Abstract
We study a putative (strange) metal-to-insulator transition in a granular array of the Sachdev–Ye–Kitaev (SYK) quantum dots, each occupied by a large number N ≫ 1 of charge-carrying fermions. Extending the previous studies, we complement the SYK couplings by the physically relevant Coulomb interactions and focus on the effects of charge fluctuations, evaluating the conductivity and density of states. The latter were found to demonstrate marked changes of behavior when the effective inter-site tunneling became comparable to the renormalized Coulomb energy, thereby signifying the transition in question.
Highlights
The recent upsurge of interest in the SYK and related models of strongly interacting dispersionless fermions with all-to-all q-body couplings has been driven, among other reasons, by the hopes of utilizing them as solvable examples of the so-called non-Fermi liquid (NFL) behavior.Originally, the SYK reincarnation [1,2,3] of the parent SY (Sachdev-Ye) [4,5,6,7,8] model was formulated in terms of neutral Majorana fermions that would be abundantly present in the recent theoretical constructs
While predicting some markedly novel features [11,12,13,14,15] in mesoscopic charge and heat transport through its proposed realizations in the irregularly shaped graphene flakes, multi-connected Quantum Hall setups, semiconductor wires and quantum dots, and topological insulator surfaces [16,17,18,19,20], the complex SYK model has still to be extended into the spatial dimensions before applying it to the analysis of any documented higher-dimensional NFL system
We demonstrate that in the problem at hand the role of such sub-Ohmic bath is played by the intra-site SYK correlations themselves, thereby enabling the metal-to-insulator transition (MIT) in the granular SYK systems even in the presence of the charging effects
Summary
The recent upsurge of interest in the SYK and related models of (super) strongly interacting dispersionless fermions with all-to-all q-body couplings has been driven, among other reasons, by the hopes of utilizing them as (asymptotically) solvable examples of the so-called non-Fermi liquid (NFL) behavior. The previous analyses were, by and large, limited to the effects of the (somewhat exotic) SYK-type entangling correlations, thereby leaving out the far more mundane (yet physically relevant and practically unavoidable) charge couplings of the Coulomb origin that are going to affect any feasible solid-state implementations of the SYK system, including those of [16,17,18,19,20]. In such electron-based simulations the SYK4 interaction itself would be simulated through the geometrically randomized intra-site Coulomb couplings. We fill in the gap by investigating the charging effects in a manner similar to that utilized in the context of the ordinary (FL) granular electronic materials [41,42,43,44,45,46,47,48]
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