Observation of interband Berry phase in laser-driven crystals.

Ever since its discovery1, the notion of the Berry phase has permeated all branches of physics and plays an important part in a variety of quantum phenomena2. However, so far all its realizations have been based on a continuous evolution of the quantum state, following a cyclic path. Here we introduce and demonstrate a conceptually new manifestation of the Berry phase in light-driven crystals, in which the electronic wavefunction accumulates a geometric phase during a discrete evolution between different bands, while preserving the coherence of the process. We experimentally reveal this phase by using a strong laser field to engineer an internal interferometer, induced during less than one cycle of the driving field, which maps the phase onto the emission of higher-order harmonics. Our work provides an opportunity for the study of geometric phases, leading to a variety of observations in light-driven topological phenomena and attosecond solid-state physics.

Imaging quantum oscillations and millitesla pseudomagnetic fields in graphene.

The exceptional control of the electronic energy bands in atomically thin quantum materials has led to the discovery of several emergent phenomena1. However, at present there is no versatile method for mapping the local band structure in advanced two-dimensional materials devices in which the active layer is commonly embedded in the insulating layers and metallic gates. Using a scanning superconducting quantum interference device, here we image the de Haas-van Alphen quantum oscillations in a model system, the Bernal-stacked trilayer graphene with dual gates, which shows several highly tunable bands2-4. By resolving thermodynamic quantum oscillations spanning more than 100 Landau levels in low magnetic fields, we reconstruct the band structure and its evolution with the displacement field with excellent precision and nanoscale spatial resolution. Moreover, by developing Landau-level interferometry, we show shear-strain-induced pseudomagnetic fields and map their spatial dependence. In contrast to artificially induced large strain, which leads to pseudomagnetic fields of hundreds of tesla5-7, we detect naturally occurring pseudomagnetic fields as low as 1 mT corresponding to graphene twisting by 1 millidegree, two orders of magnitude lower than the typical angle disorder in twisted bilayer graphene8-11. This ability to resolve the local band structure and strain at the nanoscale level enables the characterization and use of tunable band engineering in practical van der Waals devices.

Quantum-metric-induced nonlinear transport in a topological antiferromagnet.

The Berry curvature and quantum metric are the imaginary part and real part, respectively, of the quantum geometric tensor, which characterizes the topology of quantum states1. The Berry curvature is known to generate a number of important transport phenomena, such as the quantum Hall effect and the anomalous Hall effect2,3; however, the consequences of the quantum metric have rarely been probed by transport measurements. Here we report the observation of quantum-metric-induced nonlinear transport, including both a nonlinear anomalous Hall effect and a diode-like non-reciprocal longitudinal response, in thin films of a topological antiferromagnet, MnBi2Te4. Our observations reveal that the transverse and longitudinal nonlinear conductivities reverse signs when reversing the antiferromagnetic order, diminish above the Néel temperature and are insensitive to disorder scattering, thus verifying their origin in the band-structure topology. They also flip signs between electron- and hole-doped regions, in agreement with theoretical calculations. Our work provides a means to probe the quantum metric through nonlinear transport and to design magnetic nonlinear devices.

Roton pair density wave in a strong-coupling kagome superconductor.

The transition metal kagome lattice materials host frustrated, correlated and topological quantum states of matter1-9. Recently, a new family of vanadium-based kagome metals, AV3Sb5 (A = K, Rb or Cs), with topological band structures has been discovered10,11. These layered compounds are nonmagnetic and undergo charge density wave transitions before developing superconductivity at low temperatures11-19. Here we report the observation of unconventional superconductivity and a pair density wave (PDW) in CsV3Sb5 using scanning tunnelling microscope/spectroscopy and Josephson scanning tunnelling spectroscopy. We find that CsV3Sb5 exhibits a V-shaped pairing gap Δ ~ 0.5 meV and is a strong-coupling superconductor (2Δ/kBTc ~ 5) that coexists with 4a0 unidirectional and 2a0 × 2a0 charge order. Remarkably, we discover a 3Q PDW accompanied by bidirectional 4a0/3 spatial modulations of the superconducting gap, coherence peak and gap depth in the tunnelling conductance. We term this novel quantum state a roton PDW associated with an underlying vortex-antivortex lattice that can account for the observed conductance modulations. Probing the electronic states in the vortex halo in an applied magnetic field, in strong field that suppresses superconductivity and in zero field above Tc, reveals that the PDW is a primary state responsible for an emergent pseudogap and intertwined electronic order. Our findings show striking analogies and distinctions to the phenomenology of high-Tc cuprate superconductors, and provide groundwork for understanding the microscopic origin of correlated electronic states and superconductivity in vanadium-based kagome metals.

Monopole-like orbital-momentum locking and the induced orbital transport in topological chiral semimetals.

The interplay between chirality and topology nurtures many exotic electronic properties. For instance, topological chiral semimetals display multifold chiral fermions that manifest nontrivial topological charge and spin texture. They are an ideal playground for exploring chirality-driven exotic physical phenomena. In this work, we reveal a monopole-like orbital-momentum locking texture on the three-dimensional Fermi surfaces of topological chiral semimetals with B20 structures (e.g., RhSi and PdGa). This orbital texture enables a large orbital Hall effect (OHE) and a giant orbital magnetoelectric (OME) effect in the presence of current flow. Different enantiomers exhibit the same OHE which can be converted to the spin Hall effect by spin-orbit coupling in materials. In contrast, the OME effect is chirality-dependent and much larger than its spin counterpart. Our work reveals the crucial role of orbital texture for understanding OHE and OME effects in topological chiral semimetals and paves the path for applications in orbitronics, spintronics, and enantiomer recognition.

First-order quantum phase transition in the hybrid metal-Mott insulator transition metal dichalcogenide 4Hb-TaS2.

Coupling together distinct correlated and topologically nontrivial electronic phases of matter can potentially induce novel electronic orders and phase transitions among them. Transition metal dichalcogenide compounds serve as a bedrock for exploration of such hybrid systems. They host a variety of exotic electronic phases, and their Van der Waals nature enables to admix them, either by exfoliation and stacking or by stoichiometric growth, and thereby induce novel correlated complexes. Here, we investigate the compound 4Hb-TaS2 that interleaves the Mott-insulating state of 1T-TaS2 and the putative spin liquid it hosts together with the metallic state of 2H-TaS2 and the low-temperature superconducting phase it harbors using scanning tunneling spectroscopy. We reveal a thermodynamic phase diagram that hosts a first-order quantum phase transition between a correlated Kondo-like cluster state and a depleted flat band state. We demonstrate that this intrinsic transition can be induced by an electric field and temperature as well as by manipulation of the interlayer coupling with the probe tip, hence allowing to reversibly toggle between the Kondo-like cluster and the depleted flat band states. The phase transition is manifested by a discontinuous change of the complete electronic spectrum accompanied by hysteresis and low-frequency noise. We find that the shape of the transition line in the phase diagram is determined by the local compressibility and the entropy of the two electronic states. Our findings set such heterogeneous structures as an exciting platform for systematic investigation and manipulation of Mott-metal transitions and strongly correlated phases and quantum phase transitions therein.

Direct observation of the collective modes of the charge density wave in the kagome metal CsV3Sb5.

A recently discovered group of kagome metals AV[Formula: see text]Sb[Formula: see text] (A = K, Rb, Cs) exhibit a variety of intertwined unconventional electronic phases, which emerge from a puzzling charge density wave phase. Understanding of this charge-ordered parent phase is crucial for deciphering the entire phase diagram. However, the mechanism of the charge density wave is still controversial, and its primary source of fluctuations-the collective modes-has not been experimentally observed. Here, we use ultrashort laser pulses to melt the charge order in CsV[Formula: see text]Sb[Formula: see text] and record the resulting dynamics using femtosecond angle-resolved photoemission. We resolve the melting time of the charge order and directly observe its amplitude mode, imposing a fundamental limit for the fastest possible lattice rearrangement time. These observations together with ab initio calculations provide clear evidence for a structural rather than electronic mechanism of the charge density wave. Our findings pave the way for a better understanding of the unconventional phases hosted on the kagome lattice.

Single-crystalline van der Waals layered dielectric with high dielectric constant.

The scaling of silicon-based transistors at sub-ten-nanometre technology nodes faces challenges such as interface imperfection and gate current leakage for an ultrathin silicon channel1,2. For next-generation nanoelectronics, high-mobility two-dimensional (2D) layered semiconductors with an atomic thickness and dangling-bond-free surfaces are expected as channel materials to achieve smaller channel sizes, less interfacial scattering and more efficient gate-field penetration1,2. However, further progress towards 2D electronics is hindered by factors such as the lack of a high dielectric constant (κ) dielectric with an atomically flat and dangling-bond-free surface3,4. Here, we report a facile synthesis of a single-crystalline high-κ (κ of roughly 16.5) van der Waals layered dielectric Bi2SeO5. The centimetre-scale single crystal of Bi2SeO5 can be efficiently exfoliated to an atomically flat nanosheet as large as 250 × 200 µm2 and as thin as monolayer. With these Bi2SeO5 nanosheets as dielectric and encapsulation layers, 2D materials such as Bi2O2Se, MoS2 and graphene show improved electronic performances. For example, in 2D Bi2O2Se, the quantum Hall effect is observed and the carrier mobility reaches 470,000 cm2 V-1 s-1 at 1.8 K. Our finding expands the realm of dielectric and opens up a new possibility for lowering the gate voltage and power consumption in 2D electronics and integrated circuits.

Unification of Nonlinear Anomalous Hall Effect and Nonreciprocal Magnetoresistance in Metals by the Quantum Geometry.

The quantum geometry has significant consequences in determining transport and optical properties in quantum materials. Here, we use a semiclassical formalism coupled with perturbative corrections unifying the nonlinear anomalous Hall effect and nonreciprocal magnetoresistance (longitudinal resistance) from the quantum geometry. In the dc limit, both transverse and longitudinal nonlinear conductivities include a term due to the normalized quantum metric dipole. The quantum metric contribution is intrinsic and does not scale with the quasiparticle lifetime. We demonstrate the coexistence of a nonlinear anomalous Hall effect and nonreciprocal magnetoresistance in films of the doped antiferromagnetic topological insulator MnBi_{2}Te_{4}. Our work indicates that both longitudinal and transverse nonlinear transport provide a sensitive probe of the quantum geometry in solids.

Atomistic Origin of Diverse Charge Density Wave States in CsV_{3}Sb_{5}.

Kagome metals AV_{3}Sb_{5} (A=K, Rb, or Cs) exhibit intriguing charge density wave (CDW) instabilities, which interplay with superconductivity and band topology. However, despite firm observations, the atomistic origins of the CDW phases, as well as hidden instabilities, remain elusive. Here, we adopt our newly developed symmetry-adapted cluster expansion method to construct a first-principles-based effective Hamiltonian of CsV_{3}Sb_{5}, which not only reproduces the established inverse star of David (ISD) phase, but also predict a series of D_{3h}-n states under mild tensile strains. With such atomistic Hamiltonians, the microscopic origins of different CDW states are revealed as the competition of the second-nearest neighbor V-V pairs versus the first-nearest neighbor V-V and V-Sb couplings. Interestingly, the effective Hamiltonians also reveal the existence of ionic Dzyaloshinskii-Moriya interaction in the high-symmetry phase of CsV_{3}Sb_{5} and drives the formation of noncollinear CDW patterns. Our work thus not only deepens the understanding of the CDW formation in AV_{3}Sb_{5}, but also demonstrates that the effective Hamiltonian is a suitable approach for investigating CDW mechanisms, which can be extended to various CDW systems.

Chiral Charge Density Wave and Backscattering-Immune Orbital Texture in Monolayer 1T-TiTe2.

Nontrivial electronic states are attracting intense attention in low-dimensional physics. Though chirality has been identified in charge states with a scalar order parameter, its intertwining with charge density waves (CDW), film thickness, and the impact on the electronic behaviors remain less well understood. Here, using scanning tunneling microscopy, we report a 2 × 2 chiral CDW as well as a strong suppression of the Te-5p hole-band backscattering in monolayer 1T-TiTe2. These exotic characters vanish in bilayer TiTe2 in a non-CDW state. Theoretical calculations prove that chirality comes from a helical stacking of the triple-q CDW components and, therefore, can persist at the two-dimensional limit. Furthermore, the chirality renders the Te-5p bands with an unconventional orbital texture that prohibits electron backscattering. Our study establishes TiTe2 as a promising playground for manipulating the chiral ground states at the monolayer limit and provides a novel path to engineer electronic properties from an orbital degree.

Abundant Lattice Instability in Kagome Metal ScV_{6}Sn_{6}.

Kagome materials are emerging platforms for studying charge and spin orders. In this Letter, we have revealed a rich lattice instability in a Z_{2} kagome metal ScV_{6}Sn_{6} by first-principles calculations. Beyond verifying the sqrt[3]×sqrt[3]×3 charge density wave (CDW) order observed by the recent experiment, we further identified three more possible CDW structures, i.e., sqrt[3]×sqrt[3]×2 CDW with P6/mmm symmetry, 2×2×2 CDW with Immm symmetry, and 2×2×2 CDW with P6/mmm symmetry. The former two are more energetically favored than the sqrt[3]×sqrt[3]×3 phase, while the third one is comparable in energy. These CDW distortions involve mainly out-of-plane motions of Sc and Sn atoms, while V atoms constituting the kagome net are almost unchanged. We attribute the lattice instability to the smallness of Sc atomic radius. In contrast, such instability disappears in its sister compounds RV_{6}Sn_{6} (R is Y, or a rare-earth element), which exhibit quite similar electronic band structures to the Sc compound, because R has a larger atomic radius. Our work indicates that ScV_{6}Sn_{6} might exhibit varied CDW phases in different experimental conditions and provides insights to explore rich charge orders in kagome materials.

Distinct Magnetic Gaps between Antiferromagnetic and Ferromagnetic Orders Driven by Surface Defects in the Topological Magnet MnBi_{2}Te_{4}.

Many experiments observed a metallic behavior at zero magnetic fields (antiferromagnetic phase, AFM) in MnBi_{2}Te_{4} thin film transport, which coincides with gapless surface states observed by angle-resolved photoemission spectroscopy, while it can become a Chern insulator at field larger than 6 T (ferromagnetic phase, FM). Thus, the zero-field surface magnetism was once speculated to be different from the bulk AFM phase. However, recent magnetic force microscopy refutes this assumption by detecting persistent AFM order on the surface. In this Letter, we propose a mechanism related to surface defects that can rationalize these contradicting observations in different experiments. We find that co-antisites (exchanging Mn and Bi atoms in the surface van der Waals layer) can strongly suppress the magnetic gap down to several meV in the AFM phase without violating the magnetic order but preserve the magnetic gap in the FM phase. The different gap sizes between AFM and FM phases are caused by the exchange interaction cancellation or collaboration of the top two van der Waals layers manifested by defect-induced surface charge redistribution among the top two van der Waals layers. This theory can be validated by the position- and field-dependent gap in future surface spectroscopy measurements. Our work suggests suppressing related defects in samples to realize the quantum anomalous Hall insulator or axion insulator at zero fields.

Experimental signatures of the mixed axial-gravitational anomaly in the Weyl semimetal NbP.

The conservation laws, such as those of charge, energy and momentum, have a central role in physics. In some special cases, classical conservation laws are broken at the quantum level by quantum fluctuations, in which case the theory is said to have quantum anomalies. One of the most prominent examples is the chiral anomaly, which involves massless chiral fermions. These particles have their spin, or internal angular momentum, aligned either parallel or antiparallel with their linear momentum, labelled as left and right chirality, respectively. In three spatial dimensions, the chiral anomaly is the breakdown (as a result of externally applied parallel electric and magnetic fields) of the classical conservation law that dictates that the number of massless fermions of each chirality are separately conserved. The current that measures the difference between left- and right-handed particles is called the axial current and is not conserved at the quantum level. In addition, an underlying curved space-time provides a distinct contribution to a chiral imbalance, an effect known as the mixed axial-gravitational anomaly, but this anomaly has yet to be confirmed experimentally. However, the presence of a mixed gauge-gravitational anomaly has recently been tied to thermoelectrical transport in a magnetic field, even in flat space-time, suggesting that such types of mixed anomaly could be experimentally probed in condensed matter systems known as Weyl semimetals. Here, using a temperature gradient, we observe experimentally a positive magneto-thermoelectric conductance in the Weyl semimetal niobium phosphide (NbP) for collinear temperature gradients and magnetic fields that vanishes in the ultra-quantum limit, when only a single Landau level is occupied. This observation is consistent with the presence of a mixed axial-gravitational anomaly, providing clear evidence for a theoretical concept that has so far eluded experimental detection.

Delicate Ferromagnetism in MnBi6Te10.

Tailoring magnetic orders in topological insulators is critical to the realization of topological quantum phenomena. An outstanding challenge is to find a material where atomic defects lead to tunable magnetic orders while maintaining a nontrivial topology. Here, by combining magnetization measurements, angle-resolved photoemission spectroscopy, and transmission electron microscopy, we reveal disorder-enabled, tunable magnetic ground states in MnBi6Te10. In the ferromagnetic phase, an energy gap of 15 meV is resolved at the Dirac point on the MnBi2Te4 termination. In contrast, antiferromagnetic MnBi6Te10 exhibits gapless topological surface states on all terminations. Transmission electron microscopy and magnetization measurements reveal substantial Mn vacancies and Mn migration in ferromagnetic MnBi6Te10. We provide a conceptual framework where a cooperative interplay of these defects drives a delicate change of overall magnetic ground state energies and leads to tunable magnetic topological orders. Our work provides a clear pathway for nanoscale defect-engineering toward the realization of topological quantum phases.

Chirality-driven topological electronic structure of DNA-like materials.

Topological aspects of the geometry of DNA and similar chiral molecules have received a lot of attention, but the topology of their electronic structure is less explored. Previous experiments revealed that DNA can efficiently filter spin-polarized electrons between metal contacts, a process called chiral-induced spin selectivity. However, the underlying correlation between chiral structure and electronic spin remains elusive. In this work, we reveal an orbital texture in the band structure, a topological characteristic induced by the chirality. We found that this orbital texture enables the chiral molecule to polarize the quantum orbital. This orbital polarization effect (OPE) induces spin polarization assisted by the spin-orbit interaction of a metal contact and leads to magnetoresistance and chiral separation. The orbital angular momentum of photoelectrons also plays an essential role in related photoemission experiments. Beyond chiral-induced spin selectivity, we predict that the orbital polarization effect could induce spin-selective phenomena even in achiral but inversion-breaking materials.

Visualizing coexisting surface states in the weak and crystalline topological insulator Bi2TeI.

Dual topological materials are unique topological phases that host coexisting surface states of different topological nature on the same or on different material facets. Here, we show that Bi2TeI is a dual topological insulator. It exhibits band inversions at two time reversal symmetry points of the bulk band, which classify it as a weak topological insulator with metallic states on its 'side' surfaces. The mirror symmetry of the crystal structure concurrently classifies it as a topological crystalline insulator. We investigated Bi2TeI spectroscopically to show the existence of both two-dimensional Dirac surface states, which are susceptible to mirror symmetry breaking, and one-dimensional channels that reside along the step edges. Their mutual coexistence on the step edge, where both facets join, is facilitated by momentum and energy segregation. Our observation of a dual topological insulator should stimulate investigations of other dual topology classes with distinct surface manifestations coexisting at their boundaries.

Charge Density Waves and Electronic Properties of Superconducting Kagome Metals.

Kagome metals AV_{3}Sb_{5} (A=K, Rb, and Cs) exhibit intriguing superconductivity below 0.9∼2.5 K, a charge density wave (CDW) transition around 80∼100 K, and Z_{2} topological surface states. The nature of the CDW phase and its relation to superconductivity remains elusive. In this work, we investigate the electronic and structural properties of CDW by first-principles calculations. We reveal an inverse Star of David deformation as the 2×2×2 CDW ground state of the kagome lattice. The kagome lattice shows softening breathing-phonon modes, indicating the structural instability. However, electrons play an essential role in the CDW transition via Fermi surface nesting and van Hove singularity. The inverse Star of David structure agrees with recent experiments by scanning tunneling microscopy (STM). The CDW phase inherits the nontrivial Z_{2}-type topological band structure. Further, we find that the electron-phonon coupling is too weak to account for the superconductivity T_{c} in all three materials. It implies the existence of unconventional pairing of these kagome metals. Our results provide essential knowledge toward understanding the superconductivity and topology in kagome metals.

Anomalous Hall effect in Weyl semimetal half-Heusler compounds RPtBi (R = Gd and Nd).

Topological materials ranging from topological insulators to Weyl and Dirac semimetals form one of the most exciting current fields in condensed-matter research. Many half-Heusler compounds, RPtBi (R = rare earth), have been theoretically predicted to be topological semimetals. Among various topological attributes envisaged in RPtBi, topological surface states, chiral anomaly, and planar Hall effect have been observed experimentally. Here, we report an unusual intrinsic anomalous Hall effect (AHE) in the antiferromagnetic Heusler Weyl semimetal compounds GdPtBi and NdPtBi that is observed over a wide temperature range. In particular, GdPtBi exhibits an anomalous Hall conductivity of up to 60 Ω-1⋅cm-1 and an anomalous Hall angle as large as 23%. Muon spin-resonance (µSR) studies of GdPtBi indicate a sharp antiferromagnetic transition (TN) at 9 K without any noticeable magnetic correlations above TN Our studies indicate that Weyl points in these half-Heuslers are induced by a magnetic field via exchange splitting of the electronic bands at or near the Fermi energy, which is the source of the chiral anomaly and the AHE.

Nonvanishing Subgap Photocurrent as a Probe of Lifetime Effects.

For semiconductors and insulators, it is commonly believed that in-gap transitions into nonlocalized states are smoothly suppressed in the clean limit; i.e., at zero temperature, their contribution vanishes due to the unavailability of states. We present a novel type of subgap response which shows that this intuition does not generalize beyond linear response. Namely, we find that the dc current due to the bulk photovoltaic effect can be finite and mostly temperature independent in an allowed window of subgap transitions. We expect that a moderate range of excitation energies lies between the bulk energy gap and the mobility edge where this effect is observable. Using a simplified relaxation time model for the band broadening, we find the subgap dc current to be temperature independent for noninteracting systems but temperature dependent for strongly interacting systems. Thus, the subgap response may be used to distinguish whether a state is single-particle localized or many-body localized.