Vertical temperature boundary of the pseudogap under the superconducting dome in the phase diagram of Bi2Sr2CaCu2O8+δ

Abstract

Combining electronic Raman scattering experiments with cellular dynamical mean field theory, we present evidence of the pseudogap in the superconducting state of various hole-doped cuprates. In Bi2Sr2CaCu2O 8+δ we track the superconducting pseudogap hallmark, a peak-dip feature, as a function of temperature T and doping p, well beyond the optimal one. We show that, at all temperatures under the superconducting dome, the pseudogap disappears at the doping pc, between 0.222 and 0.226, where also the normal-state pseudogap collapses at a Lifshitz transition. This demonstrates that the superconducting pseudogap boundary forms a vertical line in the T − p phase diagram.Discovered thirty years ago [1], the copper oxide (cuprate) superconductors have not ceased to arise interest because their critical temperature T c is incredibly high at ambient pressure in comparison with conventional superconductors. Central to the high-T c cuprate problem is the challenge to understand the pseudogap (PG) state. In the normal phase, where the PG has been studied extensively, it manifests below a characteristic temperature T * > T c as a loss of low energy spectral weight in spectroscopic responses [2][3][4][5][6][7][8][9][10][11][12][13][14][15], and indirectly in thermodynamical and transport properties [16][17][18][19]. Its properties cannot be accounted for by the standard Fermi liquid theory of metals [20,21].An even greater challenge is to establish whether the PG exists in the superconducting phase, and if yes, what its doping dependence is. This is crucial to understand the relation between superconductivity and the pseudogap [22][23][24][25][26], which remains far from being wellunderstood [27,28]. However, there are only very few probes that can disentangle a pseudogap from a superconducting gap. Note, even when the doping end-point of the normal state PG is known, it is unclear how that extrapolates in the superconducting phase, since it involves crossing a phase boundary. In the absence of an explicit method to identify the PG in the superconducting phase, this can be settled only through normal state extrapolations that require involved data analysis of heat capacity [16] and angle-resolved photo-emission spectra (ARPES) [14], or of magneto-resistivity and nuclear magnetic resonance measurements [18,[29][30][31][32] under application of very high magnetic fields.In this article, we present evidence that the PG develops in the SC state of different under-doped compounds, showing that it is a universal property of cuprates. In the case of Bi 2 Sr 2 CaCu 2 O 8+δ (Bi-2212), we are able to follow the PG evolution with doping under the superconducting dome. We show that the pseudogap end is a vertical line in the T −p phase diagram within a narrow range of doping 0.222 < p c < 0.226 [33], the doping level where a Lifshitz transition from a hole-like to an electron-like Fermi surface takes place in the underlying electronic structure [13,34]. Our experimental findings are analyzed within the cellular dynamical mean-field theory ...

Fluctuations and the Higgs Mechanism in Underdoped Cuprates

“…The PG state persists up to a temperature T * which decreases linearly with doping. The AN gap is also visible in two-body spectroscopy, for example in the B 1g channel of Raman scattering [12][13][14], which shows that below T c , the pair breaking gap of superconductivity follows the T * line with doping, in good agreement with the AN gap observed in ARPES. In contrast to the SC phase, the PG state is found to be independent of disorder or magnetic field.…”

“…Let us assume that the CDW is real, as in the first set of Eq.(4). Here the operators η and η * which enable the "rotation" from the SC to the evidence (explaining the rotational symmetry breaking) over a broad temperature range in YBa 2 Cu 3 O y (refs 14,[19][20][21][22]. Therefore, instead of being a defining property of the ordered state, the small amplitude of the charge differentiation is more likely to be a consequence of stripe order (the smectic phase of an electronic liquid crystal 17 ) remaining partly fluctuating (that is, nematic).…”

Anomalous Electron Spectrum and Its Relation to Peak Structure of Electron Scattering Rate in Cuprate Superconductors

“…In particular, this similar PDH structure has been observed in tunneling and Raman spectra [22][23][24][25] . More importantly, the Raman scattering measurements found that the remarkable PDH structure is also developed around the nodal region [25][26][27] . Therefore this well-known PDH structure now has been a hallmark of the spectral line-shape of the ARPES spectrum in cuprate superconductors.…”

Pseudogap transition within the superconducting phase in the three-band Hubbard model

“…Therefore, an important question to consider is whether the pseudogap coexists with d-wave superconductivity. Various studies have found evidence for the pseudogap within the superconducting (SC) phase [6][7][8]. Although the doping dependence is not very well understood, one view is that the magnitude of the gap does not vary much with doping, in the pseudogap phase below T c [6,7,9].…”