Signature of Quantum Criticality in Photoemission Spectroscopy

A quantum phase transition in a heavy-fermion compound may destroy the Fermi-liquid ground state. However, the conditions for this breakdown have remained obscure. We report the first direct investigation of heavy quasiparticle formation and breakdown in the canonical system ${\mathrm{CeCu}}_{6-x}{\mathrm{Au}}_x$ by ultraviolet photoemission spectroscopy at elevated temperatures without the complications of lattice coherence. Surprisingly, the single-ion Kondo energy scale $T_K$ exhibits an abrupt step near the quantum critical Au concentration of $x_c=0.1$. We show theoretically that this step is expected from a highly nonlinear renormalization of the local spin coupling at each Ce site, induced by spin fluctuations on neighboring sites. It provides a general high-temperature indicator for heavy-fermion quasiparticle breakdown at a quantum phase transition.

Figure 1

(a) Near-$E_F$ spectra of ${\mathrm{CeCu}}_{6-x}{\mathrm{Au}}_x$ for five different Au concentrations at $T=15\mathrm{K}$ ($h\nu =40.8\mathrm{eV}$, $\Delta E=4.9\mathrm{meV}$), normalized at $E_B\approx 100\mathrm{meV}$. The dashed lines describe the resolution-broadened FDD at $T=15\mathrm{K}$. The inset shows a larger energy range including the SO partner at $E_B\approx 260\mathrm{meV}$ ($\Delta E=15\mathrm{meV}$). (b) and (c) show spectra for $x=0.1$ and $x=0.2$, respectively, divided by the FDD, at various $T$. The solid lines are best NCA fits (see Table  for the resulting model parameter values). The insets in (b) and (c) show the corresponding raw data.

Figure 2

Dependence of the Kondo temperature $T_K$ on the Au content $x$, as determined by UPS (open circles), specific heat [20] (triangles), and neutron scattering [12, 14] (diamonds). The shaded area is a guide to the eye. The insets (a) and (b) show diagrammatic representations of the RKKY corrections to the local Kondo vertex. The inset (c) and the solid line in the main panel show the universal curve $T_K(y)/T_K(0)$ vs $y/y_m$ as given by Eq. (3).

Figure 3

Schematic $T=0$ phase diagram of a HF system with a magnetic QPT driven by RKKY coupling or a SDW instability in the plane of single-ion Kondo scale $T_K(0)/D_0$ and RKKY coupling strength $y$, as drawn from the high-$T$ analysis. Red line ($y_m$): Maximum RKKY coupling strength beyond which complete Kondo screening ceases to exist [Eq. (4)]. At the red line, a step occurs in $T_K(y)$. Blue line ($y_{\mathrm{SDW}}$): RKKY coupling strength at which the heavy Fermi liquid becomes unstable towards a SDW, assuming a spin-spin coupling $J_{\mathrm{SDW}}=J$. The cases $y_m<y_{\mathrm{SDW}}$ and $y_m>y_{\mathrm{SDW}}$ distinguish whether the QPT is LQC-like (yellow) or HM-like (white), respectively. The arrows indicate estimates [16] for $T_K(0)/D_0$ for ${\mathrm{CeCu}}_{6-x}{\mathrm{Au}}_x$ and for ${\mathrm{CeNi}}_{2-x}{\mathrm{Cu}}_x{\mathrm{Ge}}_2$.