Phase diagram of Bi2Sr2CaCu2O8+δ revisited

Abstract

In cuprate superconductors, the doping of carriers into the parent Mott insulator induces superconductivity and various other phases whose characteristic temperatures are typically plotted versus the doping level p. In most materials, p cannot be determined from the chemical composition, but it is derived from the superconducting transition temperature, T_c, using the assumption that the T_c dependence on doping is universal. Here, we present angle-resolved photoemission studies of Bi₂Sr₂CaCu₂O_8+δ, cleaved and annealed in vacuum or in ozone to reduce or increase the doping from the initial value corresponding to T_c = 91 K. We show that p can be determined from the underlying Fermi surfaces and that in-situ annealing allows mapping of a wide doping regime, covering the superconducting dome and the non-superconducting phase on the overdoped side. Our results show a surprisingly smooth dependence of the inferred Fermi surface with doping. In the highly overdoped regime, the superconducting gap approaches the value of 2Δ₀ = (4 ± 1)k_BT_c.

Fig. 1

Development of the electronic structure of Bi₂Sr₂CaCu₂O_8+δ at the Fermi level with doping. a Fermi surface of an as grown sample. b, c Underdoped samples, obtained by annealing of the as grown samples in vacuum. f, g Overdoped samples, obtained by annealing of as grown samples in O₃. Spectral intensity, represented by the false color contours, is integrated within ±2.5 meV around the Fermi level. Solid (dashed) lines represent the bonding (antibonding) states obtained from the tight-binding approximation that best fits the experimental data. The fitting involved the lines connecting the experimental minimal gap loci in all cases where the underlaying Fermi surface was gapped, as indicated in e. e Dispersion of states along the red dashed line in a. Fermi momenta of bonding (B, B′) and antibonding (A, A′) are marked in both a and e. Gapped Fermi momenta (A′, B′) were approximated by the points where the dispersion acquire maximum. d Intensity contour for sample UD85 (from c) at E = −20 meV and h E = −40 meV. The area enclosed by the TB lines that best represent the experimental data is calculated and used for determination of the doping parameter p_A. The superconducting transition temperature, T_c, is determined from magnetic susceptibility measurements (as grown and underdoped samples) and from ARPES data, as explained in the text. All the maps were recorded at 12–20 K

Fig. 2

Spectral gap from the anti-nodal region of Bi₂Sr₂CaCu₂O_8+δ. a Fermi surface of the UD85 sample, with the dashed red line indicating the momentum line that is probed in b–e for samples with different oxygen content. b–e ARPES intensity as a function of binding energy and momentum along the dashed line in a, taken at T = 12 K, for several different doping levels, as indicated. f The EDC curves taken at the Fermi wave-vector of the bonding state from the anti-nodal region of the Fermi surface, as indicated by bars in b–e. g Temperature dependence of ARPES spectra for the underdoped sample, UD78, (T_c = 78 K) and h for the overdoped sample, OD62 (T_c = 62 K). The spectra in g and h are taken at k_F marked with red and black dots in a, respectively. Spectra in g, h are symmetrized relative to the Fermi level. i, j Temperature dependence of several spectral parameters for the two samples shown in g, h: intensity at the Fermi level (black triangles) and at the peak energy (blue squares), Leading edge gap (LEG) of non-symmetrized spectra (red circles) and apparent quasiparticle peak position (gray diamonds). The error bars in j correspond to the fitting uncertainties in the apparent quasiparticle peak positions from h

Fig. 3

Phase diagram of Bi₂Sr₂CaCu₂O_8+δ. a Experimentally obtained superconducting transition temperature, T_c, (black circles) and the antinodal gap, 2Δ₀ (solid red diamonds) are plotted versus experimentally determined doping parameter, p_A. Also shown are gap values (open red diamonds) and T_c (turquoise circles) for different doping levels from several previously published studies^,,,. These points are placed at the corresponding p_A in accordance with our new T_c(p_A) dependence. The universal superconducting dome is shown as blue dashed line, while the corrected dome is represented by black solid line. The red dashed line indicates the transition observed in SI-STM studies. The shaded area marks the region that has not been studied before. Characteristic temperatures are displayed against the left axis, while the right axis is for the spectral gap. b Ratio of the antinodal gap and T_c for the points shown in a from the overdoped side. The red dashed line corresponds to the BCS value for d-wave gap. We have approximated the uncertainty in doping, Δp_A, (horizontal error bars in a) to be proportional to the width of the Fermi surface: Δp_A/p_A ~ 2Δk_F/k_F. The uncertainty in T_c is given by the width of superconducting transition in susceptibility measurements (underdoped samples), or by the temperature step size in T-dependent ARPES measurements that identify T_c (overdoped samples). The uncertainty in gap magnitude (red vertical error bars in a) corresponds to the standard deviation of the quasiparticle peak position determined from fitting. It serves to determine the propagated uncertainty (vertical error bars) in b

Fig. 4

Comparison of the underlying gapped FS with the gapless FS. a FS contour in the superconducting state and b fully enclosed FS contour obtained in the normal state, at T = 140 K (>T^*) for the as grown sample, OD91. The TB parameters are identical in both panels. c Constant energy contour at E = 0 and d at E = −25 meV in the superconducting state (T = 20 K) of the underdoped sample, UD87. e The normal state contour at E = 0 of the same sample (T = 125 K). The TB contours are identical in c–e. f, g show the photoemission intensities along the momentum lines indicated in d, e, k_x = −0.7 πa⁻¹ in the superconducting and normal states, respectively. h Momentum distribution curves at E = −25 meV and at E = 0, with the maxima corresponding to the gapped and gapless Fermi momenta from f and g, respectively