Local Density Of States Spectrum Research Articles

Manipulating chiral Majorana mode with additional potential in superconductor-Chern insulator heterostructures

We employed the self-consistent Bogoliubov–de Gennes equations to explore the states of chiral Majorana mode in quantum anomalous Hall insulators in proximity to a superconductor, leading to the development of an extensive topological phase diagram. Our investigation focused on how an additional potential affects the separation of chiral Majorana modes across different phase conditions. We substantiated our findings by examining the zero-energy Local Density of States spectrum and the probability distribution of the chiral Majorana modes. We established the universality of chiral Majorana mode separation by applying an additional potential. This finding serves as a vital resource for future endeavors aimed at controlling and detecting these particles, thereby contributing to the advancement of quantum computing and condensed matter physics.

Atomic collapse in graphene quantum dots in a magnetic field

We investigate finite size and external magnetic field effects on the atomic collapse due to a Coulomb impurity placed at the center of a hexagonal graphene quantum dot within tight binding and mean-field Hubbard approaches. For large quantum dots, the atomic collapse effect persists when the magnetic field is present, characterized by a series of Landau level crossings and anticrossings, in agreement with previous bulk graphene results. However, we show that a new regime arises if the size of the quantum dot is comparable to or smaller than the magnetic length: While the lowest bound states cross the Fermi level at a lower value of coupling constant β<0.5 , a size independent critical coupling constant βc∗>0.5 emerges in the local density of states spectrum, which increases with the applied magnetic field. These effects are found to be persistent in the presence of electron–electron interactions within mean-field Hubbard approximation.

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.

Scanning tunneling microscopy identification of van Hove singularities and negative thermal expansion in highly oriented pyrolytic graphite with hexagonal moiré superlattices

We report a novel investigation on the structural, electronic and magnetic properties of highly-oriented-pyrolytic-graphite (HOPG) by employing STM/S, TEM and SQUID. Van Hove singularities (vHs) were identified by STS-acquisition of local-density-of-states spectra (LDOS) acquired from moiré-superlattice-periodicities D ~0.5 nm (θrot ~28.6°), ~2 nm (θrot of ~7.08°) and ~ 4 nm (θrot ~3.6°). A possible interlayer-coupling- or moiré-thickness-induced variation of the vHs-separation-parameter was identified. Investigation of the spatial-distribution of the moiré-superlattices by exfoliation revealed also D ~13.87 nm (θrot ~1.02°), ~13.0 nm (θrot ~1.09°), ~12.65 nm (θrot ~1.12°) and ~2.03 nm (θrot ~7.0°). These observations were further supported by additional LDOS spectra acquired on HOPG from moiré-superlattice-periodicities D ~8 nm (θrot ~1.8°). In the latter, the unusual presence of four vHs peaks evidenced the existence of multiple rotational effects between internal sublattices. Extended analyses were further performed by T-XRD from 12 K to 298 K. Unknown peak-features exhibiting unusual T-dependent shifts were analysed at 2θ ~ 21° (Fig. 6A-C) and ~ 43° (Fig. 6D). ZFC and FC-signals from the exfoliated lamellae further evidenced an anisotropic ferromagnetic behaviour, possibly involving the coexistence of (1) disorder induced percolative ferromagnetism and (2) additional magnetic components arising from the locally twisted sublattices, which were found to exhibit the moiré superlattices.

Electronic structure of the ideal Si (001) surface by first-principles calculations

The electronic structure of Si nanofilms with an ideal unreconstructed surface (001) was modeled using the full-potential linearized augmented plane wave method. Total and local density of states spectra are calculated. The transformation of the electronic structure of nanofilms with an increase in their thickness from 1 to 10 silicon elementary cells along the crystallographic direction Z (4-40 monoatomic layers) is considered. A layer-by-layer analysis of a nanofilm electronic structure with a thickness of 40 atomic layers was performed.

Tailoring emission spectra by using microcavities

We present a theoretical model to describe emission spectrum of an emitter in a micro-cavity. Our model proposes that the spectrum in a metal micro-cavity depends on the product of the emission spectrum in free space and the local density of states (LDOS) in the cavity which the emitter is placed in. Since Purcell effect can enhance LDOS of a micro-cavity, the emission intensity of an emitter is directly proportional to LDOS depending on the geometry of microcavity. Thus, the model predicts that the spectrum of an emitter can be modified as a narrow spectrum in microcavity possessing sharp LDOS spectrum, also can be modified as broadband spectrum with broadband LDOS spectrum. Finite-difference time-domain (FDTD) numerical simulations support our prediction.

Nanoscale superconductors: Dual Friedel oscillations of single quasiparticles and corresponding influence on determination of the gap energy

By numerically solving the Bogoliubov-de Gennes equations, Friedel oscillations of single quasiparticles in nanoscale superconducting square disks are systematically studied. We find that Anderson's approximation, which assumes the electron- and hole-like wave functions of a quasiparticle are proportional to a certain single-electron wave function, breaks down under strong quantum confinement, i.e. the electron- and hole-like components of single quasiparticles may show Friedel oscillations with different amplitude and normalized profile, especially when the corresponding single-electron energy moves away from the Fermi level. Such oscillation behavior is referred as dual Friedel oscillations of single quasiparticles, and is expected to be observed the local density of states spectrum. The resulting density of states (DOS) becomes asymmetric and shows significant oscillations with respect to the applied bias.

Topological Fulde-Ferrell and Larkin-Ovchinnikov states in spin-orbit-coupled lattice system

The spin-orbit coupled lattice system under Zeeman fields provides an ideal platform to realize exotic pairing states. Notable examples range from the topological superfluid/superconducting (tSC) state, which is gapped in the bulk but metallic at the edge, to the Fulde-Ferrell (FF) state (having a phase-modulated order parameter with a uniform amplitude) and the Larkin-Ovchinnikov (LO) state (having a spatially varying order parameter amplitude). Here, we show that the topological FF state with Chern number ($\mathcal{C}=-1$) (tFF$_{1}$) and topological LO state with $\mathcal{C}=2$ (tLO$_{2}$) can be stabilized in Rashba spin-orbit coupled lattice systems in the presence of both in-plane and out-of-plane Zeeman fields. Besides the inhomogeneous tSC states, in the presence of a weak in-plane Zeeman field, two topological BCS phases may emerge with $\mathcal{C}=-1$ (tBCS$_{1}$) far from half filling and $\mathcal{C}=2$(tBCS$_{2}$) near half filling. We show intriguing effects such as different spatial profiles of order parameters for FF and LO states, the topological evolution among inhomogeneous tSC states, and different non-trivial Chern numbers for the tFF$_{1}$ and tLO$_{1,2}$ states, which are peculiar to the lattice system. Global phase diagrams for various topological phases are presented for both half-filling and doped cases. The edge states as well as local density of states spectra are calculated for tSC states in a 2D strip.

Novel π-type vortex in a nanoscale extreme type-II superconductor: Induced by quantum-size effect

By numerically solving the Bogoliubov-de Gennes equations, we report a novel π-type vortex state whose order parameter near the core undergoes an extraordinary π-phase change for a quantum-confined extreme type-II s-wave superconductor. Its supercurrent behaves as the cube of the radial coordinate near the core, and its local density of states spectrum exhibits a significant negative-shifted zero-bias peak. Such π-type vortex state is induced by quantum-size effect, and can survive thermal smearing at temperatures up to a critical value Tτ. The Anderson's approximation indicates that the π-type vortex may remain stable under sufficiently week magnetic field in the case less deep in the type-II limit. Moreover, we find that its appearance is governed by the sample size and kFξ0 with kF the Fermi wave number and ξ0 the zero-temperature coherence length. Similar effects may be expected in quantum-confined ultracold superfluid Fermi gasses, or even high-Tc superconductors with proper kFξ0 value.

Proposed detection of time-reversal symmetry in topological surface states

By employing T-matrix approach, we investigate a nonmagnetic impurity located on the surface of three-dimensional topological insulators, where the time reversal symmetry is preserved. It is shown that the images of the local density of states (LDOS) around the single impurity have the dip-hump structures with six-fold symmetry at different bias voltages. The peaks are produced by quasiparticle interference while the local minima at the backscattering wave vectors are due to the absence of backscatterings. With increasing the bias voltage, the peaks and dips move forward to the location of the impurity. These dips at the backscattering wave vectors in the LDOS spectra can be regarded as a signature of the time reversal symmetry in the topological surface states, which could be observed by scanning tunneling microscopy.

Impurity Effect as a Probe of the Pairing Symmetry in BiS2-Based Superconductors

The impurity effects are studied for the BiS_{2}- layered superconductors based on a two orbital model with the Bogoliubov-de-Gennes technique. The superconducting critical temperature (T_{c}) as a function of the mpurity concentration is calculated. Significant reduction of T_{c} is found for spin singlet nearest-neighboring paring d-wave state and the spin triplet next-nearest-neighboring (NNN) paring p-wave state, while no depression of T_{c} for isotropic s-wave state. The single impurity effects for various paring states are also explored. The impurity resonance peak in the local density of states spectrum is found only for the d-wave state. For the spin triplet NNN paring p-wave state, two in-gap peaks occur in the case of positive impurity potential; and a single in-gap peak is found for the negative impurity potential, which shifts towards to lower energy with decreasing the potential strength. These results can be used to detect the paring symmetry of the BiS_{2}- based superconductors.

Two-band superconductivity in doped SrTiO3films and interfaces

We investigate the possibility of multi-band superconductivity in SrTiO$_{3}$ films and interfaces using a two-dimensional two-band model. In the undoped compound, one of the bands is occupied whereas the other is empty. As the chemical potential shifts due to doping by negative charge carriers or application of an electric field, the second band becomes occupied, giving rise to a strong enhancement of the transition temperature and a sharp feature in the gap functions, which is manifested in the local density of states spectrum. By comparing our results with tunneling experiments in Nb-doped SrTiO$_{3}$, we find that intra-band pairing dominates over inter-band pairing, unlike other known multi-band superconductors. Given the similarities with the value of the transition temperature and with the band structure of LaAlO$_{3}$/SrTiO$_{3}$ heterostructures, we speculate that the superconductivity observed in SrTiO$_{3}$ interfaces may be similar in nature to that of bulk SrTiO$_{3}$, involving multiple bands with distinct electronic occupations.

Splitting of the Fano resonance by Coulomb interactions in a two-dot quantum ring

We study the splitting of the Fano resonance in a Aharonov–Bohm interferometer with a quantum dot in each of its arms. Both intra- and inter-dot Coulomb repulsions are taken into account by employing the Keldysh nonequilibrium Green’s function technique. The single narrow Fano resonance in the noninteracting case is split into two in the presence of either intra- or inter-dot Coulomb interaction. We find that four Fano peaks emerge in the conductance or local density of states spectra when the two kinds of interactions exist simultaneously. Such behavior holds true for the accompanying broad Breit–Wigner type resonance. We also show that the positions of the Fano peaks can be tuned with the aid of the magnetic flux penetrating through the ring, which might have practical applications in device design or quantum computation.

Vortex core states in a minimal two-band model for iron-based superconductors

The pairing symmetry is one of the major issues in the study of iron-based superconductors. We adopt a minimal two-band tight-binding model with various channels of pairing interaction, and derive a set of two-band Bogoliubov--de Gennes (BdG) equations. The BdG equations are implemented in real space and then solved self-consistently via exact diagonalization. In the uniform case, we find that the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave pairing state is most favorable for a nearest-neighbor pairing interaction while the ${s}_{{x}^{2}{y}^{2}}$-wave pairing state is most favorable for a next-nearest-neighbor pairing interaction, which is consistent with that reported by Seo et al. [Phys. Rev. Lett. 101, 206404 (2008)]. We then proceed to study the local electronic structure around a magnetic vortex core for both ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave and ${s}_{{x}^{2}{y}^{2}}$-wave pairing symmetry in the mixed state. It is found from the local density of states spectra and its spatial variation that the resonance core states near the Fermi energy for the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave pairing symmetry are bound while those for the ${s}_{{x}^{2}{y}^{2}}$-wave pairing symmetry can evolve from the localized states into extended ones with varying electron filling factor. Furthermore, by including an effective exchange interaction, the emergent antiferromagnetic spin-density-wave order can suppress the resonance core states, which provides one possible avenue to understand the absence of resonance peak as revealed by recent scanning tunneling microscopy experiment by Yin et al. [Phys. Rev. Lett. 102, 097002 (2009)].

Short-range spin and charge correlations and local density of states in the colossal magnetoresistance regime of the single-orbital model for manganites

The metal-insulator transition, and the associated magnetic transition, in the colossal magnetoresistance (CMR) regime of the one-orbital model for manganites is studied here using Monte Carlo (MC) techniques in two-dimensional clusters. Both cooperative oxygen lattice distortions and a finite superexchange coupling among the ${t}_{2g}$ spins are included in our investigations. Charge and spin correlations are studied. In the CMR regime, a strong competition between the ferromagnetic metallic and the antiferromagnetic charge-ordered insulating states is observed. This competition is shown to be important to understand the resistivity peak that appears near the critical temperature. Moreover, it is argued that the system is dynamically inhomogeneous with short-range charge and spin correlations that slowly evolve with MC time, producing the glassy characteristics of the CMR state. The local density of states (LDOS) is also investigated and a pseudogap (PG), identified as a dip in the LDOS at the Fermi energy, is found to exist in the CMR temperature range. The width of the PG in the LDOS is calculated and directly compared to recent scanning-tunneling-spectroscopy (STS) experimental results. The observed agreement between our calculation and the experiment suggests that the depletion of the conductance at low bias observed experimentally is a reflection on the existence of a PG in the LDOS spectra. The apparent homogeneity observed via STS techniques could be caused by the slow time characteristics of this probe. Faster experimental methods should unveil a rather inhomogeneous state in the CMR regime, as already observed in neutron-scattering experiments.

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.

Imaging of subbands in InAs/GaSb double quantum wells by low-temperature scanning tunneling spectroscopy

The spatial distribution of the electron local density of states (LDOS) in InAs/GaSb double quantum wells (DQWs) was investigated by low-temperature scanning tunneling spectroscopy on cleaved surfaces. For DQW with a thick central barrier, clear standing wave patterns corresponding to subbands confined to each InAs single quantum well appeared in the spatial variation of LDOS spectra. In contrast, for the DQW with a thin central barrier, the standing wave patterns extended over both quantum wells. The deviation of the pattern arising from the asymmetry due to a slight difference of the well thickness appeared clearly. The observed spectra are well explained by the calculated LDOS taken to be the sum of LDOS contributed from all energetically accessible subbands.

Quantum Phenomena at Compound Semiconductor Surfaces

Two-dimensional (2 D) electron systems in compound semiconductors are markedly important not only for studies of low-dimensional electron physics but also for application in recent information-oriented society. To investigate behavior of such 2 D electrons in nanometer-scale regions, the local density of states (LDOS) was characterized at the clean surfaces in ultra-high vacuum using a low-temperature scanning tunneling microscope (LT-STM). This LT-STM was equipped with a chamber for molecular beam epitaxy (MBE) of III-V compound semiconductors. At the InAs(111)A surfaces, LDOS standing waves were clearly imaged around the defects. The wave features were confirmed to originate from the Friedel oscillation of naturally formed 2 D states in the surface electron accumulation layer. Also, the electronic states of highly Si-doped InGaAs surface quantum wells (QWs), grown on the GaAs(111)A substrates, were characterized. The LDOS spectra revealed the formation of artificial 2 D subbands quantized in the QWs. The effects related to phase coherence in the QWs are discussed. It is shown that nanoprobing the clean surfaces is very useful for microscopic understanding of quantum mechanical phenomena aiming at advanced electronic devices for future communication technologies.

Proximity effects in ferromagnet/superconductor bilayers

The local density of states (LDOS) in a ferromagnet (FM)/superconductor (SC) bilayer is obtained by using the Nambu Green's function approach. Besides the transition from the “0” state to “ π” state found in the spatial variation of the LDOS in the FM, the dependence of the LDOS spectrum on the thicknesses of the FM and SC is also investigated. It is shown that the LDOS in a thin FM film in contact to the SC shows a strong superconducting feature suggesting the possible coexistence of the ferromagnetism and s-wave superconductivity induced by the proximity effects.

Fermi surface investigation in the scanning tunneling microscopy of Bi 2Sr 2CaCu 2O 8

Within the ideal Fermi liquid picture, the impurity-induced spatial modulation of local density of states (LDOS) in the d-wave superconductor Bi 2Sr 2CaCu 2O 8 is investigated at different superconducting (SC) gap sizes. These LDOS spectra are related to the finite-temperature d I/d V spectra in scanning tunneling microscopy (STM), when the Fermi distribution factor is deconvoluted away from d I/d V. We find stripe-like structures even in the zero gap case due to a local-nesting mechanism. This mechanism is different from the octet-scattering mechanism in the d-wave SC (dSC) state proposed by McElroy et al. [K. McElroy, R.W. Simmonds, J.E. Hoffman, D.H. Lee, J. Orenstein, H. Eisaki, S. Uchida, J.C. Davis, Nature 422 (2003) 592]. The zero gap LDOS is related to the normal state d I/d V. The zero gap spectra when Fourier-transformed into the reciprocal space, can reveal the information of the entire Fermi surface at a single measuring bias voltage, in contrast to the point-wise tracing out proposed by McElroy et al. This may serve as another way to check the reality of Landau quasiparticles in the normal state. We have also re-visited the octet-scattering mechanism in the dSC state and pointed out that, due to the Umklapp symmetry, there are additional peaks in the reciprocal space that experimentally yet to be found.