Observation of Kondo hybridization with an orbital-selective Mott phase in 4d Ca2-xSrxRuO4

The heavy fermion state with Kondo-hybridization (KH), usually manifested in f-electron systems with lanthanide or actinide elements, was recently discovered in several 3d transition metal compounds without f-electrons. However, KH has not yet been observed in 4d/5d transition metal compounds, since more extended 4d/5d orbitals do not usually form flat bands that supply localized electrons appropriate for Kondo pairing. Here, we report a doping- and temperature-dependent angle-resolved photoemission study on 4d Ca2-xSrxRuO4, which shows the signature of KH. We observed a spectral weight transfer in the {\gamma}-band, reminiscent of an orbital-selective Mott phase (OSMP). The Mott localized {\gamma}-band induces KH with the itinerant \b{eta}-band, resulting in spectral weight suppression around the Fermi level. Our work is the first to demonstrate the evolution of the OSMP with possible KH among 4d electrons, and thereby expands the material boundary of Kondo physics to 4d multi-orbital systems.

1B). Finally, in III with octahedral tilting, the βand γ-FS pockets are selectively suppressed while the α-pocket remains robust as seen in Fig. 1C. This behavior is reminiscent of the OSMP.
To scrutinize this OSMP-like phenomenon, we performed systematic ARPES studies as a function of x and T. Our x-dependent result (0.2 ≤ ≤ 0.5) is presented in Fig. 2 (A-D). As x decreases from = 0.5 to 0.2, gradual suppression of the spectral weight is observed near the Fermi level generating a soft gap (18), as shown in Fig. S2B (see section S2). Interestingly, the soft gap opens only for the βand γ-bands, while the α-band remains intact with variation in doping. A similar trend is also observed in the T-dependence data ( Fig. 2 (D-H)). As T decreases from 45 K, the spectral weight of the βand γ-bands is suppressed in a similar fashion to that observed for the doping dependent result.
A detailed analysis of the spectral weight suppression in Fig. 2 is provided in Fig. 3. It can be clearly seen in the momentum distribution curves (MDCs) for each x (Fig. 3A) that the βand γ-bands are selectively suppressed as a function of x. The Lorentzian-fitted peak areas are plotted in Figs. 3B (x-dependent) and C (T-dependent), showing clear suppression only for the βand γ-bands. The energy distribution curves (EDCs) in Fig. 3D also show the evolution of the soft gap in the γ-band as a function of T. As T decreases from 45 K, the spectral weight in the 'A' region (BE < 0.2 eV) is gradually suppressed, while it increases in the 'B' region (BE ~ 0.4 eV). Hence, the spectral weight is transferred from a lower to higher BE region. This behavior can be seen more clearly in Fig. 3E, which shows the EDCs with the data obtained at 45 K subtracted. The integrated areas in the 'A' and 'B' regions are found to be almost identical, but with the opposite sign, satisfying the sum rule at all T (Fig. 3F). This suggests that the T-dependent evolution originates from (Mott-like) spectral weight transfer rather than a T-driven spectral broadening effect (19).
To confirm the origin of the spectral weight suppression further, we investigated the electronic structure change for = 0.2 upon surface electron doping ( Fig. 4C and section S6). In previous studies (20)(21)(22), it has been revealed that the Mott insulating state can easily collapse with an infinitesimal electron doping, showing emergence of a quasiparticle peak. Consistent with the results, we observe appearance of clear quasiparticle bands upon doping of small amount of electron (Fig. 4C). Therefore, we conclude that the spectral weight suppression indeed originates from Mott localization (20).

Role of octahedral tilting and signature of possible Kondo-hybridization
Our observations (orbital-selective suppression and spectral weight transfer) are consistent with the previously proposed OSMP scenario (23)(24)(25). However, there are still questions to be answered, e.g., what triggers OSMP and why the β-band is suppressed in the same way as the γ-band. It was suggested in previous experimental and theoretical studies that octahedral rotation is responsible for the OSMP (10,23). A study suggested that the rotation sufficiently reduces the γ-band width for Mott localization (23) while the importance of √2 × √2 × 2 unit cell doubling due to the rotation was discussed in another (10). In both scenarios, octahedral rotation plays a significant role in the OSMP. Therefore, a larger rotation angle may lead to a stronger OSMP effect. However, the OSMP occurs after the octahedral rotation angle saturates to the maximum value at = 0.5. Our results show that the OSMP and octahedral tilting distortion appear coincidently, and that the strength of the OSMP (spectral weight suppression of the γ-band) is roughly proportional to the tilting angle (17,23). Therefore, even though octahedral rotation significantly reduces the bandwidth of the γ-band, the OSMP in CSRO is triggered by the octahedral tilting, not by the rotation.
The mechanism with which octahedral tilting triggers the OSMP can be understood by considering the effect of the octahedral distortions (rotation/tilting) to bandwidths (Fig. 5).
The key aspect of octahedral distortions is that they lead to narrower d-orbital bandwidths. The detailed explanation for the band width reduction with octahedral distortions is as follows. Without octahedral rotation/tilting, 4d orbitals (three t2g and two eg) of Sr2RuO4 possess a wide bandwidth (Fig. 5 (A-C)). Once octahedral (in-plane) rotation sets in, the dxy and dx2-y2 orbitals become hybridized, which leads to a bandwidth reduction in the γ (d*xy) band (23) while the dyz/xz orbitals remain almost unchanged (Fig. 5 (D-F)). On top of that, octahedral tilting leads to hybridization between dxy (γ-band) and dyz/zx orbitals (α-, βbands). The hybridization from the tilt distortion results in fragmented bands with narrower bandwidths (Fig. 5 (G-I)), which is similar to how octahedral rotation narrows the bandwidth of dxy (23). This explanation is supported by our density functional theory (DFT) calculation results in Fig. 5I (26,27). There are several energy regions (yellow shaded area in Fig. 5I) in which both dxy and dyz/zx have a peak in DOS. This coincidence is an evidence that dxy (γ-band) and dyz/zx (α-, β-bands) are mixed and hybridized. In other words, octahedral tilting serves as a "scissor" that cuts t2g bands into pieces of narrow bands via hybridization. The resulting narrow bands provides a sufficient condition for the generation of the OSMP.
With the understanding of the band-width reduction mechanism described above, it is important to understand why the β-band is suppressed simultaneously with the OSMP. One may consider the possibility that a Mott-localization may occur in the β-band in a similar fashion to that of the OSMP in the γ-band. However, while the electron occupation number for the γ-band ( ~ 1.5) is appropriate for Mott localization in a doubled unit cell (10) (see section S7), the electron numbers of the α-( ~ 1.8) and β-( ~ 0.7) bands are inappropriate for Mott localization (9,10). Therefore, a mechanism other than Mott localization is needed to explain the suppression of the β-band. We can gain insight into the origin of β-band suppression from previous studies (4, 6-8, 15, 16). Some experimental results on 3d iron-based superconductors (IBS) suggest that the emergence of OSMP leads to KH between itinerant (dyz/dzx) and localized (dxy) bands (4,15,16). Interestingly, CSRO (0.2 ≤ < 0.5) exhibits the OSMP (similar to IBS), as well as HFlike behavior (6)(7)(8); thus, the KH mechanism should be considered.
As seen in Fig. 4 (A and B), the β-band dispersion is significantly renormalized in a similar way to KH, as schematically illustrated in Fig. 4D. Here, the OSMP-driven localized γ-band plays the role of the localized band in KH, and the β-band provides itinerant electrons. Therefore, as the OSMP is strengthened from = 0.5 to = 0.2, the β-band is renormalized to β´ via KH with the γ-band. In this way, as shown in Fig. 2, the OSMP and KH vary simultaneously with changes in x and T. Thus, suppression of the βband can be understood as a result of incoherent-to-coherent crossover due to KH (28,29). Our FS and Fermi momentum data (Figs. 1 and 4) also support the KH scenario. The βband FS is reduced with OSMP ( Fig. 4 (E and F)) and the electron occupancy ( ) of the βband decreases from 0.72 ( = 0.5) to 0.63 ( = 0.2) with OSMP. Furthermore, our ARPES results reveal that the βand γ-bands are hybridized at temperatures lower than 40 K (Fig. 3D). Considering the logarithmic temperature dependence of Kondo effects, this temperature (< 40 K) is of a similar order to the incoherent-to-coherent crossover temperature T* (14 K for = 0.2) for resistivity (6,8,30) and the antiferromagnetic peak temperature Tp (12 K for = 0.2) for magnetic susceptibility (8,30) (see section S4). Therefore, hybridization between the βand γbands is likely due to KH which usually accompanies both incoherent-to-coherent crossover and antiferromagnetic states. Moreover, the theoretically estimated TK value is in agreement with our experimentally observed value. HF systems exhibit scaling behavior with respect to TK which is given as (5) where and are the Sommerfeld coefficient and gas constant, respectively. The value is about 200-250 /( • ) for CSRO (0.2 ≤ ≤ 0.5) (7) and thus the estimated TK is about 40-50 K, which is consistent with our experimentally estimated value (40 K). In this regard, the β-band suppression is likely due to KH between γ-(localized) and β-(itinerant) bands.
Then, the next question is why only the β-band is involved in KH, while the α-band remains unaffected. This phenomenon can be understood by reference to momentumdependent-interaction theory, which is essential for explaining ferromagnetic-Kondo systems (29,(31)(32)(33)(34). In that theory, the proximity of two bands in momentum space is one of the most important factors leading to interactions between them. As can be seen in Fig.  2, the βand γbands are located close in momentum space. Therefore, KH can occur more easily than with the α-band, as illustrated in Fig. 5D.

Discussion
CSRO was the first material for which OSMP was proposed, but the very existence of the OSMP in CSRO has not yet been universally agreed on (10,11,19). The critical reason for the controversy may arise from the fact that the OSMP gap appears as a soft gap rather than a hard gap. As can be seen in Fig. 3, x-and T-variations lead to a gradual spectral weight transfer from a lower to a higher binding energy, rather than in the form of a sudden opening of a hard gap. In other words, suppressed spectral weight as well as remnant quasiparticle peak intensity (11) are coincidentally observed in the OSMP of CSRO, explaining both observations of suppressed spectral weight (10) and the remnant γ-band at the Fermi level (11) (see section S1). Moreover, investigation of the soft gap requires quantitative analysis with a reference point where the gap is closed ( = 0.5). Therefore, we speculate that the absence of the reference point ( = 0.5) data as well as the use of improper normalization methods (see section S1 for a detailed explanation) may have led previous studies to discrepancies in the interpretations (10,11,19). Our systematic x-and T-dependent studies not only settle down this issue by demonstrating the gradual evolution of the OSMP but also provide clues to the microscopic mechanism of the OSMP by demonstrating the coincidence between octahedral tilting and OSMP.
The reason why the OSMP appears as a soft gap can be attributed to the Hund coupling in 4d-orbital systems (35). The Hund coupling in 4d CSRO is enough to generate orbitalselective behavior but is not strong enough to create a hard gap in the system (35). The soft gap nature, which can be viewed as an intermediate state between metal and a Mott insulator with a hard gap, may enable us to observe the T-dependent spectral weight transfer (Figs. 2 and 3), which is not typically seen in Mott insulators with a hard gap behavior. There have been many recent attempts to understand the moderate nature (in Coulomb repulsion and spin orbit coupling) of 4d TMOs which exhibit various exotic phenomena (36)(37)(38)(39). We believe that results of our study on 4d TMO can provide information on how the Hund coupling plays a role in the determination of the electronic structure, thereby will enable us to understand diverse and exotic phenomena in 4d-orbital compounds.
Another important aspect to be discussed is the relevance of the OSMP to the Mott insulating state in Ca2RuO4. Previous theoretical (40,41) and experimental (42)(43)(44) results in CSRO reveal that the Mott transition in Ca2RuO4 (or < 0.2 of CSRO) is triggered by structural transition (L-Pbca to S-Pbca). The Mott state exists only in the S-Pbca phase, because the L-to S-Pbca transition leads to a full occupation of dxy, which in turn gives the essential condition for the formation the Mott state in the other two bands, i.e., half-filled αand β-bands. It is interesting to note that a uniaxial strain transforms the Mott state (S-Pbca) to a metallic phase (L-Pbca) in Ca2RuO4 (44) and that the Fermi surface of the metallic phase is remarkably similar to ours in the OSMP phase shown in Fig. 1C. The similarity between the two cases suggests that there may be a correlation between the OSMP and Mott state, which calls for further investigations on this issue.
Finally, our work also has important implications for the aspects of Kondo physics as well. Even though there have been several proposals of heavy mass behavior in CSRO (6)(7)(8), absence of quantitative and comprehensive electronic structure studies has hindered observation of direct evidence for KH. Our systematic electronic structure studies on CSRO not only reveal the signature of KH in a 4d-orbital system for the first time, but also suggest that the OSMP enables the KH via interaction with other itinerant 4d-bands. Our work advances understanding of the OSMP and Kondo physics in 4d TMOs, and suggests a key role of octahedral tilting in layered perovskite as a control parameter of physical properties.

Sample growth and characterization
High quality Ca2-xSrxRuO4 ( = 0.2, 0.3, 0.4, 0.5, 1.0, 2.0) were grown using the optical floating zone method. Sample quality and stoichiometry were characterized using a physical property measurement system (PPMS), a magnetic property measurement system (MPMS), scanning electron microscopy with energy dispersive X-ray analysis (SEM-EDX), and X-ray diffractometry.

ARPES measurements
T-dependent ARPES measurements were performed at Seoul National University using a He-I photon source (ℎ = 21.2 ) and the MERLIN beam line (BL) 4.0.3 of the Advanced Light Source, Lawrence Berkeley National Laboratory using both linearly horizontal (π) and vertical (σ) polarizations of a UV photon source (ℎ = 70 ). Spectra were acquired using R4000 (SNU) and R8000 (BL 4.0.3) electron analyzers, respectively. Cleaving of the samples was conducted at 10 K in an ultra-high vacuum better than 5 × 10 −11 .

DFT calculations
To obtain the density of states, we performed the first-principles density functional theory calculations using the Perdew-Burke-Ernzerhof functional as implemented in the VASP (26,27). The structural parameters and lattice constants are employed from (17).   The zero values at each T suggest spectral weight conservation, implying spectral weight transfer from low-to high-binding energy. A detailed explanation of the normalization method is provided in section S1.

This PDF file includes:
Section S1. Intensity normalization for the ARPES data Section S2. Doping (x)-dependent evolution of orbital-selective Mott phase Section S3. Temperature (T)-dependent evolution of orbital-selective Mott phase Section S4. Electric and magnetic properties of Ca2-xSrxRuO4 (0.2 ≤ ≤ 0.5) Section S5. Breakdown of the OSMP induced by electron doping from alkali metal (K) evaporation Section S6. x-dependent electron occupancies in each band Fig. S1. T-dependent integrated EDCs for = 0.2 with different normalization methods. Fig. S2. x-dependent evolution of orbital-selective spectral weight suppression. Fig. S3. T-dependent evolution of orbital-selective spectral weight suppression. Fig. S4. In-plane resistivity and magnetic property data of Ca2-xSrxRuO4 (CSRO) (0.2 ≤ ≤ 0.5). Fig. S5. Breakdown of the OSMP on K deposition. Fig. S6. x-dependent Fermi surfaces and electron occupancies. References (46)(47)(48)(49)(50)(51)(52)(53)(54) Section S1: Intensity normalization for the ARPES data To compare the doping (x)-and temperature (T)-dependent results, the intensity of the angleresolved photoemission spectroscopy (ARPES) data must be normalized in a systematic way. For an accurate comparison, a normalization area is selected in which bands do not cross. To obtain the normalization factor, we plot momentum-integrated EDCs near the S-point (0.6 < (Å −1 ) < 0.8, region #1 in Fig. 2A)  Regarding the effect of the normalization method on the results, figure S1 (C and D) show that the T-dependent spectrum does not exhibit spectral weight transfer (the OSMP), but does show Tdependent breakdown of quasiparticles without OSMP, consistent with previous reports (11,19) ( fig. S1D). Therefore, we conclude that the OSMP and QP breakdown may co-exist independently in the γ-band. However, to observe the OSMP, intensity normalization at a binding energy higher than the energy scale of the OSMP is essential.

Section S2: Doping (x)-dependent evolution of orbital-selective Mott phase
The As shown in fig. S2C (x-dependent octahedral rotation / tilting angles (17,46)), the strength of the OSMP (spectral weight suppression of the γ-band) seems to be proportional to the tilting angle.
On the other hand, the EDC at = 1.0 does not show Mott-like (lower to higher BE) spectral weight transfer as well as spectral weight suppression around the EF ( fig. S2A). Since the octahedral tilting angle is zero and the rotation angle varies in the region between = 0.5 and 1.0 ( fig. S2C), we conclude that the OSMP does not occur only with octahedral rotation, hence octahedral tilting is the key to triggering the OSMP.

Section S3: Temperature (T)-dependent evolution of orbital-selective Mott phase
The T-dependent MDCs exhibit orbital-selective spectral weight suppression at EF. As can be seen in fig. S3A, the βand γ-bands show spectral weight suppression, but the α-band remains almost unchanged. The T-dependent orbital selectiveness is more clearly seen in fig. S3B, which shows the MDCs subtracted from that of 45 K.
This strongly suggests a possible Kondo-hybridization (KH) scenario in CSRO.

Section S5: Breakdown of the OSMP induced by electron doping from alkali metal (K) evaporation
Alkali metal evaporation is widely used to impart an electron-doping effect on a crystal (21,22,53). Previous ARPES studies on Sr2IrO4 (21,22) showed that additional electrons from potassium (K) lead to the sudden breakdown of the Mott-localized state. Motivated by those works (21,22), we performed electronic structure measurements with K evaporation to determine whether the OSMP in CSRO ( = 0.2) breaks down in the same way as the Mott state in Sr2IrO4. As shown in fig. S6, the OSMP soft gap becomes closed with infinitesimal K coverage (< 0.2 monolayer, ML), and exhibits recovered dispersive bands. This implies that the origin of spectral weight suppression in the -band is Mott-localization.