We model interactions following the Sachdev-Ye-Kitaev (SYK) framework in disordered graphene flakes up to 300 000 atoms in size (∼100 nm in diameter) subjected to an out-of-plane magnetic field B of 5-20 Tesla within the tight-binding formalism. We investigate two sources of disorder: (i) irregularities at the system boundaries, and (ii) bulk vacancies-for a combination of which we find conditions that could be favorable for the formation of the phase with Sachdev-Ye-Kitaev features under realistic experimental conditions above the liquid helium temperature.
We model interactions following the Sachdev-Ye-Kitaev (SYK) framework in disordered graphene flakes up to 300 000 atoms in size (∼100 nm in diameter) subjected to an out-of-plane magnetic field B of 5-20 Tesla within the tight-binding formalism. We investigate two sources of disorder: (i) irregularities at the system boundaries, and (ii) bulk vacancies-for a combination of which we find conditions that could be favorable for the formation of the phase with Sachdev-Ye-Kitaev features under realistic experimental conditions above the liquid helium temperature.
We address the transport properties of a mesoscopic realization of the Sachdev-Ye-Kitaev (SYK) model which is an exactly solvable system of interacting spinless fermions connected to the black hole physics through the holographic principle. Starting with a recent proposal for simulating the SYK model in a graphene flake in an external magnetic field and extending it by considering leads attached to it, we model a realistic transport experiment and calculate directly measurable quantities featuring non-Fermi liquid signatures of the SYK physics. We show that the graphene flake realization is robust in the presence of leads and that measuring the tunneling current across the leads one can experimentally observe a non-Fermi liquid - Fermi liquid transition by tuning the external magnetic field threading the flake. After establishing the transport signatures of the SYK model near equilibrium using linear response framework, we then derive a formula to extend our results for tunneling current using Keldysh formalism to explore the effects of finite bias voltage across the leads, going beyond equilibrium.
We consider a recent proposal for a physical realization of the Sachdev-Ye-Kitaev (SYK) model in the zeroth-Landau-level sector of an irregularly shaped graphene flake. We study in detail charge transport signatures of the unique non-Fermi-liquid state of such a quantum dot coupled to noninteracting leads. The properties of this setup depend essentially on the ratio p between the number of transverse modes in the lead M and the number of the fermion degrees of freedom N on the SYK dot. This ratio can be tuned via the magnetic field applied to the dot. Our proposed setup gives access to the nontrivial conformal-invariant regime associated with the SYK model as well as a more conventional Fermi-liquid regime via tuning the field. The dimensionless linear-response conductance acquires distinct p and 1/p dependencies for the two phases, respectively, in the low-temperature limit, with a universal jump at the transition. We find that corrections scale linearly and quadratically in either temperature or frequency on the two sides of the transition. In the weak-tunneling regime, we find differential conductance proportional to the inverse square root of the applied voltage bias U. This dependence is replaced by a conventional Ohmic behavior with constant conductance proportional to 1/T for bias energy eU smaller than temperature scale kBT. We also describe the out-of-equilibrium current-bias characteristics and discuss various crossovers between the limiting behaviors mentioned above.
We use stochastic expansion and exact diagonalization to study magic-angle twisted bilayer graphene (TBG) on a disordered substrate. We show that the substrate-induced strong Coulomb disorder in TBG with the chemical potential at the level of the flat bands drives the system to a network of weakly coupled Sachdev-Ye-Kitaev (SYK) bundles, stabilizing an emergent quantum chaotic strange metal (SM) phase of TBG that exhibits the absence of quasiparticles. The Gaussian orthogonal ensemble dominates TBG's long-time chaotic dynamics at strong disorder, whereas fast quantum scrambling appears in the short-time dynamics. In weak disorder, gapped phases of TBG exhibit exponentially decaying specific heat capacity and exponential decay in out-of-time-ordered correlators (OTOCs). This is the system behavior in correlated insulator and superconducting phases, in agreement with the corresponding Larkin-Ovchinnikov result for correlators. The result suggests a low-temperature transition from the superconducting and correlated insulating phases into the strange metal upon increasing the disorder strength. We propose a finite-temperature phase diagram for Coulomb-disordered TBG and discuss the experimental consequences of the emergent SM phase.
Several condensed-matter platforms have been proposed recently to realize the Sachdev-Ye-Kitaev (SYK) model in their low-energy limit. In these proposed realizations, the characteristic SYK behavior is expected to occur under certain assumptions about the underlying physical system that (i) render all bilinear terms small compared to four-fermion interactions and (ii) ensure that the coupling constants are approximately all-to-all and independent random variables. In this work we explore, both analytically and numerically, the family of models that arises when we relax these assumptions in ways motivated by real physical systems. By relaxing (i) and allowing large bilinear terms, we obtain a novel, exactly solvable cousin of the SYK model. It exhibits two distinct phases separated by a quantum phase transition characterized by a power-law, ${\ensuremath{\sim}|\ensuremath{\omega}|}^{\ensuremath{-}1/3}$, scaling of the low-energy spectral density, despite being a noninteracting model. By relaxing (ii), we obtain close relatives of the SYK model which exhibit interesting behaviors, including a chaotic non-Fermi liquid phase with continuously varying fermion scaling dimension, and a phase transition to a disordered Fermi liquid as a function of interaction range and disorder length scale.
Disorder at etched edges of graphene quantum dots (GQD) enables random all-to-all interactions between localized charges in partially filled Landau levels, providing a potential platform to realize the Sachdev-Ye-Kitaev (SYK) model. We use quantum Hall edge states in the graphene electrodes to measure electrical conductance and thermoelectric power across the GQD. In specific temperature ranges, we observe a suppression of electric conductance fluctuations and slowly decreasing thermoelectric power across the GQD with increasing temperature, consistent with recent theory for the SYK regime.
We study a description of the large N limit of the Sachdev–Ye–Kitaev (SYK) model in terms of quantum mechanics without quenched disorder. Instead of random couplings, we introduce massive scalar fields coupled to fermions, and study a small mass limit of the theory. We show that, under a certain condition, the correlation functions of fermions reproduce those of the SYK model with a temperature dependent coupling constant in the large N limit. We also discuss a supersymmetric generalization of our quantum mechanical model. As a byproduct, we develop an efficient way of estimating the large N behavior of correlators in the SYK model.