Quasiparticle echoes in scanning tunneling microscopy

Abstract

It is shown that the local density of states (LDOS), measured in an Scanning Tunneling Microscopy (STM) experiment, at a single tip position contains oscillations as a function of energy, due to quasiparticle interference, which is related to the positions of nearby scatterers. We propose a method of STM data analysis based on this idea, which can be used to locate the scatterers. In the case of a superconductor, the method can potentially distinguish the nature of the scattering by a particular impurity. PACS numbers: 74.55.+v,72.10.Fk,73.20.At,74.72.ah Scanning Tunneling Microscopy (STM), which measures the "local density of states" (LDOS) as a function of position and energy set by the bias voltage, has opened the door to imaging the sub-nanoscale topography and electronic structure of materials, including normal metals [1] and especially cuprate superconductors [2,3,4,5,6,7,8,9].The dispersion relations of (Landau or Bogoliubov) quasiparticles may be extracted from STM data on normal metals [10,11] and superconductors [13], via the inverse method called Fourier transform scanning tunneling spectroscopy (FT-STS) [10,13], or directly in real space [11]. This technique is based on the fact that impurities produce spatial modulations of the LDOS in their vicinity -standing waves in the electronic structure that generalize the Friedel oscillations found in metals at the Fermi energy. In the cuprates BSCCO and CaCuNaOCl [13], experiments showed these quasiparticle oscillations were dominated by eight wavevectors that connect the tips of "banana" shaped energy contours in reciprocal space, the so-called Octet model as explained theoretically [12]. For optimally doped samples, the dispersion inferred from these wavevectors agrees well with d-wave BCS theory indicating the existence of well-defined BCS quasiparticles in this regime.The central observation of this paper is that the same Friedel-like oscillations of the LDOS, analyzed in the space/momentum domain by FT-STS, are also manifested in the energy/time domain. Our analysis shows that the small impurity-dependent modulations of the LDOS have a period, in energy, inversely proportional to the time required by a quasiparticle wavepacket to travel to the nearby impurities and back -hence we call it "quasiparticle echo". From this, in principle, one can determine the location and (in a superconductor) the nature of the point scatterers in a particular sample.Quasiparticle echo -The basic idea of the LDOS modulations may be understood semiclassically. The LDOS N ( r; ω) is defined as −(1/π)ImG( r, r; ω), the time Fourier transform of the local (retarded) Green's function G( r, r; t). Imagine a bare electron wavepacket (centered on energy ω) is injected at time t = 0 at point r in a two-dimensional material: the Green's function expresses its subsequent evolution. Assuming there are well-defined quasiparticles at this energy with dispersion E( k); then for every wavevector k on the energy contour E( k) = ω, the wavepacket has a component spreading outwards at the...

Extracting Quasiparticle Lifetimes from STM experiments

“…In this sense, we would do better than ARPES where the signal is averaged over an area of the sample equal to the beam size, iff the STM experiment has good signal to noise. Similarly, we can overcome inhomogeneity issues for dirty systems, in which case we would concentrate this analysis on a homogeneous patch similar in spirit to Hudson's analysis [19] and to a previous work [20].…”