Observation of Mott instability at the valence transition of f-electron system

ABSTRACT Mott physics plays a critical role in materials with strong electronic correlations. Mott insulator-to-metal transition can be driven by chemical doping, external pressure, temperature and gate voltage, which is often seen in transition metal oxides with 3d electrons near the Fermi energy (e.g. cuprate superconductor). In 4f-electron systems, however, the insulator-to-metal transition is mostly driven by Kondo hybridization and the Mott physics has rarely been explored in experiments. Here, by combining the angle-resolved photoemission spectroscopy and strongly correlated band structure calculations, we show that an unusual Mott instability exists in YbInCu4 accompanying its mysterious first-order valence transition. This contrasts with the prevalent Kondo picture and demonstrates that YbInCu4 is a unique platform to explore the Mott physics in Kondo lattice systems. Our work provides important insight for the understanding and manipulation of correlated quantum phenomena in the f-electron system.


Supplementary
. Basic characterization of high-quality YbInCu4 crystals. a. X-ray diffraction patterns along (00l), (0k0) and (h00) crystalline directions. YbInCu4 crystallizes in a FCC structure with a lattice constant of a = b = c = 7.17 Å (measured at 150 K). b. Photoemission core-level measurements on YbInCu4 crystals using 100-eV photons. (i) and (ii) are the photoemission image and integrated EDC, respectively. c. Optical images of cleaved surfaces of YbInCu4 crystals after ARPES measurements.
In the main text, we have shown Laue diffraction (Fig. 2a) and transport (Fig. 2b) measurements on YbInCu4 crystals, both reflecting the crystals are of high quality, given sharp diffraction spots in the former and narrow transition width in the latter. Here we present X-ray diffraction measurements showing sharp diffraction spots (Supplementary In Supplementary Figure 1b, besides core-level peaks, we have also marked LHB belonging to Yb 3+ and f bands belonging to Yb 2+ (UHB-f' not marked). The f band is as flat (non-dispersive) as those core-levels (e.g., In 4d) in high-binding energy regions.
As YbInCu4 crystallizes in a FCC structure with a rather big unit cell, there exists no natural cleaving planes. We usually failed to get big flat cleaved surfaces but small and fractured surfaces on (111) surface (in more than forty times of experiments), which thus highly necessitates focused-beam ARPES to acquire reliable data.
Supplementary Figure 2. Dispersive α bands: Fermi surfaces and bulk state nature. a. Fermi surfaces vertically stacking (left panel), and MDCs at EF along cut_1 (right panel) measured at 7 K, 61 K, and 6 K, respectively. Stripes are not real band structures but fake features. b. Photon-energy dependence of dispersive α bands. Black circles mark Fermi crossings of the α-band in the second BZ. The EDC is extracted around ky = 0 and fitted with a Gaussian. c. Temperature-dependence of integrated EDCs including both α and f bands. Warm-up results (i) are well reproduced by a follow-up cool-back (ii). In (i) and (ii), EDCs of both warm-up and cool-back can be easily classified into two groups, well separated by TV, indicative of the valence transition. In (iii), integrated EDC at 15 K perfectly matches that of 17 K (cool-back) (area-normalization is used), which again verifies our temperature-dependence results are reliable.
In Fig. 3 of the main text, we have shown that f band suddenly jumps towards EF when heating the sample across TV. Here we show more details of these data in Fig Hybridization seems to occur between the α and f-bands (Supplementary Figure 4).
However, we could not track the α band in a convincing way when it approaches the f band, neither did we know whether the gap truly forms or the α band loses some spectral weight.
The closing of "hybridization gap" at high temperatures (e.g., 70 K) can be alternately In the main text, we have shown valence-change-related charge transfer serves as self-doping to drive the orbital-selective Mott transition. Detailed calculation results of density of states above/below TV is presented in Supplementary Figure 7a. When cooling through TV, charge transfer occurs in a quite wide binding-energy region, manifested by shifts of core-level peaks and spectral weight transferring. This is confirmed by our ARPES measurements (Supplementary Figure 7b), hard X-ray photoemission experiments [1,2] and RIXS [3] results reported previously (e.g., Cu 3p3/2 and In 3d5/2 are shifted by ~40 and ~30 meV towards higher-binding energy when heating across TV [2], respectively, while Yb 3+ 4f (~6.0 eV) moves oppositely by 65 meV [1]). Such drastic change of the spectra naturally reflects the valence change across TV, which would in turn trigger the Mott transition in the Yb 3+ band.
Supplementary Figure 8. Comparison of the total density of states for U = 2, 6 eV and v ≈ +3, 2.9, 2.7 at 30 K. The LUB and UHB are indicated for clarity. The insets show the enlarged plots near EF.
To identify the origins of different DOS peaks, we compare their respective variation with the Coulomb interaction U for different average Yb valence v ≈+3, 2.9, and 2.7 ( Supplementary Figures 8 and 9). Deviation from integer valence may be viewed as a mixture of Yb 2+ and Yb 3+ states (the true valence of Yb ions is close but not identical to +2 and +3 according to the simple ionic picture, and there is no spatial separation of Yb 2+ and Yb 3+ sites). The Coulomb interaction plays the role of tuning the Kondo coupling [4]. The temperature is fixed to avoid confusion due to thermal broadening. At U = 6 eV, the peak right below the Fermi energy disappears for v = +3 but remains sharp for other two valences, suggesting that the former comes from the Kondo quasi-particles, while the latter two are the fully occupied 4f bands of Yb 2+ ions. The peak above the Fermi energy corresponds to the hole band (UHB) of Yb 3+ and its position changes only slightly with U, while the broad LHB is located at roughly -U and moves accordingly. The Yb 2+ bands are well described by pure DFT calculations with proper renormalization. As v decreases, Yb 2+ bands grow stronger and the broad UHB shifts downward to touch the Fermi energy, as implied from the insets. These features are in qualitative (or quantitative) agreement with experiments, thus providing a most probable interpretation of the key ARPES features supporting the proposed mechanism, although the Yb 2+ bands in calculations are not as flat as that in experiment and exact positions of the calculated UHB and Yb 2+ bands are also slightly higher in energy. It is noteworthy that we did not mean to claim that the Kondo physics is completely absent. Incoherent Kondo scattering is indeed seen above TV in the insulatinglike resistivity. It is simply that the true Kondo temperature is too small (~20 K) and the Supplementary Figure 10 presents more detailed analysis of the orbital-resolved spectra. Apparently, the two peaks near the Fermi energy are from Yb 4f orbitals (Yb 3+ UHB and Yb 2+ ) with J = 7/2 and the conduction spectra are mainly from Cu d orbitals.
Although no Kondo resonance is revealed, there does exist usual hybridization between Yb 4f and Cu d bands, as the Cu d partial DOS has similar peak structure at the Yb 4f peaks (Yb 3+ UHB and Yb 2+ ). Actually, solely from ARPES data, we can also rule out the Kondo resonance as the origin of f and f' bands: above TV (42 K), YbInCu4 is shown to possess a TK of ~ 20 K; if f or f' bands are indeed of Kondo resonance origin, they should disappear at a temperature well above such TK, under the context of the Kondo physics; however, f and f' bands can persist up to 70 K (> 20 K, even to 100 K in our measurements).
Supplementary Figure 10. Orbital-resolved partial density of states for U = 6.0 eV and T = 30 K within different energy ranges in (a) and (b).