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Register a new userIntimate link between Charge Density Wave, Pseudogap and Superconducting Energy Scales in Cuprates
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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. To address this issue it is important to extract the energy scale $Delta_{CDW}$ associated with the charge modulations, and to compare it with the pseudogap (PG) $Delta_{PG}$ and the superconducting gap $Delta_{SC}$. However, while $T_{CDW}$ is well-characterized from earlier works little has been known about $Delta_{CDW}$ until now. Here, we report the extraction of $Delta_{CDW}$ for several cuprates using electronic Raman spectroscopy. Crucially, we find that, upon approaching the parent Mott state by lowering $p$, $Delta_{CDW}$ increases in a manner similar to the doping dependence of $Delta_{PG}$ and $Delta_{SC}$. 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 $Delta_{CDW} approx Delta_{SC}$ over a substantial doping range, which is suggestive of an approximate emergent symmetry connecting the charge modulated phase with superconductivity.
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We report the hole doping dependencies of the pseudogap phase energy scale, $2Delta_{rm PG}$, the anti-nodal (nodal) superconducting energy scales $2Delta^{AN}_{rm SC}$ ($2Delta^{N}_{rm SC}$) and the charge density wave energy scale, $2Delta_{rm CDW}$. They have been extracted from the electronic Raman responses of distinct copper oxide families. For all the cuprates studied, we reveal universal doping dependencies which suggest that $2Delta_{rm PG}$, $2Delta^{AN}_{rm SC}$ and $2Delta_{rm CDW}$ are governed by common microscopic interactions and that these interactions become relevant well above the superconducting transition at $T_c$. In sharp contrast, $2Delta^N_{rm SC}$ tracks the doping dependence of $T_c$, appearing to be controlled by a different kind of interactions than the energy scales above.
The pseudogap phase of high-$T_c$ cuprates is controversially attributed to preformed pairs or to a phase which coexists and competes with superconductivity. One of the challenges is to develop theoretical and experimental studies in order to distinguish between both proposals. Very recently, researchers at Stanford have reported [M. Hashimoto {it et al.}, Nat. Phys. {bf 6}, 414 (2010); R.-H. He {it et al.}, Science {bf 331}, 1579 (2011)] angle-resolved photoemission spectroscopy experiments on Pb-Bi2201 supporting the point of view that the pseudogap is distinct from superconductivity and associated to a spacial symmetry breaking without long-range order. In this paper we show that many features reported by these experiments can be described in the framework of the t-J model considering self-energy effects in the proximity to a d charge-density-wave instability.
We have studied the momentum dependence of the energy gap of Bi2(Sr,R)2CuOy by angleresolved photoemission spectroscopy (ARPES), particularly focusing on the difference between R=La and Eu. By comparing the gap function and characteristic temperatures between the two sets of samples, we show that there exist three distinct energy scales, {Delta}pg, {Delta}sc0, and {Delta}eff sc0, which correspond to T* (pseudogap temperature), Tonset (onset temperature of fluctuating superconductivity), and Tc (critical temperature of coherent superconductivity). The results not only support the existence of a pseudogap state below T* that competes with superconductivity but also the duality of competition and superconducting fluctuation at momenta around the antinode below Tonset.
Large pulsed magnetic fields up to 60 Tesla are used to suppress the contribution of superconducting fluctuations (SCF) to the ab-plane conductivity above Tc in a series of YBa2Cu3O(6+x). These experiments allow us to determine the field Hc(T) and the temperature Tc above which the SCFs are fully suppressed. A careful investigation near optimal doping shows that Tc is higher than the pseudogap temperature T*, which is an unambiguous evidence that the pseudogap cannot be assigned to preformed pairs. Accurate determinations of the SCF contribution to the conductivity versus temperature and magnetic field have been achieved. They can be accounted for by thermal fluctuations following the Ginzburg-Landau scheme for nearly optimally doped samples. A phase fluctuation contribution might be invoked for the most underdoped samples in a T range which increases when controlled disorder is introduced by electron irradiation. Quantitative analysis of the fluctuating magnetoconductance allows us to determine the critical field Hc2(0) which is found to be be quite similar to Hc(0) and to increase with hole doping. Studies of the incidence of disorder on both Tc and T* allow us to propose a three dimensional phase diagram including a disorder axis, which allows to explain most observations done in other cuprate families.
This paper consists of two important theoretical observations on the interplay between l = 2 condensates; d-density wave (ddw), electronic nematic and d-wave superconducting states. (1) There is SO(4) invariance at a transition between the nematic and d-wave superconducting states. The nematic and d-wave pairing operators can be rotated into each other by pseudospin SU(2) generators, which are s-wave pairing and electron density operators. The difference between the current work and the previous O(4) symmetry at a transition between the ddw and d-wave superconducting states (Nayak 2000 Phys. Rev. B 62 R6135) is presented. (2) The nematic and ddw operators transform into each other under a unitary transformation. Thus, when a Hamiltonian is invariant under such a transformation, the two states are exactly degenerate. The competition between the nematic and ddw states in the presence of a degeneracy breaking term is discussed.
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