PTCDA molecular monolayer on Pb thin films: An unusual π-electron Kondo system and its interplay with a quantum-confined superconductor
Shuangzan Lu, Hyoungdo Nam, Penghao Xiao, Mengke Liu, Yanping Guo, Yusong Bai, Zhengbo Cheng, Jinghao Deng, Yanxing Li, Haitao Zhou, Graeme Henkelman, Gregory A. Fiete, Hong-Jun Gao, Allan H. MacDonald, Chendong Zhang, Chih-Kang Shih
11 PTCDA molecular monolayer on Pb thin films: An unusual -electron Kondo system and its interplay with quantum-confined superconductor Shuangzan Lu , Hyoungdo Nam , Penghao Xiao , Mengke Liu , Yanping Guo , Yusong Bai , Zhengbo Cheng , Jinghao Deng , Yanxing Li , Haitao Zhou , Graeme Henkelman , Gregory A. Fiete , Hong-Jun Gao , Allan H. MacDonald , Chendong Zhang and Chih-Kang Shih School of Physics and Technology, Wuhan University, Wuhan 430072, China Department of Physics, University of Texas at Austin, Austin, TX 78712, USA Department of Chemistry, University of Texas at Austin, Austin, TX 78712, USA Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China Department of Physics, Northeastern University, Boston, MA 02115, USA Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Present address:
Materials Science Division, Lawrence Livermore National Laboratory, Livermore, California 94550, USA *[email protected] (C.D.Z) *[email protected] (C.K.S.)
The hybridization of magnetism and superconductivity has been an intriguing playground for correlated electron systems, hosting various novel physics. Usually, localized d - or f -electrons are central to magnetism. In this study, by placing a PTCDA (3,4,9,10-perylene tetracarboxylic dianhydride) molecular monolayer on ultra-thin Pb films, we built a hybrid magnetism/superconductivity (M/SC) system consisting of only sp electronic levels participating in the magnetic and superconducting (SC) states. Through experimental and theoretical investigations, we found that the magnetic moments originating from interfacial charge-transfers reside in the unpaired molecular orbital. Kondo screening and its interplay with the superconductivity show several striking spectroscopic features in scanning tunneling spectroscopy measurements that illustrate the distinctiveness of delocalized -electron magnetic moments with substantial lateral coupling. Moreover, moiré superlattices with tunable commensurate twist angle and the quantum confinement in the ultra-thin Pb films provide easy and flexible implementations to tune the magnetic moment concentration, the SC order parameters, and the competition between them, which are rarely present in previous studied M/SC hybrid systems. The combination of magnetism and superconductivity, which are normally mutually exclusive, provides an intriguing platform involving rich quantum phenomena, such as the Yu-Shiba-Rusinov (YSR) bound states [1-3], the topological superconductivity harboring exotic Majorana modes [4,5], and the heavy-fermion behavior [6,7]. Among the hybrid systems experimentally explored thus far, the magnetism is mostly derived from unpaired d- or f- electrons in transition metal atoms. Compared with d / f electrons, the s/p -electrons show distinctively different behaviors, such as more delocalized wavefunctions (therefore, larger spin correlation lengths) [8] and hyperfine spin-orbit couplings [9,10]. The creation of magnetic properties by -electrons has attracted significant interest, particularly inspired by the rise of graphene, which is expected to exhibit improved performance in spin-based information processing [10,11]. Various attempts have been made to achieve magnetism in graphene nanostructures by introducing sublattice imbalance [12-15] or topological frustration [16,17]. Also, charge transfer is another approach to introduce unpaired -electron in pure-organic molecules [18-20]; however, it has strict requirements on the work-function matching. Thus, only scarce examples were reported so far. By either of these two approaches, -electron magnetic moments associated with a superconductor has not yet been realized. Moreover, little possibility was known to readily tune the -electron magnetism, limiting the in-depth explorations to novel physics within variable regimes of the moment concentrations and the interaction strengths. Here, we report a hybrid bilayer system comprising a monolayer (ML) of the organic molecule (3,4,9,10-perylenetetracarboxylic-dianhydride, i.e., PTCDA) and a superconducting (SC) Pb thin film. Although none of these two materials contains magnetism, surprisingly, we experimentally found that net spin moments formed in the molecular film, resulting in Kondo resonances near the Fermi level. First-principle calculations support the formation of spin-polarized lowest unoccupied molecular orbital (LUMO) states induced by charge transfer from the Pb surface to the molecules. Distinguishing characteristics of the combination of -electron magnetic moment and superconductors were revealed in thorough STS investigations. More interestingly, we found moiré superlattices forming in this bilayer system, while the commensurate twist angles are tunable. A twist angle dependent moiré modulation for the Kondo-superconductivity interplay was reported. In addition, the quantum confinement effect in Pb film provides another tuning nob to the interfacial charge transferring. Combining these two appealing features, we demonstrated versatile and effective manipulations of the crucial physical parameters for an M/SC hybrid system, such as the magnetic moment concentration and the SC pairing strength, the on-site Coulomb scattering potential, and the exchange coupling strength. Figure 1(a) is a scanning tunneling microscopy (STM) image showing a crystalline PTCDA layer formed on a Pb(111) thin film (23 ML here), which is grown epitaxially on Si(111) (refer Methods in Supplementary Material [21]). The herringbone structure of a PTCDA layer has a rectangular unit cell with unit vectors 𝒂⃗⃗ = 1.29 ± 0.02 nm and 𝒂⃗⃗ = 1.81 ± 0.02 nm. The angle between 𝒂⃗⃗ and Pb<
11⃗ 0 > is defined as in the inset of Fig. 1(a). In Fig. 1(b), we show a typical tunneling spectrum (blue curve) taken on the ML PTCDA/Pb(111) film at a sample temperature T S above the T C of 23 ML Pb film. A resonance peak appears at the Fermi level. The superconducting gap can coexist with this resonance peak (grey curve) when T S < T C . Based on the temperature dependence of the resonance and the interplay of the resonance with superconductivity, we believe this resonance resulted from the Kondo effect [21]. Note that the monolayer PTCDA with the herringbone structure can form on many metallic surfaces, yet no study has reported the observation of Kondo resonances in the pristine molecule film [20,31]. To support this hypothesis, we grew a PTCDA monolayer on the Ag(111) surface and found that the Kondo resonance was absent [red curve in Fig. 1(b)]. In addition, the Kondo resonance was absent for a single molecule on the Pb film [green curve in Fig. 1(b)] but emerged only after in-plane molecular hybridization occurred. To understand the origin of the local magnetic moment, we performed DFT calculations for a single PTCDA molecule/Pb(111), ML PTCDA/Pb(111), and ML PTCDA/Ag(111) (details in [21]). In Fig. 1(d), we plot the charge transfer Q and the magnetic moment m for each molecule as a function of the interlayer separation d for all three systems. At the equilibrium distance, the calculations show a result consistent with the experimental observation that only monolayer PTCDA on Pb(111) possessed magnetic moments. In a conventional magnetic impurity, the unpaired spin resides in a d or f atomic orbital. Therefore, it results in a relatively large intra-orbital Coulomb repulsion energy U (4–7 eV) compared with the impurity-state bandwidth w (0.1–0.3 eV) [3]. Here, the LUMO states comprised relatively delocalized s and p electrons, leading to a smaller U . Figure 1(c) shows the partial density of states (DOS) at various substrate distances, d . As shown, the value of U in a PTCDA molecule was ~ comparable to the DFT impurity state ( i.e., singly occupied LUMO) bandwidth w and energy level ( imp ). This explains why the DFT magnetic moment does not scale linearly with the charge transfer [21]. As we discussed in Supplementary Material [21], the twist angle can be tuned by thermal annealing procedures. Nearly commensurate moiré superlattices with variable commensurate twist angle were observed. Figure 2(a–b) shows three typical moiré superstructures with °, = 10 a ; °, = 8 a ; and °, = 6 a . Here, represents the periodicity of the moiré lattice along the 𝒂⃗⃗ direction. The upper panel in Fig. 2(c) shows a color rendering of the d I /d V spectra for 20 molecules along the bright row- I in Fig. 2(a). An oscillation of the spectroscopic features associated with the moiré superlattice can be seen. Representative spectra are displayed in Fig. S4(a). Here, we use the spectra acquired at the C-H bond location to represent the inter-molecular difference. For the convenience of data analysis, a small magnetic field (0.5 T) was applied to quench superconductivity. These d I /d V spectra can be fitted with the widely adopted Fano line shape [24,25]. In the lower panel of Fig. 2(c), we show a plot of the half-width at half-maximum of the resonance ( for each molecule. The peak value occurs at the location with the lowest topographic height (index °, varies from a minimum of 6.3 meV to a maximum of 20.5 meV, corresponding to a variation of T K from 72 K to 238 K (Fig. S8). A similar spatial mapping of the Kondo resonance for ° is displayed in Fig. S4(b). The maximum of is found to be 14.9 meV ( T K = 173 K), and the oscillation amplitude is about 6 meV. Both are significantly smaller than that in the situation with °. When a single localized magnetic moment is coupled to a superconductor, its exchange interaction with the Cooper pairs results in in-gap states, referred to as YSR states [1-3]. Matsuura extended the original framework of YSR to include the Kondo screening, and the in-gap states are referred to as “bound states” [32,33]. With a finite >> , the quasiparticle excitations would be dominated by the order parameters and also contain remnants of bound states. Figure 3(a) shows d I /d V spectra for selective molecules [index I in Fig. 2(a)], focusing on the energy range from −4.0 mV to +4.0 mV. An SC Nb tip was used here. Figure 3(b) shows sample DOSs after the deconvolution of the SC state of the Nb tip (details of the deconvolution and additional data in [21]). In fitting the Nb-Pb tunneling spectrum, only a tiny Dynes broadening parameter of 0.0626 meV is needed, reflecting excellent RF noise shielding in our STM [34]. The deconvoluted DOSs appear to resemble that for an intrinsic SC gap; however, a spectral difference exists in the experimental ones: two extra dips occur outside two spectral peaks. The origin of the dips can be understood by using the sample DOS of molecule S and S , respectively. For molecule S / S ratio is about 2.5. As discussed in Supplementary Material [21], the depth of spectral dips measured using the SC tip is directly proportional to the S / S ratio. For a Bardeen-Cooper-Schrieffer (BCS)-like sample DOS, the missing spectral weight in the gap is transferred to the coherent peak, and thus, S / S = 1 at all times. Indeed, such a spectral dip is completely missing for Nb-Pb tunneling [black curve in Fig. 3(a)]. Thus, the observed dip structure provides a quantitative signature of the deviation of the sample DOS from the BCS DOS. The shoulder peaks in Fig 3(b) represent the remnant bound states whose energy locations are labeled as . A color-coded spectrum mapping of the superconductivity along the bright row- I is displayed in Fig. 3(c). is measured to range from 0.73 meV to 1.04 meV, which directly correlates with the modulation of [lower panel in Fig. 2(c)]. This is consistent with the notion that the larger the Kondo screening, the more the order parameter dominates the pairing interaction. Along the moiré dark row, the variations in both and are relatively small [21]. A large ensemble of datasets of vs. * (including more than 150 molecules over the surface) can be fitted well to the theoretical model of Matsuura [32]:
2* 0 2 , with ln( ) e , using the asymptotic value of the SC order parameter /230 PTCDA ML = 1.06 meV at = ∞ [Fig. 3(d)]. This asymptotic limit denotes the “pristine” SC gap of the hybrid bilayer system. This value is significantly smaller than the value measured on the bare 23 ML Pb film ( ML = 1.31 meV, Fig. S10). The reduction in the SC gap is confirmed by the proximity effect (Fig. S11), where the bare Pb surface experiences a gradual gap reduction as one laterally approaches a PTCDA island. We attribute this diminution of the SC order parameter to the finite magnetic impurity concentration, as proposed in the original model by Matsuura [33], which is beyond the YSR picture in the dilute limit. In most previous studies on bound states, the spectral weight between hole-like and electron-like quasiparticle excitations is highly asymmetric. However, in the present system comprising -electron magnetic moment, the particle/hole spectral weight is nearly symmetric, with a ratio of 0.93 in the most asymmetric case. Two controlling parameters influence the particle/hole quasiparticle spectral function [35]: the spin-exchange interaction ( J ) and Coulomb scattering potential ( K U ). The Coulomb potential breaks the particle-hole symmetry, and the exchange interaction contributes to pair breaking [36]. Adopting the theory of Salkola and Schrieffer, we can extract J and K U by analyzing * and the particle/hole spectral weight ratio [37,38] (details in [21]). The oscillations of N F | J | and 𝐾 𝑈 |𝐽| along the bright row- I are displayed in Fig. 2(d). We find that N F | J | = 10.92 and N F | K U | = 0.15 at spectrum N F is the DOS at E F in the normal phase). The largest value of 𝐾 𝑈 |𝐽| (~0.05) occurs at the location with the smallest gap. In other locations, the value of 𝐾 𝑈 |𝐽| is even smaller, explaining the nearly symmetric particle/hole spectral weight. The weak potential scattering is a characteristic feature of the magnetic moments residing in the relatively delocalized orbitals. The delocalized nature of spin-polarized orbital is further illustrated in Fig. S13, where the d I /d V spectra mapping with a fine step size shows that the bound states and Kondo resonance are continuous throughout the whole two-dimensional (2D) interface, existing even on the sites between molecules. This is fundamentally different from the case of the MnPc/Pb system, where the bound states occur only on the Mn atoms [39]. In addition, the bound states in our sample system have relatively broad bandwidths and merge with the continuum band. As predicted in Shiba’s early work [3], when the locally excited states can overlap with each other, an “impurity band” of the bound states can form and show a finite bandwidth. Our observation suggests the formation of 2D-band-like bound states. We emphasize that the picture we have presented above is consistent with established, non-perturbative theoretical results for local moments, where the on-site Coulomb interactions are small and the system is in the so-called “mixed-valence regime” [40]. The lateral coupling of the Kondo-screened bound states does not change the basic picture of the single-impurity Kondo effect until the moment concentration is of the same order of magnitude as the free carrier concentration [41]. Finally, we show that the quantum confinement effect (QCE) in ultra-thin Pb film, can dramatically affect the behavior of the Kondo/superconductivity interplay. Figure 4(a) shows large-energy-scale d I /d V spectra taken on 22ML and 23ML Pb films, for both the bare Pb and PTCDA/Pb hybrid system. The thickness-dependent quantum well states are clearly seen [42,43]. The values were respectively 17.4 meV and 38.1 meV for the highest and lowest molecules within a moiré periodicity on 22ML Pb [Fig. 4(b)], which represents an enhancement by a factor of 2 in the Kondo screening energy and moiré modulation amplitude, compared with the results on 23 ML. The corresponding values of * were 0.97 mV and 1.16 mV, respectively [Fig. 4(c)]. The variation of * as a function of on PTCDA/22ML-Pb yields an asymptotic /220 PTCDA ML of 1.23 mV [Fig. 3(d)], which is significantly larger than the value of 1.06 mV for PTCDA/23ML Pb. The QCE only leads to a 3% change in SC transition temperature T C between 22 ML and 23 ML bare Pb [21, 42]. After the Pb films were covered with a monolayer of PTCDA, the “pristine” pairing strength (fully Kondo-screened) show a difference of 15% (1.23 meV vs. E F ) dictates the average magnetic moment [43] and then determines the “impurity” concentration and the screening strength by the surrounding itinerant electrons, which in turn facilitates a much more effective tuning of the SC pairing strength. In conclusion, we have established an unusual magnetism/superconductivity hybrid bilayer with pure -electrons that are carrying the magnetic moments. Owing to the relatively delocalized nature of electrons, this hybrid system presents 2D-like behaviors for the interlayer stacking registry, the Kondo screening, and the bound state formation, which qualitatively distinguishes it from d -electron- and f -electron-based moment systems and thus opens new avenues for novel correlated physics. Moreover, the control over the twist angle offers a rare opportunity to explore the physics of the moiré modulated Kondo and superconductivity in a single system. In addition to combining moiré physics with the quantum confinement effect, we demonstrated an effective tuning approach for the magnetic moment concentration and the SC pairing strength. Rich emergent quantum phenomena are anticipated with the combination of all these intriguing elements, as well as possibilities for topological and exotic fractionalized states. We acknowledge funding from the National Science Foundation through the Center for Dynamics and Control of Materials: an NSF MRSEC under Cooperative Agreement No. DMR-1720595 and NSF Grant Nos. DMR-1808751, DMR-1949701; the Welch Foundation F-1672 and F-1841. We also acknowledge computing time from the Texas Advanced Computing Center. 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The twist angle is defined as labeled. (b) d I /d V spectra for the ML PTCDA/Pb at sample temperature T S = 0.4 K (gray) and 6.5 K (blue), the single molecule on Pb at 0.4 K (green), and the ML PTCDA on Ag(111) at 4.2 K (red). Spectra are shifted vertically for clarity. (c) Partial density of states at various molecule-substrate distances d. The dashed lines indicate the Fermi levels. (d) The charge transfer and the magnetic moment as a function of the d for all three situations. (a) Sample bias V s = 1.0 V, set-point current I = 25 pA. Setpoint in (b): V s = 95 mV, I = 200 pA, and the lock-in modulation V rms = 0.8 mV. FIG. 2 (a)–(b) Typical Moiré superlattice for º, º, and º. The green parallelogram in (a) represents the moiré supercell. is the periodicity along 𝒂⃗⃗ direction. The Pb<