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Many-body effects play an important role in enhancing and modifying optical absorption and other excited-state properties of solids in the perturbative regime, but their role in high harmonic generation (HHG) and other nonlinear response beyond the perturbative regime is not well-understood. We develop here an ab initio many-body method to study nonperturbative HHG based on the real-time propagation of the non-equilibrium Green’s function with the GW self energy. We calculate the HHG of monolayer MoS 2 and obtain good agreement with experiment, including the reproduction of characteristic patterns of monotonic and nonmonotonic harmonic yield in the parallel and perpendicular responses, respectively. Here, we show that many-body effects are especially important to accurately reproduce the spectral features in the perpendicular response, which reflect a complex interplay of electron-hole interactions (or exciton effects) in tandem with the many-body renormalization and Berry curvature of the independent quasiparticle bandstructure. Many-body effects may be crucial for describing high harmonic generation in solids, but previous work did not fully account for many-body effects. Here the authors develop a non-perturbative, ab initio theory and apply it to monolayer MoS2, showing significant many-body effects in the perpendicular response.

Moiré patterns of transition metal dichalcogenide heterobilayers have proved to be an ideal platform on which to host unusual correlated electronic phases, emerging magnetism and correlated exciton physics. Whereas the existence of new moiré excitonic states is established 1 – 4 through optical measurements, the microscopic nature of these states is still poorly understood, often relying on empirically fit models. Here, combining large-scale first-principles GW (where G and W denote the one-particle Green's function and the screened Coulomb interaction, respectively) plus Bethe–Salpeter calculations and micro-reflection spectroscopy, we identify the nature of the exciton resonances in WSe 2 /WS 2 moiré superlattices, discovering a rich set of moiré excitons that cannot be captured by prevailing continuum models. Our calculations show moiré excitons with distinct characters, including modulated Wannier excitons and previously unidentified intralayer charge-transfer excitons. Signatures of these distinct excitonic characters are confirmed experimentally by the unique carrier-density and magnetic-field dependences of different moiré exciton resonances. Our study highlights the highly non-trivial exciton states that can emerge in transition metal dichalcogenide moiré superlattices, and suggests new ways of tuning many-body physics in moiré systems by engineering excited-states with specific spatial characters. By combining large-scale first-principles GW -BSE calculations and micro-reflection spectroscopy, the nature of the exciton resonances in WSe 2 /WS 2 moiré superlattices is identified, highlighting non-trivial exciton states and suggesting new ways of tuning many-body physics.

Electrons and holes can spontaneously form excitons and condense in a semimetal or semiconductor, as predicted decades ago. This type of Bose condensation can happen at much higher temperatures in comparison with dilute atomic gases. Two-dimensional (2D) materials with reduced Coulomb screening around the Fermi level are promising for realizing such a system. Here we report a change in the band structure accompanied by a phase transition at about 180 K in single-layer ZrTe 2 based on angle-resolved photoemission spectroscopy (ARPES) measurements. Below the transition temperature, gap opening and development of an ultra-flat band top around the zone center are observed. This gap and the phase transition are rapidly suppressed with extra carrier densities introduced by adding more layers or dopants on the surface. The results suggest the formation of an excitonic insulating ground state in single-layer ZrTe 2 , and the findings are rationalized by first-principles calculations and a self-consistent mean-field theory. Our study provides evidence for exciton condensation in a 2D semimetal and demonstrates strong dimensionality effects on the formation of intrinsic bound electron–hole pairs in solids. Two-dimensional materials are promising platforms for the realization of an excitonic insulator state. Here the authors report evidence for an excitonic insulator in a single-layer ZrTe2 based on ARPES measurements.

Electronic and optical properties of materials are affected by atomic motion through the electron–phonon interaction: not only band gaps change with temperature, but even at absolute zero temperature, zero-point motion causes band-gap renormalization. We present a large-scale first-principles evaluation of the zero-point renormalization of band edges beyond the adiabatic approximation. For materials with light elements, the band gap renormalization is often larger than 0.3 eV, and up to 0.7 eV. This effect cannot be ignored if accurate band gaps are sought. For infrared-active materials, global agreement with available experimental data is obtained only when non-adiabatic effects are taken into account. They even dominate zero-point renormalization for many materials, as shown by a generalized Fröhlich model that includes multiple phonon branches, anisotropic and degenerate electronic extrema, whose range of validity is established by comparison with first-principles results.

In solids, the condensation of electron and hole pairs with finite momentum leads to an ordered state known as a charge density wave, in which the charge has spatial modulation. However, lattice symmetry breaking and the accompanying relocation of the ions, which changes the charge distribution, can also occur simultaneously, making it difficult to disentangle the origin of the transition. Here we demonstrate a condensed phase in low-dimensional HfTe 2 . Angle-resolved photoemission spectroscopy measurements reveal a metal–insulator transition upon lowering the temperature. The observation of an opening gap, the renormalization of the bands and the emergence of replica bands in the low-temperature regime suggests that a charge density wave formed in the ground state. Raman spectroscopy shows no sign of lattice distortion within the detection limit. A small amount of electron doping substantially raises the transition temperature due to a reduced screening effect and a more balanced carrier density for electrons and holes. Our results indicate that the formation mechanism of the charge density wave is consistent with the excitonic insulator phase in low-dimensional HfTe 2 without any structural modification. The mechanism of charge density wave formation has been hard to explain due to accompanying structural distortions. Now low-dimensional HfTe 2 is revealed to host a purely electronic exitonic charge density wave driven by reduced screening effects.

Excitons are fundamental quasiparticles that are ubiquitous in photoexcited semiconductors and insulators. Despite causing a sharp and strong photoabsorption near the interband absorption edge, charge-neutral excitons do not yield photocurrent in conventional photovoltaic processes unless dissociated into free charge carriers. Here, we experimentally demonstrate that excitons can directly contribute to photocurrent generation through a nonlinear light−matter interaction in a noncentrosymmetric semiconductor CuI. Epitaxial thin films of CuI exhibit a substantial enhancement of photocurrent at exciton resonance energies even below the bandgap. From the light polarization dependence, this photocurrent is identified to be shift current, a nonlinear photocurrent driven by the change in the geometric Berry phase of electron wave functions upon the optical transition. The shift current at the exciton resonance is much larger than that induced above the band gap by free electron−hole excitation, and their signs are opposite. First-principles calculations elucidate that the sign and magnitude of the exciton shift current are strongly dependent on the strain in the thin film. The present study reveals the crucial role of excitons in enhancing the shift current magnitude and its strain sensitivity, and will open an unprecedented route for efficient manipulation of nonlinear optical effects. Quantum geometry effects in condensed matter physics are a topic of growing interest. Here, the authors show that the quantum geometry associated with excitons can generate detectable shift currents in a wide-gap semiconductor.

Strong electron-electron interaction can induce Mott insulating state, which is believed to host unusual correlated phenomena such as quantum spin liquid when quantum fluctuation dominates and unconventional superconductivity through doping. Transition metal compounds as correlated materials provide a versatile platform to engineer the Mott insulating state. Previous studies mostly focused on the controlling of the repulsive interaction and bandwidth of the electrons by gating or doping. Here, we performed angle-resolved photoemission spectroscopy (ARPES) on monolayer 1T phase NbSe 2 , TaSe 2 , and TaS 2 and directly observed their band structures with characteristic lower Hubbard bands. By systematically investigating the orbital textures and temperature dependence of the energy gap of the materials in this family, we discovered that hybridization of the chalcogen p states with lower Hubbard band stabilizes the Mott phase via tuning of the bandwidth, as shown by a significant increase of the transition temperature ( T C ) at a stronger hybridization strength. Our findings reveal a mechanism for realizing a robust Mott insulating phase and establish monolayer 1T phase transition metal dichalcogenide family as a promising platform for exploring correlated electron problems. Transition metal compounds provide a versatile platform for tailoring Mott physics. Here, the authors reveal that hybridization between the lower Hubbard band and the chalcogen band stabilizes the Mott state through bandwidth tuning in the 1T-MX 2 (M = Nb, Ta; X = S, Se) family.

Materials modelling and design using computational quantum and classical approaches is by now well established as an essential pillar in condensed matter physics, chemistry and materials science research, in addition to experiments and analytical theories. The past few decades have witnessed tremendous advances in methodology development and applications to understand and predict the ground-state, excited-state and dynamical properties of materials, ranging from molecules to nanoscopic/mesoscopic materials to bulk and reduced-dimensional systems. This issue of Nature Materials presents four in-depth Review Articles on the field. This Perspective aims to give a brief overview of the progress, as well as provide some comments on future challenges and opportunities. We envision that increasingly powerful and versatile computational approaches, coupled with new conceptual understandings and the growth of techniques such as machine learning, will play a guiding role in the future search and discovery of materials for science and technology. This Perspective provides an overview of the different approaches used to understand the behaviour of materials at different length scales and timescales through computation, and outlines future challenges in the description of complex systems or ultrafast non-equilibrium behaviour.

Shift current is a direct current generated from nonlinear light–matter interaction in a noncentrosymmetric crystal and is considered a promising candidate for next-generation photovoltaic devices. The mechanism for shift currents in real materials is, however, still not well understood, especially if electron–hole interactions are included. Here, we employ a first-principles interacting Green’s-function approach on the Keldysh contour with real-time propagation to study photocurrents generated by nonlinear optical processes under continuous wave illumination in real materials. We demonstrate a strong direct current shift current at subbandgap excitation frequencies in monolayer GeS due to strongly bound excitons, as well as a giant excitonic enhancement in the shift current coefficients at above bandgap photon frequencies. Our results suggest that atomically thin two-dimensional materials may be promising building blocks for next-generation shift current devices.

Atomically thin indium selenide (InSe) exhibits a sombrero-like valence band, leading to distinctive excitonic behaviors. It is known that the indirect band gap of atomically thin InSe leads to a weak emission from the lowest-energy excitonic state (A peak). However, the A peak emission of monolayer (ML) InSe was observed to be either absent or very weak, rendering the nature of its excitonic states largely unknown. Intriguingly, we demonstrate that ML InSe exhibits pronounced PL emission because of the efficient brightening of the momentum-indirect dark excitons. The mechanism is attributed to acoustic phonon-assisted radiative recombination facilitated by strong exciton-acoustic phonon coupling and extended wavefunction in momentum space. Systematic analysis of layer-, power-, and temperature-dependent PL demonstrates that a carrier localization model can account for the asymmetric line shape of the lowest-energy excitonic emission for atomically thin InSe. Our work reveals that atomically thin InSe is a promising platform for manipulating the tightly bound dark excitons in two-dimensional semiconductor-based optoelectronic devices.