Suppression of electronic correlations by chemical pressure from FeSe to FeS

TL;DR

This study uses high-resolution spectroscopy to show that sulfur substitution in FeSe reduces electronic correlations and alters the Fermi surface, providing insights into tuning superconductivity in iron-based chalcogenides.

Contribution

It demonstrates how chemical pressure via sulfur substitution suppresses electronic correlations and modifies the Fermi surface in FeSe, offering a new way to tune superconducting properties.

Findings

Fermi velocities increase with sulfur substitution.

Band renormalizations are suppressed towards 1.5-2 in FeS.

Fermi surface size increases but remains smaller than theoretical predictions.

Abstract

Iron-based chalcogenides are complex superconducting systems in which orbitally-dependent electronic correlations play an important role. Here, using high-resolution angle-resolved photoemission spectroscopy, we investigate the effect of these electronic correlations outside the nematic phase in the tetragonal phase of superconducting FeSe1-xSx (x = 0; 0:18; 1). With increasing sulfur substitution, the Fermi velocities increase significantly and the band renormalizations are suppressed towards a factor of 1.5-2 for FeS. Furthermore, the chemical pressure leads to an increase in the size of the quasi-two dimensional Fermi surface, compared with that of FeSe, however, it remains smaller than the predicted one from first principle calculations for FeS. Our results show that the isoelectronic substitution is an effective way to tune electronic correlations in FeSe1-xSx, being weakened for FeS with a lower superconducting transition temperature. This suggests indirectly that electronic correlations could help to promote higher-Tc superconductivity in FeSe.

Full text

Iron-based superconductors offer an interesting playground to explore the competition of low-energy electronic ground states, such as superconductivity, spin-density wave and nematic states. These low energy electronic states are strongly influenced by the presence of the different 3$d$ orbitals of Fe, the Hund’s coupling, Coulomb interactions and band filling Yin et al. (2011); de’ Medici et al. (2014). The orbitally-selective nature of these interactions often leads to different bandwidth renormalizations and an unusual relative energy shift of various bands with respect to each other and the Fermi level due to the pronounced particle-hole asymmetry of the electronic structure Fanfarillo et al. (2016). Iron-chalcogenides are among the most correlated iron-based superconductors, displaying the largest spread of orbitally-dependent bandwidth renormalization. The most pronounced renormalization is observed for the band with $d_{xy}$ orbital character, reaching a factor of 17 and being sensitive to the isoelectronic substitution, as for FeSe1-xTex Yi et al. (2015); Tamai et al. (2010).

FeSe is a unique system in which the role of correlations on nematicity and superconductivity can be explored, in the absence of a competing long-range spin-density wave order. Superconductivity in FeSe around $T_{c}\approx 9$ K emerges out of a nematic electronic state, showing strong anisotropy in the electronic and superconducting properties Watson et al. (2015a); Tanatar et al. (2016); Sprau et al. (2016). The origin of this nematic phase below $T_{s}\approx 90$ K, which coincides with a tetragonal-orthorhombic structural phase transition McQueen et al. (2009), is the orbital order that breaks the four-fold rotational symmetry and thus leads to the lifting of the $d_{xz}/d_{yz}$ orbital degeneracy Shimojima et al. (2014); Watson et al. (2015a). Previous studies in the tetragonal phase found orbitally-dependent band renormalizations for FeSe reaching values from 3-4 for the degenerate $d_{xz}/d_{yz}$ bands, to 7-9 for the $d_{xy}$ band Maletz et al. (2014); Watson et al. (2015a). Furthermore, the strength of electronic correlations manifests by the existence of a lower Hubbard band at large binding energies, recently detected in FeSe Watson et al. (2017a); Evtushinsky et al. (2016).

Superconductivity in bulk FeSe can be strongly enhanced using various tuning parameters, such as applied physical pressures Medvedev et al. (2009); Terashima et al. (2015), chemical intercalations Burrard-Lucas et al. (2013) and in-situ potassium dosing Wen et al. (2016). The enhancement in superconductivity by doping of the surface Wen et al. (2016) was found to be directly linked to the increase of electronic correlations. However, sulfur substitution in FeSe1-xSx completely suppresses the nematic state for $x\geq 0.18$(1) Watson et al. (2015a, b); Coldea et al. (2017), without promoting a high-$T_{c}$ superconducting phase or stabilizing a magnetic order, in contrast to applied pressure Medvedev et al. (2009); Terashima et al. (2015). The end member of this series, the tetragonal FeS, with a lower $T_{c}\approx 4$ K, is suggested to be less correlated Man et al. (2017); Terashima et al. (2016), emphasizing the important role of chemical pressure in tuning electronic ground states and the strength of electronic correlations.

In this paper, we study the suppression of electronic correlations and the changes in band structure as a function of isoelectronic substitution in the tetragonal phase of FeSe1-xSx using high-resolution angle-resolved photoemission spectroscopy (ARPES). The low temperature Fermi surface of the tetragonal phase with $x=0.18$ resembles that of FeSe at high temperatures ($T>T_{s}$), and it expands towards FeS, but it does not reach the size predicted by first principle calculations. The Fermi velocities increase and the band renormalizations decrease significantly with increasing $x$. At the same time, superconductivity is weakened as the electronic correlations of the $d_{xz}/d_{yz}$ bands are reduced from a factor of 3–4 for FeSe ($T_{c}\approx 9$ K) to 1.5–2 for FeS ($T_{c}\approx 4$ K).

Experimental details FeSe1-xSx single crystals with $x$=0 and $x$=0.18 were grown by the KCl/AlCl3 chemical vapour transport method Chareev et al. (2013); Böhmer et al. (2016). FeS and other single crystals with $0.5\leq x\leq 1$ were grown by the hydrothermal method, using K0.8Fe1.6(Se1-xSx)2 precursors Lai et al. (2015). ARPES measurements were performed at the I05 beamline at the Diamond Light Source Hoesch et al. (2017), using horizontally and vertically linearly-polarised synchrotron light (LH and LV) between 20 and 120 eV, with $\approx$6 to 19  meV resolution. Band structure calculations for FeS were performed with Wien2K using GGA, spin-orbit coupling and experimental lattice parameters, ($a$ = 3.6802(5) Å, $c$ = 5.0307(7) Å  and $z_{S}$ = 0.2523 Lai et al. (2015)).

Hole bands of tetragonal FeSe1-xSx. Fig. 1(a)-(c) compares the hole band dispersions at the top of the Brillouin zone, centered at the $Z$ point, in the tetragonal phase of FeSe at $120\,$K ($T>T_{s}$) with those of $x$=0.18 and FeS at $10\,$ K. The photon energies corresponding to high-symmetry points along $k_{z}$ were established by analysis of the $d_{z^{2}}$ intensity well below $E_{F}$, shown in Fig.SM1 in the Supplemental Material (SM). Despite the significant amount of sulfur substitution in $x$=0.18, the linewidths of the band dispersions in the ARPES spectra remain narrow due to the high quality of these crystals, that also allows quantum oscillations to be observed Coldea et al. (2017). This is in contrast to the much broader ARPES spectrum of FeS, shown in Fig. 1(c), likely caused by the larger degree of disorder in crystals grown by the hydrothermal method with residual resistivity ratios varying between 5 to 17 (Fig. 3(e)).

Band dispersions and the Fermi surface maps in Fig. 1 show that the high-$T$ band structure of FeSe and the low-$T$ band structure of $x$=0.18 are very similar, confirming the absence of the nematic state for $x$=0.18 at 10 K. The shape of the Fermi surface is isotropic in the $k_{x}-k_{y}$ plane for all three compositions (Fig. 1 (d)-(f)), in contrast to the elliptical Fermi surface found in the nematic phase of FeSe Watson et al. (2016) and for $x\leq 0.15$ Watson et al. (2015b). Two hole-like dispersions cross the Fermi level close to the $Z$ point, separated only by the spin-orbit coupling estimated $\sim 20$ meV in FeSe Watson et al. (2015a, 2017b).

For a quantitative analysis of the band structure, band positions were extracted by performing simultaneous constrained Lorentzian fits to the momentum distribution curves (MDC) for different light polarizations at a fixed energy, shown in Fig. 1(i) and (k). For FeS, best fits were obtained also using two hole-like bands at the Fermi level, as expected from the band structure calculations (Fig. 1(g)), even though the two bands are harder to separate (see also Fig.SM3 in SM). We find a measurable increase of the $k_{F}$ values and the Fermi surface areas with increasing S substitution (Fig. 1(i)), in agreement with the trends found in quantum oscillations up to $x\approx 0.19$ Coldea et al. (2017).

One unusual feature of the electronic structure of FeSe is the existence of a small 3D hole pocket centered only around the $Z$ point at 100 K (Fig. 1(a) and (d)). This innermost hole band is pushed below the Fermi level at low temperatures, due to the combined effects of orbital order and spin-orbit coupling Watson et al. (2015b); Fernandes and Vafek (2014). As orbital ordering is reduced with S substitution, this small 3D pocket reappears at $Z$ for $x\sim 0.11$ at low temperatures Watson et al. (2015b), consistent with our observations for $x=0.18$ (Fig. 1(b) and (e) and Fig.SM3). However, in FeS, due to the significant increase in bandwidths, we find that this pocket has become two-dimensional, as evidenced by two bands crossing the Fermi level both at the $\Gamma$ and $Z$ point (Fig.SM3).

Next, we compare the change in the electronic correlations as a function of S substitution. The strongest renormalizations are expected for bands with $d_{xy}$ character, but in ARPES, they are notoriously difficult to observe due to matrix element effects. However, their dispersions can be revealed due to band hybridization caused by the spin-orbit coupling effects Watson et al. (2015a, 2016); Fanfarillo et al. (2016); Fedorov et al. (2016). This allows us to identify the $d_{xy}$ hole band in FeSe and FeSe0.82S0.18, and we find it significantly pushed below the Fermi level ($\sim 50$ meV), in contrast to band structure calculations where it crosses the Fermi level (see Fig. SM2). In FeS, the $d_{xy}$ band is not resolved due to disorder effects, as found in other iron-based superconductors Ye et al. (2014), rather than due to the increase in correlations when it can become incoherent, as observed in FeSexTe1-x Liu et al. (2015).

In FeSe, the $d_{xy}$ band renormalization is rather large (a factor 7-9), in contrast to the $d_{xz}$/$d_{yz}$ band renormalization (a factor 3-4) Watson et al. (2015a); Maletz et al. (2014) and we find that they do not change significantly when comparing to $x$=0.18, shown in Fig. 1(i). However, for FeS we extract a significantly reduced band renormalization of 1.7(1) for the $d_{xz}$/$d_{yz}$ bands, reflecting moderate electronic correlations for FeS with a low $T_{c}\sim 4$ K. An additional band present in FeS is the $d_{z^{2}}$ band, which lies closer to the Fermi level ($\approx 150\,$meV) as compared with DFT (350 meV), also suggestive of finite correlations effects in FeS (renormalized by a factor $\approx 2$ from the $k_{z}$ dependence in Fig.SM1 in SM). Furthermore, the Fermi velocities $v_{F}$ extracted from the band dispersion slopes (Fig. 1(i) and Fig. 3(d)) significantly increase from FeSe towards FeS, whereas the quasiparticle effective masses, $m^{\star}$, of the outer hole-like bands decrease from 3-4 $m_{e}$ for $x=0.18$ to 1-2 $m_{e}$ for FeS. These findings agree with the reduction of the effective masses detected in quantum oscillations studies in FeSe1-xSx (outside the nematic phase) Coldea et al. (2017) and in FeS Terashima et al. (2016).

Electron bands of tetragonal FeSe1-xSx. Fig. 2(a)-(c) compares the evolution of the band structure at the A point in the tetragonal phase of FeSe at 100 K, and of $x$=0.18 and FeS at 10 K. As for the hole-like bands at the Z point, the ARPES spectra of FeSe and FeSe0.82S0.18 are very similar, confirming that for $x\sim 0.18$, the Fermi surface deformation observed in the nematic state of FeSe is completely suppressed Watson et al. (2015a, b). The spectra of all samples display two electron-like bands crossing the Fermi level, but they are much harder to separate for FeS (Fig.SM3). For FeS we use a single band fit to the MDCs in Fig.2(k), whereas the outer electron band size with $d_{xy}$ character is affected by matrix elements and disorder effects. Fermi surface maps in Fig. 2(d-f) display a four-fold symmetric shape, with small differences between the inner electron-like Fermi surface pocket between $x$=0.18 and FeSe at 100 K, whereas a significant expansion is detected for FeS (Fig. 2(f)).

At the corners of the tetragonal Brillouin zone, there are two degenerate states, $A_{1}$ and $A_{2}$ (Fig.2(g)), which are the bottom of the inner and outer electron bands and are not split by the spin-orbit interaction Fernandes and Vafek (2014). The increased separation between these states upon cooling through the nematic transition has caused a significant debate about the origin of the nematic phase Fernandes and Vafek (2014); Watson et al. (2016, 2017b); Evtushinsky et al. (2016). Here we find the bottom of the inner electron band is $\approx 19$ meV below the Fermi level for $x$=0 and $x$=0.18, with slight variation for the outer electron band ($\approx 42$ meV for $x$=0 and $\approx 34$ meV for $x$=0.18). Notably in FeS, these two degenerate states are significantly lower in energy compared with the other two compositions ($\approx 70$ meV and $\approx 120$ meV, respectively), a direct consequences of the increased bandwidths (identified from the energy distribution curves (EDC) shown in Fig. 2(h)). This extended bandwidth, in conjunction with the equally significant increase of the Fermi velocity (Fig. 2(i) and Fig. 3(d)) and a decrease of the quasiparticle effective masses, highlight the significant reduction in the electronic correlations in FeS.

The phase diagram of FeSe1-xSx together with the evolution of the Fermi surface in the tetragonal phase from FeSe to FeS is shown in Fig.3(c) and Fig.3(a), respectively. While the size of the quasi-two dimensional Fermi surface increases with chemical pressure, the most important change is the increase in Fermi velocities (and bandwidths) (Fig.3d), which reflects the reduction of the electronic correlations. These findings agree with the reduction of the effective masses determined from quantum oscillations in FeSe1-xSex outside the nematic phase Coldea et al. (2017); Reiss et al. (2017) and FeS Terashima et al. (2016); Man et al. (2017). Furthermore, the low temperature resistivity shows a $T^{2}$ Fermi-liquid-like behavior for FeS, in contrast to the other compositions closer to the nematic phase, as shown in Fig.3(e) and also reported in Ref.Urata et al. (2017). The low-$T_{c}$ superconductivity in FeSe1-xSx has a small dome inside the nematic region, being gently suppressed towards FeS (Fig.3(c)). This behavior is in contrast to FeSe under applied pressure Sun et al. (2016) or in-situ K dosing Wen et al. (2016), where superconductivity is enhanced once the nematic phase is suppressed, with an additional magnetic phase being stabilized under pressure Sun et al. (2016); Terashima et al. (2015); Medvedev et al. (2009).

Our results on the electronic structure of FeS are in good agreement with a recent ARPES study Miao et al. (2017). Quantum oscillations in FeS reported only small frequencies below 200 T Terashima et al. (2016), a factor 2.5 smaller than the smallest area of the inner hole band predicted by band structure calculations Coldea et al. (2017). Our ARPES data do not reveal the presence of such a small band (with a $k_{F}\sim 0.0780$Å*-1*), but the $d_{xy}$ is not visible due to the matrix effects or impurity line broadening. This $d_{xy}$ band is predicted to lie very close to the Fermi level in FeS (Fig. 1f). Furthermore, due to the complex de-intercalation procedure to prepare FeS, other byproducts could form Kirschner et al. (2016). Recently, a quantum oscillations study suggested that FeS has a 3D Fermi surface Man et al. (2017), not supported by the current ARPES studies.

As FeS remains in the tetragonal phase and the electronic correlations are reduced, one would expect a better agreement between the experimental and calculated Fermi surface of FeS (see Fig.3b). However, we find that the Fermi surface areas and the quasiparticle masses of FeS are still a factor $\sim 2$ smaller than predicted by DFT calculations (Fig.3b and Fig.SM2). This band shrinking thus also manifests in FeS, but is weaker than in FeSe Watson et al. (2015a). Furthermore, FeS is reminiscent of other iron-based superconductors with a low $T_{c}$, LaFePO and LiFeP, where the renormalization effects extracted from quantum oscillations were rather moderate ($\approx 2$) Coldea et al. (2008); Putzke et al. (2012). Interestingly, all these end member compounds, LaFePO and LiFeP and FeS, display nodal superconductivity Fletcher et al. (2009); Hashimoto et al. (2012); Xing et al. (2016); Yang et al. (2016) and the pnictogen and chalcogen position is closer to the iron planes compared to their isoelectronic sister-compounds. These trends have been captured theoretically by Kuroki et al. Kuroki et al. (2009), where the height of the pictogen acts as a switch between high-$T_{c}$ nodeless and low-$T_{c}$ nodal pairings and that superconductivity is suppressed once the lattice constants are reduced, as in the case of FeS. Substituting smaller S ions onto the Se site shrinks the unit cell Lai et al. (2015); Mizuguchi et al. (2009), decreases the Fe chalcogen bond lengths and brings the chalcogen closer to the iron planes. This would result in a greater orbital overlap causing an increase in the bandwidth and the degree of electronic correlations will reduced significantly, like in FeS.

Summary. Our high-resolution ARPES study on FeSe1-xSx single crystals reveal the suppression of the electronic correlations, demonstrated by the increase in Fermi velocities and bandwidth, while the superconductivity is weakened away from the nematic phase. The chemical pressure effects in FeSe1-xSx lead to the increase in the size of the quasi-two dimensional Fermi surface, however, its size still remains smaller than predicted from first principle band structure calculations. Our results suggest that electronic correlations may be important for enhancing superconductivity in iron-based superconductors and chemical pressure offers an ideal tuning parameter to control them.

Acknowledgements We thank Moritz Hoesch for technical support. This work was mainly supported by EPSRC (EP/L001772/1, EP/I004475/1, EP/I017836/1). A.A.H. acknowledges the financial support of the Oxford Quantum Materials Platform Grant (EP/M020517/1). We thank Diamond Light Source for access to Beamline I05 (proposal number SI15471) that contributed to the results presented here. The authors would like to acknowledge the use of the University of Oxford Advanced Research Computing (ARC) facility in carrying out part of this work. A.I.C. acknowledges an EPSRC Career Acceleration Fellowship (EP/I004475/1).