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We report transport measurements of infinite-layer cuprate Sr$_{1-x}$Eu$_{x}$CuO$_{2+y}$ films with controlled electron (by trivalent europium) and hole (by interstitial apical oxygen) carriers grown on SrTiO$_3$(001) with molecular beam epitaxy. An unusual enhancement of superconductivity upon moderate electron-hole coexistence in the films is found, which spans over the whole superconducting phase diagram and becomes more prominent in the underdoped regime. The superconductivity exhibits a two-dimensional nature with a thickness of approximately 5.2 nm, irrespective of the varying carriers, confirmed by angle-resolved magnetoresistance measurements and the Berzzinsky-Kosterlitz-Thouless transition. Nevertheless, the electron-hole coexistence enlarges the thermal activation energy of vortex motion that deviates obviously from the usual logarithmic evolution with the magnetic field. Our results offer a promising perspective to understand and enhance the high-temperature superconductivity in cuprates., Comment: 6 pages, 4 figures

Unconventional superconductors that spontaneously break space-group symmetries of their underlying crystal lattice are distinguished by spatial modulations of the superconducting order parameter. These states have recently captured significant attention in various strongly correlated materials, where the breaking of translational or intra-unit-cell symmetries results in the emergence of pair density waves with wavelengths extending across one or multiple unit cells. Here, we employ a spectroscopic-imaging scanning tunneling microscope to identify robust half-unit-cell modulations of the superconducting gap magnitude, coherence strength and subgap states in tunable 1T$^{\prime}$-MoTe$_2$ monolayer. The modulations are oriented perpendicular to the zigzag Mo chains and coexist with three-unit-cell primary pair density wave modulations along the Mo chains, both of which attenuate with increasing temperature and the application of external magnetic fields. Importantly, we find that the superconductivity modulations are strongly linked to unconventional electron pairing mechanisms, which significantly deviate from the Cooper pairing observed in traditional Bardeen-Cooper-Schrieffer superconductors. Our results advance the knowledge of Cooper-pair density modulations and the intricate interplay with other symmetry-breaking states in strongly correlated superconductors., Comment: 31 pages,4 figures

Magnetic impurities in superconductors are of increasing interest due to emergent Yu-Shiba-Rusinov (YSR) states and Majorana zero modes for fault-tolerant quantum computation. However, a direct relationship between the YSR multiple states and magnetic anisotropy splitting of quantum impurity spins remains poorly characterized. By using scanning tunneling microscopy, we resolve systematically individual transition-metal (Fe, Cr and Ni) impurities induced YSR multiplets as well as their Zeeman effects in K$_3$C$_{60}$ superconductor. The YSR multiplets show identical $d$ orbital-like wave functions that are symmetry-mismatched to the threefold K$_3$C$_{60}$(111) host surface, breaking point-group symmetries of the spatial distribution of YSR bound states in real space. Remarkably, we identify an unprecedented fermion-parity-preserving quantum phase transition between ground states with opposite signs of the uniaxial magnetic anisotropy that can be manipulated by an external magnetic field. These findings can be readily understood in terms of anisotropy splitting of quantum impurity spins, and thus elucidate the intricate interplay between the magnetic anisotropy and YSR multiplets., Comment: 38 pages, 4 figures in the main text

YBa$_2$Cu$_3$O$_{7-\delta}$ (YBCO) has favorable macroscopic superconducting properties of $T_\mathrm{c}$ up to 93 K and $H_{c2}$ up to 150 T. However, its nanoscale electronic structure remains mysterious because bulk-like electronic properties are not preserved near the surface of cleaved samples for easy access by local or surface-sensitive probes. It has been hypothesized that Ca-doping at the Y site could induce an alternate cleavage plane that mitigates this issue. We use scanning tunneling microscopy (STM) to study both Ca-free and 10% Ca-doped YBCO, and find that the Ca-doped samples do indeed cleave on an alternate plane, yielding a spatially-disordered partial (Y,Ca) layer. Our density functional theory calculations support the increased likelihood of this new cleavage plane in Ca-doped YBCO. On this surface, we image a superconducting gap with average value 24 $\pm$ 3 meV and characteristic length scale 1-2 nm, similar to Bi-based high-$T_\mathrm{c}$ cuprates, but the first map of gap inhomogeneity in the YBCO family., Comment: corrected typo in metadata author name

Non-trivial electronic states are attracting intense attention in low-dimensional physics. Though chirality has been identified in charge states with a scalar order parameter, its intertwining with charge density waves (CDW), film thickness and the impact on the electronic behaviors remain less well understood. Here, using scanning tunneling microscopy, we report a 2 x 2 chiral CDW as well as a strong suppression of the Te-5p hole-band backscattering in monolayer 1T-TiTe2. These exotic characters vanish in bilayer TiTe2 with a non-CDW state. Theoretical calculations approve that chirality comes from a helical stacking of the triple-q CDW components and therefore can persist at the two-dimensional limit. Furthermore, the chirality renders the Te-5p bands an unconventional orbital texture that prohibits electron backscattering. Our study establishes TiTe2 as a promising playground for manipulating the chiral ground states at the monolayer limit and provides a novel path to engineer electronic properties from an orbital degree., Comment: 21 pages, 5 figures

Electronic liquid-crystal phases are observed in numerous strongly-correlated systems including high-temperature superconductors. However, identifying these exotic phases and understanding their interplay with superconductivity in topological materials remain challenging. Here we employ a cryogenic scanning tunneling microscopy to discover a smectic (stripe) charge order (CO) and a primary pair-density-wave (PDW) in topological monolayer 1T$^\prime$-MoTe$_2$. The two orders are spatially modulated unidirectionally at the same wavevector, but have a marked spatial phase difference of about 2$\pi$/5. Importantly, the primary PDW state features a two-gap superconductivity below the transition temperature of 6.0 K and induces another unique particle-hole-symmetric CO at twice the PDW wavevector. Combining these results and our density functional calculations, we reveal that the two smectic orders are primarily driven by nesting behaviors between electron and hole pockets. Our findings establish monolayer 1T$^\prime$-MoTe$_2$ as a topological paradigm for exploring electronic smecticity, which intertwines with multiple preexisting symmetry-breaking states., Comment: 16 pages, 4 figures, Supplementary materials

Motivated by the discovery of superconductivity in the infinite-layer nickelate family, we report an experimental endeavor to clean the surface of nickelate superconductor Pr0.8Sr0.2NiO2 films by Ar+ ion sputtering and subsequent annealing, and we study their electronic structures by cryogenic scanning tunneling microscopy and spectroscopy. The annealed surfaces are characterized by nano-sized clusters and Coulomb staircases with periodicity inversely proportional to the projected area of the nanoclusters, consistent with a double-barrier tunneling junction model. Moreover, the dynamical Coulomb blockade effects are observed and result in well-defined energy gaps around the Fermi level, which correlate closely with the specific configuration of the junctions. These Coulomb blockade-related phenomena provide an alternative plausible cause of the observed gap structure that should be considered in the spectroscopic understanding of nickelate superconductors with the nano-clustered surface., Comment: 7 pages, 5 figures

Physics-informed neural networks (PINNs) have effectively been demonstrated in solving forward and inverse differential equation problems, but they are still trapped in training failures when the target functions to be approximated exhibit high-frequency or multi-scale features. In this paper, we propose to employ implicit stochastic gradient descent (ISGD) method to train PINNs for improving the stability of training process. We heuristically analyze how ISGD overcome stiffness in the gradient flow dynamics of PINNs, especially for problems with multi-scale solutions. We theoretically prove that for two-layer fully connected neural networks with large hidden nodes, randomly initialized ISGD converges to a globally optimal solution for the quadratic loss function. Empirical results demonstrate that ISGD works well in practice and compares favorably to other gradient-based optimization methods such as SGD and Adam, while can also effectively address the numerical stiffness in training dynamics via gradient descent., Comment: 17 pages, published as a conference paper at AAAI23

The tilted viewing nature of the off-nadir aerial images brings severe challenges to the building change detection (BCD) problem: the mismatch of the nearby buildings and the semantic ambiguity of the building facades. To tackle these challenges, we present a multi-task guided change detection network model, named as MTGCD-Net. The proposed model approaches the specific BCD problem by designing three auxiliary tasks, including: (1) a pixel-wise classification task to predict the roofs and facades of buildings; (2) an auxiliary task for learning the roof-to-footprint offsets of each building to account for the misalignment between building roof instances; and (3) an auxiliary task for learning the identical roof matching flow between bi-temporal aerial images to tackle the building roof mismatch problem. These auxiliary tasks provide indispensable and complementary building parsing and matching information. The predictions of the auxiliary tasks are finally fused to the main building change detection branch with a multi-modal distillation module. To train and test models for the BCD problem with off-nadir aerial images, we create a new benchmark dataset, named BANDON. Extensive experiments demonstrate that our model achieves superior performance over the previous state-of-the-art competitors.

Interest in superconducting proximity effect has been revived by the exploitation of Andreev states and by the possible emergence of Majorana bound states at the interface. Spectroscopy of these states has been so far restricted to just a handful of superconductor-metal systems in the diffusion regime, whereas reports in otherwise clean superconductor-superconductor heterojunctions are scarce. Here, we realize molecular beam epitaxy growth of atomically sharp planar heterojunctions between Pb and a topological superconductor candidate RhPb2 that allows us to spectroscopically image the proximity effect in the clean limit. The measured energy spectra of RhPb2 vary with the spatial separation from proximal Pb, and exhibit unusual modifications in the pairing gap structure and size that extend over a distance far beyond the coherence length. This anomalously long-range proximity (LRP) effect breaks the rotational symmetry of Cooper pair potential in real space and largely deforms the Abrikosov vortex cores. Our work opens promising avenues for fundamental studies of the Andreev physics and extraordinary states in clean superconducting heterojunctions., Comment: 8 pages, 4 figures

It is predicted that a vortex in a topological superconductor contains a Majorana zero mode (MZM). The confirmative Majorana signature, i.e., the $2e^2/h$ quantized conductance, however is easily sabotaged by unavoidable interruptions, e.g. instrument broadening, non-Majorana signal, and extra particle channels. We propose to avoid the signal interruption by introducing disorder-induced dissipation that couples to the tip-sample tunneling. With dissipation involved, we highlight three features, each of which alone can provide a strong evidence to identify MZM. Firstly, dissipation suppresses a finite-energy Caroli-de Gennes-Matricon (CdGM) conductance peak into a valley, while it does not split MZM zero-bias conductance peak. Secondly, we predict a dissipation-dependent scaling feature of the zero-bias conductance peak. Thirdly, the introduced dissipation manifests the MZM signal by suppressing non-topological CdGM modes. Importantly, the observation of these features does not require a quantized conductance value $2e^2/h$., Comment: We express our gratitude to Dr. Odobesko for bringing to our attention an intriguing and pertinent experimental paper: Phys. Rev. B 102, 174502 (2020), which is Ref. [71] of the current arXiv version

Electron-doped infinite-layer Sr$_{1-x}$Eu$_{x}$CuO$_{2+y}$ films over a wide doping range have been prepared epitaxially on SrTiO$_3$(001) using reactive molecular beam epitaxy. In-plane transport measurements of the single crystalline samples reveal a dome-shaped nodeless superconducting phase centered at $x$ $\sim$ 0.15, a Fermi-liquid behavior and pronounced upturn in low temperature resistivity. We show that the resistivity upturn follows square-root temperature dependence, suggesting the emergence of superconductivity via a three-dimensional percolation process. The percolative superconductivity is corroborated spectroscopically by imaging the electronic phase separation between superconducting and metallic phases with low-temperature scanning tunneling microscopy. Furthermore, we visualize interstitial and apical oxygen anions that rapidly increase in number as $x>$ 0.12, and elucidate their impacts on the superconductivity and normal-state resistivity., Comment: 5 pages, 4 figures, 9 supplemental figures

The microscopic understanding of high-temperature superconductivity in cuprates has been hindered by the apparent complexity of crystal structures in these materials. We used scanning tunneling microscopy and spectroscopy to study an electron-doped copper oxide compound Sr$_{1-x}$Nd$_x$CuO$_2$ that has only bare cations separating the CuO$_2$ planes and thus the simplest infinite-layer structure among all cuprate superconductors. Tunneling conductance spectra of the major CuO$_2$ planes in the superconducting state revealed direct evidence for a nodeless pairing gap, regardless of variation of its magnitude with the local doping of trivalent neodymium. Furthermore, three distinct bosonic modes are observed as multiple peak-dip-hump features outside the superconducting gaps and their respective energies depend little on the spatially varying gaps. Along with the bosonic modes with energies identical to those of the external, bending and stretching phonons of copper oxides, our findings indicate their origin from lattice vibrations rather than spin excitations., Comment: 16 Pages, 4 figures, 5 supplemental figures

The successful preparation of superconducting alkali fulleride (A$_x$C$_{60}$, A = K, Rb, Cs) films using state-of-the-art molecular beam epitaxy overcomes the disadvantages of the air-sensitivity and phase separation in bulk A$_x$C$_{60}$, enabling for the first time a direct investigation of the superconductivity in alkali fullerides on the molecular scale. In this paper, we briefly review recent cryogenic scanning tunneling microscopy results of the structural, electronic, and superconducting properties of the fcc A$_x$C$_{60}$ films grown on graphitized SiC substrates. Robust $s$-wave superconductivity is revealed against the pseudogap, electronic correlation, non-magnetic impurities, and merohedral disorder. By controlling the alkali metal species, film thickness, and electron doping, we systematically tune the C$_{60}^{x-}$ orientational orderings and superconductivity in A$_x$C$_{60}$ films and then complete a unified phase diagram of superconducting gap size vs electronic correlation and doping. These investigations are conclusive and elucidated that the $s$-wave superconductivity retains in alkali fullerides despite of the electronic correlation and presence of pseudogap., Comment: 20 pages, 19 figures

Charge modulations have been widely observed in cuprates, suggesting their centrality for understanding the high-$T_c$ superconductivity in these materials. However, the dimensionality of these modulations remains controversial, including whether their wavevector is unidirectional or bidirectional, and also whether they extend seamlessly from the surface of the material into the bulk. Material disorder presents severe challenges to understanding the charge modulations through bulk scattering techniques. We use a local technique, scanning tunneling microscopy, to image the static charge modulations on Bi$_{2-z}$Pb$_z$Sr$_{2-y}$La$_y$CuO$_{6+x}$. By comparing the phase correlation length $\xi_{\mathrm{CDW}}$ with the orientation correlation length $\xi_{\mathrm{orient}}$, we show that the charge modulations are more consistent with an underlying unidirectional wave vector. Using cluster techniques, we show that these locally 1D charge modulations are actually a bulk effect resulting from 3D criticality throughout the entire superconducting doping range.

Two-dimensional honeycomb crystals have inspired intense research interest for their novel properties and great potential in electronics and optoelectronics. Here, through molecular beam epitaxy on SrTiO3(001), we report successful epitaxial growth of metal-rich chalcogenide Fe2Te, a honeycomb-structured film that has no direct bulk analogue, under Te-limited growth conditions. The structural morphology and electronic properties of Fe2Te are explored with scanning tunneling microscopy and angle resolved photoemission spectroscopy, which reveal electronic bands cross the Fermi level and nearly flat bands. Moreover, we find a weak interfacial interaction between Fe2Te and the underlying substrates, paving a newly developed alternative avenue for honeycomb-based electronic devices., Comment: 12 pages,5 figures

Unusual quantum phenomena usually emerge upon doping Mott insulators. Using a combinatorial molecular beam epitaxy system integrated with cryogenic scanning tunneling microscopy, we investigate the electronic structure of a modulation-doped Mott insulator Sn/Si(111)-($\sqrt{3}\times \sqrt{3}$)-R30$^\textrm{o}$. In underdoped regions, we observe a universal pseudogap opening around the Fermi level, which changes little with the applied magnetic field and the occurrence of Sn vacancies. The pseudogap gets smeared out at elevated temperatures and alters in size with the spatial confinement of the Mott insulating phase. Our findings, along with the previously observed superconductivity at a higher doping level, are highly reminiscent of the electronic phase diagram in the doped copper oxide compounds., Comment: 5 pages, 4 figures

Interface phonon modes that are generated by several atomic layers at the heterointerface play a major role in the interface thermal conductance for nanoscale high-power devices such as nitride-based high-electron-mobility transistors and light emitting diodes. Here we measure the local phonon spectra across AlN/Si and AlN/Al interfaces using atomically resolved vibrational electron energy-loss spectroscopy in a scanning transmission electron microscope. At the AlN/Si interface, we observe various localized phonon modes, of which the extended and interfacial modes act as bridges to connect the bulk AlN modes and bulk Si modes, and are expected to boost the inelastic phonon transport thus substantially contribute to interface thermal conductance. In comparison, no such phonon bridge is observed at the AlN/Al interface, for which partially extended modes dominate the interface thermal conductivity. This work provides valuable insights into understanding the interfacial thermal transport in nitride semiconductors and useful guidance for thermal management via interface engineering.

Charge density wave (CDW) is a collective quantum phenomenon in metals and features a wave-like modulation of the conduction electron density. A microscopic understanding and experimental control of this many-body electronic state in atomically thin materials remain hot topics in materials physics. By means of material engineering, we realized a dimensionality and Zr intercalation induced semiconductor-metal phase transition in 1T-ZrX$_2$ (X = Se, Te) ultra-thin films, accompanied by a commensurate 2 $\times$ 2 CDW order. Furthermore, we observed a CDW energy gap up to 22 meV around the Fermi level. Fourier-transformed scanning tunneling microscopy and angle-resolved photoemission spectroscopy reveal that 1T-ZrX$_2$ films exhibit the simplest Fermi surface among the known CDW materials in TMDCs, consisting only of Zr 4d-derived elliptical electron conduction band at the corners of the Brillouin zone., Comment: 29 pages, 4 figures, 4 Supplementary notes

Materials with reduced dimensionality often exhibit exceptional properties that are different from their bulk counterparts. Here we report the emergence of a commensurate 2 $\times$ 2 charge density wave (CDW) in monolayer and bilayer SnSe$_2$ films by scanning tunneling microscope. The visualized spatial modulation of CDW phase becomes prominent near the Fermi level, which is pinned inside the semiconductor band gap of SnSe$_2$. We show that both CDW and Fermi level pinning are intimately correlated with band bending and virtual induced gap states at the semiconductor heterointerface. Through interface engineering, the electron-density-dependent phase diagram is established in SnSe$_2$. Fermi surface nesting between symmetry inequivalent electron pockets is revealed to drive the CDW formation and to provide an alternative CDW mechanism that might work in other compounds., Comment: 5 pages, 5 figures

Local quasiparticle states around impurities provide essential insight into the mechanism of unconventional superconductivity, especially when the candidate materials are proximate to an antiferromagnetic Mott-insulating phase. While such states have been reported in atom-based cuprates and iron-based compounds, they are unexplored in organic superconductors which feature tunable molecular orientation. Here we employ scanning tunneling microscopy and spectroscopy to reveal multiple forms of robustness of an exotic $s$-wave superconductivity in epitaxial Rb$_3$C$_{60}$ films against merohedral disorder, non-magnetic single impurities and step edges at the atomic scale. Also observed have been Yu-Shiba-Rusinov (YSR) states induced by deliberately incurred Fe adatoms that act as magnetic scatters. The bound states display abrupt spatial decay and vary in energy with the Fe adatom registry. Our results and the universal optimal superconductivity at half-filling point towards local electron pairing in which the multiorbital electronic correlations and intramolecular phonons together drive the high-temperature superconductivity of doped fullerenes., Comment: 25 pages, 5 figures, 5 supplemental figures

Scanning tunneling microscopy and spectroscopy are utilized to study the atomic-scale structure and electronic properties of infinite-layer Sr0.94La0.06CuO2+y films prepared on SrRuO3-buffered SrTiO3(001) substrate by ozone-assisted molecular beam epitaxy. Incommensurate structural supermodulation with a period of 24.5{\AA} is identified on the CuO2-terminated surface, leading to characteristic stripes running along the 45o direction with respect to the Cu-O-Cu bonds. Spatially resolved tunneling spectra reveal substantial inhomogeneity on a nanometer length scale and emergence of in-gap states at sufficient doping. Despite the Fermi level shifting up to 0.7 eV, the charge-transfer energy gap of the CuO2 planes remains fundamentally unchanged at different doping levels. The occurrence of the CuO2 superstructure is constrained in the surface region and its formation is found to link with oxygen intake that serves as doping agent of holes in the epitaxial films., Comment: 5 pages, 4 figures, also see arXiv:1904.12280

We report on the epitaxial growth and surface structure of infinite-layer cuprate Sr1-xNdxCuO2 films on SrTiO3(001) substrates by combining ozone-assisted molecular beam epitaxy and in situ scanning tunneling microscopy. Careful substrate temperature and flux control has been used to achieve single-phase, stoichiometric, and c-axis oriented films. The surface of the films is usually characterized by a mixed CuO2 surface and gridlike superstructure. The superstructure exhibits a periodicity of 3.47 nm that corresponds to a coincidence lattice between the overlayer peroxide SrO2 and underlying CuO2 plane, and gives rise to a conductance spectrum that is distinct from the Mott-Hubbard band structure of CuO2. At a higher Nd composition x > 0.1, a (2 x 2) surface characteristic of the hole-doped CuO2 emerges, which we ascribe to the intake of apical oxygens in the intervening Sr planes., Comment: 5 pages, 4 figures

Cryogenic scanning tunneling microscopy is employed to investigate the stoichiometry and defects of epitaxial FeSe thin films on SrTiO3(001) substrates under various post-growth annealing conditions. Low-temperature annealing with an excess supply of Se leads to formation of Fe vacancies and superstructures, accompanied by a superconductivity (metal)-to-insulator transition in FeSe films. By contrast, high-temperature annealing could eliminate the Fe vacancies and superstructures, and thus recover the high-temperature superconducting phase of monolayer FeSe films. We also observe multilayer FeSe during low-temperature annealing, which is revealed to link with Fe vacancy formation and adatom migration. Our results document very special roles of film stoichiometry and help unravel several controversies in the properties of monolayer FeSe films., Comment: 5 pages, 4 figures

Alkali-fulleride superconductors with a maximum critical temperature Tc of 40 K exhibit similar electronic phase diagram with unconventional high-Tc superconductors where the superconductivity resides proximate to a magnetic Mott-insulating state. However, distinct from cuprate compounds, which superconduct through two-dimensional (2D) CuO2 planes, alkali fullerides are attributed to the three-dimensional (3D) members of high-Tc family. Here, we employ scanning tunneling microscopy to show that trilayer K3C60 displays fully gapped strong coupling s-wave superconductivity that coexists spatially with a cuprate-like pseudogap state above Tc = 22 K and within vortices. A precise control of electronic correlations and doping reveals that superconductivity occurs near a superconductor-Mott insulator transition and reaches maximum at half-filling. The s-wave symmetry retains over the entire phase diagram, which, in conjunction with an abrupt decline of superconductivity below half-filling, demonstrates that alkali fullerides are predominantly phonon-mediated superconductors, although the multiorbital electronic correlations also come into play., Comment: 10 pages, 5 figures, supplementary materials

Alkali-doped fullerides exhibit a wealth of unusual phases that remain controversial by nature. Here we report a cryogenic scanning tunneling microscopy study of the sub-molecular structural and electronic properties of expanded fullerene C60 films with various cesium (Cs) doping. By varying the discrete charge states and film thicknesses, we reveal a large tunability of orientational ordering of C60 anions, yet the tunneling conductance spectra are all robustly characteristic of energy gaps, hallmarks of Jahn-Teller instability and electronic correlations. The Fermi level lies halfway within the insulating gap for stoichiometric Cs doping level of n = 1, 2, 3 and 4, apart from which it moves toward band edges with concomitant electronic states within the energy gap. Our findings establish the universality of Jahn-Teller instability, and clarify the relationship among the doping, structural and electronic structures in CsnC60 fullerides., Comment: 9 pages, 6 figures

The cuprate superconductors exhibit ubiquitous instabilities toward charge-ordered states. These unusual electronic states break the spatial symmetries of the host crystal, and have been widely appreciated as essential ingredients for constructing a theory for high-temperature superconductivity in cuprates. Here we report real-space imaging of the doping-dependent charge orders in the epitaxial thin films of a canonical cuprate compound La2-xSrxCuO4 using scanning tunneling microscopy. As the films are moderately doped, we observe a crossover from incommensurate to commensurate (4a0, where a0 is the Cu-O-Cu distance) stripes. Furthermore, at lower and higher doping levels, the charge orders occur in the form of distorted Wigner crystal and grid phase of crossed vertical and horizontal stripes. We discuss how the charge orders are stabilized, and their interplay with superconductivity., Comment: 15 pages, 4 figures plus supplementary materials

Identifying the essence of doped Mott insulators is one of the major outstanding problems in condensed matter physics and the key to understanding the high-temperature superconductivity in cuprates. We report real space visualization of Mott transition in Sr1-xLaxCuO2+y cuprate films that cover the entire electron- and hole-doped regimes. Tunneling conductance measurements directly on the cooper-oxide (CuO2) planes reveal a systematic shift in the Fermi level, while the fundamental Mott-Hubbard band structure remains unchanged. This is further demonstrated by exploring atomic-scale electronic response of CuO2 to substitutional dopants and intrinsic defects in a sister compound Sr0.92Nd0.08CuO2. The results could be better explained in the framework of self-modulation doping, similar to that in semiconductor heterostructures, and form a basis for developing any microscopic theories for cuprate superconductivity., Comment: 5 pages, 4 figures, See Supplemental Material at https://journals.aps.org/prl/supplemental/10.1103/PhysRevLett.125.077002

The single-layer FeSe/SrTiO3 (FeSe/STO) films have attracted much attention because of their simple crystal structure, distinct electronic structure and record high superconducting transition temperature (Tc). The origin of the dramatic Tc enhancement in single-layer FeSe/STO films and the dichotomy of superconductivity between single-layer and multiple-layer FeSe/STO films are still under debate. Here we report a comprehensive high resolution angle-resolved photoemission spectroscopy and scanning tunneling microscopy/spectroscopy measurements on the electronic structure evolution with doping in single-layer and multiple-layer FeSe/STO films. We find that the single-layer FeSe/STO films have a distinct parent phase and a route of doping evolution to superconductivity that are fundamentally different from multiple-layer FeSe/STO films. The parent phase of the single-layer FeSe/STO films is insulating, and its doping evolution is very similar to that of doping a Mott insulator in cuprate superconductors. In multiple-layer FeSe/STO films, high-Tc superconductivity occurs by suppressing the nematic order in the parent compound with electron doping. The single-layer FeSe/STO films represent the first clear case in the iron-based superconductors that the parent compound is an insulator. Our observations of the unique parent state and doping evolution in the single-layer FeSe/STO films provide key insight in understanding its record high-Tc superconductivity. They also provide a new route of realizing superconductivity in iron-based superconductors that is common in high temperature cuprate superconductors.

The structural or electronic symmetry breaking of the host lattice is a recurrent phenomenon in many quantum materials, including superconductors. Yet, how these broken symmetry states affect the electronic pair wave function of superconductivity have been rarely elucidated. Here, using low-temperature scanning tunneling microscopy and first-principles calculations, we identify the broken rotational symmetry via stripe ordering on the (001) surface of perovskite BaBi3 films grown by molecular beam epitaxy, and show that it consequently leads to anisotropic superconductivity with twofold symmetry. In contrast, the structural disorder smears out the anisotropy of electron pairing and fills superconducting subgap density of states as the film thickness is reduced. A quasi-long range model of superconducting fluctuations is revealed to describe the tunneling conductance spectra of thin BaBi3 films well, and to exemplify how disorders contribute to the low-energy quasiparticle excitations in superconductors. Our findings help understand the effects of symmetry breaking states and disorders on superconductivity, particularly the existing tunneling conductance spectra there., Comment: 38 pages, 15 figures