Local Density Of States Pattern Research Articles

Making an artificial px,y -orbital honeycomb electron lattice on a metal surface

We theoretically demonstrate that the desired ${p}_{x,y}$-orbital honeycomb electron lattice can be readily realized by arranging CO molecules into a hexagonal lattice on a Cu(111) surface with scanning tunneling microscopy (STM). The electronic structure of the Cu surface states in the presence of CO molecules is calculated with various methods, i.e., density functional theory (DFT) simulations, the muffin-tin potential model, and the tight-binding model. Our calculations indicate that, by measuring the local density of states (LDOS) pattern using STM, the $p$-orbital surface bands can be immediately identified in experiment. We also give an analytic interpretation of the $p$-orbital LDOS pattern with the $k\ifmmode\cdot\else\textperiodcentered\fi{}p$ method. Meanwhile, different from the case of graphene, the $p$-orbital honeycomb lattice has two kinds of edge states, which can also be directly observed in STM experiment. Our work points out a feasible way to construct a ${p}_{x,y}$-orbital honeycomb electron lattice in a real system, which may have exotic properties, such as Wigner crystal, ferromagnetism, $f$-wave superconductivity, and the quantum anomalous Hall effect. Furthermore, we also propose a simple way to calculate and identify the modified Cu surface bands in the Cu/CO systems with the DFT simulations. Considering the recent works about a $p$-orbital square lattice in similar systems [M. R. Slot et al., Nat. Phys. 13, 672 (2017); L. Ma et al., Phys. Rev. B 99, 205403 (2019)], our work once again illustrates that the artificial electron lattice on a metal surface is an ideal platform to study the orbital physics in a controllable way.

Quasiparticle Bound States around Fractional Vortices in s-wave Superconductor

Since the experimental formation of a vortex with a fractional quantized magnetic flux in a thin superconducting $s$-wave bi-layer was recently reported, we calculate the local density of states (LDOS) around two half quantum vortices in a $s$-wave superconductor on the basis of the quasiclassical Eilenberger theory to investigate the effect of the phase discontinuity. We show that the LDOS pattern around fractional vortices is qualitatively different from that around conventional vortex. We find that the novel bow-tie-shaped bound states appear in the high energy region, which can be an evidence for the fractional vortices through scanning tunneling microscopy/spectroscopy. We also show that the system with $n$ fractional vortices with the vorticity $1/n$ has a similarity to the Josephson junctions.

Quasiparticle scattering off phase boundaries in epitaxial graphene

We investigate the electronic structure of terraces of single layer graphene (SLG) by scanning tunnelling microscopy (STM) on samples grown by thermal decomposition of 6H-SiC(0001) crystals in ultra-high vacuum. We focus on the perturbations of the local density of states (LDOS) in the vicinity of edges of SLG terraces. Armchair edges are found to favour intervalley quasiparticle scattering, leading to the LDOS superstructure already reported for graphite edges and more recently for SLG on SiC(0001). Using the Fourier transform of LDOS images, we demonstrate that the intrinsic doping of SLG is responsible for a LDOS pattern at the Fermi energy which is more complex than for neutral graphene or graphite, since it combines local superstructure and long range beating modulation. Although these features have already been reported by Yang et al (2010 Nano Lett. 10 943–7) we propose here an alternative interpretation based on simple arguments classically used to describe standing wave patterns in standard two-dimensional systems. Finally, we discuss the absence of intervalley scattering off other typical boundaries: zig-zag edges and SLG/bilayer graphene junctions.

Spatial Imaging of Two-Dimensional Electronic States in Semiconductor Quantum Wells

We measure the spatial distribution of the local density of states (LDOS) at cleaved surfaces of InAs/GaSb isolated quantum wells and double quantum wells (DQWs) by low-temperature scanning tunneling spectroscopy. Distinct standing wave patterns of LDOS corresponding to subbands are observed. These LDOS patterns and subband energies agree remarkably well with simple calculations with tip-induced band bending. Furthermore, for the DQWs, coupling of electronic states between the quantum wells is also clearly observed.

Andreev States near Short-Ranged Pairing Potential Impurities

We study Andreev states near atomic scale modulations in the pairing potential in both s- and d-wave superconductors with short coherence lengths. For a moderate reduction of the local gap, the states exist only close to the gap edge. If one allows for local sign changes of the order parameter, however, resonances can occur at energies close to the Fermi level. The local density of states (LDOS) around such pairing potential defects strongly resembles the patterns observed by tunneling measurements around Zn impurities in Bi2Sr2CaCu2O8+x (BSCCO). We discuss how this phase impurity model of the Zn LDOS pattern can be distinguished from other proposals experimentally.

Comparing measured and calculated local density of states in a disordered two-dimensional electron system

The local density of states (LDOS) of the adsorbate induced two-dimensional electron system (2DES) on n-InAs(110) is studied by low-temperature scanning tunneling spectroscopy. In contrast to a similar 3DES, the 2DES LDOS exhibits 20 times stronger corrugations and rather irregular structures. Both results are interpreted as a consequence of weak localization. Fourier transforms of the LDOS reveal that the k-values of the unperturbed 2DES still dominate the 2DES, but additional lower k-values contribute significantly. To clarify the origin of the LDOS patterns, we measure the potential landscape of the same 2DES area allowing to calculate the expected LDOS from the single particle Schrödinger equation and to directly compare it with the measured one.

Direct comparison between potential landscape and local density of states in a disordered two-dimensional electron system.

The local density of states (LDOS) of the adsorbate-induced two-dimensional electron system (2DES) on n-InAs(110) is studied by scanning tunneling spectroscopy. In contrast to a similar 3DES, the 2DES LDOS exhibits 20 times stronger corrugations and rather irregular structures. Both results are interpreted as consequences of weak localization. Fourier transforms of the LDOS reveal that the k values of the unperturbed 2DES still dominate the 2DES, but additional lower k values contribute. To clarify the origin of the LDOS patterns, we measure the potential landscape of the 2DES area. We use it to calculate the expected LDOS and find reasonable agreement between calculation and experiment.