Infrared pseudogap in cuprate and pnictide high-temperature superconductors

We investigate infrared manifestations of the pseudogap in the prototypical cuprate and pnictide superconductors, ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_y$ and ${\mathrm{BaFe}}_2$${\mathrm{As}}_2$ (Ba122) systems. We find remarkable similarities between the spectroscopic features attributable to the pseudogap in these two classes of superconductors. The hallmarks of the pseudogap state in both systems include a weak absorption feature at about $500{\mathrm{cm}}^{-1}$ followed by a featureless continuum between 500 and $1500{\mathrm{cm}}^{-1}$ in the conductivity data and a significant suppression in the scattering rate below 700–900 ${\mathrm{cm}}^{-1}$. The latter result allows us to identify the energy scale associated with the pseudogap ${\Delta }_{\mathrm{PG}}$. We find that in the Ba122-based materials the superconductivity-induced changes of the infrared spectra occur in the frequency region below 100–200 ${\mathrm{cm}}^{-1}$, which is much lower than the energy scale of the pseudogap. We performed theoretical analysis of the scattering rate data of the two compounds using the same model, which accounts for the effects of the pseudogap and electron-boson coupling. We find that the scattering rate suppression in Ba122-based compounds below ${\Delta }_{\mathrm{PG}}$ is solely due to the pseudogap formation, whereas the impact of the electron-boson coupling effects is limited to lower frequencies. The magnetic resonance modes used as inputs in our modeling are found to evolve with the development of the pseudogap, suggesting an intimate correlation between the pseudogap and magnetism.

Figure 1

Room-temperature in-plane reflectance $R\left(\omega \right)$ spectra of ${\mathrm{YBCO}}_y$ [57] and Co-/P-doped Ba122.

Figure 2

Doping dependence of the real part of the room-temperature in-plane optical conductivity ${\sigma }_1\left(\omega \right)$ spectra of (a) ${\mathrm{YBCO}}_y$ [57] and (b) Ba122 systems. Insets of (a) and (b) show the spectral weight obtained from the integration of ${\sigma }_1\left(\omega \right)$ of ${\mathrm{YBCO}}_y$ up to $8000{\mathrm{cm}}^{-1}$ and that of Ba122 up to $1500{\mathrm{cm}}^{-1}$, respectively.

Figure 3

In-plane electrodynamics of ${\mathrm{YBCO}}_y$ and Ba122 superconductors. (a), (b) $T$-dependent optical conductivity. (c), (d) Scattering rate 1/τ(ω). (e), (f) Calculated scattering rate. (g), (h) Bosonic spectral function ${\alpha }^{2}F\left(\omega \right)$ employed in the electron-boson-coupling analysis. Insets: normalized DOS. Top panels: ${\mathrm{YBCO}}_{6.65}$. Bottom panels: P-Ba112.

Figure 4

Top panel: real part of optical conductivity of (a) ${\mathrm{YBCO}}_{6.65}$, (b) BCS superconductor, (c) Cr, (d) ${\mathrm{YbFe}}_4$${\mathrm{Sb}}_{12}$, (e) κ-(BEDT-TTF)${}_2$Cu[N(CN)${}_2$${\mathrm{]Br}}_{1-x}$${\mathrm{Cl}}_x$, and (f) graphene. $T^{*}$: pseudogap temperature; $T_c$: superconducting transition temperature; $T_{\mathrm{SDW}}$: spin-density-wave transition temperature; $T_{\mathrm{h}}$: hybridization gap formation temperature; $V$: applied voltage. Middle panel: scattering rate (g)–(k) and the imaginary part of optical conductivity for graphene (l). Bottom panel: (m)–(q) normalized DOS, (r) density of states. ${\Delta }_{\mathrm{PG}}$: pseudogap; $2{\Delta }_{\mathrm{SC}}$: superconducting gap; $\Delta {}_{\mathrm{DW}}$: density-wave gap; $\Delta {}_{\mathrm{h}}$: hybridization gap; $U$: on-site Coulomb interaction; $E_{\mathrm{F}}$: Fermi level. Thick dashed line indicates the Fermi level, which is set to zero in (m)–(q). The DOS plot in (o) is for an ideal SDW case where the full gap is developed. In Cr, some bands are not impacted by SDW order, and there remains finite DOS at the Fermi level in the SDW state. Cr [47], ${\mathrm{YbFe}}_4$${\mathrm{Sb}}_{12}$ [70], κ-(BEDT-TTF)${}_2$Cu[N(CN)${}_2$${\mathrm{]Br}}_{1-x}$Cl [71, 72], and graphene [76].

Figure 5

Optical conductivity (top) and scattering rate (bottom) for the underdoped ${\mathrm{YBCO}}_{6.50}$ with $T_c$ = 31 K (left column) and OPD Co-Ba112 with $T_c$ = 22 K (right column).

Figure 6

Optical conductivity spectra of (a) Ba$({\mathrm{Fe}}_{0.92}$${\mathrm{Co}}_{0.08})$${}_2$${\mathrm{As}}_2$ and (c) ${\mathrm{Nd}}_{1.9}$${\mathrm{Ce}}_{0.1}$${\mathrm{CuO}}_4$ [106]. Ratio of the spectral weight $K$$(\omega ,T)/K$(ω, 295 K) of (b) Ba$({\mathrm{Fe}}_{0.92}$${\mathrm{Co}}_{0.08})$${}_2$${\mathrm{As}}_2$ $(T_c=22\text{K})$ and (d) ${\mathrm{Nd}}_{1.9}$${\mathrm{Ce}}_{0.1}$${\mathrm{CuO}}_4$ (nonsuperconducting).

Figure 7

(a) Phase diagram of ${\mathrm{YBCO}}_y$ [26, 148]. $T^{*}$: the pseudogap onset temperature determined from the in-plane resistivity (open triangles, [149]) and Nernst experiments (solid triangles, [124]). Solid triangles are $T_{\mathrm{SDW}}$: the onset temperature for SDW order measured by neutron scattering (open squares, [150]) and muon spin rotation experiments (solid squares, [151]). $T_{\mathrm{CDW}}$: the onset temperature of the charge-density-wave order measured by x-ray scattering experiments (solid diamonds, [23]). (b) Phase diagram of Co-Ba122 [53, 152] and P-Ba122 [50, 115]. The lower and upper horizontal axes are for P-Ba122 and Co-Ba122, respectively. The boundary of AFM and superconducting states are indicated by thick black lines for Co-Ba122 and thick red lines for P-Ba122. The structural transition temperature $T_{\mathrm{S}}$ of Co-Ba122 is represented by black dashed line. $T^{**}$ (open squares): a crossover temperature at which the behavior of the $c$-axis resistivity of Co-Ba122 changes from nonmetallic to metallic with decreasing $T$ [54]. $T_{\mathrm{CG}}$ (open triangles): a crossover temperature at which the behavior of the $c$ xis resistivity of Co-Ba122 changes from metallic to nonmetallic with decreasing $T$ [54]. $T_{\mathrm{pc}}$ (solid diamonds): a temperature below which the point-contact experiments of Co-Ba122 show conductance enhancement [141, 142]. $T_{\mathrm{Nem}}$ (solid circles): the temperature below which the twofold torque component appears in the magnetic torque experiments of P-Ba122 [115]. In both panels, $T_{\mathrm{N}}$ represents AFM transition temperature and $T_c$ stands for superconducting transition temperature.