Unusual Temperature Evolution of Quasiparticle Band Dispersion in Electron-Doped FeSe Films

Abstract

The discovery of high-temperature (high-T_c) superconductivity in one-monolayer FeSe on SrTiO₃ has attracted tremendous attention. Subsequent studies suggested the importance of cooperation between intra-FeSe-layer and interfacial interactions to enhance T_c. However, the nature of intra-FeSe-layer interactions, which would play a primary role in determining the pairing symmetry, remains unclear. Here we have performed high-resolution angle-resolved photoemission spectroscopy of one-monolayer and alkaline-metal-deposited multilayer FeSe films on SrTiO₃, and determined the evolution of quasiparticle band dispersion across T_c. We found that the band dispersion in the superconducting state deviates from the Bogoliubov-quasiparticle dispersion expected from the normal-state band dispersion with a constant gap size. This suggests highly anisotropic pairing originating from small momentum transfer and/or mass renormalization due to electron–boson coupling. This band anomaly is interpreted in terms of the electronic interactions within the FeSe layers that may be related to the high-T_c superconductivity in electron-doped FeSe.

1. Introduction

Iron selenide (FeSe) is structurally the simplest iron-based superconductor with the superconducting-transition temperature (T_c) of ~9 K [1]. Intriguingly, one-monolayer (1 ML) film of FeSe grown on SrTiO₃ substrate exhibits exceptionally high T_c [2]. The T_c value reported by transport measurements reaches 40 K [2,3], which is about five times higher than the bulk counterpart. In addition, Cooper pairing at a higher temperature of 65 K, which exceeds the highest T_c (56 K) ever achieved in iron-based superconductors, has been suggested from a gap-closing temperature by angle-resolved photoemission spectroscopy (ARPES) [4,5,6,7] and Meissner effect by mutual conductance measurements [8]. These observations triggered fierce debates on the origin of the T_c enhancement in 1 ML-FeSe film. One key ingredient is a novel cross-interface electron–phonon coupling. The strong coupling between electrons in the FeSe layer and optical phonons of SrTiO₃ has been verified via the observation of replica bands by ARPES and theoretically proposed to enhance T_c in most of possible pairing symmetries [9,10]. Later, the close link between strong electron–phonon coupling and T_c enhancement has been supported experimentally, e.g., by isotope effects [11,12]. With these findings as a guiding principle, the search for high T_c in atomically thin films of other iron-based superconductors interfaced with SrTiO₃ [13,14,15] has been accelerated. Another key ingredient for T_c enhancement is a charge transfer from SrTiO₃. Heavy electron doping to the FeSe layer leads to unique electronic structure consisting only of electron-like Fermi surfaces [4,5,16], in contrast to the semimetallic nature of bulk FeSe [17,18]. The electron doping is essential for the high-T_c superconductivity, as established by the observation of high T_c above 40 K even in multilayer and bulk FeSe by doping electron carriers [19,20,21]. Therefore, there is accumulated evidence that the FeSe layer has the capability of inducing 40-K superconductivity through electron doping and the interfacial electron–phonon coupling will assist further T_c or pairing enhancement. However, little is known about why electron doping leads to the high T_c’s above 40 K. In particular, interactions within the FeSe layer, which would primarily determine the pairing symmetry, remain unclear.

In this study, we performed a comparative ARPES experiment on the surface of 1 ML- and Cs-deposited 20 ML-FeSe films on SrTiO₃, where the interfacial effects were present and absent, respectively. We demonstrated anomaly in the quasiparticle-band dispersions in the superconducting state, which is not expected from the Bogoliubov-quasiparticle (BQP) dispersion induced by a simple s-wave-gap opening. We discuss implications of our observation in relation to intra-FeSe-layer interactions.

2. Materials and Methods

The molecular beam epitaxy method was used to obtain 1 ML- and 20 ML-FeSe films; the films were grown on a TiO₂-terminated Nb(0.05 wt%)-SrTiO₃ substrate (SHINKOSHA) by simultaneously evaporating Fe and Se atoms while keeping a substrate temperature at 430 °C with a deposition rate of 0.01 ML/s [19]. Electron doping to 20 ML-FeSe was realized by evaporating Cs atoms onto the film surface at room temperature using a Cs dispenser (SAES Getters) [22]. After the growth, the film was transferred to the ARPES-measurement chamber without exposure to air. ARPES measurements were performed with a SES2002 spectrometer (Scienta Omicron) with the He-Iα resonance line (hν = 21.218 eV) at Tohoku University. The film was kept under an ultrahigh vacuum of 5 × 10⁻¹¹ Torr during the ARPES measurement, and no remarkable surface degradation was observed for a typical measurement time of 1 day. The energy and angular resolutions were set to be 7–12 meV and 0.2°, respectively. A gold film which made electrical contact with the film was referenced to calibrate the Fermi level (E_F).

3. Results

First, we present the electronic structure of Cs-deposited 20 ML-FeSe film measured at T = 50 K. As shown in Figure 1a,b, there was a circular-shaped large Fermi surface at the Brillouin-zone corner (M point) which originated from E_F crossing of an electron band with the bottom of the dispersion around 50 meV below E_F. The top of a hole-like band around the zone center (Γ point) was about 50 meV below E_F, resulting in the absence of a hole-like Fermi surface in contrast to the as-grown multilayer FeSe film [4,5] or bulk FeSe [17,18]. These observations confirmed a successful electron doping by Cs deposition onto the FeSe surface. The electron carrier concentration (n_e) calculated from the Fermi-surface volume was ~0.11 electrons/Fe, which corresponds to the optimal doping level with T_c value of ~40 K [22]. To investigate how the band structure changes by the superconducting transition, we performed high-resolution measurements across T_c (50 and 13 K) along a momentum (k) cut A indicated by a blue line in Figure 1a. The results displayed in Figure 1c,d show that while the electron band above T_c crossed E_F at the Fermi wave vector (k_F) of ~0.17 π/a, the band dispersion below T_c had a local maximum below E_F so as not to cross E_F due to a superconducting-gap opening. It is noted that the k location of the electron-band top below T_c coincided with the k_F point above T_c, consistent with the Cooper-pairing origin of the observed gap. The superconducting-gap opening is also clearly seen in energy distribution curves (EDCs) in Figure 1e, in which the peak position at k_F (k₃ defined in Figure 1c,d) was shifted from E_F to a high binding energy by ~10 meV with decreasing the temperature to form a superconducting gap. Since the nodeless s-wave superconductivity is realized in electron-doped multilayer FeSe [19,20], one can see the superconducting-gap opening below T_c irrespective of the k cut, e.g., along the k cut crossing the M point (cut B), as shown in Figure 1f–h, where essentially the same behavior with cut A was recognized.

An important finding manifests itself when we compare the band dispersions of the normal and superconducting states. Figure 2a displays a direct comparison of the experimental band dispersions extracted from the peak position of EDCs in cut A. As mentioned above, the band dispersion below T_c exhibited an opening of the superconducting gap and resultant bending-back behavior with the top of the dispersion at k_F. Such a characteristic band dispersion below T_c was qualitatively consistent with the dispersion relation of BQPs in the Bardeen–Cooper–Schrieffer (BCS) theory, where BQP dispersion (E_k) is expressed as $E_k=\sqrt{{\epsilon }_k{}^2+{\left|\mathsf{\Delta }\right|}^2}$ (ε_k and ∆ are the normal-state band dispersion and the superconducting-gap size, respectively) [24]. For a quantitative comparison, we determined ε_k by performing a polynomial fitting to the ARPES data above T_c (magenta curve) and simulated E_k by assuming a k-independent superconducting-gap size of 10 meV (light blue curve). Intriguingly, the band dispersion below T_c shows a clear deviation from the simulated BQP dispersion E_k; specifically, although the simulation predicted a finite downward energy shift of BQP dispersion compared with ε_k even in the k region far away from k_F (at least down to k_y = 0.05 π/a) because of a large ∆ value with respect to the shallow electron-band bottom, the experimental dispersion below T_c became nearly identical to ε_k as soon as it moved away from k_F. Almost temperature-insensitive band position away from k_F was also clearly visible in the comparison of raw EDCs in Figure 1e (see EDCs at k₁ and k₂). The same behavior was observed at different momentum, e.g., we found that the band dispersion measured below T_c along cut B deviated from the simulated BQP dispersion over a wide k region (see Figure 2b; also see a comparison of EDCs in Figure 1h).

To clarify whether the energy difference between the experimental and simulated BQP dispersions below T_c was an essential ingredient of electron-doped high-T_c FeSe films, we investigated the band-structure evolution in 1 ML-FeSe (Figure 3). For this purpose, we performed high-resolution measurements on slightly underdoped 1 ML-FeSe (n_e = 0.09) with T_c~40 K because a sharp spectral line shape compared with the heavily doped sample (T_c~65 K; n_e~0.12) [4] is suited for accurately determining the quasiparticle band dispersion. As is well known, 1 ML-FeSe has a large electron-like Fermi surface centered at the M point. The electron band which forms the Fermi surface showed an opening of the superconducting gap (∆~10 meV) below T_c, as highlighted by the characteristic bending-back behavior with the minimum-gap locus at k_F (see Figure 3b). A direct comparison of the band dispersions above and below T_c in Figure 3c demonstrates that an energy shift due to the superconducting-gap opening was limited to the k region around k_F~0.16 π/a (compare red and blue circles), in sharp contrast to a clear downward shift of the simulated BQP dispersion for k_y ≤ 0.1 π/a (light blue curve). Similarly, the case of Cs-deposited 20 ML-FeSe suggested that the deviation of the experimental band dispersion from the simulated BQP dispersion below T_c is a common feature of electron-doped FeSe films irrespective of film thickness.

4. Discussion and Conclusions

Now we are going to discuss the origin of the observed anomaly in quasiparticle dispersion. To simulate BQP dispersion $E_k=\sqrt{{\epsilon }_k{}^2+{\left|\mathsf{\Delta }\right|}^2}$, we assumed that ε_k is the same as the dispersion above T_c and ∆ is k-independent. It would be natural to consider that one or both of these assumptions are incorrect, rather than thinking that the BQP picture was broken in the electron-doped FeSe. For simplicity, we consider in the following the two extreme cases that the deviation was induced by a change in either ε_k or Δ. First, to examine the k dependence of Δ as the origin, we put the experimental band dispersions below and above T_c into E_k and ε_k, respectively, and estimated ∆(k) which reproduces the experimental band dispersion below T_c. The obtained ∆(k) was strongly k-dependent as seen from Figure 4a,b for 1 ML- and Cs-deposited 20 ML-FeSe, respectively; namely, ∆(k) was finite only in the narrow k region centered at k_F (within ±0.02 π/a of k_F), so that band dispersion only around E_F was shifted toward high binding energies by the superconducting transition, consistent with our observations. An unusual Cooper pairing in the limited k space near k_F may be caused by pairing interactions which have small momentum transfer q [25,26,27]. For instance, it has been proposed by Migdal–Eliashberg theory for 1 ML-FeSe that forward scattering with small q phonons produces highly anisotropic superconducting gap peaked at k_F and also leads to temperature-independent band structure away from k_F [25], in qualitative agreement with ∆(k) in Figure 4a as well as band dispersion in Figure 3. Although this theory assumes a cross-interface coupling between small q phonons of SrTiO₃ and electrons in 1 ML-FeSe as the key pairing interactions, our observation of anisotropic ∆(k) in 20 ML-FeSe (Figure 4b) where interfacial effects are negligible suggests that small-q interactions within the FeSe layers may be also responsible for superconductivity if the k-dependent pairing was indeed a source of the deviation from the simulated BQP dispersion.

Next, we consider another possibility that ε_k is temperature-dependent whereas k dependence of ∆(k) is small. To explain the observed deviation between the experimental and simulated BQP dispersions, ε_k below T_c must be shifted toward E_F compared with the normal-state band dispersion above T_c while keeping the same k_F position. Such an energy shift would be a consequence of mass renormalization linked to the superconducting transition, likely due to coupling with bosonic modes as reported for bulk crystals of high-T_c superconductors [28,29,30,31,32,33]. Here we defined the energy difference between the experimental and simulated BQP dispersions as ∆E (see black arrow in Figure 3c) and plotted it in Figure 4c,d for 1 ML- and 20 ML-FeSe films, respectively. As seen from Figure 4c,d, ∆E showed a broad peak around 20 meV in 1 ML- and 20 ML-FeSe. The obtained ∆E value can be used as a measure of the mass enhancement similarly to the real part of self-energies. By analogy with the fact that the peak position in the real part of self-energies below T_c corresponded to ∆ + Ω, where Ω is the energy of bosonic modes coupled to electrons, the observed peak structure at ~20 meV suggests a coupling to low-energy modes with Ω~10 meV (here, ∆~10 meV). The origin of the corresponding modes is an important open question; candidates include phonons [34] and magnetic resonance [35]. Nevertheless, one important outcome from our observation is that low-energy modes intrinsic to the FeSe layer must be involved because the mass renormalization was found not only in 1 ML-FeSe, but also in 20 ML-FeSe.

In summary, we reported the evolution of low-energy band dispersion across T_c in 1 ML- and Cs-deposited 20 ML-FeSe films on SrTiO₃. We found deviation of the band dispersion below T_c from the simple BQP dispersion simulated with the temperature-independent ε_k and k-independent ∆. We proposed two possible scenarios as the origin of this observation; (i) anisotropic ∆(k) peaked around k_F due to the superconducting pairing by small q transfer and (ii) enhancement in the effective mass in the superconducting state due to the coupling to low-energy bosonic modes. In either scenario, the observed similarity between 1 ML- and 20 ML-FeSe suggested intra-FeSe-layer nature of the interactions. Our result lays a foundation for understanding the mechanism of high-T_c superconductivity in electron-doped FeSe.