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A conventional superconducting state may be replaced by another dissipationless state hosting Cooper pairs with a finite momentum, leaving thermodynamic footprints for such a phase transition. Recently, a novel type of finite momentum pairing, so-called orbital Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, has been proposed to occur in spin-orbit coupled superconductors such as bilayer $2\mathrm{H-NbSe_{2}}$. So far, a thermodynamic demonstration, which is key for establishing this exotic phase, has been lacking. Here, we reveal a first-order quantum phase transition to the orbital FFLO state in tunneling spectroscopic measurements on multilayer $2\mathrm{H-NbSe_{2}}$. The phase transition manifests itself as a sudden enhancement of the superconducting gap at an in-plane magnetic field $B_{//}$ well below the upper critical field. Furthermore, this transition shows prominent hysteresis by sweeping $B_{//}$ back and forth and quickly disappears once the magnetic field is tilted away from the sample plane by less than one degree. We obtain a comprehensive phase diagram for the orbital FFLO state and compare it with the theoretical calculation that takes into account the rearrangement of Josephson vortices. Our work elucidates the microscopic mechanism for the emergence of the orbital FFLO state.

In twisted bilayer graphene (TBG) devices, local strains often coexist and entangle with the twist-angle dependent moir\'e superlattice, both of which can significantly affect the electronic properties of TBG. Here, using low-temperature scanning tunneling microscopy, we investigate the fine evolution of the electronic structures of a TBG device with continuous variation of twist angles from 0.32{\deg} to 1.29{\deg}, spanning the first (1.1{\deg}), second (0.5{\deg}) and third (0.3{\deg}) magic angles. We reveal the exotic behavior of the flat bands and remote bands in both the energy space and real space near the magic angles. Interestingly, we observe an anomalous spectral weight transfer between the two flat band peaks in the tunneling spectra when approaching the first magic angle, suggesting strong inter-flat-bands interactions. The position of the remote band peak can be an index for the twist angle in TBG, since it positively correlates with the twist angle but is insensitive to the strain. Moreover, influences of the twist angle gradient on symmetry breaking of the flat bands are also studied.

In designing material functionality within the intricate realm of transition metal oxides, lattice structure and d-orbital occupancy are two principal determinants of the correlated physical properties, such as superconductivity. However, the modulation of these two factors is inherently limited by the need to balance thermodynamic stability, kinetic mobility, and synthesis precision, particularly for oxidation-demanding phases. We introduce a methodology, namely the gigantic-oxidative atomically layered epitaxy (GOAL-Epitaxy), enhancing oxidation power 3-4 orders of magnitude beyond oxide molecular beam epitaxy (OMBE) and pulsed laser deposition (PLD), while ensuring atomic-layer-by-layer growth of designed complex structures. Consequently, thermodynamic stability is markedly augmented at elevated temperatures, improving growth kinetics. We demonstrate the accurate synthesis of complex nickelates and cuprates, especially an artificially designed structure as a parent of high-temperature superconductivity, in which alternating single and double NiO2 layers possess distinct nominal d-orbital occupancy. The GOAL-Epitaxy enables material discovery within the vastly broadened growth parameter space.

The pairing mechanism behind the monolayer FeSe is one essential question for iron-based superconductors. In this work, we show the sublattice degree of freedoms of monolayer FeSe plays a special role in its pairing properties, namely the sublattice dichotomy. The high-quality monolayer FeSe samples with atomic flat $1\times1$ topography on the SrTiO$_3$(001) substrates are grown by molecular beam epitaxy. By comparing the tunneling spectra at $\alpha$ and $\beta$ Fe sublattices, we find the coherence peak of $\alpha$-Fe at the inner gap $+V_i$ is higher than $\beta$-Fe while the coherence peak of $\beta$-Fe at $-V_i$ is higher than $\alpha$-Fe with a similar amount. We also observed a reversed effect at the outer gap $\pm V_o$. We propose the $\eta$-pairing mechanism between $k$ and $-k+Q$ is the key mechanism for this unconventional sublattice dichotomy effect., Comment: 6 pages, 4 figures

Clean one-dimensional electron systems can exhibit quantized conductance. The plateau conductance doubles if the transport is dominated by Andreev reflection. Here, we report quantized conductance observed in both Andreev and normal-state transports in PbTe-Pb and PbTe-In hybrid nanowires. The Andreev plateau is observed at $4e^2/h$, twice of the normal plateau value of $2e^2/h$. In comparison, Andreev conductance in the best-optimized III-V nanowires is non-quantized due to mode-mixing induced dips (a disorder effect), despite the quantization of normal-state transport. The negligible mode mixing in PbTe hybrids indicates an unprecedented low-disorder transport regime for nanowire devices, beneficial for Majorana researches.

The intrinsic magnetic order, large topological-magnetic gap and rich topological phases make MnBi2Te4 a wonderful platform to study exotic topological quantum states such as axion insulator and Chern insulator. To realize and manipulate these topological phases in a MnBi2Te4 thin film, precise manipulation of the electric field across the film is essential, which requires a dual-gate structure. In this work, we achieve dual-gate tuning of MnBi2Te4 thin films grown with molecular beam epitaxy on SrTiO3(111) substrates by applying the substrate and an AlOx layer as the gate dielectrics of bottom and top gates, respectively. Under magnetic field of 9T and temperature of 20 mK, the Hall and longitudinal resistivities of the films show inversed gate-voltage dependence, for both top- and bottom-gates, signifying the existence of the dissipationless edge state contributed by Chern insulator phase in the ferromagnetic configuration. The maximum of the Hall resistivity only reaches 0.8 h/e2, even with dual-gate tuning, probably due to the high density of bulk carriers introduced by secondary phases. In the antiferromagnetic state under zero magnetic field, the films show normal insulator behavior. The dual-gated MnBi2Te4 thin films lay the foundation for developing devices based on electrically tunable topological quantum states., Comment: 24 pages, 4 figures

Vortices in superconductors can help identify emergent phenomena but certain fundamental aspects of vortices, such as their entropy, remain poorly understood. Here, we study the vortex entropy in underdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ by measuring both magneto-resistivity and Nernst effect on ultrathin flakes ($\le$2 unit-cell). We extract the London penetration depth from the magneto-transport measurements on samples with different doping levels. It reveals that the superfluid phase stiffness $\rho_s$ scales linearly with the superconducting transition temperature $T_c$, down to the extremely underdoped case. On the same batch of ultrathin flakes, we measure the Nernst effect via on-chip thermometry. Together, we obtain the vortex entropy and find that it decays exponentially with $T_c$ or $\rho_s$. We further analyze the Nernst signal above $T_c$ in the framework of Gaussian superconducting fluctuations. The combination of electrical and thermoelectric measurements in the two-dimensional limit provides fresh insight into high temperature superconductivity.

The discovery of high-mobility two-dimensional electron gas and low carrier density superconductivity in multiple SrTiO$_3$-based heterostructures has stimulated intense interest in the surface properties of SrTiO$_3$. The recent discovery of high-T$_c$ superconductivity in the monolayer FeSe/SrTiO$_3$ aroused the upsurge and underscored the atomic precision probe of the surface structure. By performing atomically resolved cryogenic scanning tunneling microscopy/spectroscopy characterization on dual-TiO$_{2}$-${\delta}$-terminated SrTiO$_3$(001) surfaces with ($\sqrt{13}$ $\times$ $\sqrt{13}$), c(4 $\times$ 2), mixed (2 $\times$ 1), and (2 $\times$ 2) reconstructions, we disclosed universally broken rotational symmetry and contrasting bias- and temperature-dependent electronic states for apical and equatorial oxygen sites. With the sequentially evolved surface reconstructions and simultaneously increasing equatorial oxygen vacancies, the surface anisotropy reduces, and the work function lowers. Intriguingly, unidirectional stripe orders appear on the c(4 $\times$ 2) surface, whereas local (4 $\times$ 4) order emerges and eventually forms long-range unidirectional c(4 $\times$ 4) charge order on the (2 $\times$ 2) surface. This work reveals robust unidirectional charge orders induced by oxygen vacancies due to strong and delicate electronic-lattice interaction under broken rotational symmetry, providing insights into understanding the complex behaviors in perovskite oxide-based heterostructures.

Superconductivity and long-range ferromagnetism hardly coexist in a uniform manner. The counter-example has been observed, in uranium-based superconductors for instance, with a coexisting temperature limited to about 1 K. Here, we report the coexistence of high temperature superconductivity and itinerant ferromagnetism in lithium intercalated FeSe flakes. In superconducting samples with transition temperature around 40 K, we observe the anomalous Hall effect with a hysteresis loop in transverse resistivity and a butterfly-like pattern of magneto-resistance. Intriguingly, such ferromagnetism persists down to a temperature at which the zero-field resistance fully vanishes. Furthermore, the superconductivity is enhanced under an in-plane magnetic field, suggestive of the participation of spin-polarized Cooper pairs. The surprising finding underscores a uniform coexistence of the two antagonistic phenomena on a record-high energy scale.

Anderson localization is anticipated to play a pivotal role in the manifestation of the quantum anomalous Hall effect, akin to its role in conventional quantum Hall effects. The significance of Anderson localization is particularly pronounced in elucidating the reasons behind the fragility of the observed quantum anomalous Hall state in the intrinsic magnetic topological insulator MnBi2Te4 with a large predicted magnetic gap. Here, employing varying sized MnBi2Te4 micro/nano-structures fabricated from a single molecular-beam-epitaxy-grown thin film, we have carried out a systematic size- and temperature-dependent study on the transport properties of the films regarding the quantum anomalous Hall states. The low-temperature transport properties of the finite-sized MnBi2Te4 samples can be quantitatively understood through Anderson localization, which plays an indispensable role in stabilizing the ground states. At higher temperatures, the failure of electron localization induced by an excessively short electronic dephasing length is identified as the cause of deviation from quantization. The work reveals that electronic dephasing and localization are non-negligible factors in designing high-temperature quantum anomalous Hall systems., Comment: 20 pages, 4 figures

Network structures by semiconductor nanowires hold great promise for advanced quantum devices, especially for applications in topological quantum computing. In this study, we created networks of PbTe nanowires arranged in loop configurations. Using shadow-wall epitaxy, we defined superconducting quantum interference devices (SQUIDs) using the superconductor Pb. These SQUIDs exhibit oscillations in supercurrent upon the scanning of a magnetic field. Most of the oscillations can be fitted assuming a sinusoidal current-phase relation for each Josephson junction. Under certain conditions, the oscillations are found to be skewed, suggesting possible deviation from a sinusoidal behavior. Our results highlight the potential of PbTe nanowires for building complex quantum devices in the form of networks.

Degeneracy and symmetry have a profound relation in quantum systems. Here, we report gate-tunable subband degeneracy in PbTe nanowires with a nearly symmetric cross-sectional shape. The degeneracy is revealed in electron transport by the absence of a quantized plateau. Utilizing a dual gate design, we can apply an electric field to lift the degeneracy, reflected as emergence of the plateau. This degeneracy and its tunable lifting were challenging to observe in previous nanowire experiments, possibly due to disorder. Numerical simulations can qualitatively capture our observation, shedding light on device parameters for future applications.

Exploration of new dielectrics with large capacitive coupling is an essential topic in modern electronics when conventional dielectrics suffer from the leakage issue near breakdown limit. To address this looming challenge, we demonstrate that rare-earth-metal fluorides with extremely-low ion migration barriers can generally exhibit an excellent capacitive coupling over 20 $\mu$F cm$^{-2}$ (with an equivalent oxide thickness of ~0.15 nm and a large effective dielectric constant near 30) and great compatibility with scalable device manufacturing processes. Such static dielectric capability of superionic fluorides is exemplified by MoS$_2$ transistors exhibiting high on/off current ratios over 10$^8$, ultralow subthreshold swing of 65 mV dec$^{-1}$, and ultralow leakage current density of ~10$^{-6}$ A cm$^{-2}$. Therefore, the fluoride-gated logic inverters can achieve significantly higher static voltage gain values, surpassing ~167, compared to conventional dielectric. Furthermore, the application of fluoride gating enables the demonstration of NAND, NOR, AND, and OR logic circuits with low static energy consumption. Notably, the superconductor-to-insulator transition at the clean-limit Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ can also be realized through fluoride gating. Our findings highlight fluoride dielectrics as a pioneering platform for advanced electronics applications and for tailoring emergent electronic states in condensed matters., Comment: 33 pages, 5 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

Superconductivity in semiconductor nanostructures contains fascinating physics due to the interplay between Andreev reflection, spin, and orbital interactions. New material hybrids can access new quantum regimes and phenomena. Here, we report the realization of epitaxial indium thin films on PbTe nanowires.The film is continuous and forms an atomically sharp interface with PbTe.Tunneling devices reveal a hard superconducting gap.The gap size, 1.08 to 1.18 meV, is twice as large as bulk indium (around 0.5 meV), due to the presence of PbTe. A similar enhancement is also observed in the critical temperature of In on a PbTe substrate. Zero bias conductance peaks appear at finite magnetic fields. The effective g-factor (15 to 45) is notably enhanced compared to bare PbTe wires (less than 10) due to the presence of In, differing from Al-hybrids. Josephson devices exhibit gate-tunable supercurrents. The PbTe-In hybrid enhances the properties of both, the superconductivity of In and g-factors of PbTe, and thus may enable exotic phases of matter such as topological superconductivity.

Material challenges are the key issue in Majorana nanowires where surface disorder constrains device performance. Here, we tackle this challenge by embedding PbTe nanowires within a latticematched crystal, an oxide-free environment. The wire edges are shaped by self-organized growth instead of lithography, resulting in nearly-atomic-flat facets along both cross-sectional and longitudinal directions. Quantized conductance plateaus are observed at zero magnetic field with channel lengths reaching 1.54 $\mu$m, significantly surpassing the state-of-the-art of III-V nanowires (nearly an order-of-magnitude improvement compared to InSb). Coupling PbTe to a Pb film unveils a flat interface spanning microns and a large superconducting gap of 1 meV. Our results meet the stringent low-disorder requirement for the definitive observation of Majoranas.

The interface-enhanced superconductivity in monolayer iron selenide (FeSe) films on SrTiO3 has been actively pursued in the past decade. Although a synergistic effect between interfacial charge transfer and interfacial electron-phonon coupling (EPC) is proposed to be responsible for the mechanism, the microscopic nature of the interfacial EPC in the enhancement of superconductivity remains highly controversial. Herein we experimentally reveal that a coherent optical phonon mode at 4.2 THz from the SrTiO3 substrate couples to FeSe electrons and modulates the quasiparticle relaxations using ultrafast pump-probe spectroscopy. This mode originates from the antiferrodistortive (AFD) transition in SrTiO3 and is significantly stronger in the presence of monolayer FeSe than that in purely FeTe-capped Nb-doped SrTiO3. Pump fluence and temperature-dependent spectroscopy measurements suggest that SrTiO3 substrate facilitates the stabilization of FeSe structure and possibly prevents the occurrence of nematic phase transition, supporting that SrTiO3 substrate modifies the electronic structure of monolayer FeSe through a strong interfacial EPC strength as large as 0.77. Our results provide unprecedented direct evidence that the strong coupling of SrTiO3 coherent phonon to FeSe electrons is indeed responsible for the high-temperature superconductivity in monolayer FeSe and SrTiO3 heterostructure.

In this study, we investigate intrinsic magnetic topological insulator MnBi2Te4 thin films grown by molecular beam epitaxy. We observe a reentrant quantum anomalous Hall effect when the Fermi energy enters the valance band and magnetic field equals zero, indicating the emergence of the Chern Anderson insulator state. The discovery opens a new avenue for realizing the QAH effect and underscores the fundamental role of both Berry curvature and Anderson localization., Comment: 15 pages, 4 figures

The interfacial FeSe/TiO$_{2-\delta}$ coupling induces high-temperature superconductivity in monolayer FeSe films. Using cryogenic atomically resolved scanning tunneling microscopy/spectroscopy, we obtained atomic-site dependent surface density of states, work function, and pairing gap in the monolayer FeSe on SrTiO$_3$(001)-($\sqrt{13} \times \sqrt{13}$)-33.7${\deg}$ surface. Our results disclosed the out-of-plane Se-Fe-Se triple layer gradient variation, switched DOS for Fe sites on and off TiO$_{5\square}$, and inequivalent Fe sublattices, which gives global spatial modulation of pairing gap contaminant with the ($\sqrt{13} \times \sqrt{13}$) pattern. Moreover, the coherent lattice coupling induces strong inversion asymmetry and in-plane anisotropy in the monolayer FeSe, which is demonstrated to correlate with the particle-hole asymmetry in coherence peaks. The strong atomic-scale correlations in lattice and electronic structure, and pairing gap in particular, put constraints on exploring the unconventional high-temperature superconductivity emerging from interface coupling, e.g., strong demand for atomic-scale interface engineering and characterization.

Planar Josephson junctions are predicted to host Majorana zero modes. The material platforms in previous studies are two dimensional electron gases (InAs, InSb, InAsSb and HgTe) coupled to a superconductor such as Al or Nb. Here, we introduce a new material platform for planar JJs, the PbTe-Pb hybrid. The semiconductor, PbTe, was grown as a thin film via selective area epitaxy. The Josephson junction was defined by a shadow wall during the deposition of the superconductor Pb. Scanning transmission electron microscopy reveals a sharp semiconductor-superconductor interface. Gate-tunable supercurrent and multiple Andreev reflections are observed. A perpendicular magnetic field causes interference patterns of the switching current, exhibiting Fraunhofer-like and SQUID-like behaviors. We further demonstrate a prototype device for Majorana detection, wherein phase bias and tunneling spectroscopy are applicable.

Josephson tunneling in twisted cuprate junctions provides a litmus test for the pairing symmetry, which is fundamental for understanding the microscopic mechanism of high temperature superconductivity. This issue is rekindled by experimental advances in van der Waals stacking and the proposal of an emergent d+id-wave. So far, all experiments have been carried out on Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ (Bi-2212) with double CuO$_2$ planes but show controversial results. Here, we investigate junctions made of Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+y}$ (Bi-2201) with single CuO$_2$ planes. Our on-site cold stacking technique ensures uncompromised crystalline quality and stoichiometry at the interface. Junctions with carefully calibrated twist angles around 45{\deg} show strong Josephson tunneling and conventional temperature dependence. Furthermore, we observe standard Fraunhofer diffraction patterns and integer Fiske steps in a junction with a twist angle of 45.0$\pm$0.2{\deg}. Together, these results pose strong constraints on the d or d+id-wave pairing and suggest an indispensable isotropic pairing component., Comment: 32 pages, 5 figures

Disorder is the primary obstacle in current Majorana nanowire experiments. Reducing disorder or achieving ballistic transport is thus of paramount importance. In clean and ballistic nanowire devices, quantized conductance is expected with plateau quality serving as a benchmark for disorder assessment. Here, we introduce ballistic PbTe nanowire devices grown using the selective-area-growth (SAG) technique. Quantized conductance plateaus in units of $2e^2/h$ are observed at zero magnetic field. This observation represents an advancement in diminishing disorder within SAG nanowires, as none of the previously studied SAG nanowires (InSb or InAs) exhibit zero-field ballistic transport. Notably, the plateau values indicate that the ubiquitous valley degeneracy in PbTe is lifted in nanowire devices. This degeneracy lifting addresses an additional concern in the pursuit of Majorana realization. Moreover, these ballistic PbTe nanowires may enable the search for clean signatures of the spin-orbit helical gap in future devices.

Semiconductor nanowires coupled to a superconductor provide a powerful testbed for quantum device physics such as Majorana zero modes and gate-tunable hybrid qubits. The performance of these quantum devices heavily relies on the quality of the induced superconducting gap. A hard gap, evident as vanishing subgap conductance in tunneling spectroscopy, is both necessary and desired. Previously, a hard gap has been achieved and extensively studied in III-V semiconductor nanowires (InAs and InSb). In this study, we present the observation of a hard superconducting gap in PbTe nanowires coupled to a superconductor Pb. The gap size ($\Delta$) is $\sim$ 1 meV (maximally 1.3 meV in one device). Additionally, subgap Andreev bound states can also be created and controlled through gate tuning. Tuning a device into the open regime can reveal Andreev enhancement of the subgap conductance, suggesting a remarkable transparent superconductor-semiconductor interface, with a transparency of $\sim$ 0.96. These results pave the way for diverse superconducting quantum devices based on PbTe nanowires.

Learning the electron scattering around atomic impurities is a fundamental step to fully understand the basic electronic transport properties of realistic conducting materials. Although many efforts have been made in this field for several decades, atomic scale transport around single point-like impurities has yet been achieved. Here, we report the direct visualization of the electric current induced dipoles around single atomic impurities in epitaxial bilayer graphene by multi-probe low temperature scanning tunneling potentiometry as the local current density is raised up to around 25 A/m, which is considerably higher than that in previous studies. We find the directions of these dipoles which are parallel or anti-parallel to local current are determined by the charge polarity of the impurities, revealing the direct evidence for the existence of the carrier density modulation effect proposed by Landauer in 1976. Furthermore, by $in$ $situ$ tuning local current direction with contact probes, these dipoles are redirected correspondingly. Our work paves the way to explore the electronic quantum transport phenomena at single atomic impurity level and the potential future electronics toward or beyond the end of Moore's Law.

Majorana bound states (MBSs) are building blocks for topological quantum computing. They can be generated via the combination of electronic topology and superconductivity. To achieve logic operations via Majorana braiding, positional control of the MBS must be established. To this end, exotic co-existing phases or collective modes in an intrinsic topological superconductor can provide a tuning knob to manipulate the MBS. Here we report the observation of a striped surface charge order coexisting with superconductivity and its controllable tuning of the MBS in the topological superconductor 2M-WS2 using low-temperature scanning tunneling microscopy. By applying an out-of-plane magnetic field, we observe that MBS is absent in vortices in the region with strong stripe order. This is in contrast to adjacent underlaying layers without charge order where vortex-bound MBSs are observed. Via theoretical simulations, we show that the surface stripe order does not destroy the bulk topology, but it can effectively modify the spatial distribution of MBS, i.e., it pushes them downward away from the 2M-WS2 surface. Our findings demonstrate that the interplay of charge order and topological superconductivity can be used to manipulate the positions of the MBS, and to explore of new states of matter., Comment: 20 pages, 4 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

PbTe nanowires coupled to a superconductor have recently been proposed as a potential Majorana platform. The hallmark of the one-dimensional nature of ballistic nanowires is their quantized conductance. Here, we report the observation of conductance plateaus at multiples of the quantized value $2e^2/h$ in PbTe nanowires at finite magnetic fields. The quantized plateaus, as a function of source-drain bias and magnetic field, allow for the extraction of the Land\'e $g$-factor, sub-band spacing and effective mass. The coefficient of 2 in the plateau conductance indicates the presence of valley degeneracy arising from the crystal orientation of the nanowires, which are grown on a (001) substrate. Occasionally, this degeneracy can be lifted by a gate voltage that breaks the mirror symmetry. Our results demonstrate the one-dimensionality of PbTe nanowires and fulfill one of the necessary conditions for the realization of Majorana zero modes., Comment: Raw data and processing codes within this paper are available at: https://doi.org/10.5281/zenodo.7848599

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

We explore the topology-disorder phase diagram by simulating one-dimensional Su-Schrieffer-Heeger (SSH) model with quasiperiodic disorder using a programmable superconducting simulator. We experimentally map out and identify various trivial and topological phases with extended and localized bulk states. We find that in the topological phase the bulk states can be critically localized without mobility edge or contain both critically and completely localized states. In addition, there exist trivial and topological intermediate phases with mobility edge and coexistence of extended and completely localized states. The presence of the surprisingly rich phases in the simple SSH model with quasiperiodic disorder sheds new light on the investigation of the topological and localization phenomena in condensed-matter physics., Comment: 5 pages, 4 figures

There is a heated debate on the Josephson effect in twisted Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ flakes. Recent experimental results suggest the presence of either anomalously isotropic pairing or exotic $d$+i$d$-wave pairing, in addition to the commonly believed $d$-wave one. Here, we address this controversy by fabricating ultraclean junctions with uncompromised crystalline quality and stoichiometry at the junction interfaces. In the optimally doped regime, we obtain prominent Josephson coupling (2-4 mV) in multiple junctions with the twist angle of 45$^\circ$, in sharp contrast to a recent report that shows two orders of magnitude suppression around 45$^\circ$ from the value at 0$^\circ$. We further extend this study to the previously unexplored overdoped regime and observe pronounced Josephson tunneling at 45$^\circ$ together with Josephson diode effect up to 50 K. Our work helps establish the persistent presence of an isotropic pairing component across the entire superconducting phase diagram., Comment: 6 pages, 5 figures

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

Semiconductor-superconductor hybrid nanowires are a leading material platform for the realization of Majorana zero modes. The semiconductors in previous studies are dominantly InAs or InSb. In this work, we show the induced superconductivity in a PbTe nanowire epitaxially coupled to a superconductor Pb. The Josephson junction device based on this hybrid reveals a gate-tunable supercurrent in the open regime and a hard superconducting gap in the tunneling regime. By demonstrating the superconducting proximity effect, our result can enable Majorana searches and other applications like gate-tunable qubits in a new semiconductor system., Comment: Raw data and processing codes within this paper are available at: https://doi.org/10.5281/zenodo.7398019

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