Coexistence of Charge-Density-Wave and Pair-Density-Wave Orders in Underdoped Cuprates

Abstract

We analyze incommensurate charge-density-wave (CDW) and pair-density-wave (PDW) orders with transferred momenta (±Q, 0)/(0, ±Q) in underdoped cuprates within the spin-fermion model. Both orders appear due to exchange of spin fluctuations before magnetic order develops. We argue that the ordered state with the lowest energy has non-zero CDW and PDW components with the same momentum. Such a state breaks C4 lattice rotational symmetry, time-reversal symmetry, and mirror symmetries. We argue that the feedback from CDW/PDW order on fermionic dispersion is consistent with ARPES data. We discuss the interplay between the CDW/PDW order and d x 2 −y 2 superconductivity and make specific predictions for experiments. Introduction.The search for competitors to d x 2 −y 2 superconductivity (d-SC) in underdoped cuprates has gained strength over the last few years due to mounting experimental evidence that some form of electronic charge order spontaneously emerges below a certain doping and competes with d-SC (Refs. [1-16]) The two most frequently discussed candidates for electronic order are incommensurate charge density-wave (CDW) order (Refs. [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]) and incommensurate pair-density-wave order (PDW), which is a SC order with a finite Cooper pair momentum Q (Refs. [33][34][35][36][37][38] CDW order in underdoped cuprates has been proposed some time ago [17] and has been analyzed in detail by several groups in the last few years within the spinfluctuation formalism [19,20,[22][23][24][26][27][28] and within t − J model [18,21]. The initial discussion was focused on near-equivalence between d-SC and d-wave charge bond order (BO) with momenta (Q, Q) along zone diagonal [19,20,27], but charge order of this type has not been observed in the experiments. It was later found [22,23,26,28] that the same magnetic model also displays a CDW order with momenta (Q, 0) or (0, Q), which is consistent with the range of CDW wave vectors extracted from experiments [1-6, 9, 10, 41]. Such CDW order is also consistent with experiments that detect the breaking of discrete rotational and time-reversal symmetries in a (T, x) range where competing order develops [11-16]. In particular, when spin-fermion coupling is strong enough, the CDW order develops in the form of a stripe and breaks C 4 lattice rotational symmetry. A stripe CDW order with (Q, 0)/(0, Q) in turn gives rise to modulations in both charge density and charge current and breaks time-reversal and mirror symmetries [23,24,28,30].The agreement with the data is encouraging, but two fundamental issues with CDW order remain. First,

Renormalization group analysis of the pair-density-wave and charge order within the fermionic hot-spot model for cuprate superconductors

“…However, as we increase the cou-plings to somewhat moderate interactions, we do find a tendency for PDW/CDW to become leading compared to BDW/SSC near the HSFP obtained in the present work. This last result would in principle agree with the experimental situation, in which the leading charge order that emerge in non-Lanthanum-based cuprates has indeed a modulation determined by Q x(y) .Therefore, it seems reasonable to speculate here that this new emergent SU (2) symmetry relating PDW and CDW may indeed have profound consequences for the physics of the underdoped cuprates, as has been recently alluded to by many authors in the literature [30][31][32]55 .…”

Subgap structures and pseudogap in cuprate superconductors: Role of density waves

“…Recent work by Agterberg and Garaud further showed that for competing dSC and PDW, a vortex core will favor PDW through the suppression of dSC, and also drive complementary charge modulation, as those seen in experiments 26 . After the observation by Lee that some photoemission results in cuprates agree better with a PDW scenario than with one based on charge density waves 27 , and after much work stating how many theoretical models are prone to several forms of PDWs [28][29][30][31][32] , experimental evidence of pair density wave was finally obtained, at zero-field, for an underdoped sample of BSCCO, through scanning Josephson tunneling spectroscopy 33 . It would be hard, at this point, to exclude PDWs from the cuprate puzzle.…”

Interplay between unidirectional and bidirectional charge-density-wave orders in underdoped cuprates

“…This order has been proposed in several theory papers [30][31][32][33][34][35][36] and was recently reported to be observed in the tunneling experiments on the cuprates 37 .…”

“…The PDW order is a superconducting order with a non-zero total momentum of a pair (like in Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state, but in zero field). Signatures of the PDW order has been detected in the tunneling experiments on the cuprates 37 , and PDW order has been obtained in various analytical [30][31][32][33][34][35][36][42][43][44] and numerical 45 theoretical calculations. It was argued that the presence of a PDW order explains several experimental features in the pseudogap phase [30][31][32]35 .…”