${\mathrm{FeTe}}_{0.55}{\mathrm{Se}}_{0.45}$: A multiband superconductor in the clean and dirty limit

The detailed optical properties of the multiband iron-chalcogenide superconductor ${\mathrm{FeTe}}_{0.55}{\mathrm{Se}}_{0.45}$ have been reexamined for a large number of temperatures above and below the critical temperature $T_c=14\mathrm{K}$ for light polarized in the $a\text{−}b$ planes. Instead of the simple Drude model that assumes a single band, above $T_c$ the normal-state optical properties are best described by the two-Drude model that considers two separate electronic subsystems; we observe a weak response $({\omega }_{p,D;1}\simeq 3000{\mathrm{cm}}^{-1})$ where the scattering rate has a strong temperature dependence ($1/{\tau }_{D,1}\simeq 32{\mathrm{cm}}^{-1}$ for $T\gtrsim T_c$), and a strong response $({\omega }_{p,D;2}\simeq 14500{\mathrm{cm}}^{-1})$ with a large scattering rate $(1/{\tau }_{D,2}\simeq 1720{\mathrm{cm}}^{-1})$ that is essentially temperature independent. The multiband nature of this material precludes the use of the popular generalized-Drude approach commonly applied to single-band materials, implying that any structure observed in the frequency-dependent scattering rate $1/\tau \left(\omega \right)$ is spurious and it cannot be used as the foundation for optical inversion techniques to determine an electron-boson spectral function ${\alpha }^{2}F\left(\omega \right)$. Below $T_c$ the optical conductivity is best described using two superconducting optical gaps of $2{\Delta }_1\simeq 45$ and $2{\Delta }_2\simeq 90{\mathrm{cm}}^{-1}$ applied to the strong and weak responses, respectively. The scattering rates for these two bands are vastly different at low temperature, placing this material simultaneously in both clean and dirty limit. Interestingly, this material falls on the universal scaling line initially observed for the cuprate superconductors.

Figure 1

The real part of the in-plane optical conductivity of ${\mathrm{FeTe}}_{0.55}{\mathrm{Se}}_{0.45}$ for a large number of temperatures in the normal state in the far- and mid-infrared region, showing the rapid emergence with decreasing temperature of a Drude-like response at low frequency.

Figure 2

The Drude-Lorentz model fit to the real part of the optical conductivity of ${\mathrm{FeTe}}_{0.55}{\mathrm{Se}}_{0.45}$ at 20 K for light polarized in the $a\text{−}b$ planes for two Drude components and two Lorentz oscillators. The inset shows the linear combination of the two Drude components in the low-frequency region; the sharp structure at $\simeq 204{\mathrm{cm}}^{-1}$ is the normally infrared-active $E_u$ mode [30].

Figure 3

The two-Drude model fit to the optical conductivity yielding the temperature dependence of the (a) plasma frequencies ${\omega }_{p,D;j}$ and (b) scattering rates $1/{\tau }_{D,j}$ for the narrow (diamonds) and broad (circles) Drude components in ${\mathrm{FeTe}}_{0.55}{\mathrm{Se}}_{0.45}$ for $T>T_c$. The filled symbols indicate fitted parameters, while the open symbols indicate that the parameter is held fixed to a constant value. Where error bars are not shown, the error is roughly the size of the symbol. The dotted lines are drawn as a guide for the eye.

Figure 4

The temperature dependence of the spectral weight normalized to the value at 295 K for a variety of choices for the cutoff frequency ${\omega }_c$; the estimated error is indicated for the ${\omega }_c=100{\mathrm{cm}}^{-1}$ points. Smaller values of ${\omega }_c$ result in a strong temperature dependence; however, within the confidence limits of the experiment, for ${\omega }_c\gtrsim 4000{\mathrm{cm}}^{-1}$ there is effectively little or no temperature dependence.

Figure 5

(a) The optical conductivity for the temperature-independent broad, strong Drude component (dot-dashed line), and the weaker Drude component (solid and dashed lines) that displays a strongly temperature-dependent scattering rate. (b) The frequency-dependent scattering rate calculated from the two-Drude model. Inset: the experimentally determined $1/\tau \left(\omega \right)$.

Figure 6

(a) The real part of the optical conductivity for ${\mathrm{FeTe}}_{0.55}{\mathrm{Se}}_{0.45}$ for light polarized in the $a\text{−}b$ planes just above $T_c$ at 20 K, and at two temperatures below $T_c$. Note the strong suppression of the low-frequency conductivity for $T\ll T_c$. (b) The spectral weight in the normal state, $N_n(\omega ,T\gtrsim T_c)$ and in the superconducting state, $N_s(\omega ,T\ll T_c)$; the expression for ${\omega }_{p,S}^2$ converges by $\omega \simeq 150{\mathrm{cm}}^{-1}$.

Figure 7

(a) The real part of the optical conductivity for ${\mathrm{FeTe}}_{0.55}{\mathrm{Se}}_{0.45}$ for light polarized in the $a\text{−}b$ planes just above $T_c$ at 20 K, and at two temperatures below $T_c$. The dash-dotted line models the smoothed contribution to the conductivity from the gapped excitations described in the discussion. (b) The real part of the optical conductivity for a Drude model with ${\omega }_{p,D;1}=2600{\mathrm{cm}}^{-1}$ and $1/{\tau }_{D,1}=32{\mathrm{cm}}^{-1}$ (solid line), and the contribution from the gapped excitations for $T\ll T_c$ with superconducting gaps of $2{\Delta }_1=45{\mathrm{cm}}^{-1}$ and $2{\Delta }_2=90{\mathrm{cm}}^{-1}$ (dashed lines). (c) The same set of calculations for ${\omega }_{p,D;2}=14500{\mathrm{cm}}^{-1}$ and $1/{\tau }_{D,2}=1720{\mathrm{cm}}^{-1}$.

Figure 8

The log-log plot of the in-plane spectral weight of the superfluid density $N_c\equiv {\rho }_{s0}/8$ vs ${\sigma }_{dc}{T}_c$, for a variety of electron and hole-doped cuprates compared with the result for ${\mathrm{FeTe}}_{0.55}{\mathrm{Se}}_{0.45}$. The dashed line corresponds to the general result for the cuprates ${\rho }_{s0}/8\simeq 4.4{\sigma }_{dc}{T}_c$, while the dotted line is the result expected for a BCS dirty-limit superconductor in the weak-coupling limit, ${\rho }_{s0}/8\simeq 8.1{\sigma }_{dc}{T}_c$. The open circles represent the different contributions to the superfluid density in ${\mathrm{FeTe}}_{0.55}{\mathrm{Se}}_{0.45}$; the solid circle is the experimental value.