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Register a new userRobust Nodal Structure of Landau Level Wave Functions Revealed by Fourier Transform Scanning Tunneling Spectroscopy
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Scanning tunneling spectroscopy is used to study the real-space local density of states (LDOS) of a two-dimensional electron system in magnetic field, in particular within higher Landau levels (LL). By Fourier transforming the LDOS, we find a set of n radial minima at fixed momenta for the nth LL. The momenta of the minima depend only on the inverse magnetic length. By comparison with analytical theory and numerical simulations, we attribute the minima to the nodes of the quantum cyclotron orbits, which decouple in Fourier representation from the random guiding center motion due to the disorder. This robustness of the nodal structure of LL wave functions should be viewed as a key property of quantum Hall states.
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Modern high-resolution microscopes, such as the scanning tunneling microscope, 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 underlying structure of fundamental motifs present in an image. However, the Fourier transform fundamentally suffers from severe phase noise when applied to aperiodic images. Here, we report the development of a new algorithm based on nonconvex optimization, applicable to any microscopy modality, 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 novel 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. Our phase sensitive quasiparticle interference imaging results indicate that the pairing symmetry in optimally doped NaFeAs is consistent with a sign-changing s+- order parameter.
Mixing of atoms at the interface was studied for Mn/Fe magnetic hetero-epitaxial layers on Cu(001) by scanning tunneling microscopy/spectroscopy. The formation of a surface alloy was observed when the Mn layer was thinner than 3 atomic layers. From the fourth layer, Fe segregation is suppressed, and a pure Mn surface appears. Accordingly, spectroscopic measurements revealed the electronic difference between the surface alloy and Mn layers. The surface electronic structure of the fourth Mn layer is slightly different from that of the fifth layers, which is attributed to the hybridization of the fourth layer with the underneath Fe-Mn alloy.
We present here an overview of the Fourier Transform Scanning Tunneling spectroscopy technique (FT-STS). This technique allows one to probe the electronic properties of a two-dimensional system by analyzing the standing waves formed in the vicinity of defects. We review both the experimental and theoretical aspects of this approach, basing our analysis on some of our previous results, as well as on other results described in the literature. We explain how the topology of the constant energy maps can be deduced from the FT of dI/dV map images which exhibit standing waves patterns. We show that not only the position of the features observed in the FT maps, but also their shape can be explained using different theoretical models of different levels of approximation. Thus, starting with the classical and well known expression of the Lindhard susceptibility which describes the screening of electron in a free electron gas, we show that from the momentum dependence of the susceptibility we can deduce the topology of the constant energy maps in a joint density of states approximation (JDOS). We describe how some of the specific features predicted by the JDOS are (or are not) observed experimentally in the FT maps. The role of the phase factors which are neglected in the rough JDOS approximation is described using the stationary phase conditions. We present also the technique of the T-matrix approximation, which takes into account accurately these phase factors. This technique has been successfully applied to normal metals, as well as to systems with more complicated constant energy contours. We present results recently obtained on graphene systems which demonstrate the power of this technique, and the usefulness of local measurements for determining the band structure, the map of the Fermi energy and the constant-energy maps.
CrBr$_{3}$ is a layered van der Waals material with magnetic ordering down to the 2D limit. For decades, based on optical measurements, it is believed that the energy gap of CrBr$_{3}$ is in the range of 1.68-2.1 eV. However, controversial results have indicated that the band gap of CrBr$_{3}$ is possibly smaller than that. An unambiguous determination of the energy gap is critical to the correct interpretations of the experimental results of CrBr$_{3}$. Here, we present the scanning tunneling microscopy and spectroscopy (STM/S) results of CrBr$_{3}$ thin and thick flakes exfoliated onto pyropytic graphite (HOPG) surfaces and density functional theory (DFT) calculations to reveal the small energy gap (peak-to-peak energy gap to be 0.57 eV $pm$ 0.04 eV; or the onset signal energy gap to be 0.29 $pm$ 0.05 eV from dI/dV spectra). Atomic resolution topography images show the defect-free crystal structure and the dI/dV spectra exhibit multiple peak features measured at 77 K. The conduction band - valence band peak pairs in the multi-peak dI/dV spectrum agree very well with all reported optical transitions. STM topography images of mono- and bi-layer CrBr$_{3}$ flakes exhibit edge degradation due to short air exposure (~15 min) during sample transfer. The unambiguously determined small energy gap settles the controversy and is the key in better understanding CrBr$_{3}$ and similar materials.
One-atom thick crystalline layers and their vertical heterostructures carry the promise of designer electronic materials that are unattainable by standard growth techniques. In order to realize their potential it is necessary to isolate them from environmental disturbances in particular those introduced by the substrate. But finding and characterizing suitable substrates, and minimizing the random potential fluctuations they introduce, has been a persistent challenge in this emerging field. Here we show that Landau-level (LL) spectroscopy is exquisitely sensitive to potential fluctuations on both local and global length scales. Harnessing this technique we demonstrate that the insertion of an intermediate graphene layer provides superior screening of substrate induced disturbances, more than doubling the electronic mean free path. Furthermore, we find that the proximity of hBN acts as a nano-scale vacuum cleaner, dramatically suppressing the global potential fluctuations. This makes it possible to fabricate high quality devices on standard SiO2 substrates.
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