Peaks In Local Density Of States Research Articles

The quantum confinement effect on the spectrum of near-field thermal radiation by quantum dots

The quantum confinement effect on the spectrum of near-field thermal radiation by periodic and random arrays of quantum dots (QDs) is investigated. The local density of states (LDOS) thermally emitted by QD arrays made of three lead chalcogenides, namely, lead sulfide, lead selenide, and lead telluride, is computed at a near-field distance from the arrays. The dielectric function of the QDs is extracted from their absorption spectra by utilizing an optimization technique. The thermal discrete dipole approximation is used for computing the LDOS. It is shown that the peak wavenumber of near-field LDOS emitted by periodic arrays of lead chalcogenide QDs can be significantly modulated (up to 4490 cm−1) by varying the size of the dots. The LDOS is proportional to the imaginary part of the QDs' polarizability, which peaks at the bandgap energy of the QDs. The bandgap energy of the QDs (and thus the LDOS peak) is significantly affected by the quantum confinement effect, which is size dependent. While the magnitude of thermal radiation by random arrays of QDs can be different from the periodic arrays with the same filling factor by up to ±26%, the LDOS spectrum and peak location are the same for both periodic and random arrays. The peak wavenumber of near-field radiative heat transfer between the QD arrays is also strongly affected by quantum confinement in the QDs, and thus, it can be tuned by changing the size of the QDs.

Odd-frequency superconducting pairing and subgap density of states at the edge of a two-dimensional topological insulator without magnetism

We investigate the emergence and consequences of odd-frequency spin-triplet s-wave pairing in superconducting hybrid junctions at the edge of a two-dimensional topological insulator without any magnetism. More specifically, we consider several different normal-superconductor hybrid systems at the topological insulator edge, where spin-singlet s-wave superconducting pairing is proximity-induced from an external conventional superconductor. We perform fully analytical calculations and show that odd-frequency mixed spin-triplet s-wave pairing arises due to the unique spin-momentum locking in the topological insulator edge state and the naturally non-constant pairing potential profile in hybrid systems. Importantly, we establish a one-to-one correspondence between the local density of states (LDOS) at low energies and the odd-frequency spin-triplet pairing in NS, NSN and SNS junctions along the topological insulator edge; at interfaces the enhancement in the LDOS can directly be attributed to the contribution of odd-frequency pairing. Furthermore, in SNS junctions we show that the emergence of the zero-energy LDOS peak at the superconducting phase $\phi=\pi$ is associated purely with odd-frequency pairing in the middle of the junction.

Electronic properties of emergent topological defects in chiralp-wave superconductivity

Chiral $p$-wave superconductors in applied magnetic field can exhibit more complex topological defects than just conventional superconducting vortices, due to the two-component order parameter (OP) and the broken time-reversal symmetry. We investigate the electronic properties of those exotic states, some of which contain clusters of one-component vortices in chiral components of the OP and/or exhibit skyrmionic character in the \textit{relative} OP space, all obtained as a self-consistent solution of the microscopic Bogoliubov-de Gennes equations. We reveal the link between the local density of states (LDOS) of the novel topological states and the behavior of the chiral domain wall between the OP components, enabling direct identification of those states in scanning tunneling microscopy. For example, a skyrmion always contains a closed chiral domain wall, which is found to be mapped exactly by zero-bias peaks in LDOS. Moreover, the LDOS exhibits electron-hole asymmetry, which is different from the LDOS of conventional vortex states with the same vorticity. Finally, we present the magnetic field and temperature dependence of the properties of a skyrmion, indicating that this topological defect can be surprisingly large in size, and can be pinned by an artificially indented non-superconducting closed path in the sample. These features are expected to facilitate the experimental observation of skyrmionic states, thereby enabling experimental verification of chirality in emerging superconducting materials.

Evidence for Time-Reversal Symmetry Breaking of the Superconducting State near Twin-Boundary Interfaces in FeSe Revealed by Scanning Tunneling Spectroscopy

Junctions and interfaces consisting of unconventional superconductors provide an excellent experimental playground to study exotic phenomena related to the phase of the order parameter. Not only the complex structure of unconventional order parameters have an impact on the Josephson effects, but also may profoundly alter the quasi-particle excitation spectrum near a junction. Here, by using spectroscopic-imaging scanning tunneling microscopy, we visualize the spatial evolution of the local density of states (LDOS) near twin boundaries (TBs) of the nodal superconductor FeSe. The $\pi/2$ rotation of the crystallographic orientation across the TB twists the structure of the unconventional order parameter, which may, in principle, bring about a zero-energy LDOS peak at the TB. The LDOS at the TB observed in our study, in contrast, does not exhibit any signature of a zero-energy peak and an apparent gap amplitude remains finite all the way across the TB. The low-energy quasiparticle excitations associated with the gap nodes are affected by the TB over a distance more than an order of magnitude larger than the coherence length $\xi_{ab}$. The modification of the low-energy states is even more prominent in the region between two neighboring TBs separated by a distance $\approx7\xi_{ab}$. In this region the spectral weight near the Fermi level ($\approx\pm$0.2~meV) due to the nodal quasiparticle spectrum is almost completely removed. These behaviors suggest that the TB induces a fully-gapped state, invoking a possible twist of the order parameter structure which breaks time-reversal symmetry.

Electronic structure for a topological insulator with a smoothly varying step on surface

We study the penetration depth (PD) of surface state into the bulk, the local density of states (LDOS) and the spin-polarized STM tip tunneling conductance (TG) for a smoothly varying step described by an asymptotic model, on the surface of a three-dimensional (3D) topological insulator (TI). Using curvilinear coordinates for calculation, we find that the PD shows two peaks near step edges with maximum surface curvature and a dip value of flat surface at step middle with zero curvature. In contrast, the LDOS exhibits a double valley (dip) pattern, in which it rapidly declines from the highest value for flat surface to the dip value near step edges, and then shows a small peak at step middle. This interesting small peak is in good agreement with experimentally observed LDOS peak within a step of definite span on a 3D TI surface. Moreover, the calculated surface spin-polarized STM tip TG also confirms the LDOS qualitatively. The findings here may provide a further understanding of 3D TI surface with step line defects.

Origin of the transition voltage in gold–vacuum–gold atomic junctions

The origin and the distance dependence of the transition voltage of gold–vacuum–gold junctions are investigated by employing first-principles quantum transport simulations. Our calculations show that atomic protrusions always exist on the electrode surface of gold–vacuum–gold junctions fabricated using the mechanically controllable break junction (MCBJ) method. The transition voltage of these gold–vacuum–gold junctions with atomically sharp electrodes is determined by the local density of states (LDOS) of the apex gold atom on the electrode surface rather than by the vacuum barrier shape. More specifically, the absolute value of the transition voltage roughly equals the rising edge of the LDOS peak contributed by the 6p atomic orbitals of the gold atoms protruding from the electrode surface, whose local Fermi level is shifted downwards when a bias voltage is applied. Since the LDOS of the apex gold atom depends strongly on the exact shape of the electrode, the transition voltage is sensitive to the variation of the atomic configuration of the junction. For asymmetric junctions, the transition voltage may also change significantly depending on the bias polarity. Considering that the occurrence of the transition voltage requires the electrode distance to be larger than a critical value, the interaction between the two electrodes is actually rather weak. Consequently, the LDOS of the apex gold atom is mainly determined by its local atomic configuration and the transition voltage only depends weakly on the electrode distance as observed in the MCBJ experiments.

Observation of Landau-level-like quantization at 77 K along a strained-induced graphene ridge

Recent studies show that the electronic structures of graphene can be modified by strain, and it was predicted that strain in graphene can induce peaks in the local density of states (LDOS), mimicking Landau levels (LLs) generated in the presence of a large magnetic field. Here we report the scanning tunneling spectroscopy (STS) observation of nine strain-induced peaks in LDOS at 77 K along a graphene ridge created when the graphene layer was cleaved from a sample of highly oriented pyrolytic graphite (HOPG). The energies of these peaks follow the progression of LLs of massless ``Dirac fermions'' (DFs) in a magnetic field of 230 T. The results presented here suggest a possible route to realize zero-field quantum Hall-like effects at 77 K.

Single vortex structure in two models of iron pnictide s± superconductivity

The structure of a single vortex in a FeAs superconductor is studied in the framework of two formulations of superconductivity for the recently proposed sign-reversed s-wave (s±) scenario: (i) a continuum model taking into account the existence of an electron and a hole band, with a repulsive local interaction between the two; (ii) a lattice tight-binding model with two orbitals per unit cell and a next-nearest-neighbour attractive interaction. In the first model, the local density of states (LDOS) at the vortex centre, as a function of energy, exhibits a peak at the Fermi level, while in the second model the LDOS peak deviates from the Fermi level, and its energy depends on band filling. An impurity located outside the vortex core has little effect on the LDOS peak, but an impurity close to the vortex core can almost suppress it and modify its position.

Bound states induced by a single donor in a semiconductor quantum well: A scanning tunneling spectroscopy study

Low-temperature scanning tunneling spectroscopy under ultrahigh vacuum was used to investigate an In 0.53Ga 0.47As surface quantum well (QW) grown by molecular beam epitaxy. The electronic local density of states (LDOS) was probed with nanometer-scale resolution around native point defects located at the QW surface. In LDOS spectra acquired in the vicinity of a single point defect, a sharp peak was observed near each subband minimum, which indicates the formation of donor bound states. The LDOS peak intensity was measured as a function of distance from the point defect in order to estimate the Bohr radius of the donor bound states.

Odd-frequency pairing in normal-metal/superconductor junctions

We theoretically study the induced odd-frequency pairing states in ballistic normal-metal/superconductor (N/S) junctions where a superconductor has even-frequency symmetry in the bulk and a normal-metal layer has an arbitrary length. Using the quasiclassical Green's function formalism, we demonstrate that, quite generally, the pair amplitude in the junction has an admixture of an odd-frequency component due to the breakdown of translational invariance near the N/S interface where the pair potential acquires spatial dependence. If a superconductor has an even-parity pair potential (spin-singlet $s$-wave or spin-singlet ${d}_{xy}$-wave state), the odd-frequency pairing component with odd parity is induced near the N/S interface, while in the case of an odd-parity pair potential (spin-triplet ${p}_{x}$ wave) the odd-frequency component with even parity is generated. We show that in conventional $s$-wave junctions, the amplitude of the odd-frequency pairing state is strongest in the case of a full-transparency N/S interface and is enhanced at energies corresponding to the peaks in the local density of states (LDOS). In ${p}_{x}$- and ${d}_{xy}$-wave junctions, the amplitude of the odd-frequency component on the S side of the N/S interface is enhanced at zero energy where the midgap Andreev resonant state (MARS) appears due to the sign change of the pair potential. The odd-frequency component extends into the N region and exceeds the even-frequency component at energies corresponding to the LDOS peak positions, including the MARS. At the edge of the N region the odd-frequency component is nonzero while the even-frequency one vanishes. We show that the concept of the odd-frequency pairing state plays a pivotal role to interpret a number of phenomena in nonuniform superconducting systems, like McMillan-Rowell and midgap Andreev resonance states.

スピン偏極走査トンネル顕微分光(SP-STM-STS)の原理とMn(001)のスピン依存局所状態密度

Development of spin-polarized scanning tunnel microscopy/spectroscopy (SP-STM/STS) is reviewed and the working principle of SP-STM/STS is discussed with paying special attention to the obtention of the spin-resolved local density of states (LDOS). We discuss the case of bct-Mn epitaxial films grown on Fe(001) whisker. The bct-Mn(001) layers couple antiferromagnetically with the adjacent layers and there is a spin-dependent LDOS peak above the Fermi level, to which highly-polarized two dz2 surface states contribute. The highest lateral magnetic resolution obtained in this system is 0.4 nm. Performing a detailed analysis of the SP-STS measurements, we conclude that the bct-Mn(001) surface has a 60±16% polarization at the energy position of the spin-dependent LDOS peak.

Scanning tunneling microscopy and spectroscopy studies of graphite edges

We studied experimentally and theoretically the electronic local density of states (LDOS) near single-step edges at the surface of exfoliated graphite. In scanning tunneling microscopy measurements, we observed the ( 3 × 3 ) R 30 ° and honeycomb superstructures extending over 3–4 nm both from the zigzag and armchair edges. Calculations based on a density-functional-derived non-orthogonal tight-binding model show that these superstructures can coexist if the two types of edges admix each other in real graphite step edges. Scanning tunneling spectroscopy measurements near the zigzag edge reveal a clear peak in the LDOS at an energy below the Fermi energy by 20 meV. No such a peak was observed near the armchair edge. We concluded that this peak corresponds to the “edge state” theoretically predicted for graphene ribbons, since a similar prominent LDOS peak due to the edge state is obtained by the first principles calculations.

Computational study of the effect of surface defects and steps on field-stimulated exoelectron emission from aluminum

The electronic structures of a clean Al (001) surface, of a stepped Al (001) surface, and of an Al(001) surface with vacancies were investigated by the first-principles calculation to elucidate the emission mechanism of field-stimulated exoelectrons from Al tip surfaces. The results show that vacancies at the Al (001) surface slightly increase local density of states (LDOS) in the occupied states, and that monoatomic steps significantly increase LDOS at 0.36 eV above Fermi level in the unoccupied states. The LDOS peak position in the unoccupied states at the stepped surface is close to the trap level of field-stimulated exoelectrons measured in our previous experiments, and it is concluded that the monoatomic steps at Al surfaces can play a role of exoelectron traps.

Scanning tunneling spectroscopy analysis with a triangular inverse transfer matrix and its application to reduced SrTiO3 (110) surface

A straightforward method to deduce sample local density of states (LDOS) from the current–voltage characteristics ( I – V ) raw data in scanning tunneling spectroscopy (STS) is presented. The method is based on the relation between the I – V spectrum and the LDOS, both of which are treated as one-dimensional vectors: the I – V is generated from the LDOS by operating a triangular transfer matrix M . Then the LDOS is readily calculated from the I – V by operating the inverse matrix M −1 , which is also triangular. The method is an alternative for the conventional method to take (d I /d V )( V / I ), which often causes artificial peaks in LDOS at the onsets of I – V . Each row of M is determined by the tip density of states (DOS) and the barrier profile for the corresponding bias voltage. The tip DOS will be calculated from the I – V values measured at different tip-to-sample distances if the tip and sample have the same DOS and the barrier profile is symmetrical. As an example, the LDOS is calculated for the reduced SrTiO 3 (110) on which the electronic states show metallic character depending on the annealing condition and sites.

First-principles calculational study of the exoelectron emission of oxygen-adsorbed aluminum surfaces

The first-principles calculation, based upon the ultrasoft pseudopotential, was carried out on clean and O-adsorbed Al surfaces in order to investigate the emission mechanism of exoelectrons from Al surfaces. The Al (001) surface was chosen to simulate the previous experiments using Al tips [Tagawa et al., Appl. Surf. Sci. 72, 259 (1993)]. The ultrasoft pseudopotential-based first-principles calculation provided a lattice constant within 1% of the difference from the experimental value and also showed good agreement with the surface states measured by an angle-resolved photoelectron spectroscopy. The computational results indicated a high local density of states (LDOS) near the Fermi level, exceeded by the O adsorption of the Al (001) surface. It was also calculated that the LDOS peak was located 0.2 eV below the Fermi level of the O-covered Al (001). Considering the work function of the clean Al (001) surface (4.4 eV) and its decrease due to the O adsorption (-0.6 eV), this electron-filled LDOS peak was located 4.0 eV below the vacuum level. Calculated results revealed good agreement with the experimental data showing the exoelectron peak at 4.0 eV below the vacuum level [Tagawa et al., Appl. Phys. Lett. 61, 1471 (1992)]. From the first-principles calculation results reported here, the low work-function patch (LWP) model was introduced to the Al surface. This LWP model explained the origin of the exoelectron emission phenomenon in the early stage of oxidation on the Al surface.

Self-consistent electronic structure of the chlorine-adsorbed silicon (111) surface

A first-principles self-consistent-field calculation of the electronic structure of the Si(111) surface with a layer of chemisorbed Cl atoms has been performed by means of the method of linear combinations of atomic orbitals. A thin-film crystal consisting of twelve infinite (111) Si layers plus one layer of Cl on each side is considered. The crystal potential is expressed as a superposition of localized function at each site, and the basis functions consist of two-dimensional Bloch sums of the $1s$,$2s$,$2p$,$3s$,$3p$ atomiclike functions and of contracted-Gaussian orbitals for each layer of the film. By means of the Gaussian techique, all the multicenter integrals are evaluated exactly and the Hamiltonian matrix elements are computed by summing these integrals over all the lattice points to convergence. The solution of the one-electron Hamiltonian is carried to self-consistency. Application of Mulliken's method of population analysis enables us to determine the fraction of electron charge allocated to each layer for a given wave function and quantitatively characterize the localization of the surface states. At the $\overline{\ensuremath{\Gamma}}$ point of the two-dimensional Brillouin zone, we find a surfacelike $\ensuremath{\sigma}$ state at -13.4 eV (relative to the vacuum level) and a $\ensuremath{\pi}$ surface state at -10.7 eV. The localized behavior of the latter persists at ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{\ensuremath{\parallel}}$ points on the $\overline{\ensuremath{\Gamma}}\overline{M}$ line. The calculated local density of states (LDS) for the valence band agrees well with the experimental photoemission data. In the lower conduction band we find one LDS peak due to surface states at -3.4 eV which corresponds closely to the electron-energy-loss data. Estimates of the LDS for the upper conduction band have been made and the results are in reasonable accord with experiment. A population-analysis calculation indicates a net charge of -0.35 $e$/ atom ($e$ being proton charge) for the Cl layer and 0.27 $e$/ atom for the adjacent Si layer with some residual ionicity in the next few layers.