Distinguishing models for the pseudo-gap in cuprate superconductors by probing the spatial distribution of impurity states

Abstract

We argue that the spatial distribution of resonant impurity states in underdoped high-Tc superconductors serves as a probe for distinguishing different theoretical models for the pseudogap state. Superconducting pairing fluctuations are characterized by off-diagonal short-range order which distinguishes them from other possible instabilities that could give rise to the pseudogap phenomena. Due to the mixture of particle and hole states in a superconductor an impurity resonant state is composed of both a particle and a hole-like component. On the contrary a state with a gap induced by a particle-hole instability, like a d-density wave (DDW) or spin-density wave (SDW), exhibits no off-diagonal short-range order and consequently a resonant impurity state consists of only one either particle or hole-like component. Furthermore, a charge-spin separated state shows no resonance state at all inside the gap region.One of the most intriguing property of the underdoped high-temperature superconductors (HTSC) is the suppression of single-particle weight around the Fermi energy [1, 2, 3] for temperatures well above T c . As a consequence the electronic behavior of these materials deviates substantially from that of conventional superconductors. The origin of this so-called pseudo-gap state is one of the key problems to be solved in order to understand the underlying microscopic mechanism of the phenomena of HTSC. As various different theoretical proposals for the pseudo-gap have been put forward the need of experimental probes that are able to distinguish between them is of great interest. Here we argue that scanning tunneling microscopy (STM) experiments in underdoped HTSC, that serve as a local probe of impurity states [4,5], can be used in order to differentiate between at least two classes of proposals.In one class of models the pseudo-gap is ascribed to a precursor pairing amplitude whose phase coherence is destroyed above T c [6,7]. Since such a state exhibits off-diagonal short-range order, particle and hole states get mixed and consequently an induced impurity state is composed of both a particle and a hole-like component. On the other hand in models where the origin of the pseudo-gap is due to a different type of instability (DDW, SDW, stripe order etc.) the property of particle and hole mixing is absent and thus an impurity state has only one either particle or hole-like component. This difference in the local electronic density of states (LDOS) around an impurity can be measured by scanning tunneling microscopy. This prediction can be readily used by STM experiments to detecd for the DDW state in the underdoped cuprates.The local differential conductance measured at bias voltage V by STM is proportional to the local electron density of states. Here we study the LDOS around a magnetic or non-magnetic (U = 0) impurity in a system with competing d-wave superconducting (DSC) and DDW order. The model Hamiltonian is given by (Q = (π, π))where k = 2t (cos k x ) + cos k y ) − 4t (cos k x cos k y ) − µ is the dispersion o...