Anisotropic scattering continuum induced by crystal symmetry reduction in atomically thin $\alpha –\mathrm{RuCl}{}_3$

Kitaev quantum spin liquids described by the Kitaev model represent an exotic state of matter with long-range entangled spins and topological order, which hold promise for quantum computation. $\alpha \text{−}{\mathrm{RuCl}}_3$, a material with van der Waals layered structure, is shown to be proximate to such a state recently. Here we report Raman spectroscopy of atomically thin $\alpha \text{−}{\mathrm{RuCl}}_3$. New phonon modes emerge at low temperature, signifying a phase transition to a crystal structure with lowered symmetry. The Fano line shape of two low-energy phonon modes and the magnetic scattering continuum in bulk $\alpha \text{−}{\mathrm{RuCl}}_3$, which evidence fractionalized Majorana fermions of the proximate quantum spin liquid, persist to the trilayer. Polarization-dependent measurements reveal increased anisotropy of the Kitaev exchange constants when approaching the two-dimensional limit. Our results demonstrate an intimate relation between the crystal structure and the symmetry of the proximate quantum spin liquid ground state.

Figure 1

(a) Schematic for the crystal structure of monolayer $\alpha \text{−}{\mathrm{RuCl}}_3$, showing edge-sharing ${\mathrm{RuCl}}_6$ octahedra forming a honeycomb lattice. (b) Three types of bonds in the Kitaev model, with exchange coupling constants $J_x$, $J_y$, and $J_z$. (c) Atomic force microscope image of a thin $\alpha \text{−}{\mathrm{RuCl}}_3$ flake on a sapphire substrate. The inset shows the height profile along the thick white line, measuring 2.3 nm and corresponding to a trilayer. (d), (e) Raman spectra for bulk and trilayer $\alpha \text{−}{\mathrm{RuCl}}_3$ in the parallel ($XX$) and perpendicular ($XY$) polarization configurations at 300 K. Phonon modes are labeled according to their symmetry, with the corresponding atomic displacement patterns shown in (f). The dashed line in (e) represents a phonon mode of the substrate.

Figure 2

(a) Raman scattering intensity map of bulk $\alpha \text{−}{\mathrm{RuCl}}_3$ in the $XX$ configuration. (b) Data in (a) at selected temperatures. (c) An expanded view of the spectral range indicated by the dashed box in (b) for 4 and 140 K. Data at 4 K in the $XY$ configuration are also included for comparison. (d)–(f) The corresponding data for trilayer $\alpha \text{−}{\mathrm{RuCl}}_3$. The modes that emerged at low temperature are marked by arrows in (e) and by shaded regions in (f).

Figure 3

(a) Raman spectrum of trilayer $\alpha \text{−}{\mathrm{RuCl}}_3$ between 220 and 350 ${\mathrm{cm}}^{-1}$ at 4 K in the $XX$ configuration. The solid line through the data is a fit, with its components represented by Lorentzians. (b) Thickness dependence of the Raman spectra at 4 K in the $XX$ configuration. (c) Temperature dependence for the integrated intensity spanning 280–293 ${\mathrm{cm}}^{-1}$ for $A_{1g}^3$ and 316–337 ${\mathrm{cm}}^{-1}$ for $A_{1g}^4$, as indicated by the shaded areas in (a). The error bars are estimated from the noise level and the integration interval. (d) Temperature dependence of the phonon linewidth for $E_g^3$ and $E_g^4$, as obtained by fitting the data in the $XY$ configuration. (e) Temperature dependence of the phonon frequencies for $E_g^3$, $E_g^4$, $A_{1g}^1$, and $A_{1g}^3$ as obtained by fitting the data in the $XX$ configuration. The solid lines in (d) and (e) are fits to the anharmonic model.

Figure 4

(a), (b) Representative Raman spectra for bulk and trilayer $\alpha \text{−}{\mathrm{RuCl}}_3$ in the $XY$ configuration, normalized to their respective intensity of the $E_g^2$ peak at 300 K. The solid lines are fits based on a model consisting of two Fano functions and a linear background (dashed lines). (c) Temperature dependence of the integrated intensity for the linear background. The dashed and dotted lines show the temperature dependence for bosonic- and fermionic-type excitations, respectively. (d), (e) Temperature dependence of the linewidth and $1/\left|q\right|$ for $E_g^2$. The solid lines are fits to the anharmonic model.

Figure 5

(a) Raman spectra for bulk $\alpha \text{−}{\mathrm{RuCl}}_3$ in the $XX$ and $XY$ polarization configurations at 4 K, normalized to the $E_g^2$ peak intensity in $XX$. Their difference spectrum ($XX-XY$) is shown in the lower panel. Intensities for the phonons do not cancel out, giving rise to peaks. Parts (b) and (c) are the results for 12-layer and trilayer samples. The difference in the collection efficiency for the two polarization configurations was measured and compensated.