussed.

-The paper primarily proposes a model without providing detailed calculations using the Kwant package. Details are not included in the paper. Additionally, it does not discuss the influence of parameters such as electric field strength, the distance between the created quantum dots, and the expected interaction strength between different dot levels. I believe the Kondo lattice model will only emerge as a low-energy theory for specific combinations of these parameters.

This study proposes a novel approach to realizing electrically tunable Kondo lattices using gate-defined superlattices in Bernal bilayer graphene. By patterning graphite gates, the author proposes to create an array of quantum dots coupled through valley-helical channels, forming a Kondo-Heisenberg model. Unlike moiré materials, which suffer from fabrication challenges, this method could offer high reproducibility and scalability.

The proposed approach in this paper presents an innovative method for realizing tunable Kondo lattices using gate-defined superlattices in Bernal bilayer graphene. The paper builds on well-established concepts in condensed matter physics, and the theoretical framework mapping the system to a Kondo-Heisenberg model appears valid.

- There should be a discussion on how variations in electric field strength, the distance between dots (related to the structure of the gates), and the interaction strength U affect the parameters of the Kondo lattice model. Given the claim that the Kondo lattice parameters are electrically tunable, it is important to demonstrate how these parameters can be modified.

- There should be a discussion on how disorder will affect the arising effective Kondo lattice model.

- I would appreciate it if the author could provide further details on the methodologies and calculations.

Ask for minor revision

This manuscript presents an interesting idea: combine semi-realistic gate designs on bilayer graphene that impose a modulation of the chemical potential and creates quantum dots. The QDs are effectively coupled to valley polarized (nearly single) channels, so as to make 1D or 2D arrays of such entities.

Under the right conditions (interdot tunneling coupling and large charging energy), the author makes the case that the low-energy physics can be seen as a lattice Kondo-Heisenberg system with tunable parameters via the gate potentials.

The manuscript presents one-body calculations that consider the electrostatics to demonstrate the feasibility of the double/stacked gate designs.

Although a well-written (if economically) paper, there are a few minor points that could be improved:

1. The author suggests that a single-layer split gate geometry might be easier to achieve experimentally. It would have been useful to at least see a simple comparison between the two designs in a 1D case, for example. Are the electrostatics able to produce a nearly-single channel coupling?

2. The paper has a few typos:
a. The energy scale in fig 2a and 2b is missing. One can estimate it from the narrative, but still.
b. Eq. 2 has $\delta \rho$ as the first term. A rogue superscript?
c. Eq. 3 has $\epsilon$ but the text below uses $\epsilon_m$.
d. Typos/spelling throughout...

3. It would be useful to cite the references the author has in mind in connection with the "Similar networks..." phrase.

I believe that the ideas put forth here are inventive and would likely motivate further work. As such, I believe it meets the criteria for publication.

See list above

Publish (meets expectations and criteria for this Journal)