Anomalous Quantum Oscillations in a Heterostructure of Graphene on a Proximate Quantum Spin Liquid

The quasi-two-dimensional Mott insulator $\alpha \text{−}{\mathrm{RuCl}}_3$ is proximate to the sought-after Kitaev quantum spin liquid (QSL). In a layer of $\alpha \text{−}{\mathrm{RuCl}}_3$ on graphene, the dominant Kitaev exchange is further enhanced by strain. Recently, quantum oscillation (QO) measurements of such $\alpha \text{−}{\mathrm{RuCl}}_3$ and graphene heterostructures showed an anomalous temperature dependence beyond the standard Lifshitz-Kosevich (LK) description. Here, we develop a theory of anomalous QO in an effective Kitaev-Kondo lattice model in which the itinerant electrons of the graphene layer interact with the correlated magnetic layer via spin interactions. At low temperatures, a heavy Fermi liquid emerges such that the neutral Majorana fermion excitations of the Kitaev QSL acquire charge by hybridizing with the graphene Dirac band. Using ab initio calculations to determine the parameters of our low-energy model, we provide a microscopic theory of anomalous QOs with a non-LK temperature dependence consistent with our measurements. We show how remnants of fractionalized spin excitations can give rise to characteristic signatures in QO experiments.

Figure 1

(a) Optical image of a typical graphene $\alpha \text{−}{\mathrm{RuCl}}_3$ device. (b) Schematic illustration of the device, consisting of a flake of hexagonal boron nitride (hBN) as top stacking basis (green), an $\alpha \text{−}{\mathrm{RuCl}}_3$ nanosheet (purple), and a graphene monolayer (grey). The stack is then transferred onto gold electrodes which are integrated within the bottom hBN flake. (c) Comparison of the electronic structure from ab initio calculations [34] and the effective low-energy model Eq. (4). Inset: Schematic picture of the Kitaev-Kondo lattice and its coupling constants, whereby we considered $K^x=K^y=K^z\equiv K$.

Figure 2

The non-LK behavior of the QO damping factor $R(T)$ is plotted as a function of the temperature and chemical potential deviation $\mu /J$. In the hFL regime for small $\mu /J$, a characteristic maximum appears around $T_{\max }\approx J/5$, and at large chemical potential the usual monotonically decreasing LK behavior (red dashed line) is recovered.

Figure 3

(a) The experimentally determined longitudinal resistance $R_{xx}$ (sample $B$ at 3.8 K, circles which are connected to guide the eye) and the analytically determined magnetization $M$ of Eq. (8) are plotted against the cyclotron frequency of graphene ${\omega }_t\propto \sqrt{B}$. The parameters for $M$ are taken from the amplitude decay fit in Fig. S4 in Supplemental Material [42], with parameters tabulated in Table SI. (b) Fit of the experimental data (open symbols) with the theoretical predicted curves of Eq. (9) (solid lines) and the LK damping factor $R_{\mathrm{LK}}\propto \chi /\sinh \chi$ (dashed lines). Fitting values and quality criteria are given in Tables SI and SII in Supplemental Material [42].