Controlling intertwined electronic orders in two-dimensional superconductors offers an effective route to answering fundamental questions and engineering new quantum devices. However, tuning the balance between competing orders typically requires complex chemistry, strain, or interface engineering. Here, we show that a pristine alternative is the dimensional reduction of the unconventional superconductor FeSe. Exfoliation suppresses the bulk electronic nematic response and switches the superconducting symmetry from bulk s-wave to d-wave-dominant. Transport, electron microscopy, and Raman spectroscopy establish the substantial weakening of nematic order in thin flakes. To probe superconductivity, we perform angle-dependent Andreev reflection spectroscopy on pristine crystal edges. As the junction's orientation is rotated, the spectra evolve from zero-energy bound states to coherence peaks. The injection angle, field, and temperature dependence, along with theoretical modeling, confirm that exfoliation switches the superconducting symmetry. Our results suggest a versatile superconducting platform for engineering quantum orders and provide fresh insights into the underlying pairing mechanisms.

Pair density modulation is a phenomenon recently observed in exfoliated flakes of iron-based superconductors, in which the superconducting gap oscillates strongly with the same periodicity as the underlying crystalline lattice. We propose a model that explains this modulation in systems with broken intra-unit-cell symmetries through the emergence of nematic superconductivity, which further breaks the four-fold rotation symmetry. This results in a sublattice texture on the Fermi surface, aligned with the anisotropic superconducting gap of the nematic s± + d state. This gives rise to distinctive gap maxima and minima located on the two inequivalent iron sublattices while still being a zero-momentum pairing state. We discuss how further investigation of such modulations can give insight into the nature of the superconducting pairing, such as the signs of the order parameters and visualization of a phase transition to a mixed two-component state using local probes.

Topological systems are defined by global properties that enforce the existence of local boundary modes. Three-dimensional topological insulators (TIs) were among the earliest proposed systems for hosting topological superconductivity, but experimental focus subsequently shifted to other platforms. Here, we revisit bulk-insulating TIs using a columnar nano-superconducting quantum interference device (nano-SQUID) architecture. This geometry optimises the proximity effect on the TI surface and enables simultaneous probing of global superconducting properties - via the critical current through the nano-SQUID - alongside the local states at the ends of the nano-SQUID via tunnel junctions. We observe several global superconducting features that appear to show a flux-driven global phase transition consistent with entering the topological regime, including periodic critical current oscillations and a sign reversal in the superconducting diode effect. Simultaneously, tunnelling spectroscopy reveals spectral jumps in local and nonlocal conductance that align with these global features. However, zero-bias peaks (ZBPs) in local conductance are present both within the predicted topological range of magnetic fields and in theoretically trivial regimes, including at zero magnetic field. Ultimately, the lack of correlation between local ZBP signatures and global signatures emphasises that conclusively identifying Majorana bound states will necessitate a combined approach, integrating the establishment of global topological properties with the use of local and other, more advanced, probes.

A Josephson diode passes current with zero resistance in one direction but is resistive in the other direction. While such an effect has been observed in several platforms, a large and tunable Josephson diode effect has been rare. Here, we report that a simple device consisting of a topological-insulator (TI) nanowire side-contacted by superconductors to form a lateral Josephson junction presents a large diode effect with the efficiency [Formula: see text] reaching 0.3 when a parallel magnetic field [Formula: see text] is applied. The sign and the magnitude of [Formula: see text] are tunable not only by [Formula: see text] but also by the back-gate voltage. This diode effect can be understood by modeling the system as a nano-superconducting quantum interference device (SQUID), in which the top and bottom surfaces of the TI nanowire each form a line junction and [Formula: see text] creates a magnetic flux to thread the SQUID loop. This model further shows that the observed diode effect marks the emergence of topological superconductivity in TI nanowire-based Josephson junction.

Strong electron-hole interactions in a semimetal or narrow-gap semiconductor may drive a ground state of condensed excitons. Monolayer WTe2 has been proposed as a host material for such an exciton condensate, but the order parameter - the key signature of a macroscopic quantum-coherent condensate - has not been observed. Here we use Fourier-transform scanning tunnelling spectroscopy (FT-STS) to study quasi-particle interference (QPI) and periodic modulations of the local density of states (LDOS) in monolayer WTe2. In WTe2 on graphene, in which the carrier density can be varied via back-gating, FT-STS shows QPI features in the 2D bulk bands, confirming the interacting nature of the bandgap in neutral WTe2 and the semi-metallic nature of highly n- and p-doped WTe2. We observe additional non-dispersive spatial modulations in the LDOS imprinted on the topological edge mode of neutral WTe2 on metallic substrates (graphene and graphite), which we interpret as the interaction of the topological edge mode with the expected charge density wave order parameter of the excitonic condensate in WTe2 at low interaction strength due to screening by the metallic substrates.

Pair density modulation is a superconducting state, recently observed in exfoliated iron-based superconductor flakes, in which the superconducting gap oscillates strongly with the same periodicity as the underlying crystalline lattice. We propose a microscopic model that explains this modulation through a combination of glide-mirror symmetry breaking and the emergence of nematic superconductivity. The first ingredient results in a sublattice texture on the Fermi surface, which is aligned with the anisotropic superconducting gap of the nematic s_±+d state. This gives rise to distinctive gap maxima and minima located on the two inequivalent iron sublattices while still being a zero-momentum pairing state. We discuss how further investigation of such modulations can give insight into the nature of the superconducting pairing, such as the signs of the order parameters and visualization of a phase transition to a mixed two-component state using local probes.

Superconducting (SC) states that break space-group symmetries of the underlying crystal can exhibit nontrivial spatial modulation of the order parameter. Previously, such states were intimately associated with the breaking of translational symmetry1,2, resulting in the density-wave orders3-8, with wavelengths spanning several unit cells9-19. However, a related basic concept has long been overlooked20: when only intra-unit-cell symmetries of the space group are broken, the SC states can show a distinct type of nontrivial modulation preserving long-range lattice translation. Here we refer to this new concept as the pair density modulation (PDM) and report the first observation of a PDM state in exfoliated thin flakes of the iron-based superconductor FeTe0.55Se0.45. Using scanning tunnelling microscopy (STM), we discover robust SC gap modulation with the wavelength corresponding to the lattice periodicity and the amplitude exceeding 30% of the gap average. Notably, we find that the observed modulation originates from the large difference in SC gaps on the two nominally equivalent iron sublattices. The experimental findings, backed up by model calculations, suggest that, in contrast to the density-wave orders, the PDM state is driven by the interplay of sublattice symmetry breaking and a peculiar nematic distortion specific to the thin flakes. Our results establish new frontiers for exploring the intertwined orders in strong-correlated electronic systems and open a new chapter for iron-based superconductors.

Superconducting states that break space-group symmetries of the underlying crystal can exhibit nontrivial spatial modulation of the order parameter. Previously, such remarkable states were intimately associated with the breaking of translational symmetry, giving rise to the density-wave orders, with wavelengths spanning several unit cells. However, a related basic concept has been long overlooked: when only intra-unit-cell symmetries of the space group are broken, the superconducting states can display a distinct type of nontrivial modulation preserving long-range lattice translation. Here, we refer to this new concept as the pair density modulation (PDM), and report the first observation of a PDM state in exfoliated thin flakes of iron-based superconductor FeTe$_{\text{0.55}}$Se$_{\text{0.45}}$. Using scanning tunneling microscopy, we discover robust superconducting gap modulation with the wavelength corresponding to the lattice periodicity and the amplitude exceeding 30% of the gap average. Importantly, we find that the observed modulation originates from the large difference in superconducting gaps on the two nominally equivalent iron sublattices. The experimental findings, backed up by model calculations, suggest that in contrast to the density-wave orders, the PDM state is driven by the interplay of sublattice symmetry breaking and a peculiar nematic distortion specific to the thin flakes. Our results establish new frontiers for exploring the intertwined orders in strong-correlated electronic systems and open a new chapter for iron-based superconductors.

Many efforts have been made in the past decade to realize topological superconductivity using superconducting proximity effect, but an ideal platform is still lacking. A 3D topological insulator (TI) is promising for this purpose due to the spin-momentum-locked surface state. Here we propose a novel yet simple TI platform which gives rise to a topological phase that is robust against disorder. It consists of a bulk-insulating rectangular TI nanowire laterally sandwiched by two superconductors. In this structure, the top and bottom surfaces individually work as SNS line junctions, forming a nanometer-scale columnar SQUID in which the nanowire cross-section defines the threading magnetic flux Φ in axial magnetic fields. We theoretically show that, when the two junctions are asymmetric, a robust topological phase occurs periodically for a wide range of Φ, independently of the chemical potential. Our experiment found that a TI device of this structure indeed behaves as a columnar nano-SQUID where the supercurrent flows only through the top and bottom surfaces with vanishing bulk contribution. Furthermore, the top/bottom asymmetry can be tuned by a back gate, a key ingredient for the topological phase.

One of the proposed ground states of monolayer WTe$_2$, a two-dimensional topological insulator, is an excitonic condensate. However, time-reversal preserving and breaking solutions are competing at the mean-field level of analysis, and it is unclear which condensate, if any, is realized in nature. In this work we analyze the experimental signatures that allow to provide evidence for the excitonic ground states and to distinguish between the two types of condensates using scanning tunneling microscopy. We provide clear experimental signatures in local mapping and quasiparticle interference patterns that visualize the expected changes in local charge and spin density, and characterize allowed backscattering processes in the presence of impurities and disorder. Our results will thus help in the determination of the nature of the WTe$_2$ ground state.

Gapless helical edge modes are a hallmark of the quantum spin Hall effect. Protected by time-reversal symmetry, each edge contributes a quantized zero-temperature conductance quantum $G_0 \equiv e^2/h$. However, the experimentally observed conductance in WTe$_2$ decreases below $G_0$ per edge already at edge lengths around 100 nm, even in the absence of explicit time-reversal breaking due to an external field or magnetic impurities. In this work, we show how a time-reversal breaking excitonic condensate with a spin-spiral order that can form in WTe$_2$ leads to the breakdown of conductance quantization. We perform Hartree-Fock calculations to compare time-reversal breaking and preserving excitonic insulators. Using these mean-field models we demonstrate via quantum transport simulations that weak non-magnetic disorder reproduces the edge length scaling of resistance observed in the experiments. We complement this by analysis in the Luttinger liquid picture, shedding additional light on the mechanism behind the quantization breakdown.

Understanding the nature of strongly correlated states in flat-band materials (such as moiré heterostructures) is at the forefront of both experimental and theoretical pursuits. While magnetotransport, scanning probe, and optical techniques are often very successful in investigating the properties of the underlying order, the exact nature of the ground state often remains unknown. Here, we propose to leverage strong light-matter coupling present in the flat-band systems to gain insight through dynamical dielectric response into the structure of the many-body ground state. We argue that because of the enlargement of the effective lattice of the system arising from correlations, conventional long-range plasmon becomes "folded" to yield a multiband plasmon spectrum. We detail several mechanisms through which the structure of the plasmon spectrum and that of the dynamical dielectric response is susceptible to the underlying order, revealing valued insights such as the interaction-driven band gaps, spin-structure, and the order periodicity.

Altermagnets are a new class of magnetic materials, which exhibit large spin splitting, but due to the combined spin and real space group symmetry protection maintain zero net macroscopic magnetization. Such a characteristic may prove them to be superior in applications in superconducting heterostructures and thus here we investigate the Andreev reflection at the altermagnet/superconductor interface. We compare and contrast altermagnets to other magnetic materials, revealing qualitative differences in the behavior of altermagnetic junction depending on the Fermi surface orientation. We study the resonant states arising in setups with strong tunneling barriers and show that sensitivity to non-magnetic disorder is also dependent on the orientation. Our results provide a building block for altermagnetic superconducting heterostructures such as Josephson $\pi$ junctions with superior properties.

The variety of correlated phenomena in moir\'e systems is incredibly rich, spanning effects such as superconductivity, a generalized form of ferromagnetism, or even charge fractionalization. This wide range of quantum phenomena is partly enabled by the large number of internal degrees of freedom in these systems, such as the valley and spin degrees of freedom, which interplay decides the precise nature of the ground state. Identifying the microscopic nature of the correlated states in the moir\'e systems is, however, challenging, as it relies on interpreting transport behavior or scanning-tunneling microscopy measurements. Here we show how the real-space structure of collective charge oscillations of the correlated orders can directly encode information about the structure of the correlated state, focusing in particular on the problem of generalized Wigner crystals in moir\'e transition metal dichalcogenides. Our analysis builds upon our earlier result [10.1126/sciadv.adg3262] that the presence of a generalized Wigner crystal modifies the plasmon spectrum of the system, giving rise to new collective modes. We focus on scanning near-field optical microscopy technique (SNOM), fundamentally a charge-sensing-based method, and introduce a regime under which SNOM can operate as a probe of the spin degree of freedom.

In most superconductors, optical excitations require impurity scattering or the presence of multiple bands. This is because in clean single-band superconductors, the combination of particle-hole and inversion symmetries prevents momentum-conserving transitions. In this work we show how the flow of supercurrent can lead to new contributions to optical conductivity. As supercurrent breaks inversion symmetry, transitions across the superconducting gap become allowed even in clean superconductors and dominate over impurity-induced contributions for energies comparable to the gap width. The response is dependent on the nature of the underlying normal state as well as on the type of superconducting order. Through use of the screening supercurrent with controllable magnitude and direction, that arises from an external magnetic field, this enables a detailed investigation of the superconducting state and possible gap symmetry determination in unconventional superconductors for which other techniques have not been practicable.

The iron-based superconductor is emerging as a promising platform for Majorana zero mode, which can be used to implement topological quantum computation. One of the most significant advances of this platform is the appearance of large vortex level spacing that strongly protects Majorana zero mode from other low-lying quasiparticles. Despite the advantages in the context of physics research, the inhomogeneity of various aspects hampers the practical construction of topological qubits in the compounds studied so far. Here we show that the stoichiometric superconductor LiFeAs is a good candidate to overcome this obstacle. By using scanning tunneling microscopy, we discover that the Majorana zero modes, which are absent on the natural clean surface, can appear in vortices influenced by native impurities. Our detailed analysis reveals a new mechanism for the emergence of those Majorana zero modes, i.e. native tuning of bulk Dirac fermions. The discovery of Majorana zero modes in this homogeneous material, with a promise of tunability, offers an ideal material platform for manipulating and braiding Majorana zero modes, pushing one step forward towards topological quantum computation.

A sufficiently large supercurrent can close the energy gap in a superconductor and create gapless quasiparticles through the Doppler shift of quasiparticle energy caused by finite Cooper pair momentum. In this gapless superconducting state, zero-energy quasiparticles reside on a segment of the normal-state Fermi surface, whereas the remaining Fermi surface is still gapped. We use quasiparticle interference to image the field-controlled Fermi surface of bismuth telluride (Bi2Te3) thin films under proximity effect from the superconductor niobium diselenide (NbSe2). A small applied in-plane magnetic field induces a screening supercurrent, which leads to finite-momentum pairing on the topological surface states of Bi2Te3. We identify distinct interference patterns that indicate a gapless superconducting state with a segmented Fermi surface. Our results reveal the strong impact of finite Cooper pair momentum on the quasiparticle spectrum.

We analyze the thermoelectric response of Dirac and Weyl semimetals using the semiclassical approach, focusing on the extrinsic contributions due to skew-scattering and side jump. Our results apply to the linear response Nernst effect in ferromagnetic Dirac materials such as Fe3Sn2 and Weyl semimetals like Co3Sn2S2. In the case of Fe3Sn2 we obtain a very good agreement with known experimental anomalous Hall effect measurements, and based on that we predict a large Nernst effect in this material. We also extend the investigation to second-order response, focusing on monolayer graphene on hBN with trigonal warping as an example. Our analysis indicates that the extrinsic contributions can be a significant component of anomalous Nernst response and may be used to explain an enhanced thermoelectric response.

Majorana bound states provide a fertile ground for both investigation of fundamental phenomena as well as for applications in quantum computation. However, despite enormous experimental and theoretical efforts, the currently available Majorana platforms suffer from a multitude of issues that prevent full realization of their potential. Therefore, improved Majorana systems are still highly sought after. Here we present a platform for creating Majorana bound states from 2D gapless superconducting state in spin-helical systems under the in-plane magnetic or Zeeman field. Topological 1D channels are formed by quantum confinement of quasiparticles via Andreev reflection from the surrounding fully gapped superconducting region. Our proposal can be realized using narrow strips of magnetic insulators on top of proximitized 3D topological insulators. This setup has key advantages that include: small required fields, no necessity of fine-tuning of chemical potential, removal of the low-energy detrimental states, and large attainable topological gap.