Quasiparticle Interference Patterns Research Articles

Distinct quasiparticle interference patterns for surface impurity scattering on various Weyl semimetals

Distinct quasiparticle interference patterns for surface impurity scattering on various Weyl semimetals

Superconductivity in monolayer and few-layer graphene. III. Impurity-induced subgap states and quasiparticle interference patterns

Superconductivity in monolayer and few-layer graphene. III. Impurity-induced subgap states and quasiparticle interference patterns

Graphene nanoribbons with hBN passivated edges grown by high-temperature molecular beam epitaxy

Integration of graphene and hexagonal boron nitride (hBN) in lateral heterostructures has provided a route to broadly engineer the material properties by quantum confinement of electrons or introduction of novel electronic and magnetic states at the interface. In this work we demonstrate lateral heteroepitaxial growth of graphene nanoribbons (GNRs) passivated by hBN using high-temperature molecular beam epitaxy (HT-MBE) to grow graphene in oriented hBN trenches formed ex-situ by catalytic nanoparticle etching. High-resolution atomic force microscopy (AFM) reveals that GNRs grow epitaxially from the etched hBN edges, and merge to form a GNR network passivated by hBN. Using conductive AFM we probe the nanoscale electrical properties of the nanoribbons and observe quasiparticle interference patterns caused by intervalley scattering at the graphene/hBN interface, which carries implications for the potential transport characteristics of hBN passivated GNR devices.

Hyperbolic Fringe Signal for Twin Impurity Quasiparticle Interference.

We study the quasiparticle interference (QPI) pattern emanating from a pair of adjacent impurities on the surface of a gapped superconductor (SC). We find that hyperbolic fringes (HFs) in the QPI signal can appear due to the loop contribution of the two-impurity scattering, where the locations of the two impurities are the hyperbolic focus points. For a single pocket Fermiology, a HF pattern signals chiral SC order for nonmagnetic impurities and requires magnetic impurities for a nonchiral SC. For a multipocket scenario, a sign-changing order parameter such as an s_{±} wave likewise yields a HF signature. We discuss twin impurity QPI as a new tool to complement the analysis of superconducting order from local spectroscopy.

Signatures of the order parameter of a superconducting adatom layer in magnetic field dependent quasiparticle interference

Experiments have observed superconductivity in atomically-thin metallic layers deposited on semiconducting substrates. As in any superconductor, it is important to determine the structure of the superconducting pairing function in order to reveal the mechanism responsible for superconductivity. To that end, we study the possible superconducting states of two-dimensional triangular lattices. We calculate the quasiparticle interference (QPI) patterns which would result from various nearest-neighbor pairing order parameters, and show how the QPI can be used to distinguish between those order parameters. The QPI patterns are the momentum-space representations of real-space local density-of-states fluctuations: the QPI signal at momentum $q$ reveals the strength of scattering processes at that momentum transfer. We show how characteristic differences between scattering from charge disorder (i.e. impurities) and from order-parameter disorder (i.e. vortices) can be used to identify the angular momentum of the superconducting pairs.

Temperature dependence of quasiparticle interference in $d$-wave superconductors

We investigate the temperature dependence of quasiparticle interference in the high T_cTc-cuprates using an exact-diagonalization + Monte-Carlo based scheme to simulate the dd-wave superconducting order parameter. The quasiparticle interference patterns have features largely resulting from the scattering vectors of the octet model at lower temperature. Our findings suggest that the features of quasiparticle interference in the pseudogap region of the phase diagram are also dominated by the set of scattering vectors belonging to the octet model because of the persisting antinodal gap beyond the superconducting transition T_cTc. However, beyond a temperature when the antinodal gap becomes very small, a set of scattering vectors different from those belonging to the octet model are responsible for the quasiparticle interference patterns. With a rise in temperature, the patterns are increasingly broadened.

Anisotropic topological surface states in thin-film monoclinic Ag2Se

Silver chalcogenide systems have recently attracted significant attention due to their promising topological insulating properties. Here we conducted systematic low-temperature local scanning tunneling microscopy/spectroscopy and first-principles studies on the surface states of monoclinic Ag2Se thin films grown using molecular beam epitaxy. Through the use of quasi-particle interference patterns, we have observed evidence for topological surface states on the selenium-terminated surfaces with different types of defect densities. The results of ab initio calculations confirm the existence of nontrivial topological surface states in the monoclinic Ag2Se structure, for which such properties have not been previously reported. The energy dispersion determined using voltage-dependent standing wave patterns suggests that these topological states have an anisotropic Dirac cone structure. This discovery may lead to new applications for monoclinic Ag2Se in the rapidly growing fields of nanoelectronics and spintronics.

Atomic-scale study of type-II Dirac semimetal PtTe2 surface

Dirac semimetals (DSM) host linear bulk bands and topologically protected surface states, giving rise to exotic and robust properties. Platinum ditelluride (PtTe2) belongs to this interesting group of topological materials. Here, we employ scanning tunneling microscopy (STM) in combination with first-principles calculations to visualize and identify the native defects at the surface of a freshly cleaved PtTe2 crystal. Around these defects, short-wavelength electron density oscillations are observed. Fourier transform analysis of the energy-dependent quasiparticle interference patterns is in good agreement with our calculated joint density of states, demonstrating the singular properties of the surface of this type-II DSM. Our results evidence the power of STM in understanding the surface of topological materials.

Fully Two-Dimensional Incommensurate Charge Modulation on the Pd-Terminated Polar Surface of PdCoO2.

Here, we use low-temperature scanning tunneling microscopy and spectroscopy to study the polar surfaces of PdCoO2. On the CoO2-terminated polar surface, we detect the quasiparticle interference pattern originating from the Rashba-like spin-split surface states. On the well-ordered Pd-terminated polar surface, we observe a regular lattice that has a larger lattice constant than the atomic lattice of PdCoO2. In comparison with the shape of the hexagonal Fermi surface on the Pd-terminated surface, we identify this regular lattice as a fully two-dimensional incommensurate charge modulation that is driven by the Fermi surface nesting. More interestingly, we also find the moiré pattern induced by the interference between the two-dimensional incommensurate charge modulation in the Pd layer and its atomic lattice. Our results not only show a new charge modulation on the Pd surface of PdCoO2 but also pave the way for fully understanding the novel electronic properties of this material.

Effective lifting of the topological protection of quantum spin Hall edge states by edge coupling

The scientific interest in two-dimensional topological insulators (2D TIs) is currently shifting from a more fundamental perspective to the exploration and design of novel functionalities. Key concepts for the use of 2D TIs in spintronics are based on the topological protection and spin-momentum locking of their helical edge states. In this study we present experimental evidence that topological protection can be (partially) lifted by pairwise coupling of 2D TI edges in close proximity. Using direct wave function mapping via scanning tunneling microscopy/spectroscopy (STM/STS) we compare isolated and coupled topological edges in the 2D TI bismuthene. The latter situation is realized by natural lattice line defects and reveals distinct quasi-particle interference (QPI) patterns, identified as electronic Fabry-Pérot resonator modes. In contrast, free edges show no sign of any single-particle backscattering. These results pave the way for novel device concepts based on active control of topological protection through inter-edge hybridization for, e.g., electronic Fabry-Pérot interferometry.

Visualizing discrete Fermi surfaces and possible nodal-line to Weyl state evolution in ZrSiTe

Topological nodal line semimetals (TNLSMs) represent a quantum state of topological matter. When the crystal/time-reversal symmetry is broken, a nodal line state is expected to evolve into a Dirac semimetal, a Weyl semimetal, or other topological phases according to theoretical studies. Here, we report scanning tunneling microscopy (STM) based quasiparticle interference (QPI) measurements performed on the surface of TNLSM ZrSiTe single crystal. A discrete Fermi surface with multiple electron/hole pockets and the impurity-induced inter-/intra- pockets scatterings are directly visualized from QPI patterns. Moreover, the degenerated Dirac points at X point evolve into the pairs of Weyl nodes when Fe atoms are deposited, suggesting a possible phase transition from the nodal line to the Weyl state. The calculated band structures and the Weyl points by applying Zeeman splitting energies along x-direction, further confirm the existence of Weyl points in the Fe-doped ZrSiTe induced by the broken of time-reversal symmetry.

Development of a near-5-Kelvin, cryogen-free, pulse-tube refrigerator-based scanning probe microscope.

We report the design and performance of a cryogen-free, pulse-tube refrigerator (PTR)-based scanning probe microscopy (SPM) system capable of operating at a base temperature of near 5 K. We achieve this by combining a home-made interface design between the PTR cold head and the SPM head, with an automatic gas-handling system. The interface design isolates the PTR vibrations by a combination of polytetrafluoroethylene and stainless-steel bellows and by placing the SPM head on a passive vibration isolation table via two cold stages that are connected to thermal radiation shields using copper heat links. The gas-handling system regulates the helium heat-exchange gas pressures, facilitating both the cooldown to and maintenance of the base temperature. We discuss the effects of each component using measured vibration, current-noise, temperature, and pressure data. We demonstrate that our SPM system performance is comparable to known liquid-helium-based systems with the measurements of the superconducting gap spectrum of Pb, atomic-resolution scanning tunneling microscopy image and quasiparticle interference pattern of Au(111) surface, and non-contact atomic force microscopy image of NaCl(100) surface. Without the need for cryogen refills, the present SPM system enables uninterrupted low-temperature measurements.

Particle–hole asymmetric superconducting coherence peaks in overdoped cuprates

To elucidate the superconductor to metal transition at the end of superconducting dome, the overdoped regime has stepped onto the center stage of cuprate research recently. Here, we use scanning tunneling microscopy to investigate the atomic-scale electronic structure of overdoped trilayer Bi-2223 and bilayer Bi-2212 cuprates. At low energies the spectroscopic maps are well described by dispersive quasiparticle interference patterns. However, as the bias increases to the superconducting coherence peak energy, a virtually non-dispersive pattern with sqrt(2)*sqrt(2) periodicity emerges. Remarkably, the position of the coherence peaks exhibits evident particle-hole asymmetry which also modulates with the same period. We propose that this is an extreme quasiparticle interference phenomenon, caused by pairing-breaking scattering between flat anti-nodal Bogoliubov bands, which is ultimately responsible for the superconductor to metal transition.

Substrate-induced broken C4 symmetry and gap variation in superconducting single-layer FeSe/SrTiO3−(13×13)

We performed scanning tunneling microscopy/spectroscopy (STM/STS) measurements to investigate the superconducting properties of single-layer FeSe grown on ${\text{SrTiO}}_{3}$ (STO) $(001)\text{\ensuremath{-}}(\sqrt{13}\ifmmode\times\else\texttimes\fi{}\sqrt{13})$. We found ``$+$'' and ``z'' patterns arranged in $\sqrt{13}\ifmmode\times\else\texttimes\fi{}\sqrt{13}$ periodicity in the STM images. Surprisingly, they show ${C}_{2}$ symmetry, although free-standing FeSe itself has ${C}_{4}$ symmetry. STS spectra and quasiparticle interference patterns near the Fermi level also indicate the broken ${C}_{4}$ symmetry with the superconducting gap showing a local variation within the STO surface unit cell because of the short coherence length. This clearly shows the non-negligible role of the substrate surface in the superconductivity of the FeSe/STO system.

Superconductivity near the saddle point in the two-dimensional Rashba system Si(111)−3×3−(Tl,Pb)

Two-dimensional Rashba superconductor Si(111)-$\sqrt{3}\times\sqrt{3}$-(Tl,Pb) is a candidate platform of mixed spin-singlet and -triplet superconductivity. A recent scanning tunneling microscope (STM) experiment revealed a pseudogap at the vortex core, suggesting the finite triplet component [T. Nakamura $\textit{et al.}$, Phys. Rev. B $\bf{ 98}$, 134505 (2018)]. Detailed spectroscopic information of the superconducting gap and the low-energy band structure is necessary to establish the putative triplet superconductivity. Here, we performed high-energy-resolution spectroscopic imaging experiments on Si(111)-$\sqrt{3}\times\sqrt{3}$-(Tl,Pb) using an ultra-low temperature STM. We found that various spectroscopic features, including the vortex-core spectrum, are consistent with spin-singlet $s$-wave superconductivity, having no sign of the triplet component. The apparent contradiction with the previous STM result suggests that the nature of superconductivity changes within the same system. From the analysis of the quasiparticle interference patterns, we found that the Fermi energy is in the close vicinity of the saddle point near the $\overline{\rm{M}}$ point. We speculate that the nature of superconductivity varies depending on the saddle-point energy with respect to the Fermi energy, which is sample-dependent due to different band filling.

Reshaped Weyl fermionic dispersions driven by Coulomb interactions inMoTe2

We report the direct evidence of impacts of the Coulomb interaction in a prototypical Weyl semimetal, MoTe2, that alter its bare bands in a wide range of energy and momentum. Our quasiparticle interference patterns measured using scanning tunneling microscopy are shown to match the joint density of states of quasiparticle energy bands including momentum-dependent self-energy corrections, while electronic energy bands based on the other simpler local approximations of the Coulomb interaction fail to explain neither the correct number of quasiparticle pockets nor shape of their dispersions observed in our spectrum. With this, we predict a transition between type-I and type-II Weyl fermions with doping and resolve its disparate quantum oscillation experiments, thus highlighting the critical roles of Coulomb interactions in layered Weyl semimetals.

Detecting the non-magnetism and magnetism switching of point defects in graphene at the atomic scale

Magnetic and non-magnetic point defects are created by irradiating energetic Ar ions on bilayer epitaxial graphene/SiC(0001), and their atomic and electronic structures are studied using scanning tunneling microscopy(STM) and q-Plus atomic force microscopy(q-Plus AFM). A strong Kondo resonance peak is observed for magnetic impurities in dI/dV spectra, with a proposed Kondo temperature of 314 K. Magnetic scatters produce stronger quasi-particle quantum interference patterns. Structural transformation between the magnetic and non-magnetic defects is observed during atomic-scale characterizations, inducing magnetic switching of the atomic imperfections. Meanwhile, using force spectra, the atomic force driving the transformations is determined to be 22 nN. This discovery paves a way for designing magnetic logic devices through graphene defect engineering at atomic scale.

Quasiparticle interference patterns in bilayer graphene with trigonal warping

We calculate the form of quasiparticle interference patterns in bilayer graphene within a low-energy description, taking into account perturbatively the trigonal warping terms. We introduce four different types of impurities localized on the A and B sublattices of the first and the second layer, and we obtain closed-form analytical expressions both in real and Fourier spaces for the oscillatory corrections to the local density of states generated by the impurities. Finally, we compare our findings with recent experimental and semi-analytical T-matrix results from arXiv:2104.10620 and we show that there is a very good agreement between our findings and the previous results, as well as with the experimental data.

Structural and electrical characterization of the monolayer Kondo-lattice compound CePt6/Pt(111)

We report the growth process, structure, and electronic states of 1 unit layer (u.l.) of a Ce-Pt intermetallic compound on Pt(111) using scanning tunneling microscopy/spectroscopy (STM/STS) and low-energy electron diffraction. An ordered $(2 \times 2)$ structure was observed in the form of films or nanoislands depending on Ce dose by annealing at around 700 K. A structural model constructed from atomically resolved STM images and quasiparticle interference (QPI) patterns indicates the formation of a new surface compound 1 u.l. CePt$_6$ on Pt(111) terminated by a Pt layer. A lateral lattice constant of the 1 u.l. CePt$_6$ on Pt(111) is expanded from the value of a bulk CePt$_5$ crystal to match the Pt(111) substrate. By measuring d$I$/d$V$ spectra and QPI, we observed an onset energy of the surface state found on Pt(111) above Fermi energy ($E_F$) shifts below $E_F$ on the Pt layer of the 1 u.l. CePt$_6$ due to charge transfer from the underneath CePt$_2$ layer. We discuss a possible two-dimensional coherent Kondo effect with the observed spectra on the 1 u.l. CePt$_6$.

Surface states and quasiparticle interference in Bernal and rhombohedral graphite with and without trigonal warping

We use an exact analytical technique [Phys. Rev. B \textbf{101}, 115405 (2020), Phys. Rev. B \textbf{102}, 165117 (2020)] to recover the surface Green's functions for Bernal (ABA) and rhombohedral (ABC) graphite. For rhombohedral graphite we recover the predicted surface flat bands. For Bernal graphite we find that the surface state spectral function is similar to the bilayer one, but the trigonal warping effects are enhanced, and the surface quasiparticles have a much shorter lifetime. We subsequently use the T-matrix formalism to study the quasiparticle interference patterns generated on the surface of semi-infinite ABA and ABC graphite in the presence of impurity scattering. We compare our predictions to experimental STM data of impurity-localized states on the surface of Bernal graphite which appear to be in a good agreement with our calculations.