Strange Metal in Magic-Angle Graphene with near Planckian Dissipation

Geometric Inhibition of Superflow in Single-Layer Graphene Suggests a Staggered-Flux Superconductivity in Bilayer and Trilayer Graphene

In great contrast to the numerous discoveries of superconductivity in layer-stacked graphene systems, the absence of superconductivity in the simplest monolayer graphene remains quite puzzling. Here, through realistic computation of the electronic structure, we identify a systematic trend that superconductivity emerges only upon alteration of the low-energy electronic lattice from the underlying honeycomb atomic structure. We then demonstrate that this inhibition can result from geometric frustration of the bond lattice that disables the quantum phase coherence of the order parameter residing on it. In comparison, upon deviation from the honeycomb lattice, relief of geometric frustration allows robust superfluidity with nontrivial spatial structures. For the specific examples of bilayer and trilayer graphene under an external electric field, such a bond-centered order parameter would develop superfluidity with staggered flux that breaks the time-reversal symmetry. Our study also suggests the possible realization of the long-sought superconductivity in single-layer graphene via the application of unidirectional strain.

Emergent phases in graphene flat bands

Electronic correlations in two-dimensional materials play a crucial role in stabilising emergent phases of matter. The realisation of correlation-driven phenomena in graphene has remained a longstanding goal, primarily due to the absence of strong electron-electron interactions within its low-energy bands. In this context, magic-angle twisted bilayer graphene has recently emerged as a novel platform featuring correlated phases favoured by the low-energy flat bands of the underlying moiré superlattice. Notably, the observation of correlated insulators and superconductivity, and the interplay between these phases have garnered significant attention. A wealth of correlated phases with unprecedented tunability was discovered subsequently, including orbital ferromagnetism, Chern insulators, strange metallicity, density waves, and nematicity. However, a comprehensive understanding of these closely competing phases remains elusive. The ability to controllably twist and stack multiple graphene layers has enabled the creation of a whole new family of moiré superlattices with myriad properties. Here, we review the progress and development achieved so far, encompassing the rich phase diagrams offered by these graphene-based moiré systems. Additionally, we discuss multiple phases recently observed in non-moiré multilayer graphene systems. Finally, we outline future opportunities and challenges for the exploration of hidden phases in this new generation of moiré materials.

Transport properties in non-Fermi liquid phases of nodal-point semimetals

In this review, we survey the current progress in computing transport properties in semimetals which harbour non-Fermi liquid (NFL) phases. We first discuss the widely-used Kubo formalism, which can be applied to the effective theory describing the stable NFL phase obtained via a renormalization group procedure and, hence, is applicable for temperatures close to zero (e.g. optical conductivity). For finite-temperature regimes, which apply to the computations of the generalized DC conductivity tensors, we elucidate the memory matrix approach. This approach is based on an effective hydrodynamic description of the system, and is especially suited for tackling transport calculations in strongly-interacting quantum field theories, because it does not rely on the existence of long-lived quasiparticles. As a concrete example, we apply these two approaches to find the response of the so-calledLuttinger-Abrikosov-Benelavskii phaseof isotropic three-dimensional Luttinger semimetals, which arises under the effects of long-ranged (unscreened) Coulomb interactions, with the chemical potential fine-tuned to cut exactly the nodal point. In particular, we focus on the electric conductivity tensors, thermal and thermoelectric response, Raman response, free energy, entropy density, and shear viscosity.

Tunable Exciton Polaritons in Band-Gap Engineered Hexagonal Boron Nitride

We show that hexagonal boron nitride (hBN), a two-dimensional insulator, when subjected to an external superlattice potential forms a paradigm for electrostatically tunable excitons in the near- and mid-ultraviolet (UV). With a combination of analytical and numerical methods, we see that the imposed potential has three consequences: (i) It renormalizes the effective mass tensor, leading to anisotropic effective masses. (ii) It renormalizes the band gap, eventually reducing it. (iii) It reduces the exciton binding energies. All these consequences depend on a single dimensionless parameter, which includes the product of strength of the external potential with its period. In addition to the excitonic energy levels, we compute the optical conductivity along two orthogonal directions and from it the absorption spectrum. The results for the latter show that our system is able to mimic a grid polarizer. These characteristics make one-dimensional hBN superlattices a viable and meaningful platform for fine-tuned polaritonics in the UV to visible spectral range.

Hidden transport phenomena in an ultraclean correlated metal

Advancements in materials synthesis have been key to unveil the quantum nature of electronic properties in solids by providing experimental reference points for a correct theoretical description. Here, we report hidden transport phenomena emerging in the ultraclean limit of the archetypical correlated electron system SrVO3. The low temperature, low magnetic field transport was found to be dominated by anisotropic scattering, whereas, at high temperature, we find a yet undiscovered phase that exhibits clear deviations from the expected Landau Fermi liquid, which is reminiscent of strange-metal physics in materials on the verge of a Mott transition. Further, the high sample purity enabled accessing the high magnetic field transport regime at low temperature, which revealed an anomalously high Hall coefficient. Taken with the strong anisotropic scattering, this presents a more complex picture of SrVO3 that deviates from a simple Landau Fermi liquid. These hidden transport anomalies observed in the ultraclean limit prompt a theoretical reexamination of this canonical correlated electron system beyond the Landau Fermi liquid paradigm, and more generally serves as an experimental basis to refine theoretical methods to capture such nontrivial experimental consequences emerging in correlated electron systems.

Tunable Non-Fermi Liquid Phase from Coupling to Two-Level Systems

We study a controlled large-N theory of electrons coupled to dynamical two-level systems (TLSs) via spatially random interactions. Such a physical situation arises when electrons scatter off low-energy excitations in a metallic glass, such as a charge or stripe glass. Our theory is governed by a non-Gaussian saddle point, which maps to the celebrated spin-boson model. By tuning the coupling strength we find that the model crosses over from a Fermi liquid at weak coupling to an extended region of non-Fermi liquid behavior at strong coupling, and realizes a marginal Fermi liquid at the crossover. Our results are valid for generic space dimensions d>1.

Moiré band renormalization due to lattice mismatch in bilayer graphene

We investigated the band renormalization caused by the compressive-strain-induced lattice mismatch in parallel AA stacked bilayer graphene using two complementary methods: the tight-binding approach and the low-energy continuum theory. While a large mismatch does not alter the low-energy bands, a small one reduces the bandwidth of the low-energy bands along with a decrease in the Fermi velocity. In the tiny-mismatch regime, the low-energy continuum theory reveals that the long-period moiré pattern extensively renormalizes the low-energy bands, resulting in a significant reduction of bandwidth. Meanwhile, the Fermi velocity exhibits an oscillatory behavior and approaches zero at specific mismatches. However, the resulting low-energy bands are not perfectly isolated flat, as seen in twisted bilayer graphene at magic angles. These findings provide a deeper understanding of moiré physics and offer valuable guidance for related experimental studies in creating moiré superlattices using two-dimensional van der Waals heterostructures.

Link between T-Linear Resistivity and Quantum Criticality in Ambipolar Black Phosphorus

The interplay between strong Coulomb interactions and kinetic energy leads to intricate many-body competing ground states owing to quantum fluctuations in 2D electron and hole gases. However, the simultaneous observation of quantum critical phenomena in both electron and hole regimes remains elusive. Here, we utilize anisotropic black phosphorus (BP) to show density-driven metal-insulator transition with a critical conductance ∼e2/h which highlights the significant role of quantum fluctuations in both hole and electron regimes. We observe a T-linear resistivity from the deep metallic phase to the metal-insulator boundary at moderate temperatures, while it turns to Fermi liquid behavior in the deep metallic phase at low temperatures in both regimes. An analysis of the resistivity suggests that disorder-dominated transport leads to T-linear behavior in the hole regime, while in the electron regime, the T-linear resistivity results from strong Coulomb interactions, suggestive of strange-metal behavior. Successful scaling collapse of the resistivity in the T-linear region demonstrates the link between quantum criticality and the T-linear resistivity in both regimes. Our study provides compelling evidence that ambipolar BP could serve as an exciting testbed for investigating exotic states and quantum critical phenomena in hole and electron regimes of 2D semiconductors.

Nonlocal Acoustic Moiré Hyperbolic Metasurfaces

The discovery of the topological transition in twisted bilayer (tBL) materials has attracted considerable attention in nano-optics. In the analogue of acoustics, however, no such topological transition has been found due to the inherent nondirectional scalar property of acoustic pressure. In this work, by using a theory-based nonlocal anisotropic design, the in-plane acoustic pressure is transformed into a spatially distributed vector field using twisted multilayer metasurfaces. So-called "acoustic magic angle"-related acoustic phenomena occur, such as nonlocal polariton hybridization and the topological Lifshitz transition. The dispersion becomes flat at the acoustic magic angle, enabling polarized excitations to propagate in a single direction. Moreover, the acoustic topological transition (from hyperbolic to elliptic dispersion) is experimentally observed for the first time as the twist angle continuously changes. This unique characteristic facilitates low-loss tunable polariton hybridization at the subwavelength scale. A twisted trilayer acoustic metasurface is also experimentally demonstrated, and more possibilities for manipulating acoustic waves are found. These discoveries not only enrich the concepts of moiré physics and topological acoustics but also provide a complete framework of theory and methodologies for explaining the phenomena that are observed.

Engineering Flat Bands in Twisted-Bilayer Graphene away from the Magic Angle with Chiral Optical Cavities

Twisted bilayer graphene (TBG) is a recently discovered two-dimensional superlattice structure which exhibits strongly correlated quantum many-body physics, including strange metallic behavior and unconventional superconductivity. Most of TBG exotic properties are connected to the emergence of a pair of isolated and topological flat electronic bands at the so-called magic angle, θ≈1.05°, which are nevertheless very fragile. In this work, we show that, by employing chiral optical cavities, the topological flat bands can be stabilized away from the magic angle in an interval of approximately 0.8°<θ<1.3°. As highlighted by a simplified theoretical model, time reversal symmetry breaking (TRSB), induced by the chiral nature of the cavity, plays a fundamental role in flattening the isolated bands and gapping out the rest of the spectrum. Additionally, TRSB suppresses the Berry curvature and induces a topological phase transition, with a gap closing at the Γ point, towards a band structure with two isolated flat bands with Chern number equal to 0. The efficiency of the cavity is discussed as a function of the twisting angle, the light-matter coupling and the optical cavity characteristic frequency. Our results demonstrate the possibility of engineering flat bands in TBG using optical devices, extending the onset of strongly correlated topological electronic phases in moiré superlattices to a wider range in the twisting angle.

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.

Torsional force microscopy of van der Waals moirés and atomic lattices

In a stack of atomically thin van der Waals layers, introducing interlayer twist creates a moiré superlattice whose period is a function of twist angle. Changes in that twist angle of even hundredths of a degree can dramatically transform the system's electronic properties. Setting a precise and uniform twist angle for a stack remains difficult; hence, determining that twist angle and mapping its spatial variation is very important. Techniques have emerged to do this by imaging the moiré, but most of these require sophisticated infrastructure, time-consuming sample preparation beyond stack synthesis, or both. In this work, we show that torsional force microscopy (TFM), a scanning probe technique sensitive to dynamic friction, can reveal surface and shallow subsurface structure of van der Waals stacks on multiple length scales: the moirés formed between bi-layers of graphene and between graphene and hexagonal boron nitride (hBN) and also the atomic crystal lattices of graphene and hBN. In TFM, torsional motion of an Atomic Force Microscope (AFM) cantilever is monitored as it is actively driven at a torsional resonance while a feedback loop maintains contact at a set force with the sample surface. TFM works at room temperature in air, with no need for an electrical bias between the tip and the sample, making it applicable to a wide array of samples. It should enable determination of precise structural information including twist angles and strain in moiré superlattices and crystallographic orientation of van der Waals flakes to support predictable moiré heterostructure fabrication.

Anomalous electrons in a metallic kagome ferromagnet

Ordinary metals contain electron liquids within well-defined 'Fermi' surfaces at which the electrons behave as if they were non-interacting. In the absence of transitions to entirely new phases such as insulators or superconductors, interactions between electrons induce scattering that is quadratic in the deviation of the binding energy from the Fermi level. A long-standing puzzle is that certain materials do not fit this 'Fermi liquid' description. A common feature is strong interactions between electrons relative to their kinetic energies. One route to this regime is special lattices to reduce the electron kinetic energies. Twisted bilayer graphene1-4 is an example, and trihexagonal tiling lattices (triangular 'kagome'), with all corner sites removed on a 2 × 2 superlattice, can also host narrow electron bands5 for which interaction effects would be enhanced. Here we describe spectroscopy revealing non-Fermi-liquid behaviour for the ferromagnetic kagome metal Fe3Sn2 (ref. 6). We discover three C3-symmetric electron pockets at the Brillouin zone centre, two of which are expected from density functional theory. The third and most sharply defined band emerges at low temperatures and binding energies by means of fractionalization of one of the other two, most likely on the account of enhanced electron-electron interactions owing to a flat band predicted to lie just above the Fermi level. Our discovery opens the topic of how such many-body physics involving flat bands7,8 could differ depending on whether they arise from lattice geometry or from strongly localized atomic orbitals9,10.

Tunable quantum interferometer for correlated moiré electrons

Magic-angle twisted bilayer graphene can host a variety of gate-tunable correlated states - including superconducting and correlated insulator states. Recently, junction-based superconducting moiré devices have been introduced, enabling the study of the charge, spin and orbital nature of superconductivity, as well as the coherence of moiré electrons in magic-angle twisted bilayer graphene. Complementary fundamental coherence effects-in particular, the Little-Parks effect in a superconducting ring and the Aharonov-Bohm effect in a normally conducting ring - have not yet been reported in moiré devices. Here, we observe both phenomena in a single gate-defined ring device, where we can embed a superconducting or normally conducting ring in a correlated or band insulator. The Little-Parks effect is seen in the superconducting phase diagram as a function of density and magnetic field, confirming the effective charge of 2e. We also find that the coherence length of conducting moiré electrons exceeds several microns at 50 mK. In addition, we identify a regime characterized by h/e-periodic oscillations but with superconductor-like nonlinear transport.

Band structure sensitive photoresponse in twisted bilayer graphene proximitized with WSe2

The ability to tune the twist angle between different layers of two-dimensional (2D) materials has enabled the creation of electronic flat bands artificially, leading to exotic quantum phases. When a twisted blilayer of graphene (tBLG) is placed at the van der Waals proximity to a semiconducting layer of transition metal dichalcogenide (TMDC), such as WSe2, the emergent phases in the tBLG can fundamentally modify the functionality of such heterostructures. Here we have performed photoresponse measurements in few-layer-WSe2/tBLG heterostructure, where the mis-orientation angle of the tBLG layer was chosen to lie close to the magic angle of 1.1°. Our experiments show that the photoresponse is extremely sensitive to the band structure of tBLG and gets strongly suppressed when the Fermi energy was placed within the low-energy moiré bands. Photoresponse could however be recovered when Fermi energy exceeded the moiré band edge where it was dominated by the photogating effect due to transfer of charge between the tBLG and the WSe2 layers. Our observations suggest the possibility of the screening effects from moiré flat bands that strongly affect the charge transfer process at the WSe2/tBLG interface, which is further supported by time-resolved photo-resistance measurements.

Shot noise in a strange metal

Strange-metal behavior has been observed in materials ranging from high-temperature superconductors to heavy fermion metals. In conventional metals, current is carried by quasiparticles; although it has been suggested that quasiparticles are absent in strange metals, direct experimental evidence is lacking. We measured shot noise to probe the granularity of the current-carrying excitations in nanowires of the heavy fermion strange metal YbRh2Si2. When compared with conventional metals, shot noise in these nanowires is strongly suppressed. This suppression cannot be attributed to either electron-phonon or electron-electron interactions in a Fermi liquid, which suggests that the current is not carried by well-defined quasiparticles in the strange-metal regime that we probed. Our work sets the stage for similar studies of other strange metals.

A criterion for strange metallicity in the Lorenz ratio

The Wiedemann-Franz (WF) law, stating that the Lorenz ratio L = κ/(Tσ) between the thermal and electrical conductivities in a metal approaches a universal constant L 0 = π 2 k B 2 / ( 3 e 2 ) at low temperatures, is often interpreted as a signature of fermionic Landau quasi-particles. In contrast, we show that various models of weakly disordered non-Fermi liquids also obey the WF law at T → 0. Instead, we propose using the leading low-temperature correction to the WF law, L(T) - L0 (proportional to the inelastic scattering rate), to distinguish different types of strange metals. As an example, we demonstrate that in a solvable model of a marginal Fermi-liquid, L(T) - L0 ∝ - T. Using the quantum Boltzmann equation (QBE) approach, we find analogous behavior in a class of marginal- and non-Fermi liquids with a weakly momentum-dependent inelastic scattering. In contrast, in a Fermi-liquid, L(T) - L0 is proportional to - T2. This holds even when the resistivity grows linearly with T, due to T - linear quasi-elastic scattering (as in the case of electron-phonon scattering at temperatures above the Debye frequency). Finally, by exploiting the QBE approach, we demonstrate that the transverse Lorenz ratio, Lxy = κxy/(Tσxy), exhibits the same behavior.

Symmetric Kondo Lattice States in Doped Strained Twisted Bilayer Graphene

We use the topological heavy fermion (THF) model and its Kondo lattice (KL) formulation to study the possibility of a symmetric Kondo (SK) state in twisted bilayer graphene. Via a large-N approximation, we find a SK state in the KL model at fillings ν=0,±1,±2 where a KL model can be constructed. In the SK state, all symmetries are preserved and the local moments are Kondo screened by the conduction electrons. At the mean-field level of the THF model at ν=0,±1,±2,±3 we also find a similar symmetric state that is adiabatically connected to the symmetric Kondo state. We study the stability of the symmetric state by comparing its energy with the ordered (symmetry-breaking) states found in [H. Hu et al., Phys. Rev. Lett. 131, 026502 (2023).PRLTAO0031-900710.1103/PhysRevLett.131.026502, Z.-D. Song and B. A. Bernevig, Phys. Rev. Lett. 129, 047601 (2022).PRLTAO0031-900710.1103/PhysRevLett.129.047601] and find the ordered states to have lower energy at ν=0,±1,±2. However, moving away from integer fillings by doping the light bands, our mean-field calculations find the energy difference between the ordered state and the symmetric state to be reduced, which suggests the loss of ordering and a tendency toward Kondo screening. In order to include many-body effects beyond the mean-field approximation, we also performed dynamical mean-field theory calculations on the THF model in the nonordered phase. The spin susceptibility follows a Curie behavior at ν=0,±1,±2 down to ∼2  K where the onset of screening of the local moment becomes visible. This hints to very low Kondo temperatures at these fillings, in agreement with the outcome of our mean-field calculations. At noninteger filling ν=±0.5,±0.8,±1.2 dynamical mean-field theory shows deviations from a 1/T susceptibility at much higher temperatures, suggesting a more effective screening of local moments with doping. Finally, we study the effect of a C_{3z}-rotational-symmetry-breaking strain via mean-field approaches and find that a symmetric phase (that only breaks C_{3z} symmetry) can be stabilized at sufficiently large strain at ν=0,±1,±2. Our results suggest that a symmetric Kondo phase is strongly suppressed at integer fillings, but could be stabilized either at noninteger fillings or by applying strain.

Recent Advances in Moiré Superlattice Systems by Angle-Resolved Photoemission Spectroscopy

The last decade has witnessed a flourish in 2D materials including graphene and transition metal dichalcogenides (TMDs) as atomic-scale Legos. Artificial moiré superlattices via stacking 2D materials with a twist angle and/or a lattice mismatch have recently become a fertile playground exhibiting a plethora of emergent properties beyond their building blocks. These rich quantum phenomena stem from their nontrivial electronic structures that are effectively tuned by the moiré periodicity. Modern angle-resolved photoemission spectroscopy (ARPES) can directly visualize electronic structures with decent momentum, energy, and spatial resolution, thus can provide enlightening insights into fundamental physics in moiré superlattice systems and guides for designing novel devices. In this review, first, a brief introduction is given on advanced ARPES techniques and basic ideas of band structures in a moiré superlattice system. Then ARPES research results of various moiré superlattice systems are highlighted, including graphene on substrates with small lattice mismatches, twisted graphene/TMD moiré systems, and high-order moiré superlattice systems. Finally, it discusses important questions that remain open, challenges in current experimental investigations, and presents an outlook on this field of research.

Coulomb Drag and Heat Transfer in Strange Metals

We address Coulomb drag and near-field heat transfer in a double-layer system of incoherent metals. Each layer is modeled by an array of tunnel-coupled SYK dots with random interlayer interactions. Depending on the strength of intradot interactions and interdot tunneling, this model captures the crossover from the Fermi liquid to a strange metal phase. The absence of quasiparticles in the strange metal leads to temperature-independent drag resistivity, which is in strong contrast with the quadratic temperature dependence in the Fermi liquid regime. We show that all the parameters can be independently measured in near-field heat transfer experiments, performed in Fermi liquid and strange metal regimes.

Superconductivity from a melted insulator in Josephson junction arrays

Arrays of Josephson junctions are governed by a competition between superconductivity and repulsive Coulomb interactions, and are expected to exhibit diverging low-temperature resistance when interactions exceed a critical level. Here we report a study of the transport and microwave response of Josephson arrays with interactions exceeding this level. Contrary to expectations, we observe that the array resistance drops dramatically as the temperature is decreased-reminiscent of superconducting behaviour-and then saturates at low temperature. Applying a magnetic field, we eventually observe a transition to a highly resistive regime. These observations can be understood within a theoretical picture that accounts for the effect of thermal fluctuations on the insulating phase. On the basis of the agreement between experiment and theory, we suggest that apparent superconductivity in our Josephson arrays arises from melting the zero-temperature insulator.

Kondo Lattice Model of Magic-Angle Twisted-Bilayer Graphene: Hund's Rule, Local-Moment Fluctuations, and Low-Energy Effective Theory

We apply a generalized Schrieffer-Wolff transformation to the extended Anderson-like topological heavy fermion (THF) model for the magic-angle (θ=1.05°) twisted bilayer graphene (MATBLG) [Phys. Rev. Lett. 129, 047601 (2022)PRLTAO0031-900710.1103/PhysRevLett.129.047601], to obtain its Kondo lattice limit. In this limit localized f electrons on a triangular lattice interact with topological conduction c electrons. By solving the exact limit of the THF model, we show that the integer fillings ν=0,±1,±2 are controlled by the heavy f electrons, while ν=±3 is at the border of a phase transition between two f-electron fillings. For ν=0,±1,±2, we then calculate the Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions between the f moments in the full model and analytically prove the SU(4) Hund's rule for the ground state which maintains that two f electrons fill the same valley-spin flavor. Our (ferromagnetic interactions in the) spin model dramatically differ from the usual Heisenberg antiferromagnetic interactions expected at strong coupling. We show the ground state in some limits can be found exactly by employing a positive semidefinite "bond-operators" method. We then compute the excitation spectrum of the f moments in the ordered ground state, prove the stability of the ground state favored by RKKY interactions, and discuss the properties of the Goldstone modes, the (reason for the accidental) degeneracy of (some of) the excitation modes, and the physics of their phase stiffness. We develop a low-energy effective theory for the f moments and obtain analytic expressions for the dispersion of the collective modes. We discuss the relevance of our results to the spin-entropy experiments in TBG.

Kondo Lattice Model in Magic-Angle Twisted Bilayer Graphene

We systematically study emergent Kondo lattice models from magic-angle twisted bilayer graphene using the topological heavy fermion representation. At the commensurate fillings, we demonstrate a series of symmetric strongly correlated metallic states driven by the hybridization between a triangular lattice of SU(8) local moments and delocalized fermions. In particular, a (fragile) topological Dirac Kondo semimetal can be realized, providing a potential explanation for the symmetry-preserving correlated state at ν=0. We further investigate the stability of the Dirac Kondo semimetal by constructing a quantum phase diagram showing the interplay between Kondo hybridization and magnetic correlation. The destruction of Kondo hybridization suggests that the magic-angle twisted bilayer graphene may be on the verge of a solid-state quantum simulator for novel magnetic orders on a triangular lattice. Experimental implications are also discussed.

The breakdown of both strange metal and superconducting states at a pressure-induced quantum critical point in iron-pnictide superconductors

Here we report the first observation of the concurrent breakdown of the strange metal (SM) normal state and superconductivity at a pressure-induced quantum critical point in Ca₁₀(Pt₄As₈)((Fe_0.97Pt_0.03)₂As₂)₅ superconductor. We find that, upon suppressing the superconducting state, the power exponent (α) changes from 1 to 2, and the slope of the temperature-linear resistivity per FeAs layer (A^□) gradually diminishes. At a critical pressure, A^□ and superconducting transition temperature (T_c) go to zero concurrently, where a quantum phase transition from a superconducting state with a SM normal state to a non-superconducting Fermi liquid state occurs. Scaling analysis reveals that the change of A^□ with T_c obeys the relation of T_c ~ (A^□)^0.5, similar to what is seen in other chemically doped unconventional superconductors. These results suggest that there is a simple but powerful organizational principle of connecting the SM normal state with the high-T_c superconductivity.

Topological Exact Flat Bands in Two-Dimensional Materials under Periodic Strain

We study flat bands and their topology in 2D materials with quadratic band crossing points under periodic strain. In contrast to Dirac points in graphene, where strain acts as a vector potential, strain for quadratic band crossing points serves as a director potential with angular momentum ℓ=2. We prove that when the strengths of the strain fields hit certain "magic" values, exact flat bands with C=±1 emerge at charge neutrality point in the chiral limit, in strong analogy to magic angle twisted-bilayer graphene. These flat bands have ideal quantum geometry for the realization of fractional Chern insulators, and they are always fragile topological. The number of flat bands can be doubled for certain point group, and the interacting Hamiltonian is exactly solvable at integer fillings. We further demonstrate the stability of these flat bands against deviations from the chiral limit, and discuss possible realization in 2D materials.

Calibrate the non-orthogonal error of AFM with two-dimensional self-traceable grating

The calibration of the non-orthogonal error in nanoscale measurements is of paramount importance for analytical measuring instruments. Particularly, the calibration of non-orthogonal errors in atomic force microscopy (AFM) is essential for the traceable measurements of novel materials and two-dimensional (2D) crystals. The 2D self-traceable grating with a theoretical non-orthogonal angle of less than 0.0027° and an expanded uncertainty of 0.003° (k = 2) are measured by the Metrological Large Range Scanning Probe Microscope (Met. LR-SPM). In this study, we characterized the local and overall non-orthogonal error in AFM scans and proposed a protocol to tune the optimal scanning parameters of AFM minimizing the non-orthogonal error. We presented the method for accurately calibrating a commercial AFM system for non-orthogonal by establishing a detailed uncertainty budget and errors analysis. Our results verified the important advantages of the 2D self-traceable grating in calibrating precision instruments.

Electrical switching of a bistable moiré superconductor

Electrical control of superconductivity is critical for nanoscale superconducting circuits including cryogenic memory elements^1-4, superconducting field-effect transistors (FETs)^5-7 and gate-tunable qubits^8-10. Superconducting FETs operate through continuous tuning of carrier density, but no bistable superconducting FET, which could serve as a new type of cryogenic memory element, has been reported. Recently, gate hysteresis and resultant bistability in Bernal-stacked bilayer graphene aligned to its insulating hexagonal boron nitride gate dielectrics were discovered^11,12. Here we report the observation of this same hysteresis in magic-angle twisted bilayer graphene (MATBG) with aligned boron nitride layers. This bistable behaviour coexists alongside the strongly correlated electron system of MATBG without disrupting its correlated insulator or superconducting states. This all-van der Waals platform enables configurable switching between different electronic states of this rich system. To illustrate this new approach, we demonstrate reproducible bistable switching between the superconducting, metallic and correlated insulator states of MATBG using gate voltage or electric displacement field. These experiments unlock the potential to broadly incorporate this new switchable moiré superconductor into highly tunable superconducting electronics.

Pair-Density-Wave and Chiral Superconductivity in Twisted Bilayer Transition Metal Dichalcogenides

We theoretically explore possible orders induced by weak repulsive interactions in twisted bilayer transition metal dichalcogenides (e.g., WSe_{2}) in the presence of an out-of-plane electric field. Using renormalization group analysis, we show that superconductivity survives even with the conventional van Hove singularities. We find that topological chiral superconducting states with Chern number N=1, 2, 4 (namely, p+ip, d+id, and g+ig) appear over a large parameter region with a moiré filling factor around n=1. At some special values of applied electric field and in the presence of a weak out-of-plane Zeeman field, spin-polarized pair-density-wave (PDW) superconductivity can emerge. This spin-polarized PDW state can be probed by experiments such as spin-polarized STM measuring spin-resolved pairing gap and quasiparticle interference. Moreover, the spin-polarized PDW could lead to a spin-polarized superconducting diode effect.

Dissipative Quantum Criticality as a Source of Strange Metal Behavior

The strange metal behavior, usually characterized by a linear-in-temperature (T) resistivity, is a still unsolved mystery in solid-state physics. It is often associated with the proximity to a quantum critical point (a second order transition at temperature T=0, leading to a broken symmetry phase) focusing on the related divergent order parameter correlation length. Here, we propose a paradigmatic shift, focusing on a divergent characteristic time scale due to a divergent dissipation acting on the fluctuating critical modes while their correlation length stays finite. To achieve a divergent dissipation, we propose a mechanism based on the coupling between a local order parameter fluctuation and electron density diffusive modes that accounts both for the linear-in-T resistivity and for the logarithmic specific heat versus temperature ratio CV/T∼log(1/T), down to low temperatures.

The scaled-invariant Planckian metal and quantum criticality in Ce1-xNdxCoIn5

The mysterious Planckian metal state, showing perfect T-linear resistivity associated with universal scattering rate, 1/τ = αk_BT/ℏ with α ~ 1, has been observed in the normal state of various strongly correlated superconductors close to a quantum critical point. However, its microscopic origin and link to quantum criticality remains an outstanding open problem. Here, we observe quantum-critical T/B-scaling of the Planckian metal state in resistivity and heat capacity of heavy-electron superconductor Ce_1-xNd_xCoIn₅ in magnetic fields near the edge of antiferromagnetism at the critical doping x_c ~ 0.03. We present clear experimental evidences of Kondo hybridization being quantum critical at x_c. We provide a generic microscopic mechanism to qualitatively account for this quantum critical Planckian state within the quasi-two dimensional Kondo-Heisenberg lattice model near Kondo breakdown transition. We find α is a non-universal constant and depends inversely on the square of Kondo hybridization strength.

Coupled ferroelectricity and superconductivity in bilayer Td-MoTe2

Achieving electrostatic control of quantum phases is at the frontier of condensed matter research. Recent investigations have revealed superconductivity tunable by electrostatic doping in twisted graphene heterostructures and in two-dimensional semimetals such as WTe₂ (refs. ^1-5). Some of these systems have a polar crystal structure that gives rise to ferroelectricity, in which the interlayer polarization exhibits bistability driven by external electric fields^6-8. Here we show that bilayer T_d-MoTe₂ simultaneously exhibits ferroelectric switching and superconductivity. Notably, a field-driven, first-order superconductor-to-normal transition is observed at its ferroelectric transition. Bilayer T_d-MoTe₂ also has a maximum in its superconducting transition temperature (T_c) as a function of carrier density and temperature, allowing independent control of the superconducting state as a function of both doping and polarization. We find that the maximum T_c is concomitant with compensated electron and hole carrier densities and vanishes when one of the Fermi pockets disappears with doping. We argue that this unusual polarization-sensitive two-dimensional superconductor is driven by an interband pairing interaction associated with nearly nested electron and hole Fermi pockets.

Quantum criticality of excitonic Mott metal-insulator transitions in black phosphorus

Quantum phase transition refers to the abrupt change of ground states of many-body systems driven by quantum fluctuations. It hosts various intriguing exotic states around its quantum critical points approaching zero temperature. Here we report the spectroscopic and transport evidences of quantum critical phenomena of an exciton Mott metal-insulator-transition in black phosphorus. Continuously tuning the interplay of electron-hole pairs by photo-excitation and using Fourier-transform photo-current spectroscopy as a probe, we measure a comprehensive phase diagram of electron-hole states in temperature and electron-hole pair density parameter space. We characterize an evolution from optical insulator with sharp excitonic transition to metallic electron-hole plasma phases featured by broad absorption and population inversion. We also observe strange metal behavior that resistivity is linear in temperature near the Mott transition boundaries. Our results exemplify an ideal platform to investigating strongly-correlated physics in semiconductors, such as crossover between superconductivity and superfluity of exciton condensation.

Atomic-Scale Confinement and Negative Refraction of Plasmons by Twisted Bilayer Graphene

Moiré superlattices provide in-plane quantum restriction for light-matter interactions in twisted bilayer graphene (tBLG), leading to the exotic photon-Moiré physics and potential applications for light manipulation. Recently, our experiment identified a highly confined slow surface plasmons polaritons (SPPs) mode in tBLG. Here, we demonstrate that the propagation of the slow SPPs mode in tBLG is spatially tailored and steered at deep subwavelengths. Analysis by the perturbation theory indicates that the coupling between the slow SPPs mode and the Moiré system is greatly strengthened, which regulates the wavefront at the atomic scale and makes tBLG serve as a universal optical metamaterial. Consequently, the negative refraction is achieved at the interface of monolayer graphene and tBLG, by which a metalens with a controllable focal length and an extremely high resolution up to 1/150 of wavelength is devised. Our work paves the way for constructing optical metamaterial at the atomic scale and develops future photon-Moiré interaction systems.

Pseudospin Paramagnons and the Superconducting Dome in Magic Angle Twisted Bilayer Graphene

We present a theory of superconductivity in twisted bilayer graphene in which attraction is generated between electrons on the same honeycomb sublattice when the system is close to a sublattice polarization instability. The resulting Cooper pairs are spin-polarized valley singlets. Because the sublattice polarizability is mainly contributed by interband fluctuations, superconductivity occurs over a wide range of filling fraction. It is suppressed by (i) applying a sublattice polarizing field (generated by an aligned BN substrate) or (ii) changing moiré band filling to favor valley polarization. The enhanced intrasublattice attraction close to sublattice polarization instability is analogous to enhanced like-spin attraction in liquid ^{3}He near the melting curve and the enhanced valley-singlet repulsion close to valley-polarization instabilities is analogous to enhanced spin-singlet repulsion in metals that are close to a ferromagnetic instability. We comment on the relationship between our pseudospin paramagnon model and the rich phenomenology of superconductivity in twisted bilayer and multilayer graphene.

Moiré modulation of charge density waves

Here we investigate how charge density waves (CDWs), inherent to a monolayer, are effected by creating twisted van der Waals structures. Homobilayers of metallic transition metal dichalcogenides (TMDs), at small twist angles where there is significant atomic reconstruction, are utilised as an example to investigate the interplay between the moiré domain structure and CDWs of different periods. For3×3CDWs, there is no geometric constraint to prevent the CDWs from propagating throughout the moiré structure. Whereas for2×2CDWs, to ensure the CDWs in each layer have the most favourable interactions in the domains, the CDW phase must be destroyed in the connecting domain walls. For3×3CDWs with twist angles close to 180^∘, moiré-scale triangular structures can form; while close to 0^∘, moiré-scale dimer domains occur. The star-of-David CDW (13×13) is found to host CDWs in the domains only, since there is one low energy stacking configuration, similar to the2×2CDWs. These predictions are offered for experimental verification in twisted bilayer metallic TMDs which host CDWs, and we hope this will stimulate further research on the interplay between the moiré superlattice and CDW phases intrinsic to the comprising 2D materials.

Criterion for photonic topological transition in two-dimensional heterostructures

The anisotropic van der Waals material α-MoO₃ has recently attracted considerable attention because of the ability to support ellipse and hyperbolic phonon polaritons with extreme field confinement and long lifetimes, which can be used in topological transition and transformation polaritonics. However, the dispersion theory of some phonon polaritons in complex heterojunctions often requires tedious computation, which makes it difficult to simply judge and analyze the physical process of the photonic topological transition. Here we obtain the equivalent permittivity distribution of two-dimensional (2D) heterostructures by the effective medium theory and analyze the rotation-induced topological transitions and stack-dependent topological transitions of phonon polaritons. Unlike the previous discussion, we can predict the topological transition points by a parameter ɛ_x/y(i.e., the permittivity ratio along the in-plane crystal axis of the equivalent medium) and design precisely the phonon polaritons in the stacked materials by controlling the equivalent permittivity after simple calculation. The feasibility of the effective medium theory is verified based on the 2D approximation model and the non-2D approximation model under the limit of an ultrathin slab. Meanwhile, we compare the field distributions and dispersions of the 2D heterostructures and the corresponding equivalent structure. The simulation suggests that the elliptic/hyperbolic responses of the stacked materials depend on the sign of ɛ_x/y. The new, to the best of our knowledge, method not only provides an easier and clearer criterion for the study of photonic topological transition in anisotropic polaritons, but also shows great potential in designing some multilayer 2D heterostructures.

Moiré Phonons in Magic-Angle Twisted Bilayer Graphene

Magic-angle twisted bilayer graphene (TBG) has attracted significant interest recently due to the discoveries of diverse correlated and topological states. In this work, we study the phonon properties in magic-angle TBG based on many-body classical potential and interatomic forces generated by a deep neural network trained with data from ab initio calculations. We have discovered a number of soft modes which can exhibit dipolar, quadrupolar, and octupolar vibrational patterns in real space, as well as some time-reversal breaking chiral phonon modes. We have further studied the phonon effects on the electronic structures by freezing certain soft phonon modes. We find that if a soft quadrupolar phonon mode is assumed to be frozen, the system would exhibit a charge order which is perfectly consistent with recent experiments. Moreover, once some low-frequency C_2z-breaking modes get frozen, the Dirac points at the charge neutrality point would be gapped out, which provides an alternative perspective to the origin of correlated insulator state at charge neutrality point.

Observation of Coexisting Dirac Bands and Moiré Flat Bands in Magic-Angle Twisted Trilayer Graphene

Moiré superlattices that consist of two or more layers of 2D materials stacked together with a small twist angle have emerged as a tunable platform to realize various correlated and topological phases, such as Mott insulators, unconventional superconductivity, and quantum anomalous Hall effect. Recently, magic-angle twisted trilayer graphene (MATTG) has shown both robust superconductivity similar to magic-angle twisted bilayer graphene and other unique properties, including the Pauli-limit violating and re-entrant superconductivity. These rich properties are deeply rooted in its electronic structure under the influence of distinct moiré potential and mirror symmetry. Here, combining nanometer-scale spatially resolved angle-resolved photoemission spectroscopy and scanning tunneling microscopy/spectroscopy, the as-yet unexplored band structure of MATTG near charge neutrality is systematically measured. These measurements reveal the coexistence of the distinct dispersive Dirac band with the emergent moiré flat band, showing nice agreement with the theoretical calculations. These results serve as a stepstone for further understanding of the unconventional superconductivity in MATTG.

Spectroscopy of Twisted Bilayer Graphene Correlated Insulators

We analytically compute the scanning tunneling microscopy (STM) signatures of integer-filled correlated ground states of the magic angle twisted bilayer graphene (TBG) narrow bands. After experimentally validating the strong-coupling approach at ±4  electrons/moiré unit cell, we consider the spatial features of the STM signal for 14 different many-body correlated states and assess the possibility of Kekulé distortion (KD) emerging at the graphene lattice scale. Remarkably, we find that coupling the two opposite graphene valleys in the intervalley-coherent (IVC) TBG insulators does not always result in KD. As an example, we show that the Kramers IVC state and its nonchiral U(4) rotations do not exhibit any KD, while the time-reversal-symmetric IVC state does. Our results, obtained over a large range of energies and model parameters, show that the STM signal and Chern number of a state can be used to uniquely determine the nature of the TBG ground state.

Tunable quantum criticalities in an isospin extended Hubbard model simulator

Studying strong electron correlations has been an essential driving force for pushing the frontiers of condensed matter physics. In particular, in the vicinity of correlation-driven quantum phase transitions (QPTs), quantum critical fluctuations of multiple degrees of freedom facilitate exotic many-body states and quantum critical behaviours beyond Landau's framework¹. Recently, moiré heterostructures of van der Waals materials have been demonstrated as highly tunable quantum platforms for exploring fascinating, strongly correlated quantum physics^2-22. Here we report the observation of tunable quantum criticalities in an experimental simulator of the extended Hubbard model with spin-valley isospins arising in chiral-stacked twisted double bilayer graphene (cTDBG). Scaling analysis shows a quantum two-stage criticality manifesting two distinct quantum critical points as the generalized Wigner crystal transits to a Fermi liquid by varying the displacement field, suggesting the emergence of a critical intermediate phase. The quantum two-stage criticality evolves into a quantum pseudo criticality as a high parallel magnetic field is applied. In such a pseudo criticality, we find that the quantum critical scaling is only valid above a critical temperature, indicating a weak first-order QPT therein. Our results demonstrate a highly tunable solid-state simulator with intricate interplay of multiple degrees of freedom for exploring exotic quantum critical states and behaviours.

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.

Studies of twisted bilayer transition metal dichalcogenides have so far focused only on those containing group-VI metals. Here, the authors predict that twisted bilayers of ZrS₂, with the group-IV metal Zr, form an emergent moiré Kagome lattice with a uniquely strong spin-orbit coupling, leading to quantum-anomalous-Hall and fractional-Chern-insulating states.

Robust superconductivity in magic-angle multilayer graphene family

The discovery of correlated states and superconductivity in magic-angle twisted bilayer graphene (MATBG) established a new platform to explore interaction-driven and topological phenomena. However, despite multitudes of correlated phases observed in moiré systems, robust superconductivity appears the least common, found only in MATBG and more recently in magic-angle twisted trilayer graphene. Here we report the experimental realization of superconducting magic-angle twisted four-layer and five-layer graphene, hence establishing alternating twist magic-angle multilayer graphene as a robust family of moiré superconductors. This finding suggests that the flat bands shared by the members play a central role in the superconductivity. Our measurements in parallel magnetic fields, in particular the investigation of Pauli limit violation and spontaneous rotational symmetry breaking, reveal a clear distinction between the N = 2 and N > 2-layer structures, consistent with the difference between their orbital responses to magnetic fields. Our results expand the emergent family of moiré superconductors, providing new insight with potential implications for design of new superconducting materials platforms.

Magic-Angle Twisted Bilayer Graphene as a Topological Heavy Fermion Problem

Magic-angle (θ=1.05°) twisted bilayer graphene (MATBG) has shown two seemingly contradictory characters: the localization and quantum-dot-like behavior in STM experiments, and delocalization in transport experiments. We construct a model, which naturally captures the two aspects, from the Bistritzer-MacDonald (BM) model in a first principle spirit. A set of local flat-band orbitals (f) centered at the AA-stacking regions are responsible to the localization. A set of extended topological semimetallic conduction bands (c), which are at small energetic separation from the local orbitals, are responsible to the delocalization and transport. The topological flat bands of the BM model appear as a result of the hybridization of f and c electrons. This model then provides a new perspective for the strong correlation physics, which is now described as strongly correlated f electrons coupled to nearly free c electrons-we hence name our model as the topological heavy fermion model. Using this model, we obtain the U(4) and U(4)×U(4) symmetries of Refs. [1-5] as well as the correlated insulator phases and their energies. Simple rules for the ground states and their Chern numbers are derived. Moreover, features such as the large dispersion of the charge ±1 excitations [2,6,7], and the minima of the charge gap at the Γ_{M} point can now, for the first time, be understood both qualitatively and quantitatively in a simple physical picture. Our mapping opens the prospect of using heavy-fermion physics machinery to the superconducting physics of MATBG.

Stranger than metals

In traditional metals, the temperature ( T ) dependence of electrical resistivity vanishes at low or high T , albeit for different reasons. Here, we review a class of materials, known as “strange” metals, that can violate both of these principles. In strange metals, the change in slope of the resistivity as the mean free path drops below the lattice constant, or as T → 0, can be imperceptible, suggesting continuity between the charge carriers at low and high T . We focus on transport and spectroscopic data on candidate strange metals in an effort to isolate and identify a unifying physical principle. Special attention is paid to quantum criticality, Planckian dissipation, Mottness, and whether a new gauge principle is needed to account for the nonlocal transport seen in these materials.

Peculiar Physics of Heavy-Fermion Metals: Theory versus Experiment

This review considers the topological fermion condensation quantum phase transition (FCQPT) that leads to flat bands and allows the elucidation of the special behavior of heavy-fermion (HF) metals that is not exhibited by common metals described within the framework of the Landau Fermi liquid (LFL) theory. We bring together theoretical consideration within the framework of the fermion condensation theory based on the FCQPT with experimental data collected on HF metals. We show that very different HF metals demonstrate universal behavior induced by the FCQPT and demonstrate that Fermi systems near the FCQPT are controlled by the Fermi quasiparticles with the effective mass M* strongly depending on temperature T, magnetic field B, pressure P, etc. Within the framework of our analysis, the experimental data regarding the thermodynamic, transport and relaxation properties of HF metal are naturally described. Based on the theory, we explain a number of experimental data and show that the considered HF metals exhibit peculiar properties such as: (1) the universal T/B scaling behavior; (2) the linear dependence of the resistivity on T, ρ(T)∝A1T (with A1 is a temperature-independent coefficient), and the negative magnetoresistance; (3) asymmetrical dependence of the tunneling differential conductivity (resistivity) on the bias voltage; (4) in the case of a flat band, the superconducting critical temperature Tc∝g with g being the coupling constant, while the M* becomes finite; (5) we show that the so called Planckian limit exhibited by HF metals with ρ(T)∝T is defined by the presence of flat bands.

Observation of Reentrant Correlated Insulators and Interaction-Driven Fermi-Surface Reconstructions at One Magnetic Flux Quantum per Moiré Unit Cell in Magic-Angle Twisted Bilayer Graphene

The discovery of flat bands with nontrivial band topology in magic-angle twisted bilayer graphene (MATBG) has provided a unique platform to study strongly correlated phenomena including superconductivity, correlated insulators, Chern insulators, and magnetism. A fundamental feature of the MATBG, so far unexplored, is its high magnetic field Hofstadter spectrum. Here, we report on a detailed magnetotransport study of a MATBG device in external magnetic fields of up to B=31  T, corresponding to one magnetic flux quantum per moiré unit cell Φ_{0}. At Φ_{0}, we observe reentrant correlated insulators at a flat band filling factors of ν=+2 and of ν=+3, and interaction-driven Fermi-surface reconstructions at other fillings, which are identified by new sets of Landau levels originating from these. These experimental observations are supplemented by theoretical work that predicts a new set of eight well-isolated flat bands at Φ_{0}, of comparable band width, but with different topology than in zero field. Overall, our magnetotransport data reveal a qualitatively new Hofstadter spectrum in MATBG, which arises due to the strong electronic correlations in the reentrant flat bands.

Quantum-Critical Resistivity of Strange Metals in a Magnetic Field

Resistivity in the quantum-critical fluctuation region of several metallic compounds such as the cuprates, the heavy fermions, Fe chalogenides and pnictides, Moiré bilayer graphene, and WSe_{2} is linear in temperature T as well as in the magnetic field H_{z} perpendicular to the planes. Scattering of fermions by the fluctuations of a time-reversal odd polar vector field Ω has been shown to give a linear in T resistivity and other marginal Fermi-liquid properties. An extension of this theory to an applied magnetic field is presented. A magnetic field is shown to generate a density of vortices in the field Ω proportional to H_{z}. The elastic scattering of fermions from the vortices gives a resistivity linear in H_{z} with the coefficient varying as the marginal Fermi-liquid susceptibility ln(ω_{c}/T). Quantitative comparison with experiments is presented for cuprates and Moiré bilayer graphene.

Correlated States in Strained Twisted Bilayer Graphenes Away from the Magic Angle

Graphene moiré superlattice formed by rotating two graphene sheets can host strongly correlated and topological states when flat bands form at so-called magic angles. Here, we report that, for a twisting angle far away from the magic angle, the heterostrain induced during stacking heterostructures can also create flat bands. Combining a direct visualization of strain effect in twisted bilayer graphene moiré superlattices and transport measurements, features of correlated states appear at "non-magic" angles in twisted bilayer graphene under the heterostrain. Observing correlated states in these "non-standard" conditions can enrich the understanding of the possible origins of the correlated states and widen the freedom in tuning the moiré heterostructures and the scope of exploring the correlated physics in moiré superlattices.

Twist-angle-controlled neutral exciton annihilation in WS2 homostructures

Exciton-exciton annihilation (EEA), as typical nonradiative recombination, plays an unpopular role in semiconductors. The nonradiative process significantly reduces the quantum yield of photoluminescence, which substantially inhibits the maximum efficiency of optoelectronic devices. Recently, laser irradiation, introducing defects and applying strain have become effective means to restrain EEA in two-dimensional (2D) transition metal dichalcogenides (TMDCs). However, these methods destroy the atomic structure of 2D materials and limit their practical applications. Fortunately, twisted structures are expected to validly suppress EEA through excellent interface quality. Here, we develop a non-destructive way to control EEA in WS₂ homostructures by changing the interlayer twist angle, and systematically study the effect of interlayer twist angle on EEA, using fluorescence lifetime imaging measurement (FLIM) technology. Due to the large moiré potential at a small interlayer twist angle, the diffusion of excitons is hindered, and the EEA rate decreases from 1.01 × 10^-1 cm² s^-1 in a 9° twisted WS₂ homostructure to 4.26 × 10^-2 cm² s^-1 in a 1° twisted WS₂ homostructure. The results reveal the important role of the interlayer twist angle and EEA interaction in high photoluminescence quantum yield optoelectronic devices based on TMDC homostructures.

Breakdown of semiclassical description of thermoelectricity in near-magic angle twisted bilayer graphene

The planar assembly of twisted bilayer graphene (tBLG) hosts multitude of interaction-driven phases when the relative rotation is close to the magic angle (θm = 1.1∘). This includes correlation-induced ground states that reveal spontaneous symmetry breaking at low temperature, as well as possibility of non-Fermi liquid (NFL) excitations. However, experimentally, manifestation of NFL effects in transport properties of twisted bilayer graphene remains ambiguous. Here we report simultaneous measurements of electrical resistivity (ρ) and thermoelectric power (S) in tBLG for several twist angles between θ ~ 1.0 − 1.7∘. We observe an emergent violation of the semiclassical Mott relation in the form of excess S close to half-filling for θ ~ 1.6∘ that vanishes for θ ≳ 2∘. The excess S (≈2 μV/K at low temperatures T ~ 10 K at θ ≈ 1.6∘) persists upto ≈40 K, and is accompanied by metallic T-linear ρ with transport scattering rate (τ−1) of near-Planckian magnitude τ−1 ~ kBT/ℏ. Closer to θm, the excess S was also observed for fractional band filling (ν ≈ 0.5). The combination of non-trivial electrical transport and violation of Mott relation provides compelling evidence of NFL physics intrinsic to tBLG.