Quasiparticle Interference Imaging Research Articles

Determining spin-orbit coupling in graphene by quasiparticle interference imaging

Inducing and controlling spin-orbit coupling (SOC) in graphene is key to create topological states of matter, and for the realization of spintronic devices. Placing graphene onto a transition metal dichalcogenide is currently the most successful strategy to achieve this goal, but there is no consensus as to the nature and the magnitude of the induced SOC. Here, we show that the presence of backscattering in graphene-on-WSe2 heterostructures can be used to probe SOC and to determine its strength quantitatively, by imaging quasiparticle interference with a scanning tunneling microscope. A detailed theoretical analysis of the Fourier transform of quasiparticle interference images reveals that the induced SOC consists of a valley-Zeeman (λvZ ≈ 2 meV) and a Rashba (λR ≈ 15 meV) term, one order of magnitude larger than what theory predicts, but in excellent agreement with earlier transport experiments. The validity of our analysis is confirmed by measurements on a 30 degree twist angle heterostructure that exhibits no backscattering, as expected from symmetry considerations. Our results demonstrate a viable strategy to determine SOC quantitatively by imaging quasiparticle interference.

Superconducting gap symmetry from Bogoliubov quasiparticle interference analysis on Sr2RuO4

The nature of the superconducting order parameter in ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ has generated intense interest in recent years. Since the superconducting gap is very small, high-resolution methods such as scanning tunneling spectroscopy might be the best chance to directly resolve the gap symmetry. Recently, a Bogoliubov quasiparticle interference imaging (BQPI) experiment has suggested that the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ gap symmetry is appropriate for ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$. In this work, we use a material-specific theoretical approach based on Wannier functions of the surface of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ to calculate the continuum density of states as detected in scanning tunneling microscopy experiments. We examine several different proposed gap order parameters and calculate the expected BQPI pattern for each case. Comparing to the available experimental data, our results suggest that a ${s}^{\ensuremath{'}}+i{d}_{xy}$ gap order parameter is the most probable state, but the measured BQPI patterns still display features unaccounted for by the theory for any of the states currently under discussion.

Evidence for chiral superconductivity on a silicon surface

Tin adatoms on a Si(111) substrate with a one-third monolayer coverage form a two-dimensional triangular lattice with one unpaired electron per site. These electrons order into an antiferromagnetic Mott-insulating state, but doping the Sn layer with holes creates a two-dimensional conductor that becomes superconducting at low temperatures. Although the pairing symmetry of the superconducting state is currently unknown, the combination of repulsive interactions and frustration inherent in the triangular adatom lattice opens up the possibility of a chiral order parameter. Here we study the superconducting state of Sn/Si(111) using scanning tunnelling microscopy, scanning tunnelling spectroscopy and quasiparticle interference imaging. We find evidence for a doping-dependent superconducting critical temperature with a fully gapped order parameter, the presence of time-reversal symmetry breaking and a strong enhancement in zero-bias conductance near the edges of the superconducting domains. Although each individual piece of evidence could have a more mundane interpretation, our combined results suggest the possibility that Sn/Si(111) is an unconventional chiral d-wave superconductor.

Nature of quasiparticle interference in three dimensions

Quasiparticle interference (QPI) imaging is a powerful tool for the study of the low-energy electronic structure of quantum materials. However, the measurement of QPI by scanning tunneling microscopy (STM) is restricted to surfaces and is thus inherently constrained to two dimensions. QPI has proved immensely successful for the study of materials that exhibit a quasi-two-dimensional electronic structure, yet it raises questions about how to interpret QPI in materials that have a highly three-dimensional electronic structure. In this paper, we address this question and establish the methodology required to simulate and understand QPI arising from three-dimensional systems as measured by STM. We calculate the continuum surface Green's function in the presence of a defect, which captures the role of the surface and the vacuum decay of the wave functions. We find that defects at different depths from the surface will produce unique sets of scattering vectors for three-dimensional systems, which nevertheless can be related to the three-dimensional electronic structure of the bulk material. We illustrate the consequences that the three-dimensionality of the electronic structure has on the measured QPI for a simple cubic nearest-neighbor tight-binding model, and then demonstrate application to a real material using a realistic model for PbS. Our method unlocks the use of QPI imaging for the study of quantum materials with three-dimensional electronic structures and introduces a framework to generically account for ${k}_{z}$ dispersions within QPI simulations.

Atomic-scale imaging of emergent order at a magnetic field-induced Lifshitz transition.

The phenomenology and radical changes seen in material properties traversing a quantum phase transition have captivated condensed matter research over the past decades. Strong electronic correlations lead to exotic electronic ground states, including magnetic order, nematicity, and unconventional superconductivity. Providing a microscopic model for these requires detailed knowledge of the electronic structure in the vicinity of the Fermi energy, promising a complete understanding of the physics of the quantum critical point. Here, we demonstrate such a measurement at the surface of Sr3Ru2O7. Our results show that, even in zero field, the electronic structure is strongly C2 symmetric and that a magnetic field drives a Lifshitz transition and induces a charge-stripe order. We track the changes of the electronic structure as a function of field via quasiparticle interference imaging at ultralow temperatures. Our results provide a complete microscopic picture of the field-induced changes of the electronic structure across the Lifshitz transition.

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

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.

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.

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.

Visualizing superconductivity in a doped Weyl semimetal with broken inversion symmetry

The Weyl semimetal $\mathrm{Mo}{\mathrm{Te}}_{2}$ offers a rare opportunity to study the interplay between Weyl physics and superconductivity. Recent studies have found that Se substitution can boost the superconductivity up to 1.5 K, but suppresses the ${T}_{d}$ structure phase that is essential for the emergence of the Weyl state. A microscopic understanding of the possible coexistence of enhanced superconductivity and the ${T}_{d}$ phase has not been established so far. Here, we use scanning tunneling microscopy to study an optimally doped superconductor $\mathrm{Mo}{\mathrm{Te}}_{1.85}{\mathrm{Se}}_{0.15}$ with bulk ${T}_{c}\ensuremath{\sim}1.5\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. By means of quasiparticle interference imaging, we identify the existence of a low-temperature ${T}_{d}$ phase with broken inversion symmetry where superconductivity globally coexists. Furthermore, we find that the superconducting coherence length, extracted from both the upper critical field and the decay of density of states near a vortex, is much larger than the characteristic length scale of the existing chemical disorder. Our findings of robust superconductivity arising from a Weyl semimetal normal phase in $\mathrm{Mo}{\mathrm{Te}}_{1.85}{\mathrm{Se}}_{0.15}$ make it a promising candidate for realizing topological superconductivity.

Quasiparticle interference and quantum confinement in a correlated Rashba spin-split 2D electron liquid.

Exploiting inversion symmetry breaking (ISB) in systems with strong spin-orbit coupling promises control of spin through electric fields-crucial to achieve miniaturization in spintronic devices. Delivering on this promise requires a two-dimensional electron gas with a spin precession length shorter than the spin coherence length and a large spin splitting so that spin manipulation can be achieved over length scales of nanometers. Recently, the transition metal oxide terminations of delafossite oxides were found to exhibit a large Rashba spin splitting dominated by ISB. In this limit, the Fermi surface exhibits the same spin texture as for weak ISB, but the orbital texture is completely different, raising questions about the effect on quasiparticle scattering. We demonstrate that the spin-orbital selection rules relevant for conventional Rashba system are obeyed as true spin selection rules in this correlated electron liquid and determine its spin coherence length from quasiparticle interference imaging.

Momentum-resolved superconducting energy gaps of Sr2RuO4 from quasiparticle interference imaging

Sr2RuO4 has long been the focus of intense research interest because of conjectures that it is a correlated topological superconductor. It is the momentum space (k-space) structure of the superconducting energy gap [Formula: see text] on each band i that encodes its unknown superconducting order parameter. However, because the energy scales are so low, it has never been possible to directly measure the [Formula: see text] of Sr2RuO4 Here, we implement Bogoliubov quasiparticle interference (BQPI) imaging, a technique capable of high-precision measurement of multiband [Formula: see text] At T = 90 mK, we visualize a set of Bogoliubov scattering interference wavevectors [Formula: see text] consistent with eight gap nodes/minima that are all closely aligned to the [Formula: see text] crystal lattice directions on both the α and β bands. Taking these observations in combination with other very recent advances in directional thermal conductivity [E. Hassinger et al., Phys. Rev. X 7, 011032 (2017)], temperature-dependent Knight shift [A. Pustogow et al., Nature 574, 72-75 (2019)], time-reversal symmetry conservation [S. Kashiwaya et al., Phys. Rev B, 100, 094530 (2019)], and theory [A. T. Rømer et al., Phys. Rev. Lett. 123, 247001 (2019); H. S. Roising, T. Scaffidi, F. Flicker, G. F. Lange, S. H. Simon, Phys. Rev. Res. 1, 033108 (2019); and O. Gingras, R. Nourafkan, A. S. Tremblay, M. Côté, Phys. Rev. Lett. 123, 217005 (2019)], the BQPI signature of Sr2RuO4 appears most consistent with [Formula: see text] having [Formula: see text] [Formula: see text] symmetry.

Quasiparticle Interference Studies of Quantum Materials.

Exotic electronic states are realized in novel quantum materials. This field is revolutionized by the topological classification of materials. Such compounds necessarily host unique states on their boundaries. Scanning tunneling microscopy studies of these surface states have provided a wealth of spectroscopic characterization, with the successful cooperation of ab initio calculations. The method of quasiparticle interference imaging proves to be particularly useful for probing the dispersion relation of the surface bands. Herein, how a variety of additional fundamental electronic properties can be probed via this method is reviewed. It is demonstrated how quasiparticle interference measurements entail mesoscopic size quantization and the electronic phase coherence in semiconducting nanowires; helical spin protection and energy-momentum fluctuations in a topological insulator; and the structure of the Bloch wave function and the relative insusceptibility of topological electronic states to surface potential in a topological Weyl semimetal.

Design and performance of an ultra-high vacuum spin-polarized scanning tunneling microscope operating at 30 mK and in a vector magnetic field.

We describe the design and performance of a scanning tunneling microscope (STM) that operates at a base temperature of 30 mK in a vector magnetic field. The cryogenics is based on an ultra-high vacuum (UHV) top-loading wet dilution refrigerator that contains a vector magnet allowing for fields up to 9 T perpendicular and 4 T parallel to the sample. The STM is placed in a multi-chamber UHV system, which allows in situ preparation and exchange of samples and tips. The entire system rests on a 150-ton concrete block suspended by pneumatic isolators, which is housed in an acoustically isolated and electromagnetically shielded laboratory optimized for extremely low noise scanning probe measurements. We demonstrate the overall performance by illustrating atomic resolution and quasiparticle interference imaging and detail the vibrational noise of both the laboratory and microscope. We also determine the electron temperature via measurement of the superconducting gap of Re(0001) and illustrate magnetic field-dependent measurements of the spin excitations of individual Fe atoms on Pt(111). Finally, we demonstrate spin resolution by imaging the magnetic structure of the Fe double layer on W(110).

Femtosecond electron-phonon lock-in by photoemission and x-ray free-electron laser.

The interactions that lead to the emergence of superconductivity in iron-based materials remain a subject of debate. It has been suggested that electron-electron correlations enhance electron-phonon coupling in iron selenide (FeSe) and related pnictides, but direct experimental verification has been lacking. Here we show that the electron-phonon coupling strength in FeSe can be quantified by combining two time-domain experiments into a "coherent lock-in" measurement in the terahertz regime. X-ray diffraction tracks the light-induced femtosecond coherent lattice motion at a single phonon frequency, and photoemission monitors the subsequent coherent changes in the electronic band structure. Comparison with theory reveals a strong enhancement of the coupling strength in FeSe owing to correlation effects. Given that the electron-phonon coupling affects superconductivity exponentially, this enhancement highlights the importance of the cooperative interplay between electron-electron and electron-phonon interactions.

Discovery of orbital-selective Cooper pairing in FeSe.

The superconductor iron selenide (FeSe) is of intense interest owing to its unusual nonmagnetic nematic state and potential for high-temperature superconductivity. But its Cooper pairing mechanism has not been determined. We used Bogoliubov quasiparticle interference imaging to determine the Fermi surface geometry of the electronic bands surrounding the Γ = (0, 0) and X = (π/aFe, 0) points of FeSe and to measure the corresponding superconducting energy gaps. We show that both gaps are extremely anisotropic but nodeless and that they exhibit gap maxima oriented orthogonally in momentum space. Moreover, by implementing a novel technique, we demonstrate that these gaps have opposite sign with respect to each other. This complex gap configuration reveals the existence of orbital-selective Cooper pairing that, in FeSe, is based preferentially on electrons from the d yz orbitals of the iron atoms.

Aspects of electron–phonon interactions with strong forward scattering in FeSe Thin Films on SrTiO3 substrates

Mono- and multilayer FeSe thin films grown on SrTiO3 and BiTiO3 substrates exhibit a greatly enhanced superconductivity over that found in bulk FeSe. A number of proposals have been advanced for the mechanism of this enhancement. One possibility is the introduction of a cross-interface electron–phonon (e–ph) interaction between the FeSe electrons and oxygen phonons in the substrates that is peaked in the forward scattering (small direction due to the two-dimensional nature of the interface system. Motivated by this, we explore the consequences of such an interaction on the superconducting state and electronic structure of a two-dimensional system using Migdal–Eliashberg (ME) theory. This interaction produces not only deviations from the expectations of conventional phonon-mediated pairing but also replica structures in the spectral function and density of states, as probed by angle-resolved photoemission spectroscopy, scanning tunneling microscopy/spectroscopy, and quasiparticle interference imaging. We also discuss the applicability of ME theory for a situation where the e–ph interaction is peaked at small momentum transfer and in the FeSe/STO system.

Revealing the Empty-State Electronic Structure of Single-Unit-Cell FeSe/SrTiO3.

We use scanning tunneling spectroscopy to investigate the filled and empty electronic states of superconducting single-unit-cell FeSe deposited on SrTiO3(001). We map the momentum-space band structure by combining quasiparticle interference imaging with decay length spectroscopy. In addition to quantifying the filled-state bands, we discover a Γ-centered electron pocket 75 meV above the Fermi energy. Our density functional theory calculations show the orbital nature of empty states at Γ and explain how the Se height is a key tuning parameter of their energies, with broad implications for electronic properties.

Direct evidence for a magnetic f-electron-mediated pairing mechanism of heavy-fermion superconductivity in CeCoIn5.

To identify the microscopic mechanism of heavy-fermion Cooper pairing is an unresolved challenge in quantum matter studies; it may also relate closely to finding the pairing mechanism of high-temperature superconductivity. Magnetically mediated Cooper pairing has long been the conjectured basis of heavy-fermion superconductivity but no direct verification of this hypothesis was achievable. Here, we use a novel approach based on precision measurements of the heavy-fermion band structure using quasiparticle interference imaging to reveal quantitatively the momentum space (k-space) structure of the f-electron magnetic interactions of CeCoIn5. Then, by solving the superconducting gap equations on the two heavy-fermion bands Ek(α,β) with these magnetic interactions as mediators of the Cooper pairing, we derive a series of quantitative predictions about the superconductive state. The agreement found between these diverse predictions and the measured characteristics of superconducting CeCoIn5 then provides direct evidence that the heavy-fermion Cooper pairing is indeed mediated by f-electron magnetism.

Quasiparticle interference in antiferromagnetic parent compounds of iron-based superconductors

Recently reported quasiparticle interference imaging in underdoped Ca(Fe${}_{1\ensuremath{-}x}$Co${}_{x}$)${}_{2}$As${}_{2}$ shows pronounced $C$${}_{2}$ asymmetry, which is interpreted as an indication of an electronic nematic phase with a unidirectional electron band, dispersive predominantly along the $b$ axis of this orthorhombic material. On the other hand, even more recent transport measurements on untwinned samples show near isotropy of the resistivity in the $\mathit{ab}$ plane, with slightly larger conductivity along $a$ (and not $b$). We show that, in fact, both sets of data are consistent with the calculated ab initio Fermi surfaces, which have a decisively broken $C$${}_{4}$ and yet similar Fermi velocity in both directions. This reconciles completely the apparent contradiction between the conclusions of the scanning tunneling microscopy and the transport experiments.