Observation of the Hybridization Gap and Fano Resonance in the Kondo Lattice ${\mathrm{URu}}_2{\mathrm{Si}}_2$

The nature of the second-order phase transition that occurs in ${\mathrm{URu}}_2{\mathrm{Si}}_2$ at 17.5 K remains puzzling despite intensive research. A key question emerging in the field is whether a hybridization gap between the renormalized bands can be identified as the “hidden” order parameter. We report on the measurement of a hybridization gap in ${\mathrm{URu}}_2{\mathrm{Si}}_2$ employing a spectroscopic technique based on quasiparticle scattering. The differential conductance exhibits an asymmetric double-peak structure, a clear signature for a Fano resonance in a Kondo lattice. The hybridization gap opens well above 17.5 K, indicating that it is not the hidden order parameter. Our results put stringent constraints on the origin of the hidden order transition in ${\mathrm{URu}}_2{\mathrm{Si}}_2$ and demonstrate that quasiparticle scattering spectroscopy can probe the band renormalizations in a Kondo lattice via detection of a novel type of Fano resonance.

Figure 1

(a) Single-impurity Fano resonance. $T_{\mathrm{K}}$, Kondo temperature. (b) Hybridization between a conduction band (${\epsilon }_k$) and localized states (${\epsilon }_f$) (see the text). $\mu$ is the chemical potential. (c) DOS for the renormalized heavy bands (thick line), DOS broadened due to correlation effects (dotted line), and $dI/dV$ (thin line) simulating our data at $T<T_{\mathrm{HO}}$. (d) Fano resonance in a Kondo lattice. $T_{\mathrm{K}}$, characteristic temperature for the Kondo lattice. Inset: Schematic for QPS.

Figure 2

(a) $ab$-plane resistivity (resistance) for ${\mathrm{URu}}_2{\mathrm{Si}}_2$ ($\mathrm{U}({\mathrm{Ru}}_{0.985}{\mathrm{Rh}}_{0.015}{)}_2{\mathrm{Si}}_2$). $T^{*}$ for resistance maximum is 82 and 70 K, respectively. Note that the ratio $R_{300\mathrm{K}}/R_{T\to 0\mathrm{K}}$ is large: 248 for ${\mathrm{URu}}_2{\mathrm{Si}}_2$ and 5.8 for $\mathrm{U}({\mathrm{Ru}}_{0.985}{\mathrm{Rh}}_{0.015}{)}_2{\mathrm{Si}}_2$. $T_{\mathrm{HO}}$, taken for minimum in $dR/dT$, is 17.56 and 12.8 K, respectively. The lines are best fits with gapped AFM excitations: ${\rho }_{\mathrm{AFM}1}$ (solid red line, $\Delta =4.9\mathrm{meV}$) and ${\rho }_{\mathrm{AFM}2}$ (dotted blue line, $\Delta =5.1\mathrm{meV}$) (see the text). (b) Specific heat divided by temperature for ${\mathrm{URu}}_2{\mathrm{Si}}_2$.

Figure 3

(a),(b) Differential conductance (normalized by $dI/dV$ at $-50\mathrm{mV}$) curves for junctions along the $c$ axis of ${\mathrm{URu}}_2{\mathrm{Si}}_2$ and $\mathrm{U}({\mathrm{Ru}}_{0.985}{\mathrm{Rh}}_{0.015}{)}_2{\mathrm{Si}}_2$, respectively. Curves are shifted vertically. Dotted lines are a guide to the eye. (a) The measurement temperature (the differential junction resistance $R_J$ at $-50\mathrm{mV}$) is 3.49 (12.3), 3.51 (18.7), 2.07 (16.7), 4.41 (55.6), and 4.35 K ($51.0\Omega$) for the curves from 1 to 5, respectively. (b) The measurement temperature is 4.34 K for all junctions, and $R_J$ is 19.5, 25.0, 23.5, 20.4, and $19.7\Omega$ for the curves from 1 to 5, respectively. (c)–(f) Typical conductance spectra for ${\mathrm{URu}}_2{\mathrm{Si}}_2$ and best fit curves with parameters shown.

Figure 4

(a) Temperature-dependent conductance (circles, normalized by $dI/dV$ at $-30\mathrm{mV}$) and fit curves (lines). The $R_J$ at the lowest temperature is $19.1\Omega$. The top three curves are plotted on an expanded vertical scale. (b) The hybridization gap (solid circles) ${\Delta }_{\mathrm{hyb}}$, opening at $T_{\mathrm{hyb}}\sim 27\mathrm{K}\gg T_{\mathrm{HO}}$ and the renormalized $f$ level $\lambda$ (right axis, open circles). (c) $R_J$ at zero bias (open circles) and at $-25\mathrm{mV}$ (crosses) and the NZBC (right axis, solid circles).