Introduction

The normal state above the superconducting transition temperatures in copper- and iron-based high-temperature superconductors is thought to provide important information on the superconducting state itself, and very often exhibits unusual properties. These properties have been interpreted as ordering phenomena of spin or charge carriers before the formation of the superconducting state1,2,3,4,5. Recently, an orbital-selective Mott transition has been suggested to occur in the normal-state phase of iron-selenide superconductors6,7,8,9, where some of the five d orbitals independently undergo metal-to-insulator-like transitions.

The selenide iron-based superconductors offer the opportunity to explore superconductivity all the way from binary FeSe with Tc=8 K (ref. 10) and the alkaline-doped A1−xFe2−ySe2 (A=K, Rb and Cs) with Tc=32 K (refs 11, 12, 13) to epitaxial single-layer FeSe films with Tc=65 K (refs 14, 15). Critical temperatures up to 46 K are obtained by intercalation16,17,18 and 48 K by applying pressure19,20.

Superconductivity in A1−xFe2−ySe2 was shown to occur only in single crystals, where a mesoscopic separation into a superconducting phase with Tc≈32 K and an antiferromagnetic phase with a Néel temperature TN≈550 K has been established11,12,13,21,22,23,24 (see Fig. 1c). The superconducting phase is electron-doped with about 0.15 electrons per Fe atom23. Angle-resolved photoemission spectroscopy (ARPES) studies determined the Fermi-surface topology with large electron-like Fermi sheets δ at the M points and small electron pocket κ at the Γ point25 (see Fig. 1d). Isotropic superconducting gaps of 2Δ≃16 and 20 meV were reported around the κ and δ pockets, respectively25. In addition, a small gap 2Δ≃2 meV was observed by scanning tunnelling spectroscopy21. Recently, the normal state of the superconducting phase was reported to exhibit an orbital-selective metal-to-insulator transition7 observed by ARPES at about 100 K (ref. 6). Moreover, interphase correlations between superconducting and antiferromagnetic layers were predicted to reduce Tc from a hypothetical 65 K to the actually observed value of 32 K owing to proximity effects26 (see Fig. 1e).

Figure 1: Photon energy dependence of dielectric constant and optical conductivity.
figure 1

(a,b) Dielectric constant ε1 and optical conductivity σ1 of Rb0.74Fe1.60Se2 in the THz spectral region at various temperatures. The arrow in b indicates the formation of a gap at about 3 meV below Tgap≈61 K. (c) Schematic sketch of the THz transmission experiment on the sample consisting of superconducting (SC) and antiferromagnetic (AFM) layers24. (d) Sketch of Brillouin zone and Fermi surface25. (e) Illustration of interphase dxz/dyz electron hopping (tJ) between Fe atoms from SC and from AFM layers (adapted from Huang et al.26).

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In this article we report on terahertz (THz) spectroscopy studies on superconducting Rb1−xFe2−ySe2. The temperature dependence of the optical conductivity and dielectric constant exhibits an isosbestic point at Tmet=90 K indicating a metal-to-insulator-type, orbital-selective transition. At Tgap=61 K, a gap-like suppression of the optical conductivity is observed and is followed by the occurrence of the superconducting transition at Tc=32 K. This hierarchy of temperatures Tc<Tgap<Tmet seems to imply that the quasiparticles in the dxy band are more strongly correlated.

Results

Dielectric constant and optical conductivity

Figure 1a,b shows the dielectric constant ε1 and the optical conductivity σ1 as a function of incident photon energy, respectively, derived from the time domain THz transmission signal (see Methods) for selected temperatures across the three characteristic temperatures Tc=32 K, Tgap=61 K and Tmet=90 K. From room temperature down to Tmet=90 K, ε1 is positive and slightly increases towards lower temperatures, which is characteristic of a semiconducting optical response (Fig. 1a). Below 90 K, the dielectric constant becomes negative with a zero-crossing point from 2.5 meV at 80 K to 6.5 meV at 8 K. This is a fingerprint of a metallic system, and the observed zero-crossing points in ε1 correspond to the reported screened plasma frequencies22,27,28,29.

Similar observations, namely, the smooth transition from an insulating to a metallic state, are made in the frequency dependence of the optical conductivity σ1 for several temperatures (Fig. 1b). Above Tmet=90 K, σ1 is low and almost energy independent, indicating a semiconducting behaviour of quasi-localized charge carriers, while below this characteristic temperature a metallic response evolves with an increase of σ1 towards lower energies. In contrast to the monotonous decrease of ε1 with decreasing temperature, σ1 decreases for temperatures below Tgap=61 K and below energies of 5 meV. Towards lower temperatures, a gap-like feature (see arrow in Fig. 1b) evolves with a minimum in σ1 close to Egap~3 meV. Its temperature dependence is shown as an inset to Fig. 2b. The gap energy appears to increase continuously across Tc=32 K. Furthermore, the spectra of ε1 and σ1 do not exhibit drastic changes at Tc=32 K, well below Tgap=61 K.

Figure 2: Temperature dependence of dielectric constant and optical conductivity.
figure 2

(a,b) Dielectric constant ε1 and optical conductivity σ1 as a function of temperature at different photon energies. The characteristic temperatures and the isosbestic points are indicated by dashed lines. Inset to a, temperature dependence of ε1 at 2.49 meV around Tc. Inset to b, temperature dependence of the gap energy Egap (the solid line is drawn to guide the eyes). Error bars indicate uncertainties larger than the data point size.

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Isosbestic points

To analyse these striking temperature-induced changes of the optical response in more detail, Fig. 2a,b shows the dielectric constant and the conductivity as a function of temperature for several photon energies. At high temperatures, the dielectric constant is positive and almost temperature independent. At the same time the optical conductivity is low and increases gradually with decreasing temperature. This increase of σ1 becomes stronger when Tmet=90 K is approached from above, while the dielectric constant ε1 decreases and becomes negative below Tmet, signalling metallic behaviour. This metal-to-insulator-like transition is indicated by two sharp isosbestic points where all curves intersect and are therefore strictly frequency independent. At these points, the dielectric constant and optical conductivity take the values =14 and =22 Ω−1 cm−1, respectively.

The increase of the optical conductivity for decreasing temperature terminates at Tgap=61 K, and after which σ1 starts to decrease, thus leading to a pronounced maximum. This signals the opening of a gap (see Fig. 1b) far above the superconducting transition temperature, Tc=32 K. Indeed, the superconducting transition at Tc=32 K leads to a weak kink (see inset of Fig. 2a for ε1) and a subsequent levelling off of both quantities.

The existence of isosbestic points in the plots of ε1(T, ω) versus T and σ1(T, ω) versus T, respectively, allows one to determine their frequency dependences as ε1(T, ω)=ε1(T, ω0)+(1/ω−1/ω0) E1(T) and σ1(T, ω)=σ1(T, ω0)+(ω−ω0) S1(T) in the vicinity of these points30,31 (see Methods). Using the parameters E1(T) and S1(T) (Fig. 3c,d), which were obtained by fitting the spectra as shown in Fig. 3a,b, the validity of the approximations is demonstrated in Fig. 3e,f. All curves are shown to collapse onto the one for ω0=1.88 meV. We note that the observed frequency dependencies can be applied to both temperature regimes, above and below Tmet=90 K. Given the intrinsic phase separation of the compound, these frequency dependences are excellent low-frequency parametrizations of the actual optical response functions. Such well-defined frequency dependencies have not been observed in previous studies27,28,29 and are valid only in the vicinity of sharp isosbestic points30.

Figure 3: Scaling of the dielectric constant and the optical conductivity.
figure 3

(a,b) Fits of the dielectric constant using ε1(ω)~E1/ω and σ1(ω)~S1ω for selected temperatures, respectively. (c,d) Temperature dependences of the respective fit parameters E1 and S1. Error bars indicate uncertainties larger than the data point size. (e,f) Scaled dielectric constant =ε1−(1/ωi−1/ω0) E1 and optical conductivity =σ1−(ωi−ω0) S1 for different frequencies ωi. The curves collapse on the ones for ω0=1.88 meV (see Methods). For comparison, the temperature dependence of the dc conductivity σdc is shown in f (scale on the right).

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The change from insulating to metallic behaviour is reflected by the sign change of E1(T) and S1(T) from positive to negative at Tmet=90 K. While E1(T) saturates below Tc, S1(T) drops strongly with decreasing temperature until a minimum is reached at Tgap=61 K. The gap-like suppression of the optical conductivity below Tgap leads to a clear deviation from a linear frequency dependence (see larger error bars in Fig. 3d), implying that the frequency dependence of σ1 derived above does not hold below a temperature of about 40 K.

Discussion

The emergence of a metallic optical response below Tmet=90 K can be understood as a consequence of an orbital-selective Mott transition, which was proposed to explain the result of a recent ARPES study in AxFe2−ySe2 with A=K, Rb (ref. 6). Specifically, for a doping of 0.15 electrons per Fe, the investigation of a five-orbital Hubbard model discovered an orbital-selective Mott transition where the dxy band contributes to the metallic properties only below a temperature of about 100 K, while the dxz/dyz bands retain their metallic features both below and above 100 K (refs 6, 7). This scenario closely follows the general physical picture of strong orbital differentiation with a low coherence temperature32.

The collapsed optical conductivity curve in Fig. 3f exhibits the same temperature dependence as the ARPES spectral weight associated with the dxy band of the electron pocket at the M point6. Thus, we conclude that the optical conductivity probes predominantly the dxy band and signals a Mott transition of this band at the temperature of the isosbestic point Tmet=90 K.

The pronounced orbital differentiation8,9 of Rb1−xFe2−ySe2 manifests itself through highly orbital-dependent mass renormalizations of about 10 for the dxy band and about 3 for the dxz/dyz bands6. Owing to the significantly stronger correlation strength, the lifetime of quasiparticles in the dxy band is much more susceptible to temperature than in the other bands. This leads to a selective reduction of the dxy quasiparticle peak, which effectively eliminates its contribution to transport processes with increasing temperature. The lighter dxz/dyz quasiparticles will, however, dominate the transport properties. Indeed, no anomaly is visible in the dc resistivity σdc at Tmet≈90 K in Fig. 3f (ref. 13). The optical conductivity is expected to be governed by all quasiparticles, but instead it determines the temperature dependence of the strongly renormalized dxy charge carriers.

To explain the orbital differentiation of the optical conductivity, we have to consider the special morphology of the phase-separated system. Huang et al.26 investigated effects of interlayer hopping at the interface of the superconducting and the antiferromagnetic phases in the dxz/dyz channels (sketched in Fig. 1e) and found that the resulting distortions of the Fermi surfaces effectively reduce Tc. We assume that these incoherent hopping processes via the dxz/dyz bands lead to large scattering rates in the optical response of the corresponding quasiparticles of the dxz/dyz bands. By contrast, the dxy channel remains almost unaffected by the proximity effect and reveals its metallic optical response at low frequencies via its larger mass normalization.

Without the distortions of the Fermi surface induced by the vicinity of the antiferromagnetic phase a value of Tc as high as 65 K is estimated26. This scenario is supported by the formation of a gap already below Tgap=61 K in the dxy-dominated optical conductivity. The upper bound for the gap at 3.2 meV must be compared with the gap value of 2Δ≃2 meV found in a scanning tunnelling microscopy study on films of K1−xFe2−ySe2 (ref. 21). The fact that the conductivity is not completely suppressed below 3.2 meV points towards an anisotropic nature of this low-frequency gap.

Our observations provide strong support for the existence of an orbital-selective Mott transition, and also point to the possibility of orbital-selective superconducting properties33. The appearance of a gap in the dxy-dominated optical conductivity at Tgap=61 K in superconducting Rb1−xFe2−ySe2 may be compared with the reported opening of a gap below 65 K in single-layer FeSe films, which was interpreted as an indication for the onset of superconducting fluctuations at this temperature14. Given the similarity of the electronic band structures of FeSe monolayer films and Rb1−xFe2−ySe2 (ref. 14), we predict that the highest possible value of Tc in Fe selenide systems is determined by the correlated quasiparticles in the dxy channel.

Methods

Crystal growth

Pure Rb and polycrystalline FeSe (99.75%), preliminarily synthesized from the high-purity elements (99.985% Fe and 99.999% Se) were used as starting materials. Crystals of Rb0.74Fe1.60Se2 were grown using the Bridgman method from the starting composition corresponding to the Rb0.8Fe2Se2 stoichiometry. The samples have been soaked at 1,070 °C for 5 h. The cooling rate is 3 mm h−1 (ref. 13).

Crystals of the same sample batch were investigated by magnetization13, resistivity, nuclear magnetic resonance23, muon spin rotation and scanning near-field microscopy24.

Scaling analysis around the isosbestic points

In general, an isosbestic point is an intersection point of a family of n curves f(x, pi), i=1, 2, …, n in the plot of f(x) (refs 30, 31). Since isosbestic behaviour is observed only in a certain parameter range around a particular value p0, we can expand around p0 as f(x, pi)=f(x, p0)+(pi−p0) F1(x, p0)+O[(pi−p0)2], where F1(x)=∂f/∂p|p=p0 is a function of x only. The scaling of f(x, pi) is calculated as (x, pi)=f(x, pi)−(pi−p0) F1(x, p0)=f(x, p0)+O[(pi−p0)2]. The validity of the expansion approximation is verified by (x, pi) curves for different pi collapsing on a single curve. Here x≡T; f≡ε1 and σ1; and ; F1≡E1 and S1; pi≡1/ωi and ωi.

THz spectroscopy measurements

Time domain THz transmission measurements were carried out on a single crystal with the THz electric field parallel to the ab plane in the spectral range 1–10 meV using a TPS spectra 3000 spectrometer (TeraView Ltd.). Transmission and phase shift were obtained from the Fourier transformation of the time domain signal. The dielectric constant and optical conductivity were calculated from the transmission and phase shift by modelling the sample as a single-phase dielectric slab. The single crystal for optical measurements was prepared with a thickness of about 45 μm and a cross-section of about 5 mm2. A 4He-flow magneto-optical cryostat (Oxford Instruments) was used to reach the temperature range 8–300 K.

Additional information

How to cite this article: Wang, Z. et al. Orbital-selective metal–insulator transition and gap formation above TC in superconducting Rb1−xFe2−ySe2. Nat. Commun. 5:3202 doi: 10.1038/ncomms4202 (2014).