Local Quasiparticle Density Of States Research Articles

STM/STS study of the local density of states in Cu doped Fe(Se,Te) superconductors

The scanning tunnel microscopy/scanning tunnel spectroscopy (STM/STS) measurements of the local quasiparticle density of states (LDOS) in Cu x -Fe1.01-x Se0.4Te0.6 (x = 0.01-0.03) superconductors were carried out. Critical temperatures Tc decrease with increasing Cu-impurity doping level x. STM images show clear regular square arrangements of spots with the lattice spacing ~ 0.38 nm as well as the randomly distributed large spots, which are most possibly due to excess Fe atoms. While the STM image resembles that of non-doped Fe(Se,Te), the LDOS map shows various extra spot structures with bright (with higher magnitudes of dI/dV) and dark (with lower magnitudes of dI/dV) regions. With increasing x, the number of such spots grows proportionally, indicating that these spots most probably correspond to the dopant Cu atoms.

Quasiparticle density of states and triplet correlations in superconductor/ferromagnetic-insulator structures across a sharp domain wall

A ferromagnetic insulator (FI) in contact with a superconductor (S) is known to induce a spin splitting of the BCS density of states at the FI/S interface. This spin splitting causes the Cooper pairs to reduce their singlet-state correlations and acquire odd-in-frequency triplet correlations. We consider a diffusive FI/S bilayer with a sharp magnetic domain wall in the FI and study the local quasiparticle density of states and triplet superconducting correlations. In the case of collinear alignment of the domains, we obtain analytical results by solving the Usadel equation. For a small enough exchange field or weak superconductivity, we also find an analytical expression for arbitrary magnetic textures, which reveals how the triplet component vector depends on the local magnetization of the FI. For an arbitrary angle between the magnetizations and the strength of the exchange field, we numerically solve the problem of a sharp domain wall. We finally propose two different setups based on FI/S/F stacks, where F is a ferromagnetic layer, to filter out singlet pairs and detect the presence of triplet correlations via tunneling differential conductance measurements.

Spatial modulation of unitary impurity-induced resonances in superconducting CeCoIn5

Motivated by recent experimental progress in high-resolution scanning tunneling microscopy (STM) techniques, we propose to investigate the local quasiparticle density of states around a unitary impurity in the heavy fermion superconductor CeCoIn$_{5}$. Based on the T-matrix approach we obtain a sharp nearly zero-energy resonance state (ZERS) in the strong impurity potential scattering localized around the impurity, and find qualitative differences in the spatial pattern of the tunneling conductance modulated by the nodal structure of the superconducting gap. These unique features may be used as a probe of the superconducting gap symmetry and in combination with the further STM measurements, may help to confirm the $d_{x^{2}-y^{2}}$ pairing in CeCoIn$_{5}$ at ambient pressure.

Research on superconductivity of epitaxial FeSe films

The newly discovered iron-based superconductors in 2008 have become the second class of high temperature superconductor besides the cuprates. Among all these iron-based compounds, β-FeSe has the simplest chemical structure and can be an archetype system for unraveling the mechanism of superconductivity. By using state-of-the-art molecular beam epitaxy (MBE) technique, high-quality superconducting FeSe single crystalline films with finely controllable topography and composition have been successfully prepared, with their superconducting properties extensively investigated. The low-temperature scanning tunneling spectra reveal that the superconducting gap in the quasiparticle density of states is visible down to two unit cells of FeSe films, and evidence for a gap function with nodal lines. Electron pairing with two-fold symmetry has also been demonstrated by direct imaging of quasiparticle excitations in the vicinity of magnetic vortex cores, Fe adatoms and Se vacancies. The two-fold pairing symmetry is supported by our observation of striped electronic nanostructures in the slightly Se-doped samples, primarily due to the orbital ordering. Twin boundaries run at approximately 45° to the Fe-Fe bond directions, and noticeably suppress the superconducting gap and pin magnetic vortices. This is likely caused by the increased Se height in the vicinity of twin boundaries, providing the first local evidence for the importance of this height to the mechanism of superconductivity. Furthermore, we reveal signatures of a bosonic mode in the local quasiparticle density of states of superconducting FeSe films, whose energy reduces with decreasing gap magnitude Ω . Recently, the growth recipe has been further extended to grow FeSe film on SrTiO3(001) substrate, leading to the high- T c superconductivity in the very FeSe/SrTiO3 interface. A superconducting gap as large as 20 meV and the magnetic field induced vortex state revealed by in situ scanning tunneling microscopy suggest that the superconductivity of single-unit-cell FeSe films could occur around 77 K. Our subsequent transport and measurements of the one-unit-cell thick FeSe films on insulating SrTiO3 substrates with non-superconducting FeTe protection layers provide definitive evidence for high temperature superconductivity with an onset T c above 40 K which are much higher than T c~9.4 K for bulk FeSe, respectively. The finding provides a completely new avenue and method to reveal the pairing mechanism of high- T c superconductors, and to further enhance T c, stirring up worldwide increasing attention in the field of high- T c superconductors and material sciences.

Vortex Core Structure in Multilayered Rashba Superconductors

We numerically study the electronic structure of a single vortex in two dimensional superconducting bilayer systems within the range of the mean-field theory. The lack of local inversion symmetry in the system is taken into account through the layer dependent Rashba spin-orbit coupling. The spatial profiles of the pair potential and the local quasiparticle density of states are calculated in the clean spin-singlet superconductor on the basis of the quasiclassical theory. In particular, we discuss the characteristic core structure in the pair-density wave state, which is spatially modulated exotic superconducting phase in a high magnetic field.

Imaging the Electron-Boson Coupling in Superconducting FeSe Films Using a Scanning Tunneling Microscope

Scanning tunneling spectroscopy has been used to reveal signatures of a bosonic mode in the local quasiparticle density of states of superconducting FeSe films. The mode appears below Tc as a "dip-hump" feature at energy Ω∼4.7kBTc beyond the superconducting gap Δ. Spectra on strained regions of the FeSe films reveal simultaneous decreases in Δ and Ω. This contrasts with all previous reports on other high-Tc superconductors, where Δ locally anticorrelates with Ω. A local strong coupling model is found to reconcile the discrepancy well, and to provide a unified picture of the electron-boson coupling in unconventional superconductors.

Nanoengineered nonuniform strain in graphene using nanopillars

Recent experiments showed that nonuniform strain can be produced by depositing graphene over pillars. We employed atomistic calculations to study the nonuniform strain and the induced pseudomagnetic field in graphene on top of nanopillars. By decreasing the distance between the nanopillars a complex distribution for the pseudomagnetic field can be generated. Furthermore, we performed tight-binding calculations of the local density of states (LDOS) by using the relaxed graphene configuration obtained from atomistic calculations. We find that the quasiparticle LDOS are strongly modified near the pillars, both at low energies showing sublattice polarization and at high energies showing shifts of the van Hove singularity. Our study shows that changing the specific pattern of the nanopillars allows us to create a desired shape of the pseudomagnetic field profile while the LDOS maps provide an input for experimental verification by scanning tunneling microscopy.

Magnetic Rare-Earth Impurity Resonance Bound States in Iron-Based Superconductors

Starting from an Anderson model for two-orbital model of electron and hole conduction bands which hybridized with the localized impurity spin, we investigate the effect of magnetic impurities on the local quasiparticle density of states (LDOS) in iron-based superconductors. We consider extended s-wave (s+−) superconducting gap symmetry with higher harmonic correction. The impurity-induced bound states are a probe for the nodal structure of the extended s-wave symmetry in ferropnictides.

Magnetic impurity resonance states and symmetry of the superconducting order parameter in iron-based superconductors

We investigate the effect of magnetic impurities on the local quasiparticle density of states (LDOS) in iron-based superconductors. Employing the two-orbital model where 3$d$ electron and hole conduction bands are hybridizing with the localized $f$-orbital of the impurity spin, we investigate how various symmetries of the superconducting gap and its nodal structure influence the quasiparticle excitations and impurity bound states. We show that the bound states behave qualitatively different for each symmetry. Most importantly we find that the impurity-induced bound states can be used to identify the nodal structure of the extended s-wave symmetry ($S^{\pm}$) that is actively discussed in ferropnictides.

Local density of states and superconducting gap in the iron chalcogenide superconductorFe1+δSe1−xTexobserved by scanning tunneling spectroscopy

We report on the investigation of the quasiparticle local density of states and superconducting gap in the iron chalcogenide superconductor ${\text{Fe}}_{1+\ensuremath{\delta}}{\text{Se}}_{1\ensuremath{-}x}{\text{Te}}_{x}({T}_{\text{c}}\ensuremath{\sim}14\text{ }\text{K})$. The surface of a cleaved crystal revealed an atomic square lattice, superimposed on the inhomogeneous background, with a lattice constant of $\ensuremath{\sim}3.8\text{ }\text{\AA{}}$ without any reconstruction. Tunneling spectra measured at 4.2 K exhibit the superconducting gap, which completely disappears at 18 K, with a magnitude of $\ensuremath{\sim}2.3\text{ }\text{meV}$, corresponding to $2\ensuremath{\Delta}/{k}_{\text{B}}{T}_{\text{c}}=3.8$. In stark contrast to the cuprate superconductors, the value of the observed superconducting gap is relatively homogeneous, following a sharp distribution with a small standard deviation of 0.23 meV. Conversely, the normal-state local density of states observed above ${T}_{\text{c}}$ shows spatial variation over a wide energy range of more than 1 eV, probably due to the excess iron present in the crystal.

Conductance characteristics of current-carrying d-wave weak links

The local quasiparticle density of states in the current-carrying d-wave superconducting structures is studied theoretically. The density of states can be accessed through the conductance of the scanning tunneling microscope. Two particular situations are considered: the current state of a homogeneous film, and a weak link between two current-carrying d-wave superconductors.

Cooper pair shape and odd-frequency pairing in superconductor junctions

Cooper pair shape is not so simple in inhomogeneous superconducting systems. It is shown that pairing function in a normal metal is surprisingly anisotropic because of quasiparticle interference. We calculate angle resolved quasiparticle local density of states in NS bilayers which reflects such anisotropic shape of the pairing function. This unusual feature can be detected by a magneto-tunneling spectroscopy experiment.

Chiral quasiparticle local density of states maps in graphene

We present a theory of momentum space local density-of-states (LDOS) maps N(q,omega) in graphene. The LDOS map has both intravalley contributions centered near zero momentum and reciprocal lattice vectors and intervalley contributions displaced by the wavevector K'-K which connects graphene's two distinct Dirac points. Using graphene's Dirac equation chiral quasiparticle continuum model, we obtain analytic results which explain the qualitative differences between these two LDOS map features. We comment on the sensitivity of both N(q,omega) features to the mix of atomic length scale and smooth disorder sources present in a particular graphene sample.

Andreev bound states in rounded corners of d-wave superconductors

Andreev bound states at boundaries of d-wave superconductors are strongly influenced by the boundary geometry itself. In this work, the zero-energy spectral weight of the local quasiparticle density of states is presented for the case of wedge-shaped boundaries with rounded corners. Generally, both orientation of the d-wave and the specific local reflection properties of the rounded wedges determine, whether Andreev bound states exist or not. For the bisecting line of the wedge being parallel to the nodal direction of the d-wave gap function, strong zero-energy Andreev bound states are expected at the round part of the boundary.

Theory of the proximity effect at the interface of a normal metal and tripletp-wave superconductor in the clean limit

The superconducting proximity effect in normal metal (N)/triplet $p$-wave superconductor (P) junctions is studied based on the quasiclassical Green's function theory. We present theoretical results for self-consistently determined pair potentials on both the N and P sides as well as the quasiparticle local density of states near the interface. In the present study, for the P side, in order to consider promising pairing symmetries as in ${\mathrm{Sr}}_{2}\mathrm{Ru}{\mathrm{O}}_{4}$, we choose three kinds of pairings: (i) ${p}_{x}$, (ii) ${p}_{y}$, or (iii) ${p}_{x}+i{p}_{y}$ waves. Here, we assume that an attractive interelectron potential on the $N$ side can induce a subdominant $s$-wave pair potential. The spatial dependencies are sensitive to the transparency of the junctions, while the proximity-induced $s$-wave component on the N side does not enhance the magnitude of the pair potential, which breaks the time-reversal symmetry on the P side. The resulting local density of states at the interface has a zero-energy peak, and its splitting depends on the transparency and symmetry of the pair potentials of the junction.

Recent progress in vortex studies by tunneling spectroscopy

Among the methods used to study the vortex state in superconductors, scanning tunneling spectroscopy (STS), is unique in its ability to measure in real space the variations in the local quasiparticle density of states. Thus, as opposed to magnetic imaging, STS gives direct access to the coherence length rather than to the penetration length. Here we discuss two novel methods which enhance the capabilities of STS as a tool for the study of the vortex state.In the first one, called Lazy Fisherman [A. Kohen et al., Appl. Phys. Lett. 86 (2005) 212503], the scanning tunneling microscope’s tip is kept fixed at a selected location while the vortices are being moved by varying the applied magnetic field. By continuously acquiring the local tunneling conductance spectra, dI/dV(V), we detect the changes in the local density of states under the tip due to the vortex motion. With no need for scanning, the method permits one to extend the study of vortices to samples in which scanning is difficult or even impossible due to surface non-uniformity and allows one to detect faster vortex dynamics. To illustrate the approach we study single crystal samples of MgB2.In the second STS method, we replace the commonly used normal metal STM tip by a superconducting (SC) tip which we produce either by mechanically breaking a Nb wire under vacuum in the STM chamber [A. Kohen et al., Physica C 49 (2005) 18] or by gluing a piece of a crystal of MgB2 [F. Giubileo et al., Phys. Rev. Lett. 87 (2001) 177008]. The use of a SC tip enhances the energy resolution of STS in comparison to that obtained with a normal metal tip. The method is illustrated by using Nb and MgB2 tips to perform a simultaneous topographic and spectroscopic imaging on 2H–NbSe2.

Kondo screening in unconventional superconductors: The role of anomalous propagators

The Kondo effect in superconductors is frequently investigated using the local quasiparticle density of states as sole bath characteristics, i.e., the presence of anomalous propagators is ignored. Here we point out that this treatment is exact for a number of situations, including pointlike impurities in $d$-wave superconductors. We comment on recent investigations [M. Matsumoto and M. Koga, J. Phys. Soc. Jpn. 70, 2860 (2001); Phys. Rev. B 65, 024508 (2002)] which reached different conclusions: while their numerical results are likely correct, their interpretation in terms of two-channel Kondo physics and an ``orbital effect of Cooper pairs'' is incorrect.

Theory of enhanced proximity effect by midgap Andreev resonant state in diffusive normal-metal/triplet superconductor junctions

Enhanced proximity effect by mid gap Andreev resonant state (MARS) in a diffusive normal metal / insulator / triplet superconductor (DN/TS) junction is studied based on the Keldysh-Nambu quasiclassical Green's function formalism. By choosing a p-wave superconductor as a typical example of TS, conductance of the junction and the spatial variation of quasiparticle local density of states (LDOS) in DN are calculated as the function of the magnitudes of the resistance $R_{d}$, Thouless energy in DN and the transparency of the insulating barrier. The resulting conductance spectrum has a zero bias conductance peak (ZBCP) and LDOS has a zero energy peak (ZEP) except for $\alpha = \pi/2$ $(0 \leq \alpha \leq \pi/2)$, where $\alpha$ denotes the angle between the lobe direction of the p-wave pair potential to the normal to the interface. These peaks are revealed to be suppressed by applying a magnetic field. When the magnitude of $R_{d}/R_{0}$ is sufficiently large, the total zero voltage resistance of the junction is almost independent of the $R_{d}$ for $\alpha \neq \pi/2$. The extreme case is $\alpha=0$, where total zero voltage resistance is always $R_{0}/2$. Based on these results, a crucial test to identify triplet pairing superconductors based on tunneling experiments is proposed.

First Observation of the Fourfold-symmetric and Quantum Regime Vortex Core in YNi2B2C by Scanning Tunneling Microscopy and Spectroscopy

The local quasi-particle density of states, N s ( E , r ), in the isolated vortex of YNi 2 B 2 C has been measured at 0.46 K by low-temperature scanning tunneling microscopy and spectroscopy. The vortex core is found to be fourfold-symmetric star-shaped in real space: Near E = 0 meV, N s ( E , r ) extends toward <100 > (the a -axis) and has a peak at the center of the vortex core. With increasing energy, N s ( E , r ) comes to extend toward <110 > and the peak of N s ( E , r ) splits into four peaks toward <110 >. N s ( E , r ) in the vortex core exhibits electron–hole asymmetry with the intensity, indicating the first observation of the vortex core in a quantum regime.

Collective modes and quasiparticle interference on the local density of states of cuprate superconductors

The energy, momentum and temperature dependence of the quasiparticle local density of states (LDOS) of a two-dimensional $d_{x^2-y^2}$-wave superconductor with random disorder is investigated using the first-order T-matrix approximation. The results suggest that collective modes such as spin/charge density waves are relevant low-energy excitations of the cuprates that contribute to the observed LDOS modulations in recent scanning tunneling microscopy studies of $\rm Bi_2Sr_2CaCu_2O_x$.