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Implementing and tuning chirality is fundamental in physics, chemistry, and material science. Chiral charge density waves (CDWs), where chirality arises from correlated charge orders, are attracting intense interest due to their exotic transport and optical properties. However, a general framework for predicting chiral CDW materials is lacking, primarily because the underlying mechanisms remain elusive. Here, we address this challenge by developing the first comprehensive predictive framework, systematically identifying chiral CDW materials via first-principles calculations. The key lies in the previously overlooked phase difference of the CDW Q-vectors between layers, which is linked to opposite collective atomic displacements across different layers. This phase difference induces a spiral arrangement of the Q-vectors, ultimately giving rise to a chiral structure in real space. We validate our framework by applying it to the kagome lattice AV$_{3}$Sb$_{5}$ (A = K, Rb, Cs), successfully predicting emergent structural chirality. To demonstrate the generality of our approach, we extend it to predict chiral CDWs in the triangular-lattice NbSe$_{2}$. Beyond material predictions, our theory uncovers a universal and unprecedented Hall effect in chiral CDW materials, occurring without external magnetic fields or intrinsic magnetization. Our experiments on CsV$_{3}$Sb$_{5}$ confirm this prediction, observing a unique signature where the Hall conductivity's sign reverses when the input current is reversed, a phenomenon distinct from known Hall effects. Our findings elucidate the mechanisms behind chiral CDWs and open new avenues for discovering materials with unconventional quantum properties, with potential applications in next-generation electronic and spintronic devices.

The convergence of topology and correlations represents a highly coveted realm in the pursuit of novel quantum states of matter. Introducing electron correlations to a quantum spin Hall (QSH) insulator can lead to the emergence of a fractional topological insulator and other exotic time-reversal-symmetric topological order, not possible in quantum Hall and Chern insulator systems. However, the QSH insulator with quantized edge conductance remains rare, let alone that with significant correlations. In this work, we report a novel dual QSH insulator within the intrinsic monolayer crystal of TaIrTe4, arising from the interplay of its single-particle topology and density-tuned electron correlations. At charge neutrality, monolayer TaIrTe4 demonstrates the QSH insulator that aligns with single-particle band structure calculations, manifesting enhanced nonlocal transport and quantized helical edge conductance. Interestingly, upon introducing electrons from charge neutrality, TaIrTe4 only shows metallic behavior in a small range of charge densities but quickly goes into a new insulating state, entirely unexpected based on TaIrTe4's single-particle band structure. This insulating state could arise from a strong electronic instability near the van Hove singularities (VHS), likely leading to a charge density wave (CDW). Remarkably, within this correlated insulating gap, we observe a resurgence of the QSH state, marked by the revival of nonlocal transport and quantized helical edge conduction. Our observation of helical edge conduction in a CDW gap could bridge spin physics and charge orders. The discovery of a dual QSH insulator introduces a new method for creating topological flat minibands via CDW superlattices, which offer a promising platform for exploring time-reversal-symmetric fractional phases and electromagnetism., Comment: 23 pages, 15 figures, submitted version

Topological materials are at the forefront of quantum materials research, offering tremendous potential for next-generation energy and information devices. However, current investigation of these materials remains largely focused on performance and often neglects the crucial aspect of sustainability. Recognizing the pivotal role of sustainability in addressing global pollution, carbon emissions, resource conservation, and ethical labor practices, we present a comprehensive evaluation of topological materials based on their sustainability and environmental impact. Our approach involves a hierarchical analysis encompassing cost, toxicity, energy demands, environmental impact, social implications, and resilience to imports. By applying this framework to over 16,000 topological materials, we establish a sustainable topological materials database. Our endeavor unveils environmental-friendly topological materials candidates which have been previously overlooked, providing insights into their environmental ramifications and feasibility for industrial scalability. The work represents a critical step toward industrial adoption of topological materials, offering the potential for significant technological advancements and broader societal benefits.

Diode effects are of great interest for both fundamental physics and modern technologies. Electrical diode effects (nonreciprocal transport) have been observed in Weyl systems. Optical diode effects arising from the Weyl fermions have been theoretically considered but not probed experimentally. Here, we report the observation of a nonlinear optical diode effect (NODE) in the magnetic Weyl semimetal CeAlSi, where the magnetization introduces a pronounced directionality in the nonlinear optical second-harmonic generation (SHG). We show demonstrate a six-fold change of the measured SHG intensity between opposite propagation directions over a bandwidth exceeding 250 meV. Supported by density-functional theory, we establish the linearly dispersive bands emerging from Weyl nodes as the origin of this broadband effect. We further demonstrate current-induced magnetization switching and thus electrical control of the NODE. Our results advance ongoing research to identify novel nonlinear optical/transport phenomena in magnetic topological materials and further opens new pathways for the unidirectional manipulation of light., Comment: 20 pages, 4 figures, SI included

Electronic ferroelectricity represents a new paradigm where spontaneous symmetry breaking driven by electronic correlations, in contrast to traditional lattice-driven ferroelectricity, leads to the formation of electric dipoles. Despite the potential application advantages arising from its electronic nature, switchable electronic ferroelectricity remains exceedingly rare. Here, we report the discovery of an electronic ratchet effect that manifests itself as switchable electronic ferroelectricity in a layer-contrasting graphene-boron nitride moir\'e heterostructure. Our engineered layer-asymmetric moir\'e potential landscapes result in layer-polarized localized and itinerant electronic subsystems. At particular fillings of the localized subsystem, we find a ratcheting injection of itinerant carriers in a non-volatile manner, leading to a highly unusual ferroelectric response. Strikingly, the remnant polarization can be stabilized at multiple (quasi-continuous) states with behavior markedly distinct from known ferroelectrics. Our experimental observations, simulations, and theoretical analysis suggest that dipolar excitons are the driving force and elementary ferroelectric units in our system. This signifies a new type of electronic ferroelectricity where the formation of dipolar excitons with aligned moments generates a macroscopic polarization and leads to an electronically-driven ferroelectric response, which we term excitonic ferroelectricity. Such new ferroelectrics, driven by quantum objects like dipolar excitons, could pave the way to innovative quantum analog memory and synaptic devices.

Using circularly-polarized light to control quantum matter is a highly intriguing topic in physics, chemistry and biology. Previous studies have demonstrated helicity-dependent optical control of spatial chirality and magnetization $M$. The former is central for asymmetric synthesis in chemistry and homochirality in bio-molecules, while the latter is of great interest for ferromagnetic spintronics. In this paper, we report the surprising observation of helicity-dependent optical control of fully-compensated antiferromagnetic (AFM) order in 2D even-layered MnBi$_2$Te$_4$, a topological Axion insulator with neither chirality nor $M$. We further demonstrate helicity-dependent optical creation of AFM domain walls by double induction beams and the direct reversal of AFM domains by ultrafast pulses. The control and reversal of AFM domains and domain walls by light helicity have never been achieved in any fully-compensated AFM. To understand this optical control, we study a novel type of circular dichroism (CD) proportional to the AFM order, which only appears in reflection but is absent in transmission. We show that the optical control and CD both arise from the optical Axion electrodynamics, which can be visualized as a Berry curvature real space dipole. Our Axion induction provides the possibility to optically control a family of $\mathcal{PT}$-symmetric AFMs such as Cr$_2$O$_3$, CrI$_3$ and possibly novel states in cuprates. In MnBi$_2$Te$_4$, this further opens the door for optical writing of dissipationless circuit formed by topological edge states.

The bulk-boundary correspondence is a key concept in topological quantum materials. For instance, a quantum spin Hall insulator features a bulk insulating gap with gapless helical boundary states protected by the underlying Z2 topology. However, the bulk-boundary dichotomy and distinction are rarely explored in optical experiments, which can provide unique information about topological charge carriers beyond transport and electronic spectroscopy techniques. Here, we utilize mid-infrared absorption micro-spectroscopy and pump-probe micro-spectroscopy to elucidate the bulk-boundary optical responses of Bi4Br4, a recently discovered room-temperature quantum spin Hall insulator. Benefiting from the low energy of infrared photons and the high spatial resolution, we unambiguously resolve a strong absorption from the boundary states while the bulk absorption is suppressed by its insulating gap. Moreover, the boundary absorption exhibits a strong polarization anisotropy, consistent with the one-dimensional nature of the topological boundary states. Our infrared pump-probe microscopy further measures a substantially increased carrier lifetime for the boundary states, which reaches one nanosecond scale. The nanosecond lifetime is about one to two orders longer than that of most topological materials and can be attributed to the linear dispersion nature of the helical boundary states. Our findings demonstrate the optical bulk-boundary dichotomy in a topological material and provide a proof-of-principal methodology for studying topological optoelectronics., Comment: 26 pages, 4 figures

Nonlinear optical responses of quantum materials have recently undergone dramatic developments to unveil nontrivial geometry and topology. A remarkable example is the quantized longitudinal circular photogalvanic effect (CPGE) associated with the Chern number of Weyl fermions, while the physics of transverse CPGE in Weyl semimetals remains exclusive. Here, we show that the transverse CPGE of Lorentz invariant Weyl fermions is forced to be zero. We find that the transverse photocurrents of Weyl fermions are associated not only with the Chern numbers but also with the degree of Lorentz-symmetry breaking in condensed matter systems. Based on the generic two-band model analysis, we provide a new powerful equation to calculate the transverse CPGE based on the tilting and warping terms of Weyl fermions. Our results are more capable in designing large transverse CPGE of Weyl semimetals in experiments and are applied to more than tens of Weyl materials to estimate their photocurrents. Our method paves the way to study the CPGE of massless or massive quasiparticles to design next-generation quantum optoelectronics.

While ferromagnets have been known and exploited for millennia, antiferromagnets (AFMs) were only discovered in the 1930s. The elusive nature indicates AFMs' unique properties: At large scale, due to the absence of global magnetization, AFMs may appear to behave like any non-magnetic material; However, such a seemingly mundane macroscopic magnetic property is highly nontrivial at microscopic level, where opposite spin alignment within the AFM unit cell forms a rich internal structure. In topological AFMs, such an internal structure leads to a new possibility, where topology and Berry phase can acquire distinct spatial textures. Here, we study this exciting possibility in an AFM Axion insulator, even-layered MnBi$_2$Te$_4$ flakes, where spatial degrees of freedom correspond to different layers. Remarkably, we report the observation of a new type of Hall effect, the layer Hall effect, where electrons from the top and bottom layers spontaneously deflect in opposite directions. Specifically, under no net electric field, even-layered MnBi$_2$Te$_4$ shows no anomalous Hall effect (AHE); However, applying an electric field isolates the response from one layer and leads to the surprising emergence of a large layer-polarized AHE (~50%$\frac{e^2}{h}$). Such a layer Hall effect uncovers a highly rare layer-locked Berry curvature, which serves as a unique character of the space-time $\mathcal{PT}$-symmetric AFM topological insulator state. Moreover, we found that the layer-locked Berry curvature can be manipulated by the Axion field, E$\cdot$B, which drives the system between the opposite AFM states. Our results achieve previously unavailable pathways to detect and manipulate the rich internal spatial structure of fully-compensated topological AFMs. The layer-locked Berry curvature represents a first step towards spatial engineering of Berry phase, such as through layer-specific moir\'e potential., Comment: A revised version of this article is published in Nature

For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their wavefunctions. A key challenge is to identify and implement experiments that probe or control these quantum properties. In this review, we describe recent progress in this direction, focusing on nonlinear electromagnetic responses that arise directly from quantum geometry and topology. We give an overview of the field by discussing new theoretical ideas, groundbreaking experiments, and the novel materials that drive them. We conclude by discussing how these techniques can be combined with new device architectures to uncover, probe, and ultimately control novel quantum phases with emergent topological and correlated properties., Comment: Nature Materials (In Press)

The observation of chirality is ubiquitous in nature. Contrary to intuition, the population of opposite chiralities is surprisingly asymmetric at fundamental levels. Examples range from parity violation in the subatomic weak force to the homochirality in essential biomolecules. The ability to achieve chirality-selective synthesis (chiral induction) is of great importance in stereochemistry, molecular biology and pharmacology. In condensed matter physics, a crystalline electronic system is geometrically chiral when it lacks any mirror plane, space inversion center or roto-inversion axis. Typically, the geometrical chirality is predefined by a material's chiral lattice structure, which is fixed upon the formation of the crystal. By contrast, a particularly unconventional scenario is the gyrotropic order, where chirality spontaneously emerges across a phase transition as the electron system breaks the relevant symmetries of an originally achiral lattice. Such a gyrotropic order, proposed as the quantum analogue of the cholesteric liquid crystals, has attracted significant interest. However, to date, a clear observation and manipulation of the gyrotropic order remain challenging. We report the realization of optical chiral induction and the observation of a gyrotropically ordered phase in the transition-metal dichalcogenide semimetal $1T$-TiSe$_2$. We show that shining mid-infrared circularly polarized light near the critical temperature leads to the preferential formation of one chiral domain. As a result, we are able to observe an out-of-plane circular photogalvanic current, whose direction depends on the optical induction. Our study provides compelling evidence for the spontaneous emergence of chirality in the correlated semimetal TiSe$_2$. Such chiral induction provides a new way of optical control over novel orders in quantum materials., Comment: 22 pages, 5 figures

Advanced microscopy and/or spectroscopy tools play indispensable role in nanoscience and nanotechnology research, as it provides rich information about the growth mechanism, chemical compositions, crystallography, and other important physical and chemical properties. However, the interpretation of imaging data heavily relies on the "intuition" of experienced researchers. As a result, many of the deep graphical features obtained through these tools are often unused because of difficulties in processing the data and finding the correlations. Such challenges can be well addressed by deep learning. In this work, we use the optical characterization of two-dimensional (2D) materials as a case study, and demonstrate a neural-network-based algorithm for the material and thickness identification of exfoliated 2D materials with high prediction accuracy and real-time processing capability. Further analysis shows that the trained network can extract deep graphical features such as contrast, color, edges, shapes, segment sizes and their distributions, based on which we develop an ensemble approach topredict the most relevant physical properties of 2D materials. Finally, a transfer learning technique is applied to adapt the pretrained network to other applications such as identifying layer numbers of a new 2D material, or materials produced by a different synthetic approach. Our artificial-intelligence-based material characterization approach is a powerful tool that would speed up the preparation, initial characterization of 2D materials and other nanomaterials and potentially accelerate new material discoveries.

Recent theoretical advances have proposed a new class of topological crystalline insulator (TCI) phases protected by rotational symmetries. Distinct from topological insulators (TIs), rotational symmetry-protected TCIs are expected to show unique topologically protected boundary modes: First, the surface normal to the rotational axis features unpinned Dirac surface states whose Dirac points are located at generic k points. Second, due to the higher-order bulk boundary correspondence, a 3D TCI also supports 1D helical edge states. Despite the unique topological electronic properties, to date, purely rotational symmetry-protected TCIs remain elusive in real materials. Using first-principles band calculations and theoretical modeling, we identify the van der Waals material $\alpha$-Bi4Br4 as a TCI purely protected by rotation symmetry. We show that the Bi4Br4's (010) surface exhibits a pair of unpinned topological Dirac fermions protected by the two-fold rotational axis. These unpinned Dirac fermions show an exotic spin texture highly favorable for spin transport and a band structure consisting of van Hove singularities due to Lifshitz transition. We also identify 1D topological hinge states along the edges of an $\alpha$-Bi4Br4 rod. We further discuss how the proposed topological electronic properties in $\alpha$-Bi4Br4 can be observed by various experimental techniques.

Topological crystalline insulators (TCI) are insulating electronic phases of matter with nontrivial topology originating from crystalline symmetries. Recent theoretical advances have provided powerful guidelines to search for TCIs in real materials. Using density functional theory, we identify a class of new TCI states in the tetragonal lattice of the Ca$_2$As material family. On both top and side surfaces, we observe topological surface states protected independently by rotational and mirror symmetries. We show that a particular lattice distortion can single out the newly proposed topological protection by the rotational symmetry. As a result, the Dirac points of the topological surface states are moved to generic locations in momentum space away from any high symmetry lines. Such topological surface states have not been seen before. Moreover, the other family members, including Ca$_2$Sb, Ca$_2$Bi and Sr$_2$Sb, feature different topological surface states due to their distinct topological invariants. We thus further propose topological phase transitions in the pseudo-binary systems such as (Ca$_{1-x}$Sr$_x$)$_2$As and Ca$_2$As$_x$Sb$_{1-x}$. Our work reveals rich and exotic TCI physics across the Ca$_2$As family of materials, and suggests the feasibility of materials database search methods to discover new TCIs., Comment: 5 pages, 4 figures

A Weyl semimetal (WSM) is a novel topological phase of matter, in which Weyl fermions (WFs) arise as pseudo-magnetic monopoles in its momentum space. The chirality of the WFs, given by the sign of the monopole charge, is central to the Weyl physics, since it directly serves as the sign of the topological number and gives rise to exotic properties such as Fermi arcs and the chiral anomaly. Despite being the defining property of a WSM, the chirality of the WFs has never been experimentally measured. Here, we directly detect the chirality of the WFs by measuring the photocurrent in response to circularly polarized mid-infrared light. The resulting photocurrent is determined by both the chirality of WFs and that of the photons. Our results pave the way for realizing a wide range of theoretical proposals for studying and controlling the WFs and their associated quantum anomalies by optical and electrical means. More broadly, the two chiralities, analogous to the two valleys in 2D materials, lead to a new degree of freedom in a 3D crystal with potential novel pathways to store and carry information., Comment: Accepted to Nature Physics. Version of original submission

Diverse parallel stitched two-dimensional heterostructures are synthesized, including metal-semiconductor (graphene-MoS2), semiconductor-semiconductor (WS2-MoS2), and insulator-semiconductor (hBN-MoS2), directly through selective sowing of aromatic molecules as the seeds in chemical vapor deposition (CVD) method. Our methodology enables the large-scale fabrication of lateral heterostructures with arbitrary patterns, and clean and precisely aligned interfaces, which offers tremendous potential for its application in integrated circuits., Comment: 30 pages, 4 figures, Accepted by Advanced Materials

Opto-electronic devices utilizing graphene have already demonstrated unique capabilities, which are much more difficult to realize with conventional technologies. However, the requirements in terms of material quality and uniformity are very demanding. A major roadblock towards high-performance devices are the nanoscale variations of graphene properties, which strongly impact the macroscopic device behaviour. Here, we present and apply opto-electronic nanoscopy to measure locally both the optical and electronic properties of graphene devices. This is achieved by combining scanning near-field infrared nanoscopy with electrical device read-out, allowing infrared photocurrent mapping at length scales of tens of nanometers. We apply this technique to study the impact of edges and grain boundaries on spatial carrier density profiles and local thermoelectric properties. Moreover, we show that the technique can also be applied to encapsulated graphene/hexagonal boron nitride (h-BN) devices, where we observe strong charge build-up near the edges, and also address a device solution to this problem. The technique enables nanoscale characterization for a broad range of common graphene devices without the need of special device architectures or invasive graphene treatment.

Graphene is a new material showing high promise in optoelectronics, photonics, and energy-harvesting applications. However, the underlying physical mechanism of optoelectronic response has not been established. Here, we report on the intrinsic optoelectronic response of high-quality dual-gated monolayer and bilayer graphene p-n junction devices. Local laser excitation at the p-n interface leads to striking six-fold photovoltage patterns as a function of bottom- and top-gate voltages. These patterns, together with the measured spatial and density dependence of the photoresponse, provide strong evidence that non-local hot-carrier transport, rather than the photovoltaic effect, dominates the intrinsic photoresponse in graphene. This novel regime, which features a long-lived and spatially distributed hot carrier population, may open the doorway for optoelectronic technologies exploiting efficient energy transport at the nanoscale., Comment: 19 pages, 4 figures