Optical properties of the iron-chalcogenide superconductor FeTe0.55Se0.45
The complex optical properties of the iron-chalcogenide superconductor FeTeSe with K have been examined over a wide frequency range for light polarized in the Fe-Te(Se) planes above and below . At room temperature the optical response may be described by a weakly-interacting Fermi liquid; however, just above this picture breaks down and the scattering rate takes on a linear frequency dependence. Below there is evidence for two gap features in the optical conductivity at meV and meV. Less than 20% of the free carriers collapse into the condensate for , and this material is observed to fall on the universal scaling line for a BCS dirty-limit superconductor in the weak-coupling limit.
keywords:Superconductivity, Infrared spectroscopy, Optical properties, Iron chalcogenides, Order parameter
Pacs:74.25.Gz, 74.70.Xa, 78.30.-j
There have been many surprises in the field of superconductivity in the last 25 years. First and foremost was the discovery of superconductivity at elevated temperatures in the copper-oxide materials (1). For conventional metals and alloys, in the model developed by Bardeen, Cooper and Schrieffer (BCS) superconductivity is mediated through lattice vibrations where electrons form bound pairs (2); the condensation below the critical temperature () is also accompanied by the formation of an isotropic s-wave energy gap at the Fermi surface. Within this framework, it was thought that the critical temperature could not exceed approximately 30 K (3). With ’s in excess of 130 K at ambient pressure and an unusual d-wave energy gap with nodes at the Fermi surface, the pairing mechanism in the cuprates remains unresolved. The discovery of superconductivity in MgB with the surprisingly high transition temperature of K (4) initially suggested an unusual pairing mechanism; however, the isotope effect established that the superconductivity in this material is likely phonon mediated (5). In this particular case, the high phonon frequencies in MgB are likely responsible for the unusually large value for (6).
The discovery of superconductivity in the iron-arsenic LaFeAsOF (1111) pnictide compound (7) was surprising because iron had long been considered detrimental to superconductivity. Different rare earth substitutions in this material quickly raised K (8); (9); (10). While such high values for do not definitively rule out a phonon-mediated pairing mechanism, the presence of magnetic order close to the superconductivity in these compounds (11) has led to the suggestion that the pairing in this class of materials may have another origin (12); (13). The highest ’s have been observed in the 1111-family of materials; however, large single crystals have only recently been obtained (14); the extended unit cell of non-superconducting LaFeAsO is shown in Fig. 1(a). As a consequence, much of the focus has shifted to the structurally-simpler FeAs (122) iron-pnictides, shown in Fig. 1(b), and the FeTe(Se) (11) iron-chalcogenide materials, shown in Fig. 1(c), where large single crystals are available. The metallic FeAs materials (where Ca, Ba or Sr) have been extensively studied; in BaFeAs the application of pressure results in K, while Co- and Ni-doping yields K at ambient pressure (15); (16); (17). Superconductivity has been observed in the arsenic-free iron-chalcogenide FeSe compound with K, which increases to K under pressure (18); (19); (20); (21). Through the substitution of Se for Te the critical temperature at ambient pressure reaches a maximum K in FeTeSe. Despite the structural differences of the iron-pnictides and the iron-chalcogenides illustrated in Fig. 1, the band structure of these materials is remarkably similar, with a minimal description consisting of an electron band at the point and a hole band centered at the point of the Brillouin zone (22).
There have been a number of studies of the FeTe and FeTeSe materials, including transport (23); (24); (25); (26), tunneling (27), and angle-resolved photoemission (ARPES) (28); (29), with particular attention on the magnetic properties (29); (30); (31); (32); (33); (34); (35); (36). While the optical properties of the superconducting iron-pnictides have been investigated in considerable detail (37); (38); (39); (40); (41); (42); (43); (44); (45), the iron-chalcogenide materials are relatively unexplored (26).
In this work we examine the in-plane complex optical properties of a single crystal of superconducting FeTeSe above and below . At room temperature this material may be described as a weakly-interacting Fermi liquid and the transport is Drude-like. However, just above this interpretation breaks down and the scattering rate adopts a linear frequency dependence. Below there are clear signatures of the superconductivity in the reflectance and the optical conductivity. Less than 20% of the free carriers collapse into the superconducting condensate, suggesting that this material is in the dirty limit, and this material is observed to fall on the scaling line predicted for a BCS dirty-limit superconductor in the weak-coupling limit. In addition, there is evidence for two gap features in at meV and meV. Some of these results have been discussed in a previous work (46).
2 Results and Discussion
Single crystals with good cleavage planes (001) were grown by a unidirectional
solidification method with a nominal composition of FeTeSe.
The normal-state resistivity is in good agreement with literature values (24).
The critical temperature determined from magnetic susceptibility is K
with a transition width of K. The temperature dependence of the reflectance
has been measured at a near-normal angle of incidence on a freshly-cleaved surface above
and below over a wide frequency
The temperature dependence of the real part of the infrared optical conductivity is shown in Fig. 3. At room temperature the conductivity is flat and relatively featureless except for an infrared-active mode at 204 cm which involves the in-plane displacements of the Fe-Te(Se) atoms (51). As the temperature is lowered there is a shift in the spectral weight from high to low frequency, where the spectral weight is defined here as the area under the conductivity curve over a given interval
This is the expected response for a metallic system where the scattering rate decreases with temperature. The optical conductivity over most of the temperature range is described quite well by a simple Drude-Lorentz model for the dielectric function ,
where is the real part of the dielectric function at high frequency, and are the square of the plasma frequency and scattering rate for the delocalized (Drude) carriers, respectively; , and are the position, width, and strength of the th vibration or excitation. The complex conductivity is .
The optical conductivity may be reproduced using this model at 295, 200 and 100 K, with fitted values of cm and and 317 cm, respectively (%). To fit the midinfrared component, Lorentzian oscillators at the somewhat arbitrary positions of 650 and 3200 cm have been introduced; the results of the fit to the data at 100 K are shown in the inset in Fig. 3. An alternative method that has been used in some of the pnictide materials considers two Drude components (44); (52). If we apply this approach to the data at 100 K, we note that the “narrow” Drude component is similar to that obtained from the Drude-Lorentz fits, while the “broad” Drude component has a width and strength similar to that of the oscillator at cm. While the scattering rates are expected to change with temperature, the plasma frequencies should remain relatively constant. However, just above at 18 K the plasma frequency of the narrow Drude component has unexpectedly decreased by more than a factor of two. In addition, at 18 K neither the Drude-Lorentz or the two-Drude model accurately the shape of the low-frequency conductivity. To address this problem, we consider the extended-Drude model in which both the scattering rate and the effective mass take on a frequency dependence, an approach that has been previously applied to several pnictide materials (38); (39). The experimentally-determined scattering rate and effective mass are (53); (54)
In this instance we set and (although the choice of has little effect on the scattering rate or the effective mass in the far-infrared region). The temperature dependence of is shown in Fig. 4, and the inset shows the temperature dependence of . At 295, 200 and 100 K the scattering rate displays little frequency dependence, and moreover . This self-consistent behavior indicates that within this temperature range, the transport may be described as a weakly-interacting Fermi liquid (Drude model). However, just above at 18 K the scattering rate develops a linear frequency dependence cm, suggesting the presence of electronic correlations. This may be due in part to magnetic correlations (31) that arise from the suppression of the magnetic transition in FeTe at K in response to Se substitution (24). We note that similar behavior of the scattering rate is observed in many optimally-doped cuprate superconductors where the electronic correlations may have a similar origin (55). Dramatic changes are also observed in below where the scattering rate is suppressed at low frequencies, but increases rapidly and overshoots the normal-state (18 K) value at about 60 cm, finally merging with the normal-state curve at about 200 cm; this behavior is in rough agreement with a recently proposed differential sum rule for the scattering-rate (56); (57); (58). We note that the overshoot in below is in general more characteristic of a material with an s-wave gap rather than a higher-order d-wave gap (59). In the normal state just above , the low-frequency limit for the effective mass is , which is comparable with ARPES estimates of (60). This mass enhancement is too large to be caused by electron-phonon interactions or coupling to spin-fluctuations alone (61), suggesting that electronic correlations play a dominant role in the low-energy excitations in this material (62); (63).
This result is quite different than the behavior of the effective mass in the sulfide analog FeTeS where over much of the far-infrared region, from which it is inferred that the carriers form an “incoherent metal” (64); (65).
The low-frequency conductivity is shown in more detail in Fig. 5. For there is a dramatic suppression of the low-frequency conductivity with a commensurate loss of spectral weight. This “missing area” is associated with the formation of a superconducting condensate, whose spectral weight may be calculated from the Ferrell-Glover-Tinkham sum rule (66); (67)
Here is the square of the superconducting plasma frequency and superfluid density is ; the cut-off frequency cm is chosen so that the integral converges smoothly. The superconducting plasma frequency has also been determined from in the low frequency limit where . Yet another method of extracting from is to determine in the limit (68). All three techniques yield cm, indicating that less than one-fifth of the free-carriers in the normal state have condensed (), implying that this material is not in the clean limit. The superfluid density can also be expressed as an effective penetration depth Å, which is in good agreement with recent tunnel-diode (69) and muon-spin spectroscopy (70) measurements on FeTeSe and FeTeSe, respectively.
The strong suppression of the conductivity for below cm is characteristic of the opening of a superconducting energy gap in the density of states at the Fermi surface; in addition, there also appears to be a shoulder at cm. As previously noted, the formation of a gap leads to a transfer of spectral weight into the condensate. Below , the optical conductivity has been calculated using a Mattis-Bardeen approach (71) for the contribution from the gapped excitations (72). This method assumes that , where the mean-free path ( is the Fermi velocity), and the coherence length for an isotropic superconducting energy gap ; this may also be expressed as . The dirty-limit approach is consistent with the observation that less than 20% of the free carriers collapse into the condensate. Initially, only a single isotropic gap meV for was considered; however, even with a moderate amount disorder scattering () and the addition of the low-frequency tail from the bound Lorentzian oscillators this fails to accurately reproduce the low-frequency conductivity, as Fig. 5(a) demonstrates. To properly model the conductivity two gap features have been considered, meV and meV with for . The observation of two gap features is consistent with recent optical (40); (41); (43), ARPES (73), microwave (74) and penetration depth (75) results on the pnictide compounds, as well as some theoretical works that propose that s-wave gaps form on the hole () and electron () pockets, possibly with a sign change between them (76); (77); (78), the so-called symmetry state. In the model, the gap on the electron pocket () may be an extended s-wave and have nodes on its Fermi surface (79). While there is some uncertainty associated with the low-frequency conductivity in this work, the apparent lack of residual conductivity in the terahertz region for suggests the absence of nodes. It is possible that disorder may lift the nodes, resulting in a nodeless extended s-wave gap (80); (81). While the optical gaps provide estimates of the gap amplitudes, they do not distinguish between and extended s-wave. The optical gaps at and 82 cm are either similar to or slightly larger than the low-frequency scattering rate observed at 18 K, cm. This might seem to suggest that the Mattis-Bardeen approach should not be used; however, the linear frequency dependence of the scattering rate complicates matters. If we consider the value of the scattering rate in the region of the optical gaps where the scattering should be important, then from Fig. 4 we have
which is actually larger than the ratio of 2 that was assumed in the calculation, indicating that the Mattis-Bardeen approach is valid. While the value of is close the value of 3.5 expected for a BCS superconductor in the weak-coupling limit, is significantly larger.
It was recently noted that in a number of the pnictide materials (82) the superfluid density falls on a recently proposed empirical scaling relation for the cuprate superconductors shown by the dashed line in Fig. 6 (83); (84),
From the estimate of cm for (determined from Fig. 3, as well as Drude-Lorentz fits), and the previously determined value of cm, we can see that FeTeSe also falls close to this scaling line. In fact, in a BCS dirty-limit superconductor in the weak-coupling limit, the numerical constant in the scaling relation is calculated to be slightly larger (84)
(dotted line in Fig. 6); the result for this material is actually closer to the BCS dirty-limit line than the one established for the cuprate superconductors.
To summarize, the optical properties of FeTeSe ( K) have been examined for light polarized in the Fe-Te(Se) planes above and below . Well above the transport may be described by a weakly-interacting Fermi liquid (Drude model); however, this picture breaks down close to when the scattering rate takes on a linear frequency dependence, similar to what is observed in the cuprate superconductors. Below , less than one-fifth of the free carriers collapse into the condensate ( Å), indicating that this material is in the dirty limit, and indeed this material falls on the general scaling line predicted for a BCS dirty-limit superconductor in the weak coupling limit. To successfully model the optical conductivity in the superconducting state, two gaps of meV and meV are considered using a Mattis-Bardeen formalism (with moderate disorder scattering), suggesting either an or a nodeless extended s-wave gap.
We would like to acknowledge useful discussions with D. N. Basov, J. P. Carbotte, A. V. Chubukov, S. V. Dordevic, D. C. Johnson, D. J. Singh, J. M. Tranquada, and J. J. Tu. JSW and ZJX are supported by the Center for Emergent Superconductivity, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Basic Energy Sciences. This work is supported by the Office of Science, U.S. DOE under Contract No. DE-AC02-98CH10886.
- journal: Journal of Physics and Chemistry of Solids
- Some useful conversions used in this text are 1 eV = 8066 cm, 1 THz = 33.4 cm, 1 K = 0.695 cm, and 1 cm = 4.78 cm.
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