Modulation of the local density of states within thed-density wave theory of the underdoped cuprates

Abstract

The low temperature scanning tunneling microscopy spectra in the underdoped regime is analyzed from the perspective of coexisting d-density wave (DDW) and d-wave superconducting states (DSC). The calculations are carried out in the presence of a low concentration of unitary impurities and within the framework of the fully self-consistent Bogoliubov-de Gennes theory, which allows local modulations of the magnitude of the order parameters in response to the impurities. Our theory captures the essential aspects of the experiments in the underdoped BSCCO at very low temperatures.PACS numbers: PACS numbers: 73.23. Hk, 73.63.Kv, 02.70.Ss A fundamental tension in the field of high temperature superconductors is the notion of a competing order parameter in the underdoped regime, which can provide a natural explanation of why the superconducting dome exists and shed light on the nature of the pseudogap. While a charge ordered state is a candidate [1], one of us has proposed, and extensively studied, a new order parameter, which results in circulating currents arranged in a staggered pattern(DDW) [2]. Many experiments are consistent with this order parameter, as demonstrated in studies of the superfluid density, the polarized neutron scattering, the Hall number in pulsed 60 T magnetic field, the angle resolved photoemission spectroscopy (ARPES), the lack of specific heat anomaly at the pseudogap temperature, the transition temperature in multilayer cuprates, and the infrared Hall angle measurements [3]. So far the clinching direct experiment, the polarized neutron scattering, has remained suggestive [4] because of the difficulty of detecting weak signals from the small magnetic moments generated by the circulating orbital currents. Recently, another novel experimental test has been suggested that takes advantage of the spin-orbit coupling in the DDW state [5].Here we turn to the intriguing scanning tunneling microscopy (STM) measurements [6,7,8,9,10,11]. In spite of numerous theoretical analyses of this problem [1,12,13,14,15,16,17,18,19,20,21,22], no comprehensive theoretical picture has yet emerged, although certain aspects are captured by some of them. For example, earlier measurements in the slightly overdoped samples at very low temperatures have been elegantly explained in terms of a quasiparticle scattering interference model, named the octet model [8,14]. At the same time, an interpretation in terms of dynamic charge fluctuations has also been advanced [1,11]. The focus here, however, is on an extensive set of experiments as a function of doping in BSCCO at very low temperatures [9]. The exciting finding of these experiments is the emergence of a new order, present along with the d-wave superconductivity (DSC). The salient signature is a sudden development of a relatively non-dispersive incommensurate wave vector, q * , at higher energies in the underdoped regime.In this Letter we explain the experiments by adopting a view that is orthogonal to the notion of charge order and consider DDW. At first sight, this w...

Spectral signatures of modulatedd-wave superconducting phases

“…Similar structures were also found in a mean-field study of the DSC resonating valence bond phase of the t−J model 24 . Finally, we supplement the extensive literature on the Fourier-transformed local density of states (FT-LDOS) of disordered superconducting phases, with and without coexisting inhomogeneous orders [25][26][27][28][29][30][31][32][33][34][35][36][37] , by calculating the FT-LDOS of a system with anti-phase modulated superconductivity.…”

Complementary pair-density-wave andd-wave-checkerboard orderings in high-temperature superconductors

“…In these theories, the origin of the nondispersive modulations are tied to the existence of particular order parameters. The theories include pair density modulation, 5,6,[19][20][21] currentdensity modulation, 22,23 spin modulation, 2 stripe charge modulation, 7,24 impurity scattering, 25 and so on. Among the proposed mechanisms, the pair density wave has been shown to capture important characteristics of the checkerboard density modulation.…”

Competing ferromagnetism in high-temperature copper oxide superconductors

“…We emphasize, however, that the gap inhomogeneity in the underdoped regime (51) is entirely different (49). There the large gap regions reflect a pseudogap caused by a competing order, in our opinion, the d-density wave (3), whereas the narrow gap regions reflect the DSC.…”

“…We used a self-consistent Bogoliubov-de Gennes theory to calculate the local density of states (LDOS) for a DSC modified to include an effective Zeeman field. The calculational method has been described in detail (49). Here, we simply note the modifications necessary for the present problem.…”