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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.

Magic-angle twisted bilayer graphene (MATBG) exhibits a rich variety of electronic states, including correlated insulators, superconductors, and topological phases. Understanding the microscopic mechanisms responsible for these phases requires determining the interplay between electron-electron interactions and quantum degeneracy due to spin and valley degrees of freedom. Signatures of strong electron-electron correlations have been observed at partial fillings of the flat electronic bands in recent spectroscopic measurements. Transport experiments have shown changes in the Landau level degeneracy at fillings corresponding to an integer number of electrons per moir\'e unit cell. However, the interplay between interaction effects and the degeneracy of the system is currently unclear. Using high-resolution scanning tunneling microscopy (STM), we observed a cascade of transitions in the spectroscopic properties of MATBG as a function of electron filling. We find distinct changes in the chemical potential and a rearrangement of the low-energy excitations at each integer filling of the moir\'e flat bands. These spectroscopic features are a direct consequence of Coulomb interactions, which split the degenerate flat bands into Hubbard sub-bands. We find these interactions, the strength of which we can extract experimentally, to be surprisingly sensitive to the presence of a perpendicular magnetic field, which strongly modifies the spectroscopic transitions. The cascade of transitions we report here characterizes the correlated high-temperature parent phase from which various insulating and superconducting ground-state phases emerge at low temperatures in MATBG.

We describe the design, construction, and performance of an ultra-high vacuum (UHV) scanning tunneling microscope (STM) capable of imaging at dilution-refrigerator temperatures and equipped with a vector magnet. The primary objective of our design is to achieve a high level of modularity by partitioning the STM system into a set of easily separable, interchangeable components. This naturally segregates the UHV needs of STM instrumentation from the typically non-UHV construction of a dilution refrigerator, facilitating the usage of non-UHV materials while maintaining a fully bakeable UHV chamber that houses the STM. The modular design also permits speedy removal of the microscope head from the rest of the system, allowing for repairs, modifications, and even replacement of the entire microscope head to be made at any time without warming the cryostat or compromising the vacuum. Without using cryogenic filters, we measured an electron temperature of 184 mK on a superconducting Al(100) single crystal., Comment: 13 pages, 10 figures

Superconducting proximity pairing in helical edge modes, such as those of topological insulators (TI), is predicted to provide a unique platform for realizing Majorana zero modes (MZMs). We use scanning tunneling microscopy measurements to probe the influence of proximity induced superconductivity and magnetism on the helical hinge states of Bi(111) films, grown on a superconducting Nb substrate and decorated with magnetic Fe clusters. Consistent with model calculations, our measurements reveal the emergence of a localized MZM at the interface between the superconducting helical edge channel and the Fe clusters with strong magnetization component along the edge. Our experiments also resolve the MZM spin signature that distinguishes it from trivial in-gap states that may accidently occur at zero energy in a superconductor.

The mathematical field of topology has become a framework to describe the low-energy electronic structure of crystalline solids. A typical feature of a bulk insulating three-dimensional topological crystal are conducting two-dimensional surface states. This constitutes the topological bulk-boundary correspondence. Here, we establish that the electronic structure of bismuth, an element consistently described as bulk topologically trivial, is in fact topological and follows a generalized bulk-boundary correspondence of higher-order: not the surfaces of the crystal, but its hinges host topologically protected conducting modes. These hinge modes are protected against localization by time-reversal symmetry locally, and globally by the three-fold rotational symmetry and inversion symmetry of the bismuth crystal. We support our claim theoretically and experimentally. Our theoretical analysis is based on symmetry arguments, topological indices, first-principle calculations, and the recently introduced framework of topological quantum chemistry. We provide supporting evidence from two complementary experimental techniques. With scanning-tunneling spectroscopy, we probe the unique signatures of the rotational symmetry of the one-dimensional states located at step edges of the crystal surface. With Josephson interferometry, we demonstrate their universal topological contribution to the electronic transport. Our work establishes bismuth as a higher-order topological insulator., Comment: 16 pages, 6 figures, accepted manuscript

One-dimensional topological superconductors host Majorana zero modes (MZMs), the non-local property of which could be exploited for quantum computing applications. Spin- polarized scanning tunneling microscopy measurements show that MZMs realized in self- assembled Fe chains on the surface of Pb have a spin polarization that exceeds that due to the magnetism of these chains. This feature, captured by our model calculations, is a direct consequence of the nonlocality of the Hilbert space of MZMs emerging from a topological band structure. Our study establishes spin polarization measurements as a diagnostic tool to uniquely distinguish topological MZMs from trivial in-gap states of a superconductor.

In this paper, we establish that Majorana zero modes emerging from a topological band structure of a chain of magnetic atoms embedded in a superconductor can be distinguished from trivial localized zero energy states that may accidentally form in this system using spin resolved measurements. To demonstrate this key Majorana diagnostics, we study the spin composition of magnetic impurity induced in-gap Shiba states in a superconductor using a quantum impurity model (at the mean-field level). By examining the spin and spectral densities in the context of the Bogoliubov-de Gennes (BdG) particle-hole symmetry, we derive a sum rule that relates the spin densities of localized Shiba states with those in the normal state without superconductivity. Extending our investigations to ferromagnetic chain of magnetic impurities, we identify key features of the spin properties of the extended Shiba state bands, as well as those associated with a localized Majorana end mode when the effect of spin-orbit interaction is included. We then formulate a phenomenological theory for the measurement of the local spin densities with spin-polarized scanning tunneling microscopy (STM) techniques. By combining the calculated spin densities and the measurement theory, we show that spin-polarized STM measurements can reveal a sharp contrast in spin polarization between an accidentally-zero-energy trivial Shiba state and a Majorana zero mode in a topological superconducting phase in atomic chains. We further confirm our results with numerical simulations that address generic parameter settings., Comment: 22 pages, 12 figures (references updated)

Ordered assemblies of magnetic atoms on the surface of conventional superconductors can be used to engineer topological superconducting phases and realize Majorana fermion quasiparticles (MQPs) in a condensed matter setting. Recent experiments have shown that chains of Fe atoms on Pb generically have the required electronic characteristics to form a 1D topological superconductor and have revealed spatially resolved signatures of localized MQPs at the ends of such chains. Here we report higher resolution measurements of the same atomic chain system performed using a dilution refrigerator scanning tunneling microscope (STM). With significantly better energy resolution than previous studies, we show that the zero bias peak (ZBP) in Fe chains has no detectable splitting from hybridization with other states. The measurements also reveal that the ZBP exhibits a distinctive 'double eye' spatial pattern on nanometer length scales. Theoretically we show that this is a general consequence of STM measurements of MQPs with substantial spectral weight in the superconducting substrate, a conclusion further supported by measurements of Pb overlayers deposited on top of the Fe chains. Finally, we report experiments performed with superconducting tips in search of the particle-hole symmetric MQP signature expected in such measurements., Comment: Accepted to Nature Physics; available through Advance online publication

Following the intense studies on topological insulators, significant efforts have recently been devoted to the search for gapless topological systems. These materials not only broaden the topological classification of matter but also provide a condensed matter realization of various relativistic particles and phenomena previously discussed mainly in high energy physics. Weyl semimetals host massless, chiral, low-energy excitations in the bulk electronic band structure, whereas a symmetry protected pair of Weyl fermions gives rise to massless Dirac fermions. We employed scanning tunneling microscopy/spectroscopy to explore the behavior of electronic states both on the surface and in the bulk of topological semimetal phases. By mapping the quasiparticle interference and emerging Landau levels at high magnetic field in Dirac semimetals Cd$_3$As$_2$ and Na$_3$Bi, we observed extended Dirac-like bulk electronic bands. Quasiparticle interference imaged on Weyl semimetal TaAs demonstrated the predicted momentum dependent delocalization of Fermi arc surface states in the vicinity of the surface-projected Weyl nodes.

Majorana fermions are predicted to localize at the edge of a topological superconductor, a state of matter that can form when a ferromagnetic system is placed in proximity to a conventional superconductor with strong spin-orbit interaction. With the goal of realizing a one-dimensional topological superconductor, we have fabricated ferromagnetic iron (Fe) atomic chains on the surface of superconducting lead (Pb). Using high-resolution spectroscopic imaging techniques, we show that the onset of superconductivity, which gaps the electronic density of states in the bulk of the Fe chains, is accompanied by the appearance of zero energy end states. This spatially resolved signature provides strong evidence, corroborated by other observations, for the formation of a topological phase and edge-bound Majorana fermions in our atomic chains., Comment: 18 pages, 5 figures, and supplementary information. appears in Science (2014)

The hallmark of a time-reversal symmetry protected topologically insulating state of matter in two-dimensions (2D) is the existence of chiral edge modes propagating along the perimeter of the system. To date, evidence for such electronic modes has come from experiments on semiconducting heterostructures in the topological phase which showed approximately quantized values of the overall conductance as well as edge-dominated current flow. However, there have not been any spectroscopic measurements to demonstrate the one-dimensional (1D) nature of the edge modes. Among the first systems predicted to be a 2D topological insulator are bilayers of bismuth (Bi) and there have been recent experimental indications of possible topological boundary states at their edges. However, the experiments on such bilayers suffered from irregular structure of their edges or the coupling of the edge states to substrate's bulk states. Here we report scanning tunneling microscopy (STM) experiments which show that a subset of the predicted Bi-bilayers' edge states are decoupled from states of Bi substrate and provide direct spectroscopic evidence of their 1D nature. Moreover, by visualizing the quantum interference of edge mode quasi-particles in confined geometries, we demonstrate their remarkable coherent propagation along the edge with scattering properties that are consistent with strong suppression of backscattering as predicted for the propagating topological edge states., Comment: 15 pages, 5 figures, and supplementary material

Condensed matter systems provide a rich setting to realize Dirac and Majorana fermionic excitations and the possibility to manipulate them in materials for potential applications. Recently, it has been proposed that Weyl fermions, which are chiral, massless particles, can emerge in certain bulk materials or in topological insulator multilayers and can produce unusual transport properties, such as charge pumping driven by a chiral anomaly. A pair of Weyl fermions protected by crystalline symmetry, effectively forming a massless Dirac fermion, has been predicted to appear as low energy excitations in a number of candidate materials termed three-dimensional (3D) Dirac semimetals. Here we report scanning tunneling microscopy (STM) measurements at sub-Kelvin temperatures and high magnetic fields on one promising host material, the II-V semiconductor Cd3As2. Our study provides the first atomic scale probe of Cd3As2, showing that defects mostly influence the valence band, consistent with the observation of ultra-high mobility carriers in the conduction band. By combining Landau level spectroscopy and quasiparticle interference (QPI), we distinguish a large spin-splitting of the conduction band in a magnetic field and its extended Dirac-like dispersion above the expected regime. A model band structure consistent with our experimental findings suggests that for a specific orientation of the applied magnetic field, Weyl fermions are the low-energy excitations in Cd3As2., Comment: Main Text: 17 pages, 4 figures. Supplementary Materials: 12 pages, 7 figures, Nature Materials (2014)

This is a revised version of a manuscript that was originally posted here in February of 2014. It has been accepted at the journal Inorganic Chemistry after reviews that included those of two crystallographers who made sure all the t's were crossed and the i's were dotted. The old work (from 1968) that said that Cd3As2 was noncentrosymmetric was mistaken, with the authors of that study making a type of error that in the 1980s became infamous in crystallography. As a result of the increased scrutiny of the issue of centrosymmetricity of the 1980's, there are now much better analysis tools to resolve the issue fully, and its important to understand that not just our crystals are centrosymmetric, even the old guy's crystals were centrosymmetric (and by implication everyone's are). There is no shame in having made that error back in the day and those authors would not find the current centrosymmetric result controversial; their paper is excellent in all other aspects. This manuscript describes how the structure is determined, explains the structure schematically, calculates the electronic structure based on the correct centrosymmetric crystal structure, and gives the structural details that should be used for future analysis and modeling., Comment: Accepted by ACS Inorganic Chemistry