Pair Density Wave in the Pseudogap State of High Temperature Superconductors

Abstract

Recent scanning tunneling microscopy (STM) experiments of Bi2Sr2CaCu2O 8+δ have shown evidence of real-space organization of electronic states at low energies in the pseudogap state [1]. We argue based on symmetry considerations as well as model calculations that the experimentally observed modulations are due to a density wave of d-wave Cooper-pairs without global phase coherence. We show that STM measurements can distinguish a pair-density-wave from more typical electronic modulations such as those due to charge density wave ordering or scattering from an onsite periodic potential.PACS numbers: 74.25.Jb, 74.25.Dw, One of the major challenges in condensed matter physics today is to understand the electronic phase diagram of high temperature cuprate superconductors. At the center of the debate is the nature of electronic states in lightly hole-doped cuprates, which has attracted a great deal of attention because of the observation of a pseudogap in the density of states (DOS) in these compounds [2]. To understand this phenomenon, some have focused on the smooth evolution of the pseudogap into the superconducting gap[3], the anomalous high frequency conductivity [4], or the Nernst effect [5,6,7]. It was proposed that superconducting pairing fluctuations persist above T c in underdoped samples [8,9,10] and are responsible for the strange electronic behavior in this regime. Others have argued that in the underdoped regime the electronic system has a strong propensity for ordering hence proposing the possibility for antiferromagnetic order [11], combined antiferromagnetic and superconducting fluctuations [12], stripe order [13,14,15], charge density wave [16,17], staggered flux phase [18] and d-density wave [19].Recently, mapping of the electronic states with the scanning tunneling microscope (STM) has demonstrated a link between the observation of real space electronic patterns and the pseudogap in DOS of underdoped Bi 2 Sr 2 CaCu 2 O 8+δ samples [1]. In this experiment, STM was used to detect a dispersionless modulation of the low energy electronic states, showing an unusual enhancement of the intensity of modulated patterns within the pseudogap energy scale. The pseudogap modulations bears similarity to those observed near the vortex cores [20], but seems to be distinct from the STM features in the superconducting state [1,21,22], which exhibit energy dispersion. The origin of DOS modulation in the superconducting state has been for the most part attributed to quantum interference of quasi-particles [23], although potential relevance of electronic ordering has also been considered [21,24,25,26,27,28]. In Refs. [21,26], it was argued that the energy dependence of the tunneling intensity can be used to identify the type of ordering in the superconducting state.In this Letter, we focus on the STM resolved modulations of the DOS in the pseudogap state and propose that these are a consequence of a novel density wave associated with d-wave Cooper pairs, first proposed in the context of the charge ordering in the vicini...

Nernst effect in high-Tcsuperconductors

“…In the striped model, the competing state involves quasi-1D dynamic stripes [3]. Vortex excitations are also fundamental to other recent theories of the pseudogap/charge-ordered states above the T c dome [27,28,30,31,32]. We anticipate that detailed experiments on e N and M in intense fields, in combination with STM experiments above T c , should allow these theories to be tested.…”

“…In defining an extended region above the "T c dome" in which vorticity exists (which we call the "Nernst region"), the Nernst results are increasingly influencing the ongoing pseudogap debate [2,3,26,27,28,29,30,31,32,33]. Nonetheless, acceptance of a vortex origin for e N above T c is by no means unanimous; several models interpreting the Nernst results strictly in terms of quasiparticles have appeared [34,35,36,37,38].…”

Scanning tunneling microscopy and spectroscopy study of4a×4aelectronic charge order and the inhomogeneous pairing gap in superconductingBi2Hashimoto1, Momono2, Oda3 et al. 2006Phys. Rev. B371320View full textAdd to dashboardCite

“…9,10,[33][34][35] The appearance of the charge order within the pairing gap is not inconsistent with the models of pair density waves, electronic supersolids, paired-hole Wigner crystallization, or the coexistence of multitype SC and spin density wave. [36][37][38][39][40][41][42][43][44][45][46] On the other hand, Vershinin et al have claimed that the nondispersive ϳ4a ϫ 4a charge order at T Ͼ T c is a hidden order of the electron system in the pseudogap state ͑T Ͼ T c ͒. 3 In that case, the observation that the nondispersive charge order survives even in the SC state means that the hidden order of the pseudogap state will remain essentially unchanged down to below T c .…”

Quasiparticle interference and the interplay between superconductivity and density wave order in the cuprates

“…The symmetry of the LDOS modulation due to superconducting gap and site energy variations already was described in Ref. 48 using the Bogoliubov-de Gennes equations for a d-wave superconductor with classical phase fluctuations. We take a different approach: we derive the LDOS modulation due to scattering from a single impurity site using a momentum space T -matrix formalism.…”