Local Density Of States Modulations Research Articles

Electronic stripe patterns near the fermi level of tetragonal Fe(Se,S)

FeSe1−xSx remains one of the most enigmatic systems of Fe-based superconductors. While much is known about the orthorhombic parent compound, FeSe, the tetragonal samples, FeSe1−xSx with x > 0.17, remain relatively unexplored. Here, we provide an in-depth investigation of the electronic states of tetragonal FeSe0.81S0.19, using scanning tunneling microscopy and spectroscopy (STM/S) measurements, supported by angle-resolved photoemission spectroscopy (ARPES) and theoretical modeling. We analyze modulations of the local density of states (LDOS) near and away from Fe vacancy defects separately and identify quasiparticle interference (QPI) signals originating from multiple regions of the Brillouin zone, including the bands at the zone corners. We also observe that QPI signals coexist with a much stronger LDOS modulation for states near the Fermi level whose period is independent of energy. Our measurements further reveal that this strong pattern appears in the STS measurements as short range stripe patterns that are locally two-fold symmetric. Since these stripe patterns coexist with four-fold symmetric QPI around Fe-vacancies, the origin of their local two-fold symmetry must be distinct from that of nematic states in orthorhombic samples. We explore several aspects related to the stripes, such as the role of S and Fe-vacancy defects, and whether they can be explained by QPI. We consider the possibility that the observed stripe patterns may represent incipient charge order correlations, similar to those observed in the cuprates.

Nano-scale periodic structures and gap distribution in Pb-doped Bi2223 cuprate superconductors observed by STM/STS

The first systematic study of the nano-scale periodic local density of states (LDOS) and the inhomogeneous gap distributions for the Pb doped Bi2Sr2Ca2Cu3O10 + y (PbBi2223) microcrystals was carried out using the low-temperature scanning tunneling microscopy/spectroscopy. The spatially inhomogeneous gap distributions with patchy structures of several nm size reveal the average gap magnitude Δave ≃ 46 meV with the standard deviation σ = 8 meV. Those features are similar to properties of the widely investigated two-layer Bi-based cuprates. The energy dispersive types of the LDOS modulations are identified as being due to the quasiparticle interference. The relevant scattering vectors seem to testify that the PbBi2223 superconductors are ones, which was shown earlier to be most probable for Bi2212. Three types of energy non-dispersive modulations manifest themselves. Among them, the modulation in the diagonal direction with the period of ∼2.1a0 [ (2π/a0)] seems to be observed for the first time.

Enhancing superconductivity by disorder

We study two mechanisms for enhancing the superconducting transition temperature Tc by nonmagnetic disorder in both conventional (sign-preserving gaps) and unconventional (sign-changing gaps) superconductors (SC). In the first scenario, relevant to multi-band systems in the dilute impurity limit of both conventional and unconventional SC, we demonstrate how favorable density of states enhancements driven by resonant states in off-Fermi-level bands, lead to significant enhancements of Tc in the condensate formed by the near-Fermi-level bands. The second scenario focuses on the dense impurity limit where random disorder-generated local density of states modulations cause a boosted Tc for conventional SC with short coherence lengths. We analyze the basic physics of both mechanisms within simplified models, and discuss the relevance to existing materials.

Surface reconstruction induced Co Kondo resonance width modulation on one monolayer Ag covered Cu(111)

We present a systematic study of the Kondo effect of single Co adatom placed on one monolayer (ML) Ag covered Cu(111) surface. The 1-ML Ag/Cu(111) shows apparent local density of states (LDOS) modulation which associated with the surface reconstruction. Interestingly, we find the Kondo resonance width of the Co adatom on 1-ML Ag/Cu(111) is position-dependent. When the Co adatom is placed near the triangular dislocation loop (hcp/fcc boundary), the Kondo resonance width is generally wider than the one measured at fcc site. At the fcc region, the measured Kondo resonance width is closely related to the LDOS variation. In conjunction with the tight binding approximation calculation, we identify that the main contribution of the LDOS modulation is the surface-reconstruction-regulated surface states. With a recently developed model, we further determine the contributions of the bulk and surface states to the Kondo resonance. These findings clarify the role of surface reconstruction on the Kondo effect.

Impact of step defects on surface states of topological insulators

The eigenstates in the presence of a step defect (SD) along the $x$ or $y$ axis on the surface of topological insulators are exactly solved. It is shown that unlike the electronic states in conventional metals, the topological surface states across the SD can produce spin rotations. The magnitudes of the spin rotations depend on the height and direction of the SD. The oscillations of local density of states (LDOS) are characterized by a wave vector connecting two points on the hexagonal constant-energy contour at higher energies. The period of the oscillation caused by the SD along the $y$ axis is $\sqrt{3}$ ($\frac{1}{\sqrt{3}}$) times that induced by the SD along the $x$ axis at a larger positive (negative) bias voltage. With increasing the bias voltage, the period of the oscillation, insensitive to the strength of the SD, becomes smaller. At lower energies near the Fermi surface, the two types of wave vectors coexist in the LDOS modulations. These results are consistent qualitatively with recent observations of scanning tunneling microscopy.

Multifractal nature of the surface local density of states in three-dimensional topological insulators with magnetic and nonmagnetic disorder

We compute the multifractal spectra associated to local density of states (LDOS) fluctuations due to weak quenched disorder for a single Dirac fermion in two spatial dimensions. Our results are relevant to the surfaces of ${\mathbb{Z}}_{2}$ topological insulators such as ${\text{Bi}}_{2}{\text{Se}}_{3}$ and ${\text{Bi}}_{2}{\text{Te}}_{3}$, where LDOS modulations can be directly probed via scanning tunneling microscopy. We find a qualitative difference in spectra obtained for magnetic versus nonmagnetic disorder. Randomly polarized magnetic impurities induce quadratic multifractality at first order in the impurity density; by contrast, no operator exhibits multifractal scaling at this order for a nonmagnetic impurity profile. For the time-reversal invariant case, we compute the first nontrivial multifractal correction, which appears at two loops (impurity density squared). We discuss spectral enhancement approaching the Dirac point due to renormalization, and we survey known results for the opposite limit of strong disorder.

Spatial correlation between the LDOS modulation and electronic inhomogeneity in Bi2Sr2-xLaxCuO6+δ

Low-temperature scanning tunneling microscopy has been performed on underdoped Bi2Sr1.4La0.6CuO6+δ (Tc ∼ 29 K) at 4.2 K to observe the non-dispersive spatial modulation of local density of states (LDOS). The LDOS modulation is along the Cu-O-Cu directions and its period is about 4a0, though the period is slightly distributed over the surface. The correlation between the modulation period and the nanoscale electronic inhomogeneity, which is represented by the spatial variation of the low-energy integrated LDOS (ILDOS), was analyzed. The result exhibits clear tendency of that the period in the low-ILDOS region is slightly shorter than that in the high-ILDOS region.

Coulomb interaction-induced checkerboard patterns in disordered cuprates

We study the effect of the Coulomb interaction on the local density of states (LDOS) and its Fourier component in disordered cuprates. It is shown that the Coulomb interaction suppresses strongly the maximum value of the LDOS induced by the dopant impurity at each energy value and expands significantly the Friedel oscillation in real space. The existence of the Coulomb interaction with a moderate strength yields an energy-dependent checkerboard LDOS modulation around the impurity, which is very different from that produced by pure quasiparticle interference. The orientation and transformation of the checkerboard pattern with energy and the relations among the modulation vectors, dopings and the bias voltages agree qualitatively with the recent scanning tunneling microscopy (STM) experiments.

STM observation of local density-of-states modulation in lanthanide substituted Bi2Sr1.6Ln0.4CuO6+δ

We performed scanning tunneling microscopy (STM) experiments on optimally doped Bi2Sr1.6Ln0.4CuO6+δ (Ln=La, Nd, and Gd) at 4.2K to explore the lanthanide ion dependence of the local density-of-states (LDOS) modulation. STM image at high bias voltage showed the structural superlattice modulation along the b-axis. At low bias voltage, we observed the LDOS modulation along the Cu–O–Cu direction in all materials. The period of the modulation was independent of the lanthanide ion substituted, and was about 5a0 (a0 is the lattice constant).

Scanning tunneling spectroscopy of high-temperature superconductors

Tunneling spectroscopy played a central role in the experimental verification of the microscopic theory of superconductivity in the classical superconductors. Initial attempts to apply the same approach to high-temperature superconductors were hampered by various problems related to the complexity of these materials. The use of scanning tunneling microscopy/spectroscopy (STM/STS) on these compounds allowed to overcome the main difficulties. This success motivated a rapidly growing scientific community to apply this technique to high-temperature superconductors. This paper reviews the experimental highlights obtained over the last decade. We first recall the crucial efforts to gain control over the technique and to obtain reproducible results. We then discuss how the STM/STS technique has contributed to the study of some of the most unusual and remarkable properties of high-temperature superconductors: the unusual large gap values and the absence of scaling with the critical temperature; the pseudogap and its relation to superconductivity; the unprecedented small size of the vortex cores and its influence on vortex matter; the unexpected electronic properties of the vortex cores; the combination of atomic resolution and spectroscopy leading to the observation of periodic local density of states modulations in the superconducting and pseudogap states, and in the vortex cores.

Putting competing orders in their place near the Mott transition

We describe the localization transition of superfluids on two-dimensional lattices into commensurate Mott insulators with average particle density p/q (p, q relatively prime integers) per lattice site. For bosons on the square lattice, we argue that the superfluid has at least q degenerate species of vortices which transform under a projective representation of the square lattice space group (a PSG). The formation of a single vortex condensate produces the Mott insulator, which is required by the PSG to have density wave order at wavelengths of q/n lattice sites (n integer) along the principle axes; such a second-order transition is forbidden in the Landau-Ginzburg-Wilson framework. We also discuss the superfluid-insulator transition in the direct boson representation, and find that an interpretation of the quantum criticality in terms of deconfined fractionalized bosons is only permitted at special values of q for which a permutative representation of the PSG exists. We argue (and demonstrate in detail in a companion paper: L. Balents et al., cond-mat/0409470) that our results apply essentially unchanged to electronic systems with short-range pairing, with the PSG determined by the particle density of Cooper pairs. We also describe the effect of static impurities in the superfluid: the impurities locally break the degeneracy between the q vortex species, and this induces density wave order near each vortex. We suggest that such a theory offers an appealing rationale for the local density of states modulations observed by Hoffman et al. (cond-mat/0201348) in STM studies of the vortex lattice of BSCCO, and allows a unified description of the nucleation of density wave order in zero and finite magnetic fields. We note signatures of our theory that may be tested by future STM experiments.

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 $\rm Bi_2Sr_2CaCu_2O_x$.

Spin collective mode and quasiparticle contributions to STM spectra of d-wave superconductors with pinning

We present additional details of the scanning tunneling microscopy spectra predicted by the model of pinning of dynamic spin collective modes in d-wave superconductor proposed by Polkovnikov et al. [Phys. Rev. B 65 (2002) 220509]. Along with modulations at the twice the wavevector of the spin collective mode, the local density of states (LDOS) displays features linked to the spectrum of the Bogoliubov quasiparticles. The former is expected to depend more strongly on an applied magnetic field or the doping concentration. The spin collective mode and the quasiparticles are distinct, co-existing, low energy excitations of the d-wave superconductor (strongly coupled only in some sectors of the Brillouin zone), and should not be viewed as mutually exclusive sources of LDOS modulation.