Interpretation of Scanning Tunneling Quasiparticle Interference and Impurity States in Cuprates

Abstract

We apply a recently developed method combining first principles based Wannier functions with solutions to the Bogoliubov-de Gennes equations to the problem of interpreting STM data in cuprate superconductors. We show that the observed images of Zn on the surface of Bi2Sr2CaCu2O8 can only be understood by accounting for the tails of the Cu Wannier functions, which include significant weight on apical O sites in neighboring unit cells. This calculation thus puts earlier crude "filter" theories on a microscopic foundation and solves a long standing puzzle. We then study quasiparticle interference phenomena induced by out-of-plane weak potential scatterers, and show how patterns long observed in cuprates can be understood in terms of the interference of Wannier functions above the surface. Our results show excellent agreement with experiment and enable a better understanding of novel phenomena in the cuprates via STM imaging.PACS numbers: 74.70.Xa, 74.62.En, Scanning tunneling microscopy (STM) methods were applied to cuprates relatively early on, but dramatic improvements in energy and spatial resolution led to a new set of classic discoveries in the early part of the last decade, giving for the first time a truly local picture of the superconducting and pseudogap states at low temperatures [1,2]. These measurements revealed gaps that were much more inhomogeneous than had previously been anticipated [3][4][5][6], exhibited localized impurity resonant states [7,8], and gave important clues to the nature of competing order [9][10][11][12][13]. More recently, STM has again been at the forefront of studies of inhomogeneities, this time as a real space probe of intra-unit cell charge ordering visible in the underdoped systems [14]. While a microscopic description of such atomic scale phenomena in superconductors is available in terms of the Bogolibuov de-Gennes equations, such calculations are always performed on a lattice with sites centered on the Cu atoms, and thus do not contain intra-unit cell information.The simplest example of a problem that can arise because of the deficiencies of theory in this regard is that of the Zn impurity substituting for Cu in Bi 2 Sr 2 CaCu 2 O 8 (BSCCO), a cuprate material which cleaves well in vacuum, leaving atomically smooth surfaces ideal for STM. The observation of a spectacularly sharp impurity resonance at the impurity site [7,8,15,16] was an important local confirmation of unconventional pairing in the cuprates. The differential conductance map near the impurity exhibits a cross-shaped real-space conductance map at resonance, as expected for a pointlike potential scatterer in a d-wave superconductor, see Fig. 1(c) [17] Upon closer examination, however, the pattern deviates from the expected theoretical one on the Cu square lat- tice in some important respects [18,19]. First, it displays a central maximum on the impurity site, unlike simple models, which have a minimum ( Fig. 1(a)). Second, the longer range intensity tails are rotated 45 degrees from the nodal directions of the ...

Effects of strong disorder in strongly correlated superconductors

“…Such impurities suppress SC dramatically [36]. Zinc impurities in cuprate HTSC have traditionally been treated as strong repulsive potential [37][38][39], although recent work has shown these impurities to be attractive [10,35]. We show here that for large repulsive V 0 = 7.0 (> V c ), the n imp -dependence of ∆ OP follows the weak coupling IMT behavior, rather than the strong coupling RIMT trend [49], as shown in Fig.…”

“…We also examined a different model of disorder: Randomly located impurities of strength V 0 on n imp fraction of sites, which is more relevant to Zn doping of cuprate hightemperature superconductors (HTSC) [33][34][35]. Such impurities suppress SC dramatically [36].…”

Magnetic field dependence of the density of states in the multiband superconductorβ−Bi2Pd

“…We should note that the tunneling spectroscopy at the surface of all these materials is influenced by the quasi-2D nature of a large part of their Fermi surface, possibly favoring contributions from in-plane states [64]. As mentioned above, the Fermi surface of β-Bi 2 Pd has a pronounced 3D character.…”

Tracing the Electronic Pairing Glue in Unconventional Superconductors via Inelastic Scanning Tunneling Spectroscopy

“…A classical example is the determination of the electron-phonon pairing interaction in conventional superconductors [1,2]. More recently, quasi-particles interference spectroscopy managed to exploit the local resolution of scanning tunneling microscopy (STM) to obtain momentum space information [3][4][5]. Both examples are based on elastic tunneling theory [6,7] where one interprets the low-temperature conductance to be proportional to the electronic density of states (DOS), including renormalizations of the DOS that occur for example within the strong coupling Eliashberg formalism [8].…”