SciPost Submission Page
Universal relations in flat band superconducting bipartite lattices
by G. Bouzerar and M. Thumin
|Authors (as registered SciPost users):||Georges Bouzerar|
|Preprint Link:||scipost_202308_00024v1 (pdf)|
|Date submitted:||2023-08-17 16:33|
|Submitted by:||Bouzerar, Georges|
|Submitted to:||SciPost Physics|
Unconventional flat band (FB) superconductivity, as observed in van der Waals heterostructures, could open promising avenues towards high-T$_c$ materials. Indeed, in FBs, pairings and superfluid weight scale linearly with the interaction parameter, such an unusual behaviour justifies strategies to promote FB engineering. Bipartite lattices (BLs) which naturally host FBs could be particularly interesting candidates. By revealing a hidden symmetry of the quasi-particle eigenstates, we demonstrate that pairings and superfluid weight obey universal relations in BLs. Remarkably, these general properties are insensitive to disorder as long as the bipartite character is protected.
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This manuscript studies some aspects of superconductivity, specifically various "universal" relations between the pairing amplitudes and superfluid stiffness, in “flat-band” systems in the presence of *only* an on-site attractive-U Hubbard interaction, and assuming (without any justification; see below) that mean-field theory is applicable. Unfortunately, the paper does make some misleading statements (perhaps unintentionally), especially when it comes to presenting results using the said mean-field theory as if they hold well beyond this uncontrolled and unjustified limit. At the same time, the paper fails to cite many important papers, including an early paper by Tovmasyan et al, Phys. Rev. B 94, 245149 (2016), which beautifully highlighted many important aspects of the flat-band problem with on-site attractive-U Hubbard interaction, including where BCS theory is valid. As shown by these authors, the only limit where the BCS wavefunction is the actual ground-state wavefunction, thereby providing some a posteriori justification, is tied to an emergent SU(2) symmetry in the problem. Furthermore, they also derived relations between the superfluid stiffness and pairing amplitudes (they are both related to the interaction strength, as well as some other invariants). However, in this limit even though the stiffness is finite, the transition temperature vanishes.
I do not find this manuscript well written/presented and contributing any fundamental new insights into the problem (though it tries to present results in a “rigorous” fashion, even when the starting point of the approach lacks much rigor). Ultimately, all of the calculations involve various manipulations of the same BdG equations. At this point, based on the large existing literature of similar analysis of the FB problem using mean-field theory, I find that this work is just a straightforward extension of these ideas and does not meet the criteria for acceptance in SciPost.
Interestingly, there is repeated mention of how well BCS mean-field theory apparently agrees with DMRG. However, as has been pointed out in various unbiased, large-scale two-dimensional QMC simulations, BCS mean-field theory also fails in dramatic ways once the on-site attraction is perturbed by infinitesimal nearest-neighbor interactions (Hofmann et al., ‘20, ‘23; Peri et al., ‘21). The authors do not cite any of these papers as well.