The quantum Hall effect in gapped systems represents a defining signature of nontrivial topology. Realizing this principle in gapless matter has remained a central challenge in quantum materials. Chiral topological semimetals provide a unique platform to achieve this aim via symmetry-protected multifold crossings that act as Berry-curvature monopoles. When optical transitions are confined to a single multifold node, the resulting circular photogalvanic effect is predicted to be quantized in terms of the topological charge of the node. In real materials, however, this phenomenon remains experimentally elusive, obscured by trivial band transitions, the energy separation between the node pairs, and their relative positions with respect to the Fermi level. Here we observe a quantized circular photogalvanic effect in the chiral topological semimetal Rh0.95Ni0.05Si. Ni substitution opens a photon-energy window dominated by interband optical transitions at the Γ-point multifold node. This allows circularly polarized near- to mid-infrared pulses to drive a helicity-odd terahertz response that manifests three hallmarks of quantization: a sharp onset, a wavelength-independent plateau governed by the magnitude of monopole charge, and an abrupt cutoff imposed by Pauli blocking. Our work establishes an all-optical analogue for the quantum Hall effect and a new paradigm for topological quantization in gapless matter.

Charge-density-wave implies a periodic modulation of the charge density. Typically observed in metallic systems, charge-density-wave arise from Fermi surface instabilities, resulting in the total or partial gapping of the Fermi surface. Here, we present experimental evidence for a charge-density-wave state emerging in a band insulator which has no Fermi surface. The bulk and surface of our material platform, α -Bi4Br4, is gapped over the entire Brillouin zone. Through topographic and spectroscopic imaging at low temperatures, we unveil an unexpected unidirectional charge modulation in α -Bi4Br4, breaking the lattice translation symmetry. The charge-density-wave develops at temperatures below 40 K and adds an energy gap atop the existing insulating gap of α -Bi4Br4. Furthermore, our transport measurements reveal nonlinear electrical conduction, a phenomenon conventionally associated with the sliding or phason mode of incommensurate charge-density-waves. These unusual observations represent a different type of charge-density-wave.

By sidestepping the intractable calculations of many-body wave functions, density functional theory has revolutionized the prediction of ground states of materials. However, predicting nonlinear responses-critical for next-generation quantum devices-still relies heavily on explicit wave functions, limiting computational efficiency. In this Letter, using the circular photogalvanic effect in Weyl semimetals as a representative example, we realize a 1000-fold computational speedup by eliminating the explicit dependence on wave functions. Our approach leverages the one-to-one correspondence between free parameters of Weyl fermions and the associated responses to obtain precise wave-function-free formulations. Applying our methodology, we systematically investigated known Weyl semimetals and revealed that Ta_{3}S_{2} exhibits photocurrents an order of magnitude greater than those observed in TaAs, with potential for an additional order-of-magnitude enhancement under strain. To further demonstrate the generality of our approach, we obtained a wave-function-free formula for the Berry-curvature dipole in Weyl semimetals. Our Letter paves the way for substantially more efficient screening and optimization of nonlinear electromagnetic properties in topological quantum materials.

Topological materials hold immense promise for exhibiting exotic quantum phenomena, yet achieving controllable topological phase transitions remains challenging. Here, we demonstrate a structurally driven, reversible topological phase transition in the distorted square net material GdPS, induced via in situ potassium dosing. Using angle-resolved photoemission spectroscopy and first principles calculations, we demonstrate a cascade of topological phases in the sub-surface P layer: from a large, topologically trivial band gap to a gapless Dirac cone state with a 2 eV dispersion, and finally to a two-dimensional topological insulator as inferred from theory. This evolution is driven by subtle structural distortions in the first P layer caused by potassium adsorption, which in turn contribute to the band gap closure and topological phase transition. Furthermore, the ability to manipulate the topology of a sub-surface layer in GdPS offers a unique route for exploring and controlling topological states in bulk materials.

The Kondo lattice model, as one of the most fundamental models in condensed matter physics, has been employed to describe a wide range of quantum materials. Discovering new phases on the Kondo lattice and unveiling their mechanisms are crucial to the understanding of strongly correlated systems. Here, in a layered Kondo magnet USbTe, we observe a spin-textured nematic state and visualize a heavy electronic liquid-crystal phase. Employing scanning tunneling microscopy and spectroscopy (STM/STS), we visualize a tetragonal symmetry breaking of heavy electronic states around the Fermi level, which coincides with the formation of heavy quasi-particles driven by band hybridization. Remarkably, using spin-polarized STM, we demonstrate that the nematic state is spin-polarized, which not only suggests its intrinsically electronic nature but also represents the unique magnetic texture of nematic heavy fermions. Our findings unveil a novel correlation-mediated order whose mechanism is inherently tied to Kondo-lattice physics. The observation of heavy nematic states enriches the phase diagram of correlated systems and provides a rare platform to explore the interplay of Kondo physics, spontaneous symmetry breaking, and quantum criticality. The authors study the layered Kondo magnet USbTe by spin-polarized scanning tunneling microscopy and spectroscopy. They discover a spin-polarized nematic state below 15 K, coinciding with the formation of heavy quasi-particles driven by band hybridization.

On the kagome lattice, electrons benefit from the simultaneous presence of band topology, flat electronic bands, and van Hove singularities, forming competing or cooperating orders. Understanding the interrelation between these distinct order parameters remains a significant challenge, leaving much of the associated physics unexplored. In the kagome superconductor KV3Sb5, which exhibits a charge density wave (CDW) state below T = 78 K, we uncover an unpredicted field-induced phase transition below 6 K. The observed transition is marked by a hysteretic anomaly in the resistivity, nonlinear electrical transport, and a change in the symmetry of the electronic response as probed via the angular dependence of the magnetoresistivity. These observations surprisingly suggest the emergence of an unanticipated broken symmetry state coexisting with the original CDW. To understand this experimental observation, we developed a theoretical minimal model for the normal state inside the high-temperature parent CDW phase where an incommensurate CDW order emerges as an instability sub-leading to superconductivity. The incommensurate CDW emerges when superconducting fluctuations become fully suppressed by large magnetic fields. Our results suggest that, in kagome superconductors, quantum states can either coexist or are nearly degenerate in energy, indicating that these are rich platforms to expose new correlated phenomena.

The Kondo lattice mode, as one of the most fundamental models in condensed matter physics, has been employed to describe a wide range of quantum materials such as heavy fermions, transition metal dichalcogenides and two-dimensional Moire systems. Discovering new phases on Kondo lattice and unveiling their mechanisms are crucial to the understanding of strongly correlated systems. Here, in a layered Kondo magnet USbTe, we observe a spin-textured nematic state and visualize a heavy electronic liquid-crystal phase. Employing scanning tunneling microscopy and spectroscopy (STM/STS), we visualize a tetragonal symmetry breaking of heavy electronic states around the Fermi level. Through systematically investigating the temperature and energy dependence of spectroscopic data, we find that the nematic state coincides with the formation of heavy quasi-particles driven by band hybridization. Remarkably, using spin polarized STM, we demonstrate that the nematic state is spin polarized, which not only suggests its intrinsically electronic nature, but also represents the unique magnetic texture of nematic heavy fermions. Our findings unveil a novel correlation-mediated order whose mechanism is inherently tied to Kondo-lattice physics. The observation of heavy nematic states enriches the phase diagram of correlated systems and provides a rare platform to explore the interplay of Kondo physics, spontaneous symmetry breaking and quantum criticality.

The interplay between electronic topology and superconductivity is the subject of great current interest in condensed matter physics. For example, superconductivity induced on the surface of topological insulators is predicted to be triplet in nature, while the interplay between electronic correlations and topology may lead to unconventional superconductivity as in twisted bilayer graphene. Here, we unveil an unconventional two-dimensional superconducting state in the recently discovered Dirac nodal line semimetal ZrAs2 which is exclusively confined to the top and bottom surfaces within the crystal's ab plane. As a remarkable consequence of this emergent state, we observe a Berezinskii-Kosterlitz-Thouless (BKT) transition, the hallmark of two-dimensional superconductivity. Notably, this is the first observation of a BKT transition on the surface of a three-dimensional system. Furthermore, employing angle-resolved photoemission spectroscopy and first-principles calculations, we find that these same surfaces also host a two-dimensional van Hove singularity near the Fermi energy. The proximity of van Hove singularity to the Fermi level leads to enhanced electronic correlations contributing to the stabilization of superconductivity at the surface of ZrAs2, a unique phenomenon among topological semimetals. The surface-confined nature of the van Hove singularity, and associated superconductivity, realized for the first time, opens new avenues to explore the interplay between low-dimensional quantum topology, correlations, and superconductivity in a bulk material without resorting to the superconducting proximity effect.

Correlated topological materials often maintain a delicate balance among physical symmetries. Many topological orders are symmetry protected, whereas most correlated phenomena arise from spontaneous symmetry breaking. Cases where symmetry breaking induces a non-trivial topological phase are rare. Here we demonstrate the presence of two such phases in Ta2Pd3Te5, where Coulomb interactions form excitons that condense below 100 K, one with zero and the other with finite momentum. We observed a full spectral bulk gap, which stems from exciton condensation. This topological excitonic insulator state spontaneously breaks mirror symmetries but involves a weak structural coupling. Scanning tunnelling microscopy shows gapless boundary modes in the bulk insulating phase. Their magnetic field response, together with theoretical modelling, indicates a topological origin. These observations establish Ta2Pd3Te5 as a topological excitonic insulator in a three-dimensional crystal. Thus, our results manifest a unique sequence of topological exciton condensations in a bulk crystal, offering exciting opportunities to study critical behaviour and excitations.

Determining the types of superconducting order in quantum materials is a challenge, especially when multiple degrees of freedom, such as bands or orbitals, contribute to the fermiology and when superconductivity competes, intertwines, or coexists with other symmetry-breaking orders. Here, we study the Kagome-lattice superconductor CsV3Sb5, in which multiband superconductivity coexists with a charge order that substantially reduces the compound's space group symmetries. Through a combination of thermodynamic as well as electrical and thermal transport measurements, we uncover two superconducting regimes with distinct transport and thermodynamic characteristics, while finding no evidence for a phase transition separating them. Thermodynamic measurements reveal substantial quasiparticle weight in a high-temperature regime. At lower temperatures, this weight is removed via the formation of a second gap. The two regimes are sharply distinguished by a pronounced enhancement of the upper critical field at low temperatures and by a switch in the anisotropy of the longitudinal thermal conductivity as a function of in-plane magnetic field orientation. We argue that the band with a gap opening at lower temperatures continues to host low-energy quasiparticles, possibly due to a nodal structure of the gap. Taken together, our results present evidence for band-selective superconductivity with remarkable decoupling of the (two) superconducting gaps. The commonly employed multiband scenario, whereby superconductivity emerges in a primary band and is then induced in other bands appears to fail in this unconventional kagome superconductor. Instead, band-selective superconducting pairing is a paradigm that seems to unify seemingly contradicting results in this intensely studied family of materials and beyond.

Translational symmetry breaking is foundational to condensed matter physics because it is associated with crystal formation. At much lower energy scales, the breaking of crystalline translational symmetry can be driven by electronic, rather than ionic, degrees of freedom and may give rise to stripe order, a unidirectional ordered state. Such symmetry breaking has been seen in two-dimensional and strongly correlated systems. Here, for the first time, we report the observation of stripe order in an elemental solid, tellurium. Through topographic and spectroscopic imaging, we discover a commensurate 4 × 1 stripe phase. Surprisingly, this exotic order is so robust that it survives close to room temperature. Notably, our diffraction experiments confirm the bulk nature of the stripe order, showing the minuteness of potential lattice distortion associated with the order. Our discovery of the stripe order in tellurium opens new windows to understanding the spontaneous symmetry breaking in elemental solids.

Transition metal dichalcogenides are a family of quasi-two-dimensional materials that display a high technological potential due to their wide range of electronic ground states, e.g., from superconducting to semiconducting, depending on the chemical composition, crystal structure, or electrostatic doping. Here, we unveil that by tuning a single parameter, the hydrostatic pressure P, a cascade of electronic phase transitions can be induced in the few-layer transition metal dichalcogenide 1T'-WS2, including superconducting, topological, and anomalous Hall effect phases. Specifically, as P increases, we observe a dual phase transition: the suppression of superconductivity with the concomitant emergence of an anomalous Hall effect at P=1.15 GPa. Remarkably, upon further increasing the pressure above 1.6 GPa, we uncover a reentrant superconducting state that emerges out of a state still exhibiting an anomalous Hall effect. This superconducting state shows a marked increase in superconducting anisotropy with respect to the phase observed at ambient pressure, suggesting a different superconducting state with a distinct pairing symmetry. Via first-principles calculations, we demonstrate that the system concomitantly transitions into a strong topological phase with markedly different band orbital characters and Fermi surfaces contributing to the superconductivity. These findings position 1T'-WS2 as a unique, tunable superconductor, wherein superconductivity, anomalous transport, and band features can be tuned through the application of moderate pressures.

Chirality, or handedness, is ubiquitous in science, from cell biology to physics, and in condensed matter can underlie exotic phases such as chiral charge density waves and chiral superconductivity. However, detecting subtle broken symmetries that define such states is challenging, leading to debate and controversy. Here, using second-order optical response, we reveal the broken symmetries of a chiral charge density wave in the Kagome lattice KV3Sb5. Polarization-dependent mid-infrared photocurrent microscopy uncovers a longitudinal, helicity-dependent photocurrent associated with the charge order, indicating broken inversion and mirror symmetries. These findings, supported by theoretical analysis, directly establish the intrinsic chiral nature of the ordered state. Moreover, the absence of a circular photogalvanic effect perpendicular to the incident light imposes stringent constraints on the point-group symmetries. Our study not only visualizes the chiral nature of the Kagome charge order, but also highlights the nonlinear photogalvanic effect as a sensitive probe for detecting subtle symmetry breakings.

Transition metal dichalcogenides display a high technological potential due to their wide range of electronic ground states. Here, we unveil that by tuning hydrostatic pressure P, a cascade of electronic phase transitions can be induced in the few-layer transition metal dichalcogenide 1T’-WS2. As P increases, we observe the suppression of superconductivity with the concomitant emergence of an anomalous Hall effect (AHE) at $$P\approx 1.15$$ GPa. Above 1.6GPa, we uncover a reentrant superconducting state emerging from a state still exhibiting AHE. This superconducting state competes with the AHE state and shows a marked increase in superconducting anisotropy with respect to the ambient pressure phase, suggesting a distinct pairing symmetry. We demonstrate that 1T’-WS2 concomitantly transitions into a strong topological phase with different band orbital characters and Fermi surfaces contributing to the superconductivity. These findings position 1T’-WS2 as a tunable superconductor, wherein superconductivity, AHE, and band features can be tuned reversibly. Transition metal dichalcogenides exhibit diverse and tunable electronic states. Here the authors reveal a cascade of phase transitions upon increasing hydrostatic pressure in the few-layer 1T’-WS2, including a re-entrant superconducting phase emerging from a normal state exhibiting anomalous Hall effect.

Lattice gauge theories (LGTs)1-4 can be used to understand a wide range of phenomena, from elementary particle scattering in high-energy physics to effective descriptions of many-body interactions in materials5-7. Studying dynamical properties of emergent phases can be challenging, as it requires solving many-body problems that are generally beyond perturbative limits8-10. Here we investigate the dynamics of local excitations in a Z 2 LGT using a two-dimensional lattice of superconducting qubits. We first construct a simple variational circuit that prepares low-energy states that have a large overlap with the ground state; then we create charge excitations with local gates and simulate their quantum dynamics by means of a discretized time evolution. As the electric field coupling constant is increased, our measurements show signatures of transitioning from deconfined to confined dynamics. For confined excitations, the electric field induces a tension in the string connecting them. Our method allows us to experimentally image string dynamics in a (2+1)D LGT, from which we uncover two distinct regimes inside the confining phase: for weak confinement, the string fluctuates strongly in the transverse direction, whereas for strong confinement, transverse fluctuations are effectively frozen11,12. We also demonstrate a resonance condition at which dynamical string breaking is facilitated. Our LGT implementation on a quantum processor presents a new set of techniques for investigating emergent excitations and string dynamics.

Berry curvature physics is responsible for the anomalous electromagnetic responses in solids. One such response is the circular photogalvanic effect (CPGE), typically observed in systems with pronounced Berry curvature─such as flat-band systems or topological semimetals featuring band crossings near the Fermi level, where Berry curvature exhibits sharp discontinuities. To maximize CPGE, one must develop the ability to tune their electronic band dispersion without introducing disorder, which is a challenging endeavor. Here, we demonstrate that it is possible to maximize the CPGE response in a topological material by a fundamentally different approach: controlling the proximity of a given system to a symmetry-breaking phase transition that induces a reconstruction of the electronic band structure. Through measurements of the longitudinal circular photogalvanic effect in the Weyl semimetal (TaSe4)2I, we show that the circular photogalvanic effect can be amplified by a dramatic factor of 2 by tuning the proximity of this compound to charge density wave order. The first-principles calculations we present here show that this enhancement arises from the development of the CDW order parameter and the divergence of the associated relaxation time near the critical temperature. Therefore, this work provides a paradigm for boosting CPGE responses in solids─not by engineering band structure alone but by exploiting critical fluctuations near phase transitions in topological materials.

Kagome metals with charge density wave (CDW) order exhibit a broad spectrum of intriguing quantum phenomena. The recent discovery of the novel kagome CDW compound ScV$_6$Sn$_6$ has spurred significant interest. However, understanding the interplay between CDW and the bulk electronic structure has been obscured by a profusion of surface states and terminations in this quantum material. Here, we employ photoemission spectroscopy and potassium dosing to elucidate the complete bulk band structure of ScV$_6$Sn$_6$, revealing multiple van Hove singularities near the Fermi level. We surprisingly discover a robust spin-polarized topological Dirac surface resonance state at the M point within the two-fold van Hove singularities. Assisted by the first-principle calculations, the temperature dependence of the $k_z$- resolved ARPES spectrum provides unequivocal evidence for the proposed $\sqrt{3}$$\times$$\sqrt{3}$$\times3$ charge order over other candidates. Our work not only enhances the understanding of the CDW-dependent bulk and surface states in ScV$_6$Sn$_6$ but also establishes an essential foundation for potential manipulation of the CDW order in kagome materials.

Charge density waves appear in numerous condensed matter platforms ranging from high-temperature superconductors to quantum Hall systems. Despite such ubiquity, there has been a lack of direct experimental study of boundary states that can uniquely stem from the charge order. Here we directly visualize the bulk and boundary phenomenology of the charge density wave in a topological material, Ta2Se8I, using scanning tunnelling microscopy. At a monolayer step edge, we demonstrate the presence of an in-gap boundary mode persisting up to the charge ordering temperature with modulations along the edge that match the charge density wave wavevector along the edge. Furthermore, these results manifesting the presence of an edge state challenge the existing axion insulator interpretation of the charge-ordered phase in this compound. Topological boundary modes within charge-ordered states have not yet been observed experimentally. Now an in-gap boundary mode, stemming solely from the charge order, is visualized in the topological material Ta2Se8I.

Nematic quantum fluids appear in strongly interacting systems and break the rotational symmetry of the crystallographic lattice. In metals, this is connected to a well-known instability of the Fermi liquid-the Pomeranchuk instability. Using scanning tunneling microscopy, we identified this instability in a highly unusual setting: on the surface of an elemental topological metal, arsenic. By directly visualizing the Fermi surface of the surface state via scanning tunneling spectroscopy and photoemission spectroscopy, we find that the Fermi surface gets deformed and becomes elliptical at the energies where the nematic state is present. Known instances of nematic instability typically need van-Hove singularities or multi-orbital physics as drivers. In contrast, the surface states of arsenic are essentially indistinguishable from well-confined isotropic Rashba bands near the Fermi level, rendering our finding the first realization of Pomeranchuk instability of the topological surface state.