Quasiparticle Interference Research Articles

Fermi surface segmentation in the helical state of a Rashba superconductor

We investigate the quasiparticle excitations in the FFLO- type helical state of a superconductor with inversion-symmetry breaking and strong Rashba spin-orbit coupling. We restrict to a state with single finite momentum of Cooper pairs in the helical phase that is determined by minimization of the condensation energy. We derive the dependence of quasiparticle dispersions on the Rashba coupling strength and external field. It leads to a peculiar momentum-space segmentation of the corresponding Rashba Fermi surface sheets which has not yet been observed experimentally. We show that it may be directly visualized by the method of quasiparticle interference that identifies the critical points of the segmented sheets and can map their evolution with field strength, bias voltage and Rashba coupling. We also indicate a strategy how to determine the finite Cooper-pair momentum from experimental quantities. This investigation has the potential for a more detailed microscopic understanding of the helical superconducting state under the influence of Rashba spin-orbit coupling.

Orbital-Selective High-Temperature Cooper Pairing Developed in the Two-Dimensional Limit.

For multiband superconductors, the orbital multiplicity yields orbital differentiation in normal-state properties and can lead to orbital-selective spin-fluctuation Cooper pairing. The orbital-selective phenomenon has become increasingly pivotal in clarifying the pairing "enigma", particularly for multiband high-temperature superconductors. Meanwhile, in one-unit-cell (1-UC) FeSe/SrTiO3, since the standard electron-hole Fermi pocket nesting scenario is inapplicable, the actual pairing mechanism is subject to intense debate. Here, by measuring high-resolution Bogoliubov quasiparticle interference, we report observations of highly anisotropic magnetic Cooper pairing in 1-UC FeSe. Theoretically, it is important to incorporate orbitally selective effects of electronic correlations within a spin-fluctuation pairing calculation, where the dxy orbital becomes coherence-suppressed. The resulting pairing gap is compatible with the experimental findings, which suggests that high-Tc Cooper pairing with orbital selectivity applies to 2D-limit 1-UC FeSe. Our findings imply the general existence of orbital selectivity in iron-based superconductors and the universal significance of electron correlations in high-Tc superconductors.

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.

Quasiparticle interference observation of the topologically nontrivial drumhead surface state in ZrSiTe

Drumhead surface states that link together loops of nodal lines arise in Dirac nodal-line semimetals as a consequence of the topologically non-trivial band crossings. We used low-temperature scanning tunneling microscopy and Fourier-transformed scanning tunneling spectroscopy to investigate the quasiparticle interference (QPI) properties of ZrSiTe. Our results show two scattering signals across the drumhead state resolving the energy-momentum relationship through the occupied and unoccupied energy ranges it is predicted to span. Observation of this drumhead state is in contrast to previous studies on ZrSiS and ZrSiSe, where the QPI was dominated by topologically trivial bulk bands and surface states. Furthermore, we observe a near $\mathbf{k} \rightarrow -\mathbf{k}$ scattering process across the $\Gamma$-point, enabled by scattering between the spin-split drumhead bands in this material.

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.

Spin-polarized imaging of strongly interacting fermions in the ferrimagnetic state of the Weyl candidate CeBi

CeBi has an intricate magnetic phase diagram whose fully polarized state has recently been suggested as a Weyl semimetal, though the role of $f$ states in promoting strong interactions has remained elusive. Here we focus on the less-studied but also time-reversal symmetry-breaking ferrimagnetic phase of CeBi, where our density functional theory (DFT) calculations predict additional Weyl nodes near the Fermi level ${E}_{F}$. We use spin-polarized scanning tunneling microscopy and spectroscopy to image the surface ferrimagnetic order on the itinerant Bi $p$ states, indicating their orbital hybridization with localized Ce $f$ states. We observe suppression of this spin-polarized signature at ${E}_{F}$, coincident with a Fano line shape in the conductance spectra, suggesting the Bi $p$ states partially Kondo screen the $f$ magnetic moments, and this $p\ensuremath{-}f$ hybridization causes strong Fermi-level band renormalization. The $p$-band flattening is supported by our quasiparticle interference measurements, which also show band splitting in agreement with DFT, painting a consistent picture of a strongly interacting magnetic Weyl semimetal.

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.

Proximity-driven ferromagnetism and superconductivity in the triangular Rashba-Hubbard model

Bilayer Moir\'e structures are a highly tunable laboratory to investigate the physics of strongly correlated electron systems. Moir\'e transition metal dichalcogenides at low-energies, in particular, are believed to be described by a single narrow band Hubbard model on a triangular lattice with spin-orbit coupling. Motivated by recent experimental evidence for superconductivity in twisted bilayer materials, we investigate the possible superconducting pairings in a two-dimensional single band Rashba-Hubbard model. Using a random-phase approximation in the presence of nearest and next-nearest neighbor hopping, we analyze the structure of spin fluctuations and the symmetry of the superconducting gap function. We show that Rashba spin-orbit coupling favors ferromagnetic fluctuations which strengthen triplet superconductivity. If parity is violated due to the absence of spatial inversion symmetry, singlet (d-wave) and triplet (p-wave) channels of superconductivity will be mixed. Moreover, we show that time-reversal symmetry can be spontaneously broken leading to a chiral superconducting state. Finally, we consider quasiparticle interference as a possible experimental technique to observe the superconducting gap symmetry.

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.

Revealing sign-reversal s+− -wave pairing by quasiparticle interference in the heavy-fermion superconductor CeCu2Si2

Recent observations of two nodeless gaps in superconducting CeCu$_2$Si$_2$ have raised intensive debates as to its exact gap structure of either sign-reversal ($s^{+-}$) or sign-preserving ($s^{++}$) pairing. Here we investigate the quasiparticle interference (QPI) using realistic Fermi surface topology for both weak and strong interband impurity scatterings. Our calculations of the QPI and integrated antisymmetrized local density of states reveal qualitative distinctions between $s^{+-}$ and $s^{++}$ pairing states, which include the intragap impurity resonance and a significant energy-dependence difference between two gap energies. Our predictions provide a guide for phase-sensitive QPI measurements to uncover decisively the true pairing symmetry in the heavy-fermion superconductor CeCu$_2$Si$_2$.

Adaptive sparse sampling for quasiparticle interference imaging

Quasiparticle interference imaging (QPI) offers insight into the band structure of quantum materials from the Fourier transform of local density of states (LDOS) maps. Their acquisition with a scanning tunneling microscope is traditionally tedious due to the large number of required measurements that may take several days to complete. The recent demonstration of sparse sampling for QPI imaging showed how the effective measurement time could be fundamentally reduced by only sampling a small and random subset of the total LDOS. However, the amount of required sub-sampling to faithfully recover the QPI image remained a recurring question. Here we introduce an adaptive sparse sampling (ASS) approach in which we gradually accumulate sparsely sampled LDOS measurements until a desired quality level is achieved via compressive sensing recovery. The iteratively measured random subset of the LDOS can be interleaved with regular topographic images that are used for image registry and drift correction. These reference topographies also allow to resume interrupted measurements to further improve the QPI quality. Our ASS approach is a convenient extension to quasiparticle interference imaging that should remove further hesitation in the implementation of sparse sampling mapping schemes.• Accumulative sampling for unknown degree of sparsity• Controllably interrupt and resume QPI measurements• Scattering wave conserving background subtractions

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.

Charge transport spectra in superconductor-InAs/GaSb-superconductor heterostructures

Charge transport physics in InAs/GaSb bi-layer systems has recently attracted attention for the experimental search for two-dimensional topological superconducting states in solids. Here we report measurement of charge transport spectra of nano devices consisting of an InAs/GaSb quantum well sandwiched by tantalum superconductors. We explore the current-voltage relation as a function of the charge-carrier density in the quantum well controlled by a gate voltage and an external magnetic field. We observe three types of differential resistance peaks, all of which can be effectively tuned by the external magnetic field, and, however, two of which appear at electric currents independent of the gate voltage, indicating a dominant mechanism from the superconductor and the system geometry. By analyzing the spectroscopic features, we find that the three types of peaks identify Andreev reflections, quasi-particle interference, and superconducting transitions in the device, respectively. Our results provide a basis for further exploration of possible topological superconducting state in the InAs/GaSb system.

Quasi-particle interference of the van Hove singularity in Sr2RuO4

The single-layered ruthenate Sr2RuO4 is one of the most enigmatic unconventional superconductors. While for many years it was thought to be the best candidate for a chiral p-wave superconducting ground state, desirable for topological quantum computations, recent experiments suggest a singlet state, ruling out the original p-wave scenario. The superconductivity as well as the properties of the multi-layered compounds of the ruthenate perovskites are strongly influenced by a van Hove singularity in proximity of the Fermi energy. Tiny structural distortions move the van Hove singularity across the Fermi energy with dramatic consequences for the physical properties. Here, we determine the electronic structure of the van Hove singularity in the surface layer of Sr2RuO4 by quasi-particle interference imaging. We trace its dispersion and demonstrate from a model calculation accounting for the full vacuum overlap of the wave functions that its detection is facilitated through the octahedral rotations in the surface layer.

Phase diagram of CeSb2 from magnetostriction and magnetization measurements: Evidence for ferrimagnetic and antiferromagnetic states

Cerium diantimonide ($\mathrm{Ce}{\mathrm{Sb}}_{2}$) is one of a family of rare-earth-based magnetic materials that exhibit metamagnetism, enabling control of the magnetic ground state through an applied magnetic field. At low temperatures, $\mathrm{Ce}{\mathrm{Sb}}_{2}$ hosts a rich phase diagram with multiple magnetically ordered phases for many of which the order parameter is only poorly understood. In this paper, we report a study of its metamagnetic properties by scanning tunneling microscopy (STM) and magnetization measurements. We use STM measurements to characterize the sample magnetostriction with subpicometer resolution from magnetic field and temperature sweeps. This allows us to directly assess the bulk phase diagram as a function of field and temperature and relate spectroscopic features from tunneling spectroscopy to bulk phases. Our magnetostriction and magnetization measurements indicate that the low-temperature ground state at zero field is ferrimagnetic. Quasiparticle interference mapping shows evidence for a reconstruction of the electronic structure close to the Fermi energy upon entering the magnetically ordered phase.

Tomographic mapping of the hidden dimension in quasi-particle interference

Quasiparticle interference (QPI) imaging is well established to study the low-energy electronic structure in strongly correlated electron materials with unrivalled energy resolution. Yet, being a surface-sensitive technique, the interpretation of QPI only works well for anisotropic materials, where the dispersion in the direction perpendicular to the surface can be neglected and the quasiparticle interference is dominated by a quasi-2D electronic structure. Here, we explore QPI imaging of galena, a material with an electronic structure that does not exhibit pronounced anisotropy. We find that the quasiparticle interference signal is dominated by scattering vectors which are parallel to the surface plane however originate from bias-dependent cuts of the 3D electronic structure. We develop a formalism for the theoretical description of the QPI signal and demonstrate how this quasiparticle tomography can be used to obtain information about the 3D electronic structure and orbital character of the bands.

Surface step states and Majorana end states in profiled topological-insulator thin films

The protected helical surface states in thin films of topological insulators (TI) are subject to inter-surface hybridisation. This leads to gap opening and spin texture changes as witnessed in photoemission and quasiparticle interference investigations. Theoretical studies show that universally the hybridisation energy exhibits exponential decay as well as sign oscillations as a function of film thickness, depending on the effective band parameters of the material. When a step is introduced in the TI film e.g. by profiling the substrate such that the hybridisation has different signs on both sides of the step, 1D bound states appear within the hybridisation gap which decay exponentially with distance from the step. The step bound states have linear dispersion and inherit the helical spin locking from the surface states and are therefore non-degenerate. When the substrate becomes an s-wave superconductor Majorana zero modes located at the step ends are created inside the superconducting gap. The proposed scenario involves just a suitably stepped interface of superconductor and TI and therefore may be a most simple device being able to host Majorana zero modes.

Fast spectroscopic mapping of two-dimensional quantum materials

Spectroscopic mapping refers to the massive recording of spectra whilst varying an additional degree of freedom, such as: magnetic field, location, temperature, or charge carrier concentration. As this involves two serial tasks, spectroscopic mapping can become excruciatingly slow. We demonstrate exponentially faster mapping through our combination of sparse sampling and parallel spectroscopy. We exemplify our concept using quasiparticle interference imaging of Au(111) and Bi2Sr2CaCu2O8 (Bi2212), as two well-known model systems. Our method is accessible, straightforward to implement with existing scanning tunneling microscopes, and can be easily extended to enhance gate or field-mapping spectroscopy. In view of a possible four orders of magnitude speed advantage, it is setting the stage to fundamentally promote the discovery of novel quantum materials.