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The iron-based superconductor FeTe$_{0.55}$Se$_{0.45}$ is a peculiar material: it hosts a surface state with a Dirac dispersion, is a putative topological superconductor hosting Majorana modes in vortices, and has an unusually low Fermi energy. The superconducting state is generally thought to be characterized by three gaps in different bands, with the usual homogenous, spatially extended Bogoliubov excitations -- in this work, we uncover evidence that it is instead of a very different nature. Our scanning tunneling spectroscopy data shows several peaks in the density of states above a full gap, and by analyzing the spatial and junction-resistance dependence of the peaks, we conclude that the peaks above the first one are not coherence peaks from different bands. Instead, comparisons with our simulations indicate that they originate from generalized Shiba states that are spatially overlapping. This can lead to an amorphous state of Bogoliubov quasiparticles, reminiscent of impurity bands in semiconductors. We discuss the origin and implications of this new state., Comment: 6 pages, 4 figures

Vertical charge order shapes the electronic properties in layered charge density wave (CDW) materials. Various stacking orders inevitably create nanoscale domains with distinct electronic structures inaccessible to bulk probes. Here, the stacking characteristics of bulk 1$T$-TaS$2$ are analyzed using scanning tunneling spectroscopy (STS) and density functional theory (DFT) calculations. It is observed that Mott-insulating domains undergo a transition to band-insulating domains restoring vertical dimerization of the CDWs. Furthermore, STS measurements covering a wide terrace reveal two distinct band insulating domains differentiated by band edge broadening. These DFT calculations reveal that the Mott insulating layers preferably reside on the subsurface, forming broader band edges in the neighboring band insulating layers. Ultimately, buried Mott insulating layers believed to harbor the quantum spin liquid phase are identified. These results resolve persistent issues regarding vertical charge order in 1$T$-TaS$2$, providing a new perspective for investigating emergent quantum phenomena in layered CDW materials., Comment: 26 pages and 13 figures

4Hb-TaS2 has been proposed to possess unconventional superconductivity with broken time reveral symmetry due to distinctive layered structure, featuring a heterojunction between a 2D triangular Mott insulator and a charge density wave metal. However, since a frustrated spin state in the correlated insulating layer is susceptible to charge ordering with carrier doping, it is required to investigate the charge distribution driven by inter-layer charge transfer to understand its superconductivity. Here, we use scanning tunneling microscopy and spectroscopy (STM/S) to investigate the charge ordered phases of 1T-TaS2 layers within 4Hb-TaS2, explicitly focusing on the non-half-filled regime. Our STS results show an energy gap which exhibits an out-of-phase relation with the charge density. We ascribe the competition between on-site and nonlocal Coulomb repulsion as the driving force for the charge-ordered insulating phase of a doped triangular Mott insulator. In addition, we discuss the role of the insulating layer in the enhanced superconductivity of 4Hb-TaS2., Comment: 18 pages, 6 figures

Solids undergoing a transition from order to disorder experience the proliferation of topological defects. The melting process generates transient quantum states. However, their dynamical nature with femtosecond lifetime hinders exploration with atomic precision. Here, we suggest an alternative approach to the dynamical melting process by focusing on the interface created by competing degenerate quantum states. We use a scanning tunneling microscope (STM) to visualize the unidirectional charge density wave (CDW) and its spatial progression ("static melting") across a twin domain boundary (TDB) in the layered material GdTe$_{3}$. Combining STM with a spatial lock-in technique, we reveal that the order parameter amplitude attenuates with the formation of dislocations and thus two different unidirectional CDWs coexist near the TDB, reducing the CDW anisotropy. Notably, we discover a correlation between this anisotropy and the CDW gap. Our study provides valuable insight into the behavior of topological defects and transient quantum states.

Surface reconstruction plays a vital role in determining the surface electronic structure and chemistry of semiconductors and metal oxides. However, it has been commonly believed that surface reconstruction does not occur in van der Waals layered materials, as they do not undergo significant bond breaking during surface formation. In this study, we present evidence that charge density wave (CDW) order in these materials can, in fact, cause CDW surface reconstruction through interlayer coupling. Using density functional theory calculations on the 1T-TaS2 surface, we reveal that CDW reconstruction, involving concerted small atomic displacements in the subsurface layer, results in a significant modification of the surface electronic structure, transforming it from a Mott insulator to a band insulator. This new form of surface reconstruction explains several previously unexplained observations on the 1T-TaS2 surface and has important implications for interpreting surface phenomena in CDW-ordered layered materials., Comment: 20 pages, 6 figures (Supplementary Information: 5 Pages, 3 figures)

Majorana bound states are putative collective excitations in solids that exhibit the self-conjugate property of Majorana fermions - they are their own antiparticles. In iron-based superconductors, zero-energy states in vortices have been reported as potential Majorana bound states, but the evidence remains controversial. Here, we use scanning tunneling noise spectroscopy to study the tunneling process into vortex bound states in the conventional superconductor NbSe2, and in the putative Majorana platform FeTe0.55Se0.45. We find that tunneling into vortex bound states in both cases exhibits charge transfer of a single electron charge. Our data for the zero-energy bound states in FeTe0.55Se0.45 exclude the possibility of Yu-Shiba-Rusinov states and are consistent with both Majorana bound states and trivial vortex bound states. Our results open an avenue for investigating the exotic states in vortex cores and for future Majorana devices, although further theoretical investigations involving charge dynamics and superconducting tips are necessary., Comment: 15 pages, 4 figures, and 16 pages for supplementary information

The bulk-boundary correspondence is an integral feature of topological analysis and the existence of boundary or interface modes offers direct insight into the topological structure of the Bloch wave function. While only the topology of the wave function has been considered relevant to boundary modes, we demonstrate that another geometric quantity, the so-called quantum distance, can also host a bulk-interface correspondence. We consider a generic class of two-dimensional flat band systems, where the flat band has a parabolic band-crossing with another dispersive band. While such flat bands are known to be topologically trivial, we show that the nonzero maximum quantum distance between the eigenstates of the flat band around the touching point guarantees the existence of boundary modes at the interfaces between two domains with different chemical potentials or different maximum quantum distance. Moreover, the maximum quantum distance can predict even the explicit form of the dispersion relation and decay length of the interface modes., Comment: 11pages, 5 figures

The idea that preformed Cooper pairs could exist in a superconductor above its zero-resistance state has been explored for unconventional, interface, and disordered superconductors, yet direct experimental evidence is lacking. Here, we use scanning tunneling noise spectroscopy to unambiguously show that preformed Cooper pairs exist up to temperatures much higher than the zero-resistance critical temperature $T_{C}$ in the disordered superconductor titanium nitride, by observing a clear enhancement in the shot noise that is equivalent to a change of the effective charge from 1 to 2 electron charges. We further show that spectroscopic gap fills up rather than closes when increasing temperature. Our results thus demonstrate the existence of a novel state above $T_{C}$ that, much like an ordinary metal, has no (pseudo)gap, but carries charge via paired electrons.

By using scanning tunneling microscopy (STM) we find and characterize dispersive, energy-symmetric in-gap states in the iron-based superconductor $\mathrm{FeTe}_{0.55}\mathrm{Se}_{0.45}$, a material that exhibits signatures of topological superconductivity, and Majorana bound states at vortex cores or at impurity locations. We use a superconducting STM tip for enhanced energy resolution, which enables us to show that impurity states can be tuned through the Fermi level with varying tip-sample distance. We find that the impurity state is of the Yu-Shiba-Rusinov (YSR) type, and argue that the energy shift is caused by the low superfluid density in $\mathrm{FeTe}_{0.55}\mathrm{Se}_{0.45}$, which allows the electric field of the tip to slightly penetrate the sample. We model the newly introduced tip-gating scenario within the single-impurity Anderson model and find good agreement to the experimental data.

We report on the fabrication and performance of a new kind of tip for scanning tunneling microscopy. By fully incorporating a metallic tip on a silicon chip using modern micromachining and nanofabrication techniques, we realize so-called smart tips and show the possibility of device-based STM tips. Contrary to conventional etched metal wire tips, these can be integrated into lithographically defined electrical circuits. We describe a new fabrication method to create a defined apex on a silicon chip and experimentally demonstrate the high performance of the smart tips, both in stability and resolution. In situ tip preparation methods are possible and we verify that they can resolve the herringbone reconstruction and Friedel oscillations on Au(111) surfaces. We further present an overview of possible applications.

Domain walls in interacting electronic systems can have distinct localized states, which often govern physical properties and may lead to unprecedented functionalities and novel devices. However, electronic states within domain walls themselves have not been clearly identified and understood for strongly correlated electron systems. Here, we resolve the electronic states localized on domain walls in a Mott-charge-density-wave(CDW) insulator 1T-TaS2 using scanning tunneling spectroscopy. We establish that the domain wall state decomposes into two nonconducting states located at the center of domain walls and edges of domains. Theoretical calculations reveal their atomistic origin as the local reconstruction of domain walls under the strong influence of electron correlation. Our results introduce a concept for the domain wall electronic property, the wall's own internal degrees of freedom, which is potentially related to the controllability of domain wall electronic properties.

Quantum states of strongly correlated electrons are of prime importance to understand exotic properties of condensed matter systems and the controllability over those states promises unique electronic devices such as a Mott memory. As a recent example, a ultrafast switching device was demonstrated using the transition between the correlated Mott insulating state and a hidden-order metallic state of a layered transition metal dichalcogenides 1T-TaS2. However, the origin of the hidden metallic state was not clear and only the macroscopic switching by laser pulse and carrier injection was reported. Here, we demonstrate the nanoscale manipulation of the Mott insulating state of 1T-TaS2. The electron pulse from a scanning tunneling microscope switches the insulating phase locally into a metallic phase which is textured with irregular domain walls in the charge density wave (CDW) order inherent to this Mott state. The metallic state is a novel correlated phase near the Mott criticality with a coherent feature at the Fermi energy, which is induced by the moderate reduction of electron correlation due to the decoherence in CDW. This work paves the avenue toward novel nanoscale electronic devices based on correlated electrons., Comment: Corrected typos

We investigate the interplay of the electron-electron and electron-phonon interactions in the electronic structure of an exotic insulating state in the layered dichalcogenide 1T-TaS2, where the charge-density-wave (CDW) order coexists with a Mott correlation gap. Scanning tunneling microscopy and spectroscopy measurements with high spatial and energy resolution determine unambiguously the CDW and the Mott gap as 0.20-0.24 eV and 0.32 eV, respectively, through the real space electron phases measured across the multiply formed energy gaps. An unusual local reduction of the Mott gap is observed on the defect site, which indicates the renormalization of the on-site Coulomb interaction by the electron-phonon coupling as predicted by the Hubbard-Holstein model. The Mott-gap renormalization provides new insight into the disorder-induced quasi-metallic phases of 1T-TaS2.