Intimate link between charge density wave, pseudogap and superconducting energy scales in cuprates

Abstract

The cuprate high temperature superconductors develop spontaneous charge density wave (CDW) order below a temperature T CDW and over a wide range of hole doping (p). An outstanding challenge in the field is to understand whether this modulated phase is related to the more exhaustively studied pseudogap and superconducting phases [1,2]. To address this issue it is important to extract the energy scale ∆ CDW associated with the charge modulations, and to compare it with the pseudogap (PG) ∆ PG and the superconducting gap ∆ SC . However, while T CDW is well-characterized from earlier works [3] little has been known about ∆ CDW until now. Here, we report the extraction of ∆ CDW for several cuprates using electronic Raman spectroscopy.Crucially, we find that, upon approaching the parent Mott state by lowering p, ∆ CDW increases in a manner similar to the doping dependence of ∆ PG and ∆ SC . This shows that CDW is an unconventional order, and that the above three phases are controlled by the same electronic correlations. In addition, we find that ∆ CDW ≈ ∆ SC over a substantial doping range, which is suggestive of an approximate emergent symmetry connecting the charge modulated phase with superconductivity [4][5][6][7][8][9].In recent years, many experiments and different techniques have established the ubiquity of CDW order in cuprates [3]. In particular, these works have determined T CDW (p), which displays a dome-like shape on the temperature-doping (T − p) phase diagram, in a fashion reminiscent of the superconducting dome T SC (p), even though the former order is present over a much narrower p-range, and mostly below optimal doping. The CDW is found to compete with superconductivity [10-16] but there are indications that the interplay between the two phenomena might be more complex than a simple competition [17,18].The energy scale ∆ CDW associated with the CDW has attracted far less experimental attention, even though this quantity is crucial to address several important ques-tions such as the following. (a) First, whether the CDW is a conventional order i.e., a phase whose existence can be understood within a scenario of weakly interacting electrons. A tell-tale signature of it would be if T CDW (p) ∝ ∆ CDW (p). On the other hand if their doping trends are different, as is famously the case of the superconducting order, it implies unconventional order, which is a consequence of strongly interacting electrons.Here we show that this is also the case of the CDW and, therefore, it is an unconventional order. (b) Second, a comparison of the magnitudes and the doping dependencies of ∆ CDW (p), ∆ SC (p) and ∆ PG (p) is important to understand the relation between these three phenomena. We show that these three energy scales have rather similar doping evolutions, implying that it is likely that they have a common origin in terms of a driving electronic interaction. Moreover, we find that the magnitude of ∆ CDW (p) and of ∆ SC (p) are comparable over a significant doping range, which is consistent with a concept that has ...

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.…”

“…Second scale corresponds to the spectroscopy peaks at a lower energy scale seen in STM, ARPES or Raman spectroscopy. Both the "Alloul-Warren" and the spectroscopic gaps seem to be related to each other and behave similarly with doping, decreasing in a quasi-linear fashion as doping increases [13]. The argument of two PG energy scales is typical of strong coupling theories where the higher energy scale is characterized with spin singlet formation and the lower energy scale is associated with superconducting fluctuations.…”

“…A recent Raman scattering experiment performed on the compound Hg1223 shows for the first time that there is a precursor gap in the charge channel (see Fig.7a) [13]. It is seen as a spectral peak in the B 2g channel, which is visible below the ordering temperature T co but follows T * rather than T co as a function of oxygen doping.…”

“…1 and Supplementary Figs 9 and 10) and 67 6 5 K for p 5 0.12 ( Supplementary Figs 7 and 8). Within error bars, for each of the samples Tcharge coincides with T0, the temperature at which the Hall constant RH becomes negative, an indication of the Fermi surface reconstruction [11][12][13] . Thus, whatever the p charge modulation is, the reconstruction m lational symmetry breaking by the charge The absence of any splitting or broaden one-dimensional character of the modula imposes strong constraints on the charge types of modulation are compatible with a first is a commensurate short-range (2a running along the (chain) b axis.…”

“…On the other hand, in the nodal region, the spectral gap vanishes at T c as it should within the standard BCS theory. Moreover, we learn from Raman scattering spectroscopies that in the B 1g channel, which scans the ANR, the spectral gap follows the T * line as a function of doping, but is at the same time associated to the "pair breaking" below T c [13].…”