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The quantum many body states in the BCS-BEC crossover regime are of long-lasting interest. Here we report direct spectroscopic evidence of BCS-BEC crossover in real-space in a FeSe monolayer thin film by using spatially resolved scanning tunneling spectra. The crossover is driven by the shift of band structure relative to the Fermi level. The theoretical calculation based on a two-band model qualitatively reproduces the measured spectra in the whole crossover range. In addition, the Zeeman splitting of the quasi-particle states is found to be consistent with the characteristics of a condensate. Our work paves the way to study the exotic states of BCS-BEC crossover in a two-dimensional crystalline material at the atomic scale.

Determining the pairing symmetry of single-layer FeSe on SrTiO$_3$ is the key to understanding the enhanced pairing mechanism; furthermore, it guides exploring new superconductors with high transition temperatures ($T_\mathrm{c}$). Despite significant efforts, it remains controversial whether the symmetry is the sign-preserving $s$- or the sign-changed $s_{\pm}$-wave. Here, we investigate the pairing symmetry of single-layer FeSe from a topological point of view. Using low-temperature scanning tunneling microscopy/spectroscopy, we have systematically characterized the superconducting states at isolated edges and corners of single-layer FeSe. The tunneling spectra collected at edges and corners exhibit full gap and substantial dip, respectively, demonstrating the absence of topologically non-trivial edge/corner modes. According to the theoretical calculation, these spectroscopic features are strong evidence for the sign-preserving $s$-wave pairing.

Monolayer FeSe grown on SrTiO$_3$ provides a new playground for high-Tc superconductivity. A recent study shows the importance of stripy instability for superconductivity enhancement in FeSe/SrTiO3. However, it is still under debate whether such a stripe phase is ubiquitously bound to the interfacial superconductivity. Here, we report on molecular beam epitaxy growth and low-temperature scanning tunneling microscopy study of FeSe films on BaTiO$_3$(001). We find that the stripe phase is more prominent in FeSe/BaTiO$_3$. Long-range stripes exist in bilayer and triple-layer FeSe films at 4 K and even persist up to 77 K in the case of bilayer FeSe, with enlarged superconducting gaps upon alkali-metal deposition. The results point out an intimate correlation between the interfacial superconductivity and the stripe phase., Comment: Comments are welcome

The intrinsic magnetic topological insulator MnBi2Te4 provides a feasible pathway to high temperature quantum anomalous Hall (QAH) effect as well as various novel topological quantum phases. Although quantized transport properties have been observed in exfoliated MnBi2Te4 thin flakes, it remains a big challenge to achieve molecular beam epitaxy (MBE)-grown MnBi2Te4 thin films even close to the quantized regime. In this work, we report the realization of quantized anomalous Hall resistivity in MBE-grown MnBi2Te4 thin films with the chemical potential tuned by both controlled in-situ oxygen exposure and top gating. We find that elongated post-annealing obviously elevates the temperature to achieve quantization of the Hall resistivity, but also increases the residual longitudinal resistivity, indicating a picture of high-quality QAH puddles weakly coupled by tunnel barriers. These results help to clarify the puzzles in previous experimental studies on MnBi2Te4 and to find a way out of the big difficulty in obtaining MnBi2Te4 samples showing quantized transport properties., Comment: 4 figures

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

Understanding the rich and competing electronic orders in cuprate superconductors may provide important insight into the mechanism of high-temperature superconductivity. Here, by measuring Bi2Sr2CaCu2O8+x in the extremely underdoped regime, we obtain evidence for a distinct type of ordering, which manifests itself as resistance oscillations at low magnetic fields (<10 T) and at temperatures around the superconducting transition. By tuning the doping level p continuously, we reveal that these low-field oscillations occur only when p<0.1. The oscillation amplitude increases with decreasing p but the oscillation period stays almost constant. We show that these low-field oscillations can be well described by assuming a periodic superconducting structure with a mesh size of about 50 nm. Such a charge order, which is distinctly different from the well-established charge density wave and pair density wave, seems to be an unexpected piece of the puzzle on the correlated physics in cuprates.

Here we visualize the trapping of topological surface states in the circular n-p junctions on the top surface of the 7-quintuple-layer three dimensional (3D) topological insulator (TI) Sb2Te3 epitaxial films. As shown by spatially- and field-dependent tunneling spectra, these trapped resonances show field-induced splittings between the degenerate time-reversal-symmetric states at zero magnetic field. These behaviors are attributed unambiguously to Berry-phase switch by comparing the experimental data with both numerical and semi-classical simulations. The successful electrostatic trapping of topological surface states in epitaxial films and the observation of Berry-phase switch provide a rich platform of exploiting new ideas for TI-based quantum devices., Comment: 24pages,including the supplementary materials

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

The surface of a three-dimensional topological insulator (TI) hosts two-dimensional massless Dirac fermions (DFs), the gapless and spin-helical nature of which yields many exotic phenomena, such as the immunity of topological surface states (TSS) to back-scattering. This leads to their high transmission through surface defects or potential barriers. Quantum corrals, previously elaborated on metal surfaces, can act as nanometer-sized electronic resonators to trap Schr\"odinger electrons by quantum confinement. It is thus intriguing, concerning their peculiar nature, to put the Dirac electrons of TSS to the test in similar circumstances. Here, we report the behaviors of TSS in a triangular quantum corral (TQC) fabricated by epitaxially growing Bi bilayer nanostructures on the surfaces of Bi2Te3 films. Unlike a circular corral, the TQC is supposed to be totally transparent for DFs. By mapping the electronic structure of TSS inside TQCs through a low-temperature scanning tunneling microscope in the real space, both the trapping and de-trapping behaviors of the TSS electrons are observed. The selection rules are found to be governed by the geometry and spin texture of the constant energy contour of TSS upon the strong hexagonal warping in Bi2Te3. Careful analysis of the quantum interference patterns of quasi-bound states yields the corresponding wave vectors of trapped TSS, through which two trapping mechanisms favoring momenta in different directions are uncovered. Our work indicates the extended nature of TSS and elucidates the selection rules of the trapping of TSS in the presence of a complicated surface state structure, giving insights into the effective engineering of DFs in TIs., Comment: 31pages, 12figures(including supplementary materials)

We report phase coherent electron transport in PbTe nanowire networks with a loop geometry. Magneto-conductance shows Aharonov-Bohm (AB) oscillations with periods of $h/e$ and $h/2e$ in flux. The amplitude of $h/2e$ oscillations is enhanced near zero magnetic field, possibly due to interference between time-reversal paths. Temperature dependence of the AB amplitudes suggests a phase coherence length $\sim$ 8 - 12 $\mu$m at 50 mK. This length scale is larger than the typical geometry of PbTe-based hybrid semiconductor-superconductor nanowire devices., Comment: Raw data and processing codes within this paper are available at https://zenodo.org/record/5798424

The chirality associated with broken time reversal symmetry in magnetically doped topological insulators has important implications to the quantum transport phenomena. Here we report the anomalous Hall effect studies in Mn- and Cr-doped Bi$_2$Te$_3$ topological insulators with varied thickness and doping content. By tracing the chirality of the Hall loops, we find that the Mn-type anomalous Hall effect with clockwise chirality is strengthened by the reduction of film thickness, which is opposite to that of the Cr-type anomalous Hall effect with counterclockwise chirality. We provide a phenomenological model to explain the evolution of magnetic order and anomalous Hall effect chirality in magnetically doped topological insulators., Comment: 11 pages, 5 figures

The nature of the anomalous metal state has been a major puzzle in condensed matter physics for more than three decades. Here, we report systematic investigation and modulation of the anomalous metal states in high-temperature interface superconductor FeSe films on SrTiO3 substrate. Remarkably, under zero magnetic field, the anomalous metal state persists up to 20 K in pristine FeSe films, an exceptionally high temperature standing out from previous observations. In stark contrast, for the FeSe films with nano-hole arrays, the characteristic temperature of the anomalous metal state is considerably reduced. We demonstrate that the observed anomalous metal states originate from the quantum tunneling of vortices adjusted by the Ohmic dissipation. Our work offers a perspective for understanding the origin and modulation of the anomalous metal states in two-dimensional bosonic systems.

Topological quantum computing is based on braiding of Majorana zero modes encoding topological qubits. A promising candidate platform for Majorana zero modes is semiconductor-superconductor hybrid nanowires. The realization of topological qubits and braiding operations requires scalable and disorder-free nanowire networks. Selective area growth of in-plane InAs and InSb nanowires, together with shadow-wall growth of superconductor structures, have demonstrated this scalability by achieving various network structures. However, the noticeable lattice mismatch at the nanowire-substrate interface, acting as a disorder source, imposes a serious obstacle along with this roadmap. Here, combining selective area and shadow-wall growth, we demonstrate the fabrication of PbTe-Pb hybrid nanowires - another potentially promising Majorana system - on a nearly perfectly lattice-matched substrate CdTe, all done in one molecular beam epitaxy chamber. Transmission electron microscopy shows the single-crystal nature of the PbTe nanowire and its atomically sharp and clean interfaces to the CdTe substrate and the Pb overlayer, without noticeable inter-diffusion or strain. The nearly ideal interface condition, together with the strong screening of charge impurities due to the large dielectric constant of PbTe, hold promise towards a clean nanowire system to study Majorana zero modes and topological quantum computing., Comment: 19 pages, 4+7 figures

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

We report on in situ low-temperature (4 K) scanning tunneling microscope measurements of atomic and electronic structures of the cleaved surfaces of an alkali-based kagome metal RbV$_3$Sb$_5$ single crystals. We find that the dominant pristine surface exhibits Rb-1x1 structure, in which a unique unidirectional $\sqrt{3}a_0$ charge order is discovered. As the sample temperature slightly rises, Rb-$\sqrt{3}$x1 and Rb-$\sqrt{3}$x$\sqrt{3}$ reconstructions form due to desorption of surface Rb atoms. Our conductance mapping results demonstrate that Rb desorption not only gives rise to hole doping, but also renormalizes the electronic band structures. Surprisingly, we find a ubiquitous gap opening near the Fermi level in tunneling spectra on all the surfaces despite their large differences of hole-carrier concentration, indicating an orbital-selective band reconstruction in RbV$_3$Sb$_5$., Comment: Comments are welcome

Superconductivity and charge density wave (CDW) appear in the phase diagram of a variety of materials including the high - $T$$_c$ cuprate family and many transition metal dichalcogenides (TMDs). Their interplay may give rise to exotic quantum phenomena. Here, we show that superconducting arrays can spontaneously form in TiSe$_2$ - a TMD with coexisting superconductivity and CDW - after lithium ion intercalation. We induce a superconducting dome in the phase diagram of Li$_x$TiSe$_2$ by using the ionic solid-state gating technique. Around optimal doping, we observe magnetoresistance oscillations, indicating the emergence of periodically arranged domains. In the same temperature, magnetic field and carrier density regime where the resistance oscillations occur, we observe signatures for the anomalous metal - a state with a resistance plateau across a wide temperature range below the superconducting transition. Our study not only sheds further insight into the mechanism for the periodic electronic structure, but also reveals the interplay between the anomalous metal and superconducting fluctuations.

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.

Superconductivity is significantly enhanced in monolayer FeSe grown on SrTiO3, but not for multilayer films, in which large strength of nematicity develops. However, the link between the high-transition temperature superconductivity in monolayer and the correlation related nematicity in multilayer FeSe films is not well understood. Here, we use low-temperature scanning tunneling microscopy to study few-layer FeSe thin films grown by molecular beam epitaxy. We observe an incommensurate long-range smectic phase, which solely appears in bilayer FeSe films. The smectic order still locally exists and gradually fades away with increasing film thickness, while it suddenly vanishes in monolayer FeSe, indicative of an abrupt smectic phase transition. Surface alkali-metal doping can suppress the smectic phase and induce high-Tc superconductivity in bilayer FeSe. Our observations provide evidence that the monolayer FeSe is in close proximity to the smectic phase, and its superconductivity is likely enhanced by this electronic instability as well., Comment: Comments are welcome: )

We report transport measurements on Josephson junctions consisting of Bi2Te3 topological insulator (TI) thin films contacted by superconducting Nb electrodes. For a device with junction length L = 134 nm, the critical supercurrent Ic can be modulated by an electrical gate which tunes the carrier type and density of the TI film. Ic can reach a minimum when the TI is near the charge neutrality regime with the Fermi energy lying close to the Dirac point of the surface state. In the p-type regime the Josephson current can be well described by a short ballistic junction model. In the n-type regime the junction is ballistic at 0.7 K < T < 3.8 K while for T < 0.7 K the diffusive bulk modes emerge and contribute a larger Ic than the ballistic model. We attribute the lack of diffusive bulk modes in the p-type regime to the formation of p-n junctions. Our work provides new clues for search of Majorana zero mode in TI-based superconducting devices., Comment: 6 pages, 4 figures, The manuscript with the same title will be published by Chinese Physics Letters

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

The accurate theoretical description of the underlying electronic structures is essential for understanding the superconducting mechanism of iron-based superconductors. Compared to bulk FeSe, the superconducting single-layer FeSe/SrTiO3 films exhibit a distinct electronic structure consisting of only electron Fermi pockets, due to the formation of a new band gap at the Brillouin zone (BZ) corners and an indirect band gap between the BZ center and corners. Although intensive studies have been carried out, the origin of such a distinct electronic structure and its connection to bulk FeSe remain unclear. Here we report a systematic study on the temperature evolution of the electronic structure in single-layer FeSe/SrTiO3 films by angle-resolved photoemission spectroscopy. A temperature-induced electronic phase transition was clearly observed at 200 K, above which the electronic structure of single-layer FeSe/SrTiO3 films restored to that of bulk FeSe, characterized by the closing of the new band gap and the vanishing of the indirect band gap. Moreover, the interfacial charge transfer effect induced band shift of ~ 60 meV was determined for the first time. These observations not only show the first direct evidence that the electronic structure of single-layer FeSe/SrTiO3 films originates from bulk FeSe through a combined effect of an electronic phase transition and an interfacial charge transfer, but also provide a quantitative basis for theoretical models in describing the electronic structure and understanding the superconducting mechanism in single-layer FeSe/SrTiO3 films., Comment: 18 pages, 4 figures

Quantum Griffiths singularity (QGS) reveals the profound influence of quenched disorder on the quantum phase transitions, characterized by the divergence of the dynamical critical exponent at the boundary of the vortex glass-like phase, named as quantum Griffiths phase. However, in the absence of vortices, whether the QGS can exist under parallel magnetic field remains a puzzle. Here we study the magnetic field induced superconductor-metal transition in ultrathin crystalline PdTe2 films grown by molecular beam epitaxy. Remarkably, the QGS emerges under both perpendicular and parallel magnetic field in 4-monolayer PdTe2 films. The direct activated scaling analysis with a new irrelevant correction has been proposed, providing important evidence of QGS. With increasing film thickness to 6 monolayers, the QGS disappears under perpendicular field but persists under parallel field, and this discordance may originate from the differences in microscopic processes. Our work demonstrates the universality of parallel field induced QGS and can stimulate further investigations on novel quantum phase transitions under parallel magnetic field.

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

One-dimensional (1D) metallic mirror-twin boundaries (MTBs) in monolayer transition metal dichalcogenides (TMDCs) exhibit a periodic charge modulation and provide an ideal platform for exploring collective electron behavior in the confined system. The underlying mechanism of the charge modulation and how the electrons travel in 1D structures remain controversial. Here, for the first time, we observed atomic-scale structures of the charge distribution within one period in MTB of monolayer MoTe2 by using scanning tunneling microscopy/spectroscopy (STM/STS). The coexisting apparent periodic lattice distortions and U-shaped energy gap clearly demonstrate a Peierls-type charge density wave (CDW). Equidistant quantized energy levels with varied periodicity are further discovered outside the CDW gap along the metallic MTB. Density functional theory (DFT) calculations are in good agreement with the gapped electronic structures and reveal they originate mainly from Mo 4d orbital. Our work presents hallmark evidence of the 1D Peierls-type CDW on the metallic MTBs and offers opportunities to study the underlying physics of 1D charge modulation., Comment: 19pages,5figures

Exotic quantum phenomena have been demonstrated in recently discovered intrinsic magnetic topological insulator MnBi2Te4. At its two-dimensional limit, quantum anomalous Hall (QAH) effect and axion insulator state are observed in odd and even layers of MnBi2Te4, respectively. The measured band structures exhibit intriguing and complex properties. Here we employ low-temperature scanning tunneling microscopy to study its surface states and magnetic response. The quasiparticle interference patterns indicate that the electronic structures on the topmost layer of MnBi2Te4 is different from that of the expected out-of-plane A-type antiferromagnetic phase. The topological surface states may be embedded in deeper layers beneath the topmost surface. Such novel electronic structure presumably related to the modification of crystalline structure during sample cleaving and re-orientation of magnetic moment of Mn atoms near the surface. Mn dopants substituted at the Bi site on the second atomic layer are observed. The ratio of Mn/Bi substitutions is 5%. The electronic structures are fluctuating at atomic scale on the surface, which can affect the magnetism of MnBi2Te4. Our findings shed new lights on the magnetic property of MnBi2Te4 and thus the design of magnetic topological insulators.

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

We show that topological equivalence classes of circles in a two-dimensional square lattice can be used to design dynamical decoupling procedures to protect qubits attached on the edges of the lattice. Based on the circles of the topologically trivial class in the original and the dual lattices, we devise a procedure which removes all kinds of local Hamiltonians from the dynamics of the qubits while keeping information stored in the homological degrees of freedom unchanged. If only the linearly independent interaction and nearest-neighbor two-qubit interactions are concerned, a much simpler procedure which involves the four equivalence classes of circles can be designed. This procedure is compatible with Eulerian and concatenated dynamical decouplings, which make it possible to implement the procedure with bounded-strength controls and for a long time period. As an application, it is shown that our method can be directly generalized to finite square lattices to suppress uncorrectable errors in surface codes., Comment: 8 pages, 8 figues

Identification and control of topological phases in topological thin films offer great opportunity for fundamental research and the fabrication of topology-based devices. Here, combining molecular beam epitaxy, angle-resolved photoemission spectroscopy and ab-initio calculations, we investigate the electronic structure evolution in (Bi1-xInx)2Se3 films with thickness from 2 to 13 quintuple layers. We identify several phases with their characteristic topological nature and evolution between them, i.e., dimensional crossover from a three-dimensional topological insulator with gapless surface state to its two-dimensional counterpart with gapped surface state, and topological phase transition from topological insulator to a normal semiconductor with increasing In concentration x. Furthermore, by introducing In alloying as an external knob of band gap engineering, we experimentally demonstrated the trivial topological nature of Bi2Se3 thin films (below 6 quintuple layers) as two-dimensional gapped systems, in consistent with our theoretical calculations. Our results provide not only a comprehensive phase diagram of (Bi1-xInx)2Se3 and a route to control its phase evolution, but also a practical way to experimentally determine the topological properties of a gapped compound by topological phase transition and band gap engineering., Comment: 24 pages, 4 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 interplay between disorder and superconductivity is a subtle and fascinating phenomenon in quantum many body physics. The conventional superconductors are insensitive to dilute nonmagnetic impurities, known as the Anderson's theorem. Destruction of superconductivity and even superconductor-insulator transitions occur in the regime of strong disorder. Hence disorder-enhanced superconductivity is rare and has only been observed in some alloys or granular states. Because of the entanglement of various effects, the mechanism of enhancement is still under debate. Here we report well-controlled disorder effect in the recently discovered monolayer NbSe$_2$ superconductor. The superconducting transition temperatures of NbSe$_2$ monolayers are substantially increased by disorder. Realistic theoretical modeling shows that the unusual enhancement possibly arises from the multifractality of electron wave functions. This work provides the first experimental evidence of the multifractal superconducting state.

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.

SnTe hosts ferroelectricity that competes with its weak non-trivial band topology: in the high-symmetry rocksalt structure--in which its intrinsic electric dipole is quenched--this material develops metallic surface bands, but in its rhombic ground-state configuration--that hosts a non-zero spontaneous electric dipole--the crystalline symmetry is lowered and the presence of surface electronic bands is not guaranteed. Here, the type of ferroelectric coupling and the atomistic and electronic structure of SnTe films ranging from 2 to 40 ALs are examined on freestanding samples, to which atomic layers were gradually added. 4 AL SnTe films are antiferroelectrically-coupled, while thicker freestanding SnTe films are ferroelectrically-coupled. The electronic band gap reduces its magnitude in going from 2 ALs to 40 ALs but it does not close due to the rhombic nature of the structure. These results bridge the structure of SnTe films from the monolayer to the bulk.

Since the discovery of high temperature superconductivity in cuprates, Josephson junction based phase-sensitive experiments are believed and used to provide the most convincing evidence for determining the pairing symmetry. Regardless of different junction materials and geometries used, quantum tunneling involved in these experiments is essentially a nanoscale process, and thus, actual experimental results are extremely sensitive to atomic details of the junction structures. The situation has led to controversial results as to the nature of the pairing symmetry of cuprates: while in-plane junction experiments generally support $d$-wave pairing symmetry, those based on out-of-plane ($c$-axis) Josephson junctions between two rotated cuprate blocks favor $s$-wave pairing. In this work, we revisit the $c$-axis experiment by fabricating Josephson junctions with atomic-level control in their interface structure. We fabricate over 90 junctions of ultrathin Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ (BSCCO) flakes by state-of-the-art exfoliation technique and obtain atomically flat junction interfaces in the whole junction regions as characterized by high resolution transmission electron microscopy (TEM). Notably, the resultant uniform junctions at various twist angles all exhibit a single tunneling branch behavior, suggesting that only the first half a unit cell on both sides of the twisted flakes is involved in Josephson tunneling process. With such well-defined geometry/structure and the characteristic single tunneling branch, we repeatedly observe Josephson tunneling at a nominal twist angle of 45 degrees, which is against the expectation from a purely $d$-wave pairing scenario. Our results strongly favor the scenario of a persistent $s$-wave order parameter in the junction., Comment: 11 pages, 10 figures

Spin-orbit coupling has proven indispensable in realizing topological materials and more recently Ising pairing in two-dimensional superconductors. This pairing mechanism relies on inversion symmetry breaking and sustains anomalously large in-plane polarizing magnetic fields whose upper limit is expected to diverge at low temperatures, although experimental demonstration of this has remained elusive due to the required fields. In this work, the recently discovered superconductor few-layer stanene, i.e. epitaxially strained $\alpha$-Sn, is shown to exhibit a new type of Ising pairing between carriers residing in bands with different orbital indices near the $\Gamma$-point. The bands are split as a result of spin-orbit locking without the participation of inversion symmetry breaking. The in-plane upper critical field is strongly enhanced at ultra-low temperature and reveals the sought for upturn.

We report high-resolution scanning tunneling microscopy (STM) study of nano-sized Pb islands grown on SrTiO3, where three distinct types of gaps with different energy scales are revealed. At low temperature, an enlarged superconducting gap ({\Delta}s) emerges while there is no enhancement in superconducting transition temperature (Tc), giving rise to a larger BCS ratio 2{\Delta}s/kBTc ~ 6.22. The strong coupling here may originate from the electron-phonon coupling on the metal-oxide interface. As the superconducting gap is suppressed under applied magnetic field or at elevated temperature, Coulomb gap and pseudogap appear, respectively. The Coulomb gap is sensitive to the lateral size of Pb islands, indicating that quantum size effect is able to influence electronic correlation, which is usually ignored in low-dimensional superconductivity. Our experimental results shall shed important light on the interplay between quantum size effect and correlations in nano-sized superconductors.

We prepared single unit cell FeSe films on GaO$_{2-\delta}$ terminated perovskite NdGaO$_{3}$(110) substrates and performed ex situ transport and scanning transmission electron microscopy measurements on the FeTe protected films. Our experimental measurements showed that the single unit cell FeSe films interfaced with GaO$_{2-{\delta}}$ layer are electron doped via interface charge transfer. Most importantly, this type of heterostructure can host interface enhanced superconductivity with an onset temperature of about 28 K, which is much higher than the value of 8 K in bulk FeSe. Our work indicates that FeSe/GaO$_{2-{\delta}}$can be a comparative platform with the FeSe/TiO$_{2-{\delta}}$ family for understanding the mechanism of interface enhanced high temperature superconductivity.

Quantum spin Hall (QSH) effect is an intriguing phenomenon arising from the helical edge states in two-dimensional topological insulators. We use molecular beam epitaxy (MBE) to prepare FeSe films with atomically sharp nematic domain boundaries, where tensile strains, nematicity suppression and topological band inversion are simultaneously achieved. Using scanning tunneling microscopy (STM), we observe edge states at the Fermi level that spatially distribute as two distinct strips in the vicinity of the domain boundaries. At the endpoint of the boundaries, a bound state at the Fermi level is further observed. The topological origin of the edge states is supported by density functional theory calculations. Our findings not only demonstrate a candidate for QSH states, but also provide a new pathway to realize topological superconductivity in a single-component film.