Kondo Reshapes Multiple Orders in a $5f$ van der Waals Material

Abstract

Electron interactions can drive magnetism, superconductivity, and topology. However, the realization of these phases remains limited in van der Waals materials, and the full landscape of strong correlations remains uncharted in any context. While interactions between conduction electrons and localized spins yield a well-known competition between heavy fermions (Kondo hybridization) and magnetic order (RKKY exchange), such spin-driven competition represents only part of the correlated electron phase diagram. Here we demonstrate that a heavy-fermion state can also compete with charge order, such as the charge density wave (CDW) state typical in the van der Waals $4f$ rare-earth tritellurides (RTe$_3$). We exploit the spatially-extended $5f$ orbitals of $β$-UTe$_3$ to enhance Kondo hybridization compared to its isostructural RTe$_3$ cousins. Our scanning tunneling spectroscopy on $β$-UTe$_3$ shows Fano resonances characteristic of the heavy fermion state, while our quasiparticle interference imaging reveals the disappearance of Fermi-level nesting and the appearance of flat bands. We extend the tritelluride tight-binding model to include Kondo coupling and quantify the Fermi surface reconstruction. Consistent with the destruction of nesting, we observe no CDW in $β$-UTe$_3$. Our expansion of the Kondo phase diagram beyond spin-mediated competition opens new possibilities for proximity-induced phase engineering in correlated van der Waals heterostructures.

Figures (9)

• Figure 1: Tritelluride overview and $\beta$-UTe$_3$ structure.a, Evolution of the RKKY--Kondo crossover in the tritelluride series, governed by $f$-orbital localization. TmTe$_3$ exhibits localized $4f$ orbitals and RKKY-dominated interactions; CeTe$_3$ has more extended $4f$ orbitals and weak Kondo behavior; $\beta$-UTe$_3$ has even more extended 5$f$ orbitals and lies fully in the Kondo regime. b, Crystal structure of $\beta$-UTe$_3$, showing the van der Waals (vdW) gap and the layers exposed by cleaving. c, Cross-sectional STEM image viewed along the $a$–$c$ plane with the $b$ axis vertical; the crystal structure is overlaid. d,e, Tight-binding calculation of constant-energy contours in $\beta$-UTe$_3$ (see Methods). The nested structure at energies below $E_{\mathrm{F}}$ (d) is destroyed at the Fermi surface (e) due to Kondo hybridization. f, Top view of the $\beta$-UTe$_3$ crystal structure, highlighting the Te and U sub-lattices. g, STM topograph with the lattice overlaid; a U vacancy and a Te vacancy are indicated. h, Fourier transform of (g), showing peaks from the Te and U periodicities (calculated from the larger field of view in Extended Data Fig. \ref{['fig:full_topo']}a). STM topograph was measured at $T = 4.5$ K with sample bias $V_{\mathrm{sample}} = -200$ mV and current setpoint $I_{\mathrm{set}} = 100$ pA.
• Figure 1: STM topograph of the surface of $\beta$-UTe$_3$.a, Large field of view of the $\beta$-UTe$_3$ surface topograph. A crop from this scan was used in Fig. \ref{['fig:KS']}g. b, Fourier transformation of (a). The Bragg peaks corresponding to the U and Te periodicities are marked. STM topograph was measured at $T = 4.5$ K with sample bias $V_{\mathrm{sample}} = -200$ mV and current setpoint $I_{\mathrm{set}} = 100$ pA.
• Figure 2: $\beta$-UTe$_3$ defect imaging and Kondo spectroscopy.a, STM topograph and b, Fano $q$ map, fitted from a d$I$/d$V$ map in the same area. A representative U site and U vacancy are marked in both panels; $q$ is high on U sites and suppressed on U vacancies. c, d$I$/d$V$ spectra averaged over U sites (green) and U vacancies (cyan), and corresponding Fano line shape fits to equation (\ref{['eq:stsfit']}). The fitted hybridization energy $2\Gamma$ is approximately the same for both curves, while $q$ varies. Measurements were performed at $T = 7.2$ K with $V_{\mathrm{sample}} = 100$ mV and $I_{\mathrm{set}} = 150$ pA; spectra were acquired using a zero-to-peak lock-in modulation amplitude of $V_{\mathrm{exc}} = 4$ mV.
• Figure 2: Effect of bias and tip material on STM topography.a, Crystal structure of $\beta$-UTe$_3$, showing the vdW gap and the layers exposed by cleaving. b, Top view of the $\beta$-UTe$_3$ structure, highlighting the Te and U sub-lattices. c,d, STM topographs of the $\beta$-UTe$_3$ surface acquired with a PtIr tip (as used for all main-text data). e,f, STM topographs of the $\beta$-UTe$_3$ surface acquired with a W tip. For each tip, scans were taken on the same area at $V_\mathrm{sample}=100$ mV and $V_\mathrm{sample}=-100$ mV. g--j, Corresponding Fourier transformations of the topographs in (c--f). Bragg peaks from the Te periodicity (black circles) and the U periodicity (red circles) are visible. With the PtIr tip, the U peaks dominate at positive bias, while the Te peaks dominate at negative bias. This behavior matches the main text: in Fig. \ref{['fig:KS']}g we use negative bias and observe that the Te lattice corrugation dominates the topographs, whereas in Fig. \ref{['fig:fano']}a we use positive bias and the U lattice corrugation dominates. Since the scans shown in (c) and (d) were taken on the same area, we confirm that the bias dependence of the Bragg peaks originates from an electronic effect rather than spatial variations across the sample. In contrast to the PtIr tip measurements (g,h), both Te and U Bragg peaks are clearly resolved in the W-tip Fourier transformations (i,j) with no significant bias dependence, indicating that the tunneling into the different sub-lattices depends on the tip material in addition to the sample bias. Measurements were performed under the following conditions and setpoints: (c,d) $T=5$ K, $I_{\mathrm{set}}=200$ pA; (e,f) $T=10.3$ K, $I_{\mathrm{set}}=150$ pA.
• Figure 3: Quasiparticle interference and tight-binding model of $\beta$-UTe$_3$.a,b, QPI dispersion along the $\Gamma$–M (a) and $\Gamma$–X (b) directions, extracted from the Fourier transforms of d$I$/d$V$ energy slices acquired in $25 \times 25$ nm$^2$ area (see Methods). The dominant scattering modes are marked as $q_1^{\pm}$ (green), $q_2$ (blue), and $q_3$ (orange), with colored guides to the eye. In (b), the blue dashed circle marks the $\Gamma$–X position corresponding to the $\Gamma$–M mode $q_2$, scaled by $\sqrt{2}$. c, Energy-resolved QPI intensity obtained by integrating panels (a) and (b) over a low-$q$ window associated with the $q_1$ mode and then averaging the two directions (black curve). Green shading shows Gaussian fits to the two peaks. The hybridization gap is consistent with the energy scale $2\Gamma$ (black arrow) extracted from the Fano fits in Fig. \ref{['fig:fano']}. d, Tight-binding model of $\beta$-UTe$_3$, with five coupling terms indicated: nearest-neighbor Te $5p$ orbital couplings ($t_{\parallel}$ and $t_{\perp}$, black); next-nearest-neighbor Te $5p$ orbital diagonal couplings across underlying U ($t_\mathrm{d}^\mathrm{U}$, green) and across underlying Te ($t_\mathrm{d}^\mathrm{U}$, cyan); and effective Kondo coupling between Te $5p$ and U $5f$ orbitals ($t_\mathrm{K}$, red). The terms capture the nested tritelluride band structure and the Kondo hybridization. e, Calculated band structure cuts parallel to $\Gamma$–M, at the constant $k_y$ values marked in (g). f, Calculated band structure along $\Gamma$–X. QPI scattering modes $q_1^{\pm}$, $q_2$, and $q_3$ are labeled in colors corresponding to (a--b). g, Constant-energy contour at $-100$ mV, below the Kondo energy range. The reduced Brillouin zone is outlined by the dashed red box; linecuts used in (e--f) are marked. Measurements were performed at $T = 7.1$ K with $V_{\mathrm{sample}} = 100$ mV, $I_{\mathrm{set}} = 800$ pA, and $V_{\mathrm{exc}} = 4$ mV.