Topological semimetals are renowned for exhibiting large, unsaturated magnetoresistance arising from ultrahigh carrier mobility and electron-hole compensation. However, such behaviors remain poorly understood in iron-based superconductors that have been recently recognized to harbor rich nontrivial topology. Here, we combine angle-resolved magneto-transport measurements with first principles calculations to reveal the emergence and tunability of topological semimetals in ferropnictide Ba(Fe$_{1-x}$Co$_x$)$_{2+δ}As$_2$ epitaxial films, modulated by interstitial Fe. These states exhibit ultralow residual resistivity, coexisting high-mobility electron and hole carriers, and linear positive magnetoresistance below 110 K. Remarkably, the magnetoresistance becomes more pronounced when the magnetic field is applied parallel to the film plane, reaching an unsaturated 1206% at 56 T. Furthermore, superconductivity persists in these ferropnictide films, establishing them as a tunable platform for investigating the interplay among electron correlation, topology, and superconductivity.

Surface and bulk superconductivity may possess fundamentally different superconducting properties in quantum materials with nontrivial electronic structures, yet their superimposed spectroscopic signatures often prevent direct experimental access to each superconducting channel. Here we reveal, in epitaxial films of the kagome superconductor SrSn_3, distinct surface and bulk superconducting channels with markedly different superconducting gaps, upper critical fields, and vortex-core electronic states by tuning the tunneling junction resistance in scanning tunneling spectroscopy. The surface superconductivity is characterized by a thickness-independent superconducting gap and an enhanced upper critical field, whereas the bulk superconducting channel exhibits a larger superconducting gap that decreases with reducing film thickness and a much lower upper critical field. Within magnetic vortex cores, robust non-split zero-bias conductance peaks are observed exclusively in the surface superconducting channel, while pronounced zero-bias suppression is consistently associated with the bulk superconducting channel. These findings demonstrate that the vortex-core electronic structure depends sensitively on the underlying superconducting channel, providing new insight into vortex-bound states in topological quantum materials.

Despite being well established in cuprates, an intrinsic translational symmetry-breaking charge order has not been clearly identified in iron-based superconductors. Using spectroscopic-imaging scanning tunneling microscopy on epitaxial Ca(Fe1-xCox)2As2 (x = 0 0.055) thin films, we observe smectic, near-commensurate charge-stripe order in the underdoped regime that intervenes between the nematic parent phase and optimally doped superconductivity. Distinct from the bidirectional checkerboard-like order in cuprates, these charge stripes are unidirectional along the antiferromagnetic Fe-Fe bond direction and are accompanied by a van Hove singularity near the Fermi level, inherited from the Fermi surface reconstruction driven by intertwined antiferromagnetic and nematic correlations. Both local and global suppression of the charge-stripe instability enhance superconductivity, tunable via epitaxial strain and Co doping. These results establish charge-stripe order as an intermediate electronic phase in iron pnictides and reveal a coherent pathway from nematicity to superconductivity. Our findings highlight charge ordering as a unifying element across different families of high-temperature superconductors.

Clean, nonsplit vortex zero-bias peaks (ZBPs) can be misinterpreted as Majorana zero modes (MZMs), making static scanning tunneling microscopy intrinsically ambiguous. Here we use the STM tip coupling to drive a local boundary-renormalization-group (boundary RG) flow, turning dynamical Coulomb blockade into a falsification test for Majorana-like ZBPs. Experimentally, in a SrSn_3 thin film, normal-state spectra establish an Ohmic dissipative environment, and a common boundary-RG/thermodynamic-Bethe-ansatz analysis of the superconducting-gap and vortex-center spectra yields consistent dissipation strengths within the r < 1/2 Majorana-filter regime. Lowering the tip nevertheless drives a clean, non-split vortex-center ZBP into a zero-bias dip, opposite to the protected flow of an isolated MZM, unmasking the peak as a Majorana false positive produced by a conventional vortex-core state. The same flow selectively suppresses the strongly tip-coupled channel, resolving the two-gap superconductivity. Dissipative STM thus tests dynamical protection rather than spectral appearance.

The interplay between quantum criticality and Fermi surface reconstruction is central to elucidating the phase diagram of high-temperature cuprate superconductors. While studies on electron-doped T'-structure cuprates suggest an antiferromagnetic origin of this reconstruction, quantitative consensus has been hindered by apical oxygen instabilities and uncontrolled oxygen vacancies. Here, we overcome these limitations by utilizing ozone-assisted molecular beam epitaxy to synthesize high-quality, oxygen-stoichiometric thin films of infinite-layer cuprate Sr1-xNdxCuO2 across its entire superconducting dome. Hall transport measurements reveal a sharp carrier-type transition signaling a Fermi surface reconstruction at a critical doping xc 0.155. We show that a spin-density-wave tight-binding model quantitatively reproduces the transport evolution, supporting an antiferromagnetic origin of this quantum phase transition. Furthermore, upon suppressing superconductivity with magnetic fields, the normal-state resistivity exhibits a pristine strange metal behavior that persists down to 2 K in the vicinity of xc. Our findings establish an intrinsic, universal antiferromagnetic quantum criticality in electron-doped cuprates, positioning the structurally simplest infinite-layer cuprates as a clean benchmark platform for theories of unconventional superconductivity.

In type-II superconductors, magnetic fields modulate the amplitude and phase of the superconducting order parameter, forming quantized vortices where superconductivity is locally suppressed and exotic bound states or competing electronic orders emerge. Using spectroscopic-imaging scanning tunneling microscopy on epitaxial Ba(Fe_0.94Co_0.06)_2As_2 films, we discover an incommensurate charge-stripe order aligned with the Fe-Fe bond direction and nucleated inside magnetic vortices. These charge modulations intensify at the vortex core, extend far into the vortex halo, and persist within the superconducting gap. Strikingly, the charge order modulates Andreev bound states of vortices at non-zero energies, producing abelian vortices with half-odd-integer level quantization and non-abelian vortices with integer-quantized core states that host a Majorana zero mode. The distinct vortex types are distinguished by the registry of their centers relative to the charge-stripe pattern and remain robust in ultrathin (2.5-unit-cell) films. Our findings reveal a density-wave-textured vortex matter and provide fresh insights into the intertwined phenomena of charge-stripe order, pair-density-wave modulations, and Majorana physics in iron-based superconductors.

Two-dimensional superconductivity has become a major frontier in condensed matter physics. It holds the key to the mechanism of high-temperature superconductors and offers an exceptional arena to stabilize emergent quantum states enabled by enhanced electron correlations in reduced dimensionality. These states are frequently characterized by spatial modulations and intertwined with competing orders, calling for studies that combine real-space imaging with local spectroscopy. Scanning tunneling microscopy and spectroscopy meets this need by directly accessing local density of states with lattice-scale resolution. In this review, we summarize recent advances of the study on several representative unconventional superconductors using this technique, focusing on direct characterization of high-temperature superconducting planes, pair-density waves, and topological superconductivity in both artificial heterostructures and intrinsic materials. We conclude by outlining current challenges and future directions motivated by the microscopic insights.

We report the superconducting properties of tensile-strained infinite-layer cuprate Sr1−xEuxCuO2+y thin films fabricated on KTaO3 substrates via molecular beam epitaxy. The doping-dependent superconducting phase diagram shows an optimal doping level of x ∼ 0.184 and a broader dome shifting to higher doping range due to reduced intralayer hopping and enhanced interlayer magnetic coupling. The characteristic of two-dimensional superconductivity is observed by Berezinskii-Kosterlitz-Thouless transition and the angle-resolved magnetoresistance measurements. Moreover, the temperature-dependent upper critical field and thermally-activated vortex motion under the in-plane and out-of-plane magnetic fields exhibit strong anisotropy, which further reveal the anisotropic nature of the superconductivity in infinite-layer cuprates.

We employ cryogenic scanning tunneling microscopy to observe a tunable two-dimensional electron gas / / (2DEG) on the Sn/Si(111)-2 3 x 2 3-R30 degrees surface, where its properties are modulated by the underlying Si(111) substrates. The 2DEG resides near the conduction band edge of the Sn overlayer, which features a band gap of approximately 0.65 eV. By analyzing quasiparticle interference patterns induced by the 2DEG, we determine its energy dispersion and reveal a variation in effective mass with the Si substrate doping. Moreover, quantum interference fringes are found in spatially confined regions of the 2DEG, from which consistent band parameters are deduced. This study advances our understanding of the 2DEG and associated electronic properties in heterostructures.

We report the superconducting properties of tensile-strained infinite-layer cuprate Sr 1− x Eu x CuO 2+ y thin films fabricated on KTaO 3 substrates via molecular beam epitaxy. The doping-dependent superconducting phase diagram shows an optimal doping level of $x\ \sim $ x ∼ 0.184 and a broader dome shifting to higher doping range due to reduced intralayer hopping and enhanced interlayer magnetic coupling. The characteristic of two-dimensional superconductivity is observed by Berezinskii-Kosterlitz-Thouless transition and the angle-resolved magnetoresistance measurements. Moreover, the temperature-dependent upper critical field and thermally-activated vortex motion under the in-plane and out-of-plane magnetic fields exhibit strong anisotropy, which further reveal the anisotropic nature of the superconductivity in infinite-layer cuprates.

Interfacial interactions often promote the emergence of unusual phenomena in two-dimensional systems, including high-temperature superconductivity. Here, we report the observation of full-gap superconductivity with a maximal spectroscopic temperature up to 26 K in a BaAs monolayer grown on ferropnictide Ba(Fe_1-xCo_x)_2As_2 (abbreviated as BFCA) epitaxial films. The superconducting gap remains robust even when the thickness of underlying BFCA is reduced to the monolayer limit, in contrast to the rapid suppression of T_c in standalone BFCA thin films. We reveal that the exceptional crystallinity of the BaAs/BFCA heterostructures, featured by their remarkable electronic and geometric uniformities, is crucial for the emergent full-gap superconductivity with mean-field temperature dependence and pronounced bound states within magnetic vortices. Our findings open up new avenues to unravel the mysteries of unconventional superconductivity in ferropnictides and advance the development of FeAs-based heterostructures.

We report transport measurements of infinite-layer cuprate Sr1−xEuxCuO2+y films with controlled electron (by trivalent europium) and hole (by interstitial apical oxygen) carriers grown on SrTiO3(001) with molecular beam epitaxy. An unusual enhancement of superconductivity upon the moderate coexistence of electron and hole carriers in the films is found, which spans over the whole superconducting phase diagram and becomes more prominent in the underdoped regime. The superconductivity exhibits a two-dimensional nature with a thickness of approximately 5.2 nm, irrespective of the varying carriers, confirmed by angle-resolved magnetoresistance measurements and the Berezinskii-Kosterlitz-Thouless transition. Nevertheless, the coexisting electron and hole carriers enlarge the thermal activation energy of vortex motion that deviates obviously from the usual logarithmic evolution with the magnetic field. Our results offer a promising perspective to understand and enhance the high-temperature superconductivity in cuprates. locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon Physics Subject Headings (PhySH)MagnetoresistanceSuperconductivityCupratesSuperconductorsThin filmsResistivity measurements

We report transport measurements of infinite-layer cuprate Sr1-xEuxCuO2+y films with controlled electron (by trivalent europium) and hole (by interstitial apical oxygen) carriers grown on SrTiO3(001) with molecular beam epitaxy. An unusual enhancement of superconductivity upon the moderate coexistence of electron and hole carriers in the films is found, which spans over the whole superconducting phase diagram and becomes more prominent in the underdoped regime. The superconductivity exhibits a two-dimensional nature with a thickness of approximately 5.2 nm, irrespective of the varying carriers, confirmed by angle-resolved magnetoresistance measurements and the Berezinskii-Kosterlitz-Thouless transition. Nevertheless, the coexisting electron and hole carriers enlarge the thermal activation energy of vortex motion that deviates obviously from the usual logarithmic evolution with the magnetic field. Our results offer a promising perspective to understand and enhance the hightemperature superconductivity in cuprates.

Unconventional superconductors that spontaneously break space-group symmetries of their underlying crystal lattice are distinguished by spatial modulations of superconducting order parameter. These states have recently captured significant attention in various strongly correlated materials, where the translational or intra-unit-cell symmetry breaking results in the emergence of pair density waves with wavelength extending across one or multiple unit cells. Here, we employ a spectroscopic-imaging scanning tunneling microscopy to reveal sublattice modulations of the superconducting gap magnitude, coherence strength, and subgap states in tunable 1 T^{'}-MoTe_{2} monolayer. These modulations are uniquely oriented perpendicular to the zigzag Mo chains at the scale of half a unit cell and coexist with three-unit-cell pair density wave modulations along the Mo chains, both of which attenuate with increasing temperature and external magnetic fields. Importantly, we find that the superconductivity modulations are strongly linked to unconventional electron pairing mechanisms, which significantly deviate from the Cooper pairing observed in conventional Bardeen-Cooper-Schrieffer superconductors. Our findings advance the knowledge of Cooper-pair density modulations and their intricate interplay with other symmetry-breaking states in strongly correlated superconductors.

Unconventional superconductors that spontaneously break space-group symmetries of their underlying crystal lattice are distinguished by spatial modulations of superconducting order parameter. These states have recently captured significant attention in various strongly correlated materials, where the translational or intra-unit-cell symmetry breaking results in the emergence of pair density waves with wavelength extending across one or multiple unit cells. Here, we employ a spectroscopic-imaging scanning tunneling microscopy to reveal sublattice modulations of the superconducting gap magnitude, coherence strength, and subgap states in tunable 1 T0-MoTe2 monolayer. These modulations are uniquely oriented perpendicular to the zigzag Mo chains at the scale of half a unit cell and coexist with three-unit-cell pair density wave modulations along the Mo chains, both of which attenuate with increasing temperature and external magnetic fields. Importantly, we find that the superconductivity modulations are strongly linked to unconventional electron pairing mechanisms, which significantly deviate from the Cooper pairing observed in conventional Bardeen-Cooper-Schrieffer superconductors. Our findings advance the knowledge of Cooper-pair density modulations and their intricate interplay with other symmetry-breaking states in strongly correlated superconductors.

We employ spectroscopic-imaging scanning tunneling microscopy to investigate the electronic properties of copper-oxide (CuO2) planes in an electron-doped infinite-layer cuprate superconductor Sr1-xNdxCuO2. Tunneling conductance spectra reveal distinct Bose-Einstein condensation (BEC)-like features in underdoped regions, characterized by a small Fermi energy, broad coherence peaks, and pronounced particle-hole asymmetry. As the local electron doping level increases, these features evolve into well-defined superconducting gaps, unveiling the long-sought crossover between the BEC and Bardeen-Cooper-Schrieffer (BCS) regions in cuprate superconductors. Additionally, we observe three distinct phonon excitations within the BEC regions, which underscores the potential role of lattice vibrations in electron pairing. Our results provide direct real-space experimental evidence for the BEC-BCS crossover on CuO2 planes, offering insights into the emergent superconductivity in doped Mott cuprates.

The quest to unravel the intricacies of high-Tc superconductivity and strongly correlated electrons in cuprates has spurred a novel focus on direct probing of the CuO2 planes through scanning tunneling microscopy. Infinite-layer (IL) cuprates, featuring a CuO2-terminated surface, emerge as optimal systems for this investigation. Leveraging controllable growth via molecular beam epitaxy, both electron- and hole-doped IL cuprates are realized, with surface structure and c-axis length serving as distinctive markers. A consistent pattern in the Mott transition is established, revealing that doping merely shifts the Fermi level without inducing changes in the Mott band structure, thereby suggesting a self-modulation doping scenario. Furthermore, the identification of a nodeless superconducting gap in the CuO2 planes challenges conventional notions derived from charge reservoir layers, advocating for a quantum well interpretation of cuprate superconductivity. This review sheds light on the distinct roles played by CuO2 layers and charge reservoir layers, promising a more profound comprehension of cuprate superconductivity through the lens of the CuO2 surface.

Symmetry-breaking phenomena are identifiable in numerous strongly correlated systems including hightemperature superconductors. However, identification of these exotic states and understanding their interplay with superconductivity in topological materials remains limited. Here we employ cryogenic scanning tunneling microscopy to reveal coexistent charge and pair density waves (CDWs and PDWs) in topological monolayer 1T'-MoTe2. The two orders are modulated unidirectionally and share the same periodicity of five unit cells or a wave vector near (0, 0.4)n/b (b is the lattice constant along the zigzag Mo chains). Importantly, the PDW features a two-gap superconductivity below a transition temperature of around 6.0 K and induces a unique secondary particle-hole-symmetric CDW at twice its wave vector. Combining these results and our density functional calculations, we elucidate that the two unidirectional orders are driven by nesting behaviors between electron and hole pockets. Our findings establish monolayer 1T '-MoTe2 as a topological paradigm to explore multiple preexisting symmetry-breaking states.