Evidence of hole-electron quasiparticle interference in ErSi2 semimetal by Fourier-transform scanning tunneling spectroscopy

Dictionary learning in Fourier-transform scanning tunneling spectroscopy

Modern high-resolution microscopes are commonly used to study specimens that have dense and aperiodic spatial structure. Extracting meaningful information from images obtained from such microscopes remains a formidable challenge. Fourier analysis is commonly used to analyze the structure of such images. However, the Fourier transform fundamentally suffers from severe phase noise when applied to aperiodic images. Here, we report the development of an algorithm based on nonconvex optimization that directly uncovers the fundamental motifs present in a real-space image. Apart from being quantitatively superior to traditional Fourier analysis, we show that this algorithm also uncovers phase sensitive information about the underlying motif structure. We demonstrate its usefulness by studying scanning tunneling microscopy images of a Co-doped iron arsenide superconductor and prove that the application of the algorithm allows for the complete recovery of quasiparticle interference in this material.

Aperiodic structure imaging suffers limitations when utilizing Fourier analysis. The authors report an algorithm that quantitatively overcomes these limitations based on nonconvex optimization, demonstrated by studying aperiodic structures via the phase sensitive interference in STM images.

Long-wavelength local density of states oscillations near graphene step edges

Using scanning tunneling microscopy and spectroscopy, we have studied the local density of states (LDOS) of graphene over step edges in boron nitride. Long-wavelength oscillations in the LDOS are observed with maxima parallel to the step edge. Their wavelength and amplitude are controlled by the energy of the quasiparticles allowing a direct probe of the graphene dispersion relation. We also observe a faster decay of the LDOS oscillations away from the step edge than in conventional metals. This is due to the chiral nature of the Dirac fermions in graphene.

Electron standing waves on the GaN(0001)-pseudo (1 × 1) surface: a FT-STM study at room temperature

We report the direct imaging of standing waves on a GaN(0001)-pseudo (1 × 1) metallic surface, which consists of two atomic Ga layers with the top layer incommensurate. Two types of periodic oscillation are observed by scanning tunneling microscopy at room temperature. The longer wavelength standing waves are due to electron scattering by dislocation-induced steps and two-dimensional InN islands. The localized shorter wavelength waves are attributed to a structural transition of the incommensurate Ga bilayer to a tetrahedral Ga bilayer after the growth of the InN islands.

Effect of a single localized impurity on the local density of States in monolayer and bilayer graphene

We use the T-matrix approximation to analyze the effect of a localized impurity on the local density of states in monolayer and bilayer graphene. For monolayer graphene the Friedel oscillations generated by intranodal scattering obey an inverse-square law, while the internodal ones obey an inverse law. In the Fourier transform this translates into a filled circle of high intensity in the center of the Brillouin zone, and empty circular contours around its corners. For bilayer graphene both types of oscillations obey an inverse law.