Exploration of Hg-based cuprate superconductors by Raman spectroscopy under hydrostatic pressure

The superconducting phase of the ${\mathrm{HgBa}}_2{\mathrm{CuO}}_{4+\delta }$ (Hg-1201) and ${\mathrm{HgBa}}_2{\mathrm{Ca}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{8+\delta }$ (Hg-1223) cuprates has been investigated by Raman spectroscopy under hydrostatic pressure. Our analysis reveals that the increase of $T_{\mathrm{c}}$with pressure is slower in the Hg-1223 cuprate compared to Hg-1201 due to a charge carrier concentration imbalance accentuated by pressure in Hg-1223. We find that the energy variation under pressure of the apical oxygen mode from which the charge carriers are transferred to the ${\mathrm{CuO}}_2$ layer, is the same for both the Hg-1223 and Hg-1223 cuprates and it is controlled by the interlayer compressibility. At last, we show that the binding energy of the Cooper pairs related to the maximum amplitude of the $d$-wave superconducting gap at the antinodes does not follow $T_{\mathrm{c}}$with pressure. It decreases while $T_{\mathrm{c}}$increases. In the particular case of Hg-1201, the binding energy collapses from 10 to 2 $K_B{T}_{\mathrm{c}}$ as the pressure increases up to 10 GPa. These direct spectroscopic observations joined to the fact that the binding energy of the Cooper pairs at the antinodes does not follow $T_{\mathrm{c}}$either with doping, raises the question of its link with the pseudogap energy scale which follows the same trend with doping.

Figure 1

Schematic representation of the tetragonal crystal structures (a) Hg-1201 and (b) Hg-1223. The oxygen atoms O1 and O4 are, respectively, related to the inner and outer ${\mathrm{CuO}}_2$ planes, O2 are the apical oxygen atoms, and O3 are the oxygen atoms in excess inserted by the chemical doping in the $\mathrm{HgO}$ plane.

Figure 2

DC magnetization curves as a function of temperature of two sets of (a) Hg-1201 and (b) Hg-1223 single crystals. These crystals have been used for Raman measurements under pressure. The first derivatives of the magnetization curves are reported in the insets to underline the $T_{\mathrm{c}}$values and their full width at half maximum. The $T_{\mathrm{c}}$values of the mercurate single crystals measured by Raman spectroscopy are reported for the (c) Hg-1201 and (d) Hg-1223 systems.

Figure 3

Top view of the diamond anvil cell with diamonds of $800\text{−}\mu \mathrm{m}$ diameter before loading. The chamber between the diamonds is a cylindrical hole. After loading the chamber size is approximately $300\mu \mathrm{m}$ (dashed circle).

Figure 4

Cross polarizations of the incoming and outgoing light (a) at 45 degrees from the Cu-O bond direction of the ${\mathrm{CuO}}_2$ plane corresponding to the ${\mathrm{B}}_{1g}$geometry and (b) along the Cu-O bond direction corresponding to the ${\mathrm{B}}_{2g}$geometry. (c) The antinodal region probed by the ${\mathrm{B}}_{1g}$geometry and (d) the nodal region probed by the ${\mathrm{B}}_{2g}$geometry in the first Brillouin zone.

Figure 5

Superconducting and normal Raman responses of the UD92K Hg-1201 and OP133K Hg-1223 in three distinct geometries at ambient pressure. The straight lines and numbers indicate the locations of the vibrational modes. Dashes lines indicate the ${\mathrm{A}}_{1g}$ and ${\mathrm{B}}_{1g}$contributions. Panel (f) contains a part of one spectrum in Ref. [40].

Figure 6

Double structure of the ${\mathrm{B}}_{1g}$superconducting gap of Hg-1223 (a)–(c) as a function of doping (d)–(f) as a function of temperature for each doping. Panel (f) contains a part of one spectrum in Ref. [42].

Figure 7

Superconducting Raman responses in the ${\mathrm{A}}_{1g}+{\mathrm{B}}_{1g}$ geometry of (a) Hg-1201 and (b) Hg-1223 crystals at 0.4 GPa. Zoom on the frequency range of the ${\mathrm{A}}_{1g}+{\mathrm{B}}_{1g}$ Raman spectra of (c) Hg-1201 and (d) Hg-1223 compounds under hydrostatic pressures. The framed frequencies mark the pristine oxygen modes (see Table 1). The dotted lines are guides for the eyes.

Figure 8

The normalized frequencies of the oxygen vibrational modes of Hg-1223 and Hg-1201 as a function of pressure $P$. The normalized frequency is obtained by dividing the frequency at pressure $P$ by this value at ambient pressure. The normalized critical temperature $T_{\mathrm{c}}{}^N=T_c\left(P\right)/T_c\left(0\right)$ is also reported. The $T_c\left(P\right)$ values come from Refs. [25, 70].

Figure 9

${\mathrm{B}}_{1g}$ and ${\mathrm{B}}_{2g}$ Raman responses free of phonons under hydrostatic pressures of Hg-1223 (a) and (b), and Hg-1201 (c)–(d). The sets of Hg-1223 and Hg-1201 data were obtained at $4\mathrm{K}$ and $14\mathrm{K}$, respectively.

Figure 10

${\mathrm{B}}_{1g}$ Raman response in Hg-1223 under pressure at $T=4\mathrm{K}$. (a)–(d) Electronic Raman response featuring the superconducting peak at various pressures. At maximum $10\mathrm{GPa}$ pressures, the normal state response above $T_c$ is also displayed in order to underline the superconducting peak. (e) Contour plot highlighting the evolution of the ${\mathrm{B}}_{1g}$ spectral weight as a function of pressure. The dashed lines are guides for the eyes.

Figure 11

${\mathrm{B}}_{2g}$ Raman response in Hg-1223 under pressure at $T=4\mathrm{K}$. (a)–(d) Electronic Raman response featuring the superconducting peak. (e) Contour plot highlighting the evolution of the ${\mathrm{B}}_{2g}$ spectral weight as a function of pressure. The dashed line is a guide for the eyes.

Figure 12

Following the ${\mathrm{B}}_{1g}$SC gap in Hg-1201. (a) Difference between the ${\mathrm{B}}_{1g}$and the ${\mathrm{B}}_{2g}$Raman response (the latter one serving as a reference background), as a function of pressure. (b) Contour plot highlighting the evolution of the ${\mathrm{B}}_{1g}$ spectral weight with pressure. The dashed line is a guide for the eyes.

Figure 13

Frequency evolution of the characteristic superconducting peaks in the Raman spectra of Hg-1223 and Hg-1201 compounds.

Figure 14

Sets of the Hg-1201 and Hg-1223 Raman responses under hydrostatic pressures. The sets of Hg-1223 and Hg-1201 spectra were obtained at $4\mathrm{K}$ and $14\mathrm{K}$, respectively.

Figure 15

Splitting of the ${\mathrm{B}}_{1g}$SC peak under hydrostatic pressures in Hg-1223. (a) Comparison between the Raman responses at 0 and 0.4 GPa measured outside and inside the pressure cell; (b) superposition of several Raman responses of Hg-1223 under pressure. The based dotted line delimits the top of the ${\mathrm{B}}_{1g}$SC peak; (c)–(h) deconvolution of the ${\mathrm{B}}_{1g}$SC peak under various pressures.

Figure 16

${\mathrm{B}}_{2g}$and ${\mathrm{B}}_{1g}$Raman spectra of (UD92K) Hg-1201 compounds measured as a function of pressure.

Figure 17

${\mathrm{A}}_{1g}+{\mathrm{B}}_{1g}$ Raman response at high pressure for (a) (UD92K) Hg-1201 and (b) (UD132K) Hg-1223 compounds. The arrows indicate the location of the ${\mathrm{B}}_{1g}$SC peak. In the insets is displayed the subtraction between the Raman response above and below $T_{\mathrm{c}}$under pressure. The ${\mathrm{B}}_{1g}$SC peak for both compounds is still present well above $T_{\mathrm{c}}$at ambient pressure.

Figure 18

${\mathrm{A}}_{1g}+{\mathrm{B}}_{1g}$ Raman response in Hg-1201 under pressure at $T=14\mathrm{K}$. (a) Electronic Raman response featuring the ${\mathrm{A}}_{1g}$ peak, whose frequency decreases under pressure. (b) Contour plot highlighting the evolution of the ${\mathrm{A}}_{1g}$ spectral weight as a function of pressure. The dashed line is a guide for the eyes.