Advanced Characterization of the Spatial Variation of Moiré Heterostructures and Moiré Excitons.

In this short review, an overview of recent progress in deploying advanced characterization techniques is provided to understand the effects of spatial variation and inhomogeneities in moiré heterostructures over multiple length scales. Particular emphasis is placed on correlating the impact of twist angle misalignment, nano-scale disorder, and atomic relaxation on the moiré potential and its collective excitations, particularly moiré excitons. Finally, future technological applications leveraging moiré excitons are discussed.

Collective Charge Excitations between Moiré Minibands in Twisted WSe_{2} Bilayers Probed with Resonant Inelastic Light Scattering.

We establish low-temperature resonant inelastic light scattering (RILS) spectroscopy as a tool to probe the formation of a series of moiré bands in twisted WSe_{2} bilayers by accessing collective inter-moiré-band excitations (IMBEs). We observe resonances in RILS spectra at energies in agreement with inter-moiré-band transitions obtained from an ab initio based continuum model. Transitions between the first and second moiré band for a twist angle of about 8° are reported and between the first and the third, and higher bands for a twist of about 3°. The signatures from IMBE for the latter highlight a strong departure from parabolic bands with flat minibands exhibiting very high density of states in accord with theory. These observations allow one to quantify the transition energies at the K point where the states relevant for correlation physics are hosted.

Linear resistivity at van Hove singularities in twisted bilayer WSe2.

Different mechanisms driving a linear temperature dependence of the resistivity ρ ∼ T at van Hove singularities (VHSs) or metal-insulator transitions when doping a Mott insulator are being debated intensively with competing theoretical proposals. We experimentally investigate this using the exceptional tunability of twisted bilayer (TB) WSe2 by tracking the parameter regions where linear-in-T resistivity is found in dependency of displacement fields, filling, and magnetic fields. We find that even when the VHSs are tuned rather far away from the half-filling point and the Mott insulating transition is absent, the T-linear resistivity persists at the VHSs. When doping away from the VHSs, the T-linear behavior quickly transitions into a Fermi liquid behavior with a T2 relation. No apparent dependency of the linear-in-T resistivity, besides a rather strong change of prefactor, is found when applying displacement fields as long as the filling is tuned to the VHSs, including D ∼ 0.28 V/nm where a high-order VHS is expected. Intriguingly, such non-Fermi liquid linear-in-T resistivity persists even when magnetic fields break the spin-degeneracy of the VHSs at which point two linear in T regions emerge, for each of the split VHSs separately. This points to a mechanism of enhanced scattering at generic VHSs rather than only at high-order VHSs or by a quantum critical point during a Mott transition. Our findings provide insights into the many-body consequences arising out of VHSs, especially the non-Fermi liquid behavior found in moiré materials.

Terminable Transitions in a Topological Fermionic Ladder.

Interacting fermionic ladders are versatile platforms to study quantum phases of matter, such as different types of Mott insulators. In particular, there are D-Mott and S-Mott states that hold preformed fermion pairs and become paired-fermion liquids upon doping (d wave and s wave, respectively). We show that the D-Mott and S-Mott phases are in fact two facets of the same topological phase and that the transition between them is terminable. These results provide a quantum analog of the well-known terminable liquid-to-gas transition. However, the phenomenology we uncover is even richer, as the order of the transition may alternate between continuous and first order, depending on the interaction details. Most importantly, the terminable transition is robust in the sense that it is guaranteed to appear for weak, but arbitrary couplings. We discuss a minimal model where some analytical insights can be obtained, a generic model where the effect persists; and a model-independent field-theoretical study demonstrating the general phenomenon. The role of symmetry and the edge states is briefly discussed. The numerical results are obtained using the variational uniform matrix-product state (VUMPS) formalism for infinite systems, as well as the density-matrix renormalization group (DMRG) algorithm for finite systems.

Theory of resonantly enhanced photo-induced superconductivity.

Optical driving of materials has emerged as a versatile tool to control their properties, with photo-induced superconductivity being among the most fascinating examples. In this work, we show that light or lattice vibrations coupled to an electronic interband transition naturally give rise to electron-electron attraction that may be enhanced when the underlying boson is driven into a non-thermal state. We find this phenomenon to be resonantly amplified when tuning the boson's frequency close to the energy difference between the two electronic bands. This result offers a simple microscopic mechanism for photo-induced superconductivity and provides a recipe for designing new platforms in which light-induced superconductivity can be realized. We discuss two-dimensional heterostructures as a potential test ground for light-induced superconductivity concretely proposing a setup consisting of a graphene-hBN-SrTiO3 heterostructure, for which we estimate a superconducting Tc that may be achieved upon driving the system.

Ultrafast Spin Dynamics and Photoinduced Insulator-to-Metal Transition in α-RuCl3.

Laser-induced ultrafast demagnetization is a phenomenon of utmost interest and attracts significant attention because it enables potential applications in ultrafast optoelectronics and spintronics. As a spin-orbit coupling assisted magnetic insulator, α-RuCl3 provides an attractive platform to explore the physics of electronic correlations and unconventional magnetism. Using time-dependent density functional theory, we explore the ultrafast laser-induced dynamics of the electronic and magnetic structures in α-RuCl3. Our study unveils that laser pulses can introduce ultrafast demagnetizations, accompanied by an out-of-equilibrium insulator-to-metal transition in a few tens of femtoseconds. The spin response significantly depends on the laser wavelength and polarization on account of the electron correlations, band renormalizations, and charge redistributions. These findings provide physical insights into the coupling between the electronic and magnetic degrees of freedom in α-RuCl3 and shed light on suppressing the long-range magnetic orders and reaching a proximate spin liquid phase for two-dimensional magnets on an ultrafast time scale.

Can Neural Quantum States Learn Volume-Law Ground States?

We study whether neural quantum states based on multilayer feed-forward networks can find ground states which exhibit volume-law entanglement entropy. As a testbed, we employ the paradigmatic Sachdev-Ye-Kitaev model. We find that both shallow and deep feed-forward networks require an exponential number of parameters in order to represent the ground state of this model. This demonstrates that sufficiently complicated quantum states, although being physical solutions to relevant models and not pathological cases, can still be difficult to learn to the point of intractability at larger system sizes. Hence, the variational neural network approach offers no benefits over exact diagonalization methods in this case. This highlights the importance of further investigations into the physical properties of quantum states amenable to an efficient neural representation.

Cavity Light-Matter Entanglement through Quantum Fluctuations.

The hybridization between light and matter forms the basis to achieve cavity control over quantum materials. In this Letter we investigate a cavity coupled to a quantum chain of interacting spinless fermions by numerically exact solutions and perturbative analytical expansions. We draw two important conclusions about such systems: (i) Specific quantum fluctuations of the matter system play a pivotal role in achieving entanglement between light and matter; and (ii) in turn, light-matter entanglement is a key ingredient to modify electronic properties by the cavity. We hypothesize that quantum fluctuations of those matter operators to which the cavity modes couple are a general prerequisite for light-matter entanglement in the ground state. Implications of our findings for light-matter-entangled phases, cavity-modified phase transitions in correlated systems, and measurement of light-matter entanglement through Kubo response functions are discussed.

Witnessing Nonequilibrium Entanglement Dynamics in a Strongly Correlated Fermionic Chain.

Many-body entanglement in condensed matter systems can be diagnosed from equilibrium response functions through the use of entanglement witnesses and operator-specific quantum bounds. Here, we investigate the applicability of this approach for detecting entangled states in quantum systems driven out of equilibrium. We use a multipartite entanglement witness, the quantum Fisher information, to study the dynamics of a paradigmatic fermion chain undergoing a time-dependent change of the Coulomb interaction. Our results show that the quantum Fisher information is able to witness distinct signatures of multipartite entanglement both near and far from equilibrium that are robust against decoherence. We discuss implications of these findings for probing entanglement in light-driven quantum materials with time-resolved optical and x-ray scattering methods.

Unconventional non-local relaxation dynamics in a twisted trilayer graphene moiré superlattice.

The electronic and structural properties of atomically thin materials can be controllably tuned by assembling them with an interlayer twist. During this process, constituent layers spontaneously rearrange themselves in search of a lowest energy configuration. Such relaxation phenomena can lead to unexpected and novel material properties. Here, we study twisted double trilayer graphene (TDTG) using nano-optical and tunneling spectroscopy tools. We reveal a surprising optical and electronic contrast, as well as a stacking energy imbalance emerging between the moiré domains. We attribute this contrast to an unconventional form of lattice relaxation in which an entire graphene layer spontaneously shifts position during assembly, resulting in domains of ABABAB and BCBACA stacking. We analyze the energetics of this transition and demonstrate that it is the result of a non-local relaxation process, in which an energy gain in one domain of the moiré lattice is paid for by a relaxation that occurs in the other.

Experimental Observation of ABCB Stacked Tetralayer Graphene.

In tetralayer graphene, three inequivalent layer stackings should exist; however, only rhombohedral (ABCA) and Bernal (ABAB) stacking have so far been observed. The three stacking sequences differ in their electronic structure, with the elusive third stacking (ABCB) being unique as it is predicted to exhibit an intrinsic bandgap as well as locally flat bands around the K points. Here, we use scattering-type scanning near-field optical microscopy and confocal Raman microscopy to identify and characterize domains of ABCB stacked tetralayer graphene. We differentiate between the three stacking sequences by addressing characteristic interband contributions in the optical conductivity between 0.28 and 0.56 eV with amplitude and phase-resolved near-field nanospectroscopy. By normalizing adjacent flakes to each other, we achieve good agreement between theory and experiment, allowing for the unambiguous assignment of ABCB domains in tetralayer graphene. These results establish near-field spectroscopy at the interband transitions as a semiquantitative tool, enabling the recognition of ABCB domains in tetralayer graphene flakes and, therefore, providing a basis to study correlation physics of this exciting phase.

Ultra-strong spin-orbit coupling and topological moiré engineering in twisted ZrS2 bilayers.

We predict that twisted bilayers of 1T-ZrS2 realize a novel and tunable platform to engineer two-dimensional topological quantum phases dominated by strong spin-orbit interactions. At small twist angles, ZrS2 heterostructures give rise to an emergent and twist-controlled moiré Kagome lattice, combining geometric frustration and strong spin-orbit coupling to give rise to a moiré quantum spin Hall insulator with highly controllable and nearly-dispersionless bands. We devise a generic pseudo-spin theory for group-IV transition metal dichalcogenides that relies on the two-component character of the valence band maximum of the 1T structure at Γ, and study the emergence of a robust quantum anomalous Hall phase as well as possible fractional Chern insulating states from strong Coulomb repulsion at fractional fillings of the topological moiré Kagome bands. Our results establish group-IV transition metal dichalcogenide bilayers as a novel moiré platform to realize strongly-correlated topological phases in a twist-tunable setting.

Effective Hamiltonian for Photonic Topological Insulator with Non-Hermitian Domain Walls.

The gain and loss in photonic lattices provide possibilities for many functional phenomena. In this Letter, we consider photonic topological insulators with different types of gain-loss domain walls, which will break the translational symmetry of the lattices. A method is proposed to construct effective Hamiltonians, which accurately describe states and the corresponding energies at the domain walls for different types of photonic topological insulators and domain walls with arbitrary shapes. We also consider domain-induced higher-order topological states in two-dimensional non-Hermitian Aubry-André-Harper lattices and use our method to explain such phenomena successfully. Our results reveal the physics in photonic topological insulators with gain-loss domain walls, which provides advanced pathways for manipulation of non-Hermitian topological states in photonic systems.

Nematicity Arising from a Chiral Superconducting Ground State in Magic-Angle Twisted Bilayer Graphene under In-Plane Magnetic Fields.

Recent measurements of the resistivity in magic-angle twisted bilayer graphene near the superconducting transition temperature show twofold anisotropy, or nematicity, when changing the direction of an in-plane magnetic field [Cao et al., Science 372, 264 (2021)SCIEAS0036-807510.1126/science.abc2836]. This was interpreted as strong evidence for exotic nematic superconductivity instead of the widely proposed chiral superconductivity. Counterintuitively, we demonstrate that in two-dimensional chiral superconductors the in-plane magnetic field can hybridize the two chiral superconducting order parameters to induce a phase that shows nematicity in the transport response. Its paraconductivity is modulated as cos(2θ_{B}), with θ_{B} being the direction of the in-plane magnetic field, consistent with experiment in twisted bilayer graphene. We therefore suggest that the nematic response reported by Cao et al. does not rule out a chiral superconducting ground state.

Phonon-induced disorder in dynamics of optically pumped metals from nonlinear electron-phonon coupling.

The non-equilibrium dynamics of matter excited by light may produce electronic phases, such as laser-induced high-transition-temperature superconductivity, that do not exist in equilibrium. Here we simulate the dynamics of a metal driven at initial time by a spatially uniform pump that excites dipole-active vibrational modes which couple nonlinearly to electrons. We provide evidence for rapid loss of spatial coherence, leading to emergent effective disorder in the dynamics, which arises in a system unitarily evolving under a translation-invariant Hamiltonian, and dominates the electronic behavior as the system evolves towards a correlated electron-phonon long-time state, possibly explaining why transient superconductivity is not observed. Our framework provides a basis within which to understand correlation dynamics in current pump-probe experiments of vibrationally coupled electrons, highlight the importance of the evolution of phase coherence, and demonstrate that pumped electron-phonon systems provide a means of realizing dynamically induced disorder in translation-invariant systems.

Realization of nearly dispersionless bands with strong orbital anisotropy from destructive interference in twisted bilayer MoS2.

Recently, the twist angle between adjacent sheets of stacked van der Waals materials emerged as a new knob to engineer correlated states of matter in two-dimensional heterostructures in a controlled manner, giving rise to emergent phenomena such as superconductivity or correlated insulating states. Here, we use an ab initio based approach to characterize the electronic properties of twisted bilayer MoS2. We report that, in marked contrast to twisted bilayer graphene, slightly hole-doped MoS2 realizes a strongly asymmetric px-py Hubbard model on the honeycomb lattice, with two almost entirely dispersionless bands emerging due to destructive interference. The origin of these dispersionless bands, is similar to that of the flat bands in the prototypical Lieb or Kagome lattices and co-exists with the general band flattening at small twist angle due to the moiré interference. We study the collective behavior of twisted bilayer MoS2 in the presence of interactions, and characterize an array of different magnetic and orbitally-ordered correlated phases, which may be susceptible to quantum fluctuations giving rise to exotic, purely quantum, states of matter.

Engineering Three-Dimensional Moiré Flat Bands.

Twisting two adjacent layers of van der Waals materials with respect to each other can lead to flat two-dimensional electronic bands which enables a wealth of physical phenomena. Here, we generalize this concept of so-called moiré flat bands to engineer flat bands in all three spatial dimensions controlled by the twist angle. The basic concept is to stack the material such that the large spatial moiré interference patterns are spatially shifted from one twisted layer to the next. We exemplify the general concept by considering graphitic systems, boron nitride, and WSe2, but the approach is applicable to any two-dimensional van der Waals material. For hexagonal boron nitride, we develop an ab initio fitted tight binding model that captures the corresponding three-dimensional low-energy electronic structure. We outline that interesting three-dimensional correlated phases of matter can be induced and controlled following this route, including quantum magnets and unconventional superconducting states.

Moiréless correlations in ABCA graphene.

Atomically thin van der Waals materials stacked with an interlayer twist have proven to be an excellent platform toward achieving gate-tunable correlated phenomena linked to the formation of flat electronic bands. In this work we demonstrate the formation of emergent correlated phases in multilayer rhombohedral graphene--a simple material that also exhibits a flat electronic band edge but without the need of having a moiré superlattice induced by twisted van der Waals layers. We show that two layers of bilayer graphene that are twisted by an arbitrary tiny angle host large (micrometer-scale) regions of uniform rhombohedral four-layer (ABCA) graphene that can be independently studied. Scanning tunneling spectroscopy reveals that ABCA graphene hosts an unprecedentedly sharp van Hove singularity of 3-5-meV half-width. We demonstrate that when this van Hove singularity straddles the Fermi level, a correlated many-body gap emerges with peak-to-peak value of 9.5 meV at charge neutrality. Mean-field theoretical calculations for model with short-ranged interactions indicate that two primary candidates for the appearance of this broken symmetry state are a charge-transfer excitonic insulator and a ferrimagnet. Finally, we show that ABCA graphene hosts surface topological helical edge states at natural interfaces with ABAB graphene which can be turned on and off with gate voltage, implying that small-angle twisted double-bilayer graphene is an ideal programmable topological quantum material.

Moiré metrology of energy landscapes in van der Waals heterostructures.

The emerging field of twistronics, which harnesses the twist angle between two-dimensional materials, represents a promising route for the design of quantum materials, as the twist-angle-induced superlattices offer means to control topology and strong correlations. At the small twist limit, and particularly under strain, as atomic relaxation prevails, the emergent moiré superlattice encodes elusive insights into the local interlayer interaction. Here we introduce moiré metrology as a combined experiment-theory framework to probe the stacking energy landscape of bilayer structures at the 0.1 meV/atom scale, outperforming the gold-standard of quantum chemistry. Through studying the shapes of moiré domains with numerous nano-imaging techniques, and correlating with multi-scale modelling, we assess and refine first-principle models for the interlayer interaction. We document the prowess of moiré metrology for three representative twisted systems: bilayer graphene, double bilayer graphene and H-stacked MoSe2/WSe2. Moiré metrology establishes sought after experimental benchmarks for interlayer interaction, thus enabling accurate modelling of twisted multilayers.

Universality of Boundary Charge Fluctuations.

We establish the quantum fluctuations ΔQ_{B}^{2} of the charge Q_{B} accumulated at the boundary of an insulator as an integral tool to characterize phase transitions where a direct gap closes (and reopens), typically occurring for insulators with topological properties. The power of this characterization lies in its capability to treat different kinds of insulators on equal footing, being applicable to transitions between topological and nontopological band, Anderson, and Mott insulators alike. In the vicinity of the phase transition, we find a universal scaling ΔQ_{B}^{2}(E_{g}) as a function of the gap size E_{g} and determine its generic form in various dimensions. For prototypical phase transitions with a massive Dirac-like bulk spectrum, we demonstrate a scaling with the inverse gap in one dimension and a logarithmic one in two dimensions.