Boundary effect on CDW: Friedel oscillations, STM image

– We study the effect of open boundary condition on charge density waves (CDW). The electron density oscillates rapidly close to the boundary, and additional non-oscillating terms (∼ ln(r)) appear. The Friedel oscillations survive beyond the CDW coherence length (vF /∆), but their amplitude gets heavily suppressed. The scanning tunneling microscopy image (STM) of CDW shows clear features of the boundary. The local tunneling conductance becomes asymmetric with respect to the Fermi energy, and considerable amount of spectral weight is transferred to the lower gap edge. Also it exhibits additional zeros reflecting the influence of the boundary. Introduction. – The behaviour of charge density waves (CDW) in bulk systems has received considerable attention in the last few decades [1]. But unlike mesoscopic superconductors, only a few attempts have been made to explore the response of CDW in mesoscopic systems [2–5]. These mainly concern charge density wave junctions, and concentrate on tunneling between CDW and other systems. In this letter, we are going to study the effect of an open end along the CDW chain on the electron density and scanning tunneling microscope (STM) image, as shown in fig. 1. As a model we consider a quasi-one dimensional charge density wave, treated in the meanfield approximation. Due to quasi-one dimensionality, the effective mass of the electrons in the interchain direction is much larger than along the chains, and it is reasonable to assume that the main affect of neighbouring chains is to suppress the thermal fluctuations of the order parameter [1,4]. Impurities in low dimensional systems tend to cut the sample. So instead of introducing an external potential representing the impurity, we shall mimic its effect by a semi infinite chain, namely by open boundary condition [6]. Hence the present model is thought to describe impurities in the strong pinning limit, or the behaviour of finite CDW with open boundaries. Similar models in one dimensional systems have extensively been studied over the years [7–9]. Experimentally, in-chain tunneling studies have been made on CDW systems [10,11], and most of STM scans were performed on bulk CDW materials such as Fe doped NbSe3 [12] or NbSe2 [13], where boundary condition or single impurity results were not reported. CDW film growth and structuring have been started from oxide Rb0.30MoO3 (blue bronze) [11, 14]