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Two-dimensional flat-band systems have recently attracted considerable interest due to the rich physics unveiled by emergent phenomena and correlated electronic states at van Hove singularities. However, the difficulties in electrically detecting the flat band position in field-effect structures are slowing down the investigation of their properties. In this work, we employ Indium Selenide (InSe) as a flat-band system due to a van Hove singularity at the valence band edge in a few-layer form of the material without the requirement of a twist angle. We investigate tunneling photocurrents in gated few-layer InSe structures and relate them to ambipolar transport and photoluminescence measurements. We observe an appearance of a sharp change in tunneling mechanisms due to the presence of the van Hove singularity at the flat band. We further corroborate our findings by studying tunneling currents as a reliable probe for the flat-band position up to room temperature. Our results create an alternative approach to studying flat-band systems in heterostructures of 2D materials.

Recently, there has been growing interest in researching the use of hexagonal boron nitride (hBN) for quantum technologies. Here we investigate nitrogen isotope effects on boron vacancy (V$_\text{B}$) defects, one of the candidates for quantum sensors, in $^{15}$N isotopically enriched hBN synthesized using metathesis reaction. The Raman shifts are scaled with the reduced mass, consistent with previous work on boron isotope enrichment. We obtain nitrogen isotopic composition dependent optically detected magnetic resonance spectra of V$_\text{B}$ defects and determine the hyperfine interaction parameter of $^{15}$N spin to be -64 MHz. Our investigation provides a design policy for hBNs for quantum technologies.

Material systems that exhibit tunable spin-selective conductivity are key components of spintronic technologies. Here we demonstrate a novel type of spin-selective transport, based on the unusual Landau level (LL) sequence observed in bilayer WSe$_2$ under large applied magnetic fields. We find that the conductivity depends strongly on the relative iso-spin ordering between conducting electrons in a partially filled LL and the localized electrons of lower energy filled LLs, with conductivity observed to be almost completely suppressed when the spin-ratio and field-tuned Coulomb energy exceed a critical threshold. Switching between "on/off" states is achievable through either modulation of the external magnetic or electric fields, with many-body interaction driving a collective switching mechanism. In contrast to magnetoresistive heterostructures, this system achieves electrically tunable spin filtering within a single material, driven by interaction between free and localized spins residing in energy-separated spin/valley polarized bands. Similar spin-selective conductivity may be realizable in multi-flat band systems at zero magnetic field.

We report on the observation of a nonlinear intensity dependence of the terahertz radiation induced ratchet effects in bilayer graphene with asymmetric dual grating gate lateral lattices. These nonlinear ratchet currents are studied in structures of two designs with dual grating gate fabricated on top of encapsulated bilayer graphene and beneath it. The strength and sign of the photocurrent can be controllably varied by changing the bias voltages applied to individual dual grating subgates and the back gate. The current consists of contributions insensitive to the radiation's polarization state, defined by the orientation of the radiation electric field vector with respect to the dual grating gate metal stripes, and the circular ratchet sensitive to the radiation helicity. We show that intense terahertz radiation results in a nonlinear intensity dependence caused by electron gas heating. At room temperature the ratchet current saturates at high intensities of the order of hundreds to several hundreds of kWcm$^{-2}$. At $T = 4 {\rm K}$, the nonlinearity manifests itself at intensities that are one or two orders of magnitude lower, moreover, the photoresponse exhibits a complex dependence on the intensity, including a saturation and even a change of sign with increasing intensity. This complexity is attributed to the interplay of the Seebeck ratchet and the dynamic carrier density redistribution, which feature different intensity dependencies and a nonlinear behavior of the sample's conductivity induced by electron gas heating. Our study demonstrates that graphene-based asymmetric dual grating gate devices can be used as terahertz detectors at room temperature over a wide dynamic range, spanning many orders of magnitude of terahertz radiation power. Therefore, their integration together with current-driven read-out electronics is attractive for the operation with high-power pulsed sources., 11 pages, 13 figures

The most widely used method for obtaining high-quality two-dimensional materials is through mechanical exfoliation of bulk crystals. Manual identification of suitable flakes from the resulting random distribution of crystal thicknesses and sizes on a substrate is a time-consuming, tedious task. Here, we present a platform for fully automated scanning, detection, and classification of two-dimensional materials, the source code of which we make openly available. Our platform is designed to be accurate, reliable, fast, and versatile in integrating new materials, making it suitable for everyday laboratory work. The implementation allows fully automated scanning and analysis of wafers with an average inference time of 100 ms for images of 2.3 Mpixels. The developed detection algorithm is based on a combination of the flakes' optical contrast toward the substrate and their geometric shape. We demonstrate that it is able to detect the majority of exfoliated flakes of various materials, with an average recall (AR50) between 67% and 89%. We also show that the algorithm can be trained with as few as five flakes of a given material, which we demonstrate for the examples of few-layer graphene, WSe$_2$, MoSe$_2$, CrI$_3$, 1T-TaS$_2$ and hexagonal BN. Our platform has been tested over a two-year period, during which more than $10^6$ images of multiple different materials were acquired by over 30 individual researchers.

Two-dimensional (2D) semiconductors have attracted considerable interest for their unique physical properties. Here, we report the intrinsic cryogenic electronic transport properties in few-layer MoSe$_2$ field-effect transistors (FETs) that are simultaneously van der Waals contacted with gold electrodes and are fully encapsulated in ultraclean hexagonal boron nitride dielectrics. The FETs exhibit electronically favorable channel/dielectric interfaces with low densities of interfacial traps ($10^{10}\,$cm$^{-2}$), which lead to outstanding device characteristics at room temperature, including a near-Boltzmann-limit subthreshold swings ($\lt65\,$mV/dec), a high carrier mobility ($68\,$cm$^{2}\cdot$V$^{-1}\cdot$s$^{-1}$), and a negligible scanning hysteresis ($\lt15\,$mV). The dependence of various contact-related quantities on temperature and carrier density are also systematically characterized to understand the van der Waals contacts between gold and MoSe$_2$. The results provide insightful information on the device physics in van der Waals contacted and encapsulated 2D FETs., 14 pages, 4 figures

Twisted graphene multilayers are highly tunable flatband systems for developing new phases of matter. Thus far, while orbital ferromagnetism has been observed in valley polarized phases, the long-range orders of other correlated phases as well as the quantum phase transitions between different orders mostly remain unknown. Here, we report an observation of Coulomb interaction driven first-order quantum phase transitions and ferromagnetism in twisted double bilayer graphene (TDBG). At zero magnetic field, the transitions are revealed in a series of step-like abrupt resistance jumps with prominent hysteresis loop when either the displacement field (D) or the carrier density (n) is tuned across symmetry-breaking boundary near half filling, indicating a formation of ordered domains. It is worth noting that the good turnability and switching of these states gives a rise to a memory performance with a large on/off ratio. Moreover, when both spin and valley play the roles at finite magnetic field, we observe abundant first-order quantum phase transitions among normal metallic states from charge neutral point, orbital ferromagnetic states from quarter filling, and spin-polarized states from half filling. We interpret these first-order phase transitions in the picture of phase separations and spin domain percolations driven by multi-field tunable Coulomb interactions, in agreement with Lifshitz transition from Hartree-Fock calculations. The observed multi-filed tunable domain structure and its hysteresis resembles the characteristics of multiferroics, revealing intriguing magnetoelectric properties. Our result enriches the correlated phase diagram in TDBG for discovering novel exotic phases and quantum phase transitions, and it would benefit other twisted moir\'e systems as well.

Being able to control the neutral excitonic flux is a mandatory step for the development of future room-temperature two-dimensional excitonic devices. Semiconducting Monolayer Transition Metal Dichalcogenides (TMD-ML) with extremely robust and mobile excitons are highly attractive in this regard. However, generating an efficient and controlled exciton transport over long distances is a very challenging task. Here we demonstrate that an atomically sharp TMD-ML lateral heterostructure (MoSe$_{2}$-WSe$_{2}$) transforms the isotropic exciton diffusion into a unidirectional excitonic flow through the junction. Using tip-enhanced photoluminescence spectroscopy (TEPL) and a modified exciton transfer model, we show a discontinuity of the exciton density distribution on each side of the interface. We introduce the concept of exciton Kapitza resistance, by analogy with the interfacial thermal resistance referred to as Kapitza resistance. By comparing different heterostructures with or without top hexagonal boron nitride (hBN) layer, we deduce that the transport properties can be controlled, over distances far greater than the junction width, by the exciton density through near-field engineering and/or laser power density. This work provides a new approach for controlling the neutral exciton flow, which is key toward the conception of excitonic devices.

Van der Waals heterostructures are an excellent platform for studying intriguing interface phenomena, such as moir\'e and proximity effects. Surface science techniques like scanning tunneling microscopy (STM) have proven a powerful tool to study such heterostructures but have so far been hampered because of their high sensitivity to surface contamination. Here, we report a dry polymer-based assembly technique to fabricate van der Waals heterostructures with atomically clean surfaces. The key features of our suspended dry pick-up and flip-over technique are 1) the heterostructure surface never comes into contact with polymers, 2) it is entirely solvent-free, 3) it is entirely performed in a glovebox, and 4) it only requires temperatures below 130$^{\circ}$. By performing ambient atomic force microscopy and atomically-resolved scanning tunneling microscopy on example heterostructures, we demonstrate that we can fabricate air-sensitive heterostructures with ultra-clean interfaces and surfaces. Due to the lack of polymer melting, the technique is further compatible with heterostructure assembly under ultra-high vacuum conditions, which promises ultimate heterostructure quality.

We report on integer and fractional quantum Hall states in a stack of two twisted Bernal bilayer graphene sheets. By exploiting the momentum mismatch in reciprocal space, we suppress single particle tunneling between both bilayers. Since the bilayers are spatially separated by only 0.34 nm, the stack benefits from strong interlayer Coulomb interactions. These interactions can cause the formation of a Bose-Einstein condensate. Indeed, such a condensate is observed for half filling in each bilayer sheet. However, only when the partially filled levels have orbital index 1. It is absent for partially filled levels with orbital index 0. This discrepancy is tentatively attributed to the role of skyrmion/anti-skyrmion pair excitations and the dependence of the energy of these excitations on the orbital index. The application of asymmetric top and bottom gate voltages enables to influence the orbital nature of the electronic states of the graphene bilayers at the chemical potential and to navigate in an orbital mixed space. The latter hosts an even denominator fractional quantum Hall state at total filling -3/2. Our observations suggest a unique edge reconstruction involving both electrons and chiral p-wave composite fermions.

In recent years, correlated insulating states, unconventional superconductivity, and topologically non-trivial phases have all been observed in several moiré heterostructures. However, understanding of the physical mechanisms behind these phenomena is hampered by the lack of local electronic structure data. Here, we use scanning tunnelling microscopy and spectroscopy to demonstrate how the interplay between correlation, topology, and local atomic structure determines the behaviour of electron-doped twisted monolayer-bilayer graphene. Through gate- and magnetic field-dependent measurements, we observe local spectroscopic signatures indicating a quantum anomalous Hall insulating state with a total Chern number of $\pm 2$ at a doping level of three electrons per moiré unit cell. We show that the sign of the Chern number and associated magnetism can be electrostatically switched only over a limited range of twist angle and sample hetero-strain values. This results from a competition between the orbital magnetization of filled bulk bands and chiral edge states, which is sensitive to strain-induced distortions in the moiré superlattice., Article 14 pages, 4 figures & Supplementary Information 13 pages, 9 figures

Reliable, clean transfer and interfacing of 2D material layers is technologically as important as their growth. Bringing both together remains a challenge due to the vast, interconnected parameter space. We introduce a fast-screening descriptor approach to demonstrate holistic data-driven optimization across the entirety of process steps for the graphene-Cu model system. We map the crystallographic dependencies of graphene chemical vapor deposition, interfacial Cu oxidation to decouple graphene, and its dry delamination across inverse pole figures. Their overlay enables us to identify hitherto unexplored (168) higher index Cu orientations as overall optimal. We show the effective preparation of such Cu orientations via epitaxial close-space sublimation and achieve mechanical transfer with very high yield (>95%) and quality of graphene domains, with room-temperature electron mobilities in the range of 40000 cm$^2$/(Vs). Our approach is readily adaptable to other descriptors and 2D materials systems, and we discuss the opportunities of such holistic optimization., 56 pages, 19 figures

Bilayer graphene encapsulated in tungsten diselenide can host a weak topological phase with pairs of helical edge states. The electrical tunability of this phase makes it an ideal platform to investigate unique topological effects at zero magnetic field, such as topological superconductivity. Here we couple the helical edges of such a heterostructure to a superconductor. The inversion of the bulk gap accompanied by helical states near zero displacement field leads to the suppression of the critical current in a Josephson geometry. Using superconducting quantum interferometry we observe an even-odd effect in the Fraunhofer interference pattern within the inverted gap phase. We show theoretically that this effect is a direct consequence of the emergence of helical modes that connect the two edges of the sample. The absence of such an effect at high displacement field, as well as in bare bilayer graphene junctions, confirms this interpretation and demonstrates the topological nature of the inverted gap. Our results demonstrate the coupling of superconductivity to zero-field topological states in graphene., 13 pages, 14 figures

Rydberg excitons, the solid-state counterparts of Rydberg atoms, have sparked considerable interest in harnessing their quantum application potentials, whereas a major challenge is realizing their spatial confinement and manipulation. Lately, the rise of two-dimensional moiré superlattices with highly tunable periodic potentials provides a possible pathway. Here, we experimentally demonstrate this capability through the observation of Rydberg moiré excitons (XRM), which are moiré trapped Rydberg excitons in monolayer semiconductor WSe2 adjacent to twisted bilayer graphene. In the strong coupling regime, the XRM manifest as multiple energy splittings, pronounced redshift, and narrowed linewidth in the reflectance spectra, highlighting their charge-transfer character where electron-hole separation is enforced by the strongly asymmetric interlayer Coulomb interactions. Our findings pave the way for pursuing novel physics and quantum technology exploitation based on the excitonic Rydberg states., 24 pages, including 4 figures and 6 supplementary figures

We report on a detailed investigation of the shell-filling sequence in electrostatically defined bilayer graphene quantum dots (QDs) in the regime of low charge carrier occupation, $N < 12$, by means of magnetotransport spectroscopy. Conductance resonances, so-called Coulomb peaks, appear in groups of four in gate space in good agreement with spin and valley degenerate orbital states in bilayer graphene. Interestingly, an additional bunching into pairs of two is superimposed onto the orbital fourfold degeneracy. We conclude that the additional splitting is caused by electron-electron interaction leading to a renormalization of the QD ground state at half filling of each orbital state. Furthermore, we also report in detail on the influences of the QD geometry on the energy scales of the electron-electron interaction and the impact of the magnetic field on the QD states mainly determined by the QD size-dependent valley $g$-factor., 9 pages, 7 figures

Transistors realized on multilayers of 2D antiferromagnetic semiconductor CrPS$_4$ exhibit large, gate-tunable low-temperature magnetoconductance, due to changes in magnetic state induced by the applied magnetic field. The microscopic mechanism coupling the conductance to the magnetic state is however not understood. We identify this mechanism by analyzing the evolution with temperature and magnetic field of the parameters determining the transistor behavior, the carrier mobility and threshold voltage. We find that for temperatures $T$ close to the n\'eel temperature $T_N$, the magnetoconductance originates from the increase in mobility due to cooling or the applied magnetic field, which reduce disorder originating from spin fluctuations. For $T<

Quantum phenomena at interfaces create functionalities at the level of materials. Ferromagnetism in van der Waals systems with diverse arrangements of spins opened a pathway for utilizing proximity magnetic fields to activate properties of materials which would otherwise require external stimuli. Herewith, we realize this notion via creating heterostructures comprising bulk CrCl$_3$ ferromagnet with in-plane easy-axis magnetization and monolayer WSe$_2$ semiconductor. We demonstrate that the in-plane component of the proximity field activates the dark excitons within WSe$_2$. Zero-external-field emission from the dark states allowed us to establish the in-plane and out-of-plane components of the proximity field via inspection of the emission intensity and Zeeman effect, yielding canted orientations at the degree range of $10^{\circ}$ $-$ $30^{\circ}$ at different locations of the heterostructures, attributed to the features of interfacial topography. Our findings are relevant for the development of spintronics and valleytronics with long-lived dark states in technological timescales and sensing applications of local magnetic fields realized simultaneously in multiple dimensions., 7 pages, 5 figures + SI

The chemical potential u of an electron system is a fundamental property of a solid. A precise measurement of u plays a crucial role in understanding the electron interaction and quantum states of matter. However, thermodynamics measurements in micro and nanoscale samples are challenging because of the small sample volume and large background signals. Here, we report an optical readout technique for u of an arbitrary two-dimensional (2D) material. A monolayer semiconductor sensor is capacitively coupled to the sample. The sensor optical response determines a bias that fixes its chemical potential to the band edge and directly reads u of the sample. We demonstrate the technique in AB-stacked MoTe2/WSe2 moire bilayers. We obtain u with DC sensitivity about 20 ueV/sqrt(Hz), and the compressibility and interlayer electric polarization using AC readout. The results reveal a correlated insulating state at the doping density of one hole per moire unit cell, which evolves from a Mott to a charge-transfer insulator with increasing out-of-plane electric field. Furthermore, we image u and quantify the spatial inhomogeneity of the sample. Our work opens the door for high spatial and temporal resolution measurements of the thermodynamic properties of 2D quantum materials.

The physics of moir'e superlattices and the resulting formation of mini-bands in van der Waals materials have opened up an exciting new field in condensed matter physics. These systems exhibit a rich phase diagram of novel physical phenomena and exotic correlated phases that emerge in the low-dispersing bands. Transition metal dichalcogenides, in particular, molybdenum disulfide (MoS2), are potential candidates to extend the studies on moir'e electronics beyond graphene. Our transport spectroscopy measurements and analysis reveal a correlation-driven phase transition and the emergence of discrete mini-bands in MoS2 moir'e superlattices that remained elusive so far. We resolve these mini-bands arising from quantum mechanical tunneling through Schottky barriers between the MoS2 and its metallic leads. Energy scales deduced from a first approach exhibit an astounding agreement with our experimental observations. The behavior under thermal activation suggests a Lifshitz phase transition at low temperatures that is driven by a complete spin-valley symmetry breaking. These intriguing observations bring out the potential of twisted MoS2 to explore correlated electron states and associated physics.

In this work, we report on the growth of hexagonal boron nitride (hBN) crystals from an iron flux at atmospheric pressure and high temperature and demonstrate that (i) the entire sheet of hBN crystals can be detached from the metal in a single step using hydrochloric acid and that (ii) these hBN crystals allow the fabrication of high carrier mobility graphene devices. By combining spatially-resolved confocal Raman spectroscopy and electrical transport measurements, we confirm the excellent quality of these crystals for high-performance hBN-graphene-based van der Waals heterostructures. The full width at half maximum of the graphene Raman 2D peak is as low as 16 cm$^{-1}$, and the room temperature charge carrier mobilitiy is around 80000 cm$^2$/(Vs) at a carrier density 1$\times$10$^{12}$cm$^{-12}$. This is fully comparable with devices of similar dimensions fabricated using crystalline hBN synthesized by the high pressure and high temperature method. Finally, we show that for high quality hBN crystals the hBN Raman peak line width, in contrast to the graphene 2D line width, does not contain any useful information for benchmarking the hBN substrate or encapsulant., 7 pages, 4 figures

This letter presents our findings on the recursive band gap engineering of chiral fermions in bilayer graphene doubly aligned with hBN. By utilizing two interfering moir\'{e} potentials, we generate a supermoir\'{e} pattern which renormalizes the electronic bands of the pristine bilayer graphene, resulting in higher-order fractal gaps even at very low energies. These Bragg gaps can be mapped using a unique linear combination of periodic areas within the system. To validate our findings, we used electronic transport measurements to identify the position of these gaps as functions of the carrier density and establish their agreement with the predicted carrier densities and corresponding quantum numbers obtained using the continuum model. Our work provides direct experimental evidence of the quantization of the area of quasi-Brillouin zones in supermoir\'{e} systems. It fills essential gaps in understanding the band structure engineering of Dirac fermions by a recursive doubly periodic superlattice potential., Comment: 29 pages (including Supplementary Materials)

Interacting electrons in flat bands give rise to a variety of quantum phases. One fundamental aspect of such states is the ordering of the various flavours - such as spin or valley - that the electrons can undergo and the excitation spectrum of the broken symmetry states that they form. These properties cannot be probed directly with electrical transport measurements. The zeroth Landau level of monolayer graphene with four-fold spin-valley degeneracy is a model system for such investigations, but the nature of its broken symmetry states - particularly at partial fillings - is still not understood. Here we demonstrate a non-invasive spectroscopic technique with a scanning tunneling microscope and use it to perform measurements of the valley polarization of the electronic wavefunctions and their excitation spectrum in the partially filled zeroth Landau level of graphene. We can extract information such as the strength of Haldane pseudopotentials that characterize the repulsive interactions underlying the fractional quantum states. Our experiments also demonstrate that fractional quantum Hall phases are built upon broken symmetry states that persist at partial filling. Our experimental approach quantifies the valley phase diagram of the partially filled Landau level as a model flat band platform which is applicable to other graphene-based electronic systems.

Here, we describe synthesis of TMD crystals using a two-step flux growth method that eliminates a major potential source of contamination. Detailed characterization of TMDs grown by this two-step method reveals charged and isovalent defects with densities an order of magnitude lower than in TMDs grown by a single-step flux technique. Initial temperature-dependent electrical transport measurements of monolayer WSe2 yield room-temperature hole mobility above 840 cm2/Vs and low-temperature disorder-limited mobility above 44,000 cm2/Vs. Electrical transport measurements of graphene-WSe2 heterostructures fabricated from the two-step flux grown WSe2 also show superior performance: higher graphene mobility, lower charged impurity density, and well-resolved integer quantum Hall states.

Bilayer graphene (BLG) was recently shown to host a band-inverted phase with unconventional topology emerging from the Ising-type spin--orbit interaction (SOI) induced by the proximity of transition metal dichalcogenides with large intrinsic SOI. Here, we report the stabilization of this band-inverted phase in BLG symmetrically encapsulated in tungsten-diselenide (WSe$_2$) via hydrostatic pressure. Our observations from low temperature transport measurements are consistent with a single particle model with induced Ising SOI of opposite sign on the two graphene layers. To confirm the strengthening of the inverted phase, we present thermal activation measurements and show that the SOI-induced band gap increases by more than 100% due to the applied pressure. Finally, the investigation of Landau level spectra reveals the dependence of the level-crossings on the applied magnetic field, which further confirms the enhancement of SOI with pressure.

Moir\'e excitons are emergent optical excitations in 2D semiconductors with deep moir\'e superlattice potentials. While these excitations have been realized in several platforms, a system with dynamically tunable moir\'e potential to tailor the moir\'e exciton properties is yet to be realized. Here, we present a continuously tunable moir\'e potential in a monolayer WSe2 that is enabled by its proximity to twisted bilayer graphene (TBG) near the magic-angle. Due to its flat electronic bands, charge distribution is highly localized and forms a triangular lattice in TBG. Tuning the local charge density via electrostatic gating, TBG thus provides a spatially varying and dynamically tunable dielectric superlattice for modulating monolayer exciton wavefunctions. By performing optical reflection spectroscopy, we observe emergent moir\'e exciton Rydberg branches in monolayer WSe2 with increased energy splitting upon doping TBG. The twist-angle dependence reveals that the observation is due to a hybridization between bright and dark Rydberg states enabled by the moir\'e potential. Further, at the magic-angle near 1.1{\deg}, the moir\'e Rydberg excitons form a sawtooth pattern with doping owing to the formation of strongly correlated states in the TBG. Our study provides a new platform for engineering moir\'e excitons as well as optical accessibility to the electronic states with small correlation gaps in TBG.

The control of elastic and inelastic electron tunneling relies on materials with well defined interfaces. Van der Waals materials made of two-dimensional constituents form an ideal platform for such studies. Signatures of acoustic phonons and defect states have been observed in current-to-voltage ($I-V$) measurements. These features can be explained by direct electron-phonon or electron-defect interactions. Here, we use a novel tunneling process that involves excitons in transition metal dichalcogenides (TMDs). We study tunnel junctions consisting of graphene and gold electrodes separated by hexagonal boron nitride (hBN) with an adjacent TMD monolayer and observe prominent resonant features in $I-V$ measurements. These resonances appear at bias voltages that correspond to TMD exciton energies. By placing the TMD outside of the tunneling pathway, we demonstrate that this phonon-exciton mediated tunneling process does not require any charge injection into the TMD. This work demonstrates the appearance of optical modes in electrical transport measurements and introduces a new functionality for optoelectronic devices based on van der Waals materials., 26 pages, 23 figures, 77 references

Interactions among electrons create novel many-body quantum phases of matter with wavefunctions that often reflect electronic correlation effects, broken symmetries, and novel collective excitations. A wide range of quantum phases has been discovered in MATBG, including correlated insulating, unconventional superconducting, and magnetic topological phases. The lack of microscopic information, including precise knowledge of possible broken symmetries, has thus far hampered our understanding of MATBG's correlated phases. Here we use high-resolution scanning tunneling microscopy to directly probe the wavefunctions of the correlated phases in MATBG. The squares of the wavefunctions of gapped phases, including those of the correlated insulators, pseudogap, and superconducting phases, show distinct patterns of broken symmetry with a $\sqrt{3}$ x $\sqrt{3}$ super-periodicity on the graphene atomic lattice that has a complex spatial dependence on the moir\'e superlattice scale. We introduce a symmetry-based analysis to describe our measurements of the wavefunctions of MATBG's correlated phases with a set of complex-valued local order parameters. For the correlated insulators in MATBG, at fillings of $\nu$ = $\pm$ 2 electrons per moir\'e unit cell relative to charge neutrality, we compare the observed quantum textures to those expected for proposed theoretical ground states. In typical MATBG devices, the textures of correlated insulators' wavefunctions closely match those of the theoretically proposed IKS order, while in ultra-low-strain samples our data has local symmetries like those of a T-IVC phase. We also study the wavefunction of MATBG's superconducting state, revealing strong signatures of intervalley coherence that can only be distinguished from those of the insulator with our phase-sensitive measurements., Comment: 5 figures

Systems combining superconductors with topological insulators offer a platform for the study of Majorana bound states and a possible route to realize a topological quantum computer. Among the systems being considered in this field, monolayers of tungsten ditelluride ($\mathrm{WTe_2}$) have a rare combination of properties. Notably, it has been demonstrated to be a Quantum Spin Hall Insulator (QSHI) and can easily be gated into a superconducting state. Here we report measurements on gate-defined Josephson junction devices fabricated using monolayer $\mathrm{WTe_2}$. We find that consideration of the two dimensional superconducting leads are critical in the interpretation of magnetic interference in the resulting junctions. Our fabrication procedures suggest a facile way to produce further devices from this technically challenging material and our results mark the first step toward realizing versatile all-in-one topological Josephson junctions using monolayer $\mathrm{WTe_2}$.

Solid-state single photon sources are central building blocks in quantum communication networks and on-chip quantum information processing. Atomically thin crystals were established as possible candidates to emit non-classical states of light, however, the performance of monolayer-based single photon sources has so far been lacking behind state-of-the-art devices based on volume crystals. Here, we implement a single photon source based on an atomically thin sheet of WSe2 coupled to a spectrally tunable optical cavity. It is characterized by a high single photon purity with a $g^{(2)}(0)$ value as low as $4.7 \pm 0.7 \%$ and a record-high first lens brightness of linearly polarized photons as large as $65 \pm 4 \%$. Interestingly, the high performance of our devices allows us to observe genuine quantum interference phenomena in a Hong-Ou-Mandel experiment. Our results demonstrate that open cavities and two-dimensional materials constitute an excellent platform for ultra-bright quantum light sources: the unique properties of such two-dimensional materials and the versatility of open cavities open an inspiring avenue for novel quantum optoelectronic devices., 12 pages, 7 figures

The low-temperature phase diagram of multilayer graphene heterostructures is largely defined by the exchange-driven instability that lifts the four-fold isospin degeneracy. Such instability gives rise to the quarter- and half-metal phases, which are key to our understanding of other emergent phenomena. Recent theoretical works shed light on a new type of Coulomb-driven instability. It is proposed that the exchange interaction between trigonal-warping-induced Fermi pockets could induce charge carriers to condense into one of the Fermi pockets, giving rise to a net polarization in the momentum space. Here, we report the observation of spontaneous momentum polarization in Bernal bilayer graphene using angle-resolved nonlinear transport measurement at the second-harmonic frequency. With excellent angular precision, we show that the polar axis of the momentum polarization is tunable with varying carrier density, electric field, and magnetic field. The dominating influence of the momentum-space instability reveals a natural connection between broken symmetries, and the isospin degeneracy lifting in the half- and quarter-metal phases.

Hexagonal boron nitride (hBN) is a van der Waals material with excellent mechanical properties hosting quantum emitters and optically active spin defects, several of them being sensitive to strain. Establishing optomechanical control of hBN will enable hybrid quantum devices that combine the spin degree of freedom with the cavity optomechanical toolbox. In this letter, we report the first observation of radiation pressure backaction at telecom wavelengths with a hBN drum-head mechanical resonator. The thermomechanical motion of the resonator is coupled to the optical mode of a high finesse fiber-based Fabry-P\'erot microcavity in a membrane-in-the-middle configuration. We are able to resolve the optical spring effect and optomechanical damping with a single photon coupling strength of $g_0/2\pi = 1200$ Hz. Our results pave the way for tailoring the mechanical properties of hBN resonators with light.

Monolayer transition metal dichalcogenide (TMDC) semiconductors exhibit strong excitonic optical resonances which serve as a microscopic, non-invasive probe into their fundamental properties. Like the hydrogen atom, such excitons can exhibit an entire Rydberg series of resonances. Excitons have been extensively studied in most TMDCs (MoS$_2$, MoSe$_2$, WS$_2$ and WSe$_2$), but detailed exploration of excitonic phenomena has been lacking in the important TMDC material molybdenum ditelluride (MoTe$_2$). Here, we report an experimental investigation of excitonic luminescence properties of monolayer MoTe$_2$ to understand the excitonic Rydberg series, up to 3s. We report significant modification of emission energies with temperature (4K to 300K), quantifying the exciton-phonon coupling. Furthermore, we observe a strongly gate-tunable exciton-trion interplay for all the Rydberg states governed mainly by free-carrier screening, Pauli blocking, and band-gap renormalization in agreement with the results of first-principles GW plus Bethe-Salpeter equation approach calculations. Our results help bring monolayer MoTe$_2$ closer to its potential applications in near-infrared optoelectronics and photonic devices., 5 figures (main text)

We report on multiterminal measurements in a ballistic bilayer graphene (BLG) channel where multiple spin and valley-degenerate quantum point contacts (QPCs) are defined by electrostatic gating. By patterning QPCs of different shapes and along different crystallographic directions, we study the effect of size quantization and trigonal warping on the transverse electron focusing (TEF) spectra. Our TEF spectra show eight clear peaks with comparable amplitude and weak signatures of quantum interference at the lowest temperature, indicating that reflections at the gate-defined edges are specular and transport is phase coherent. The temperature dependence of the scattering rate indicates that electron-electron interactions play a dominant role in the charge relaxation process for electron doping and temperatures below 100 K. The achievement of specular reflection, which is expected to preserve the pseudospin information of the electron jets, is promising for the realization of ballistic interconnects for new valleytronic devices., 22 pages, 16 figures

Carrier relaxation measurements in moir\'e materials offer a unique probe of the microscopic interactions, in particular the ones that are not easily measured by transport. Umklapp scattering between phonons is a ubiquitous momentum-nonconserving process that governs the thermal conductivity of semiconductors and insulators. In contrast, Umklapp scattering between electrons and phonons has not been demonstrated experimentally. Here, we study the cooling of hot electrons in moir\'e graphene using time- and frequency-resolved photovoltage measurements as a direct probe of its complex energy pathways including electron-phonon coupling. We report on a dramatic speedup in hot carrier cooling of twisted bilayer graphene near the magic angle: the cooling time is a few picoseconds from room temperature down to 5 K, whereas in pristine graphene coupling to acoustic phonons takes nanoseconds. Our analysis indicates that this ultrafast cooling is a combined effect of the formation of a superlattice with low-energy moir\'e phonons, spatially compressed electronic Wannier orbitals, and a reduced superlattice Brillouin zone, enabling Umklapp scattering that overcomes electron-phonon momentum mismatch. These results demonstrate a way to engineer electron-phonon coupling in twistronic systems, an approach that could contribute to the fundamental understanding of their transport properties and enable applications in thermal management and ultrafast photodetection., Comment: 19 pages, 4 figures, 10 supporting figures

Placing a sensor close to the target at the nano-level is a central challenge in quantum sensing. We demonstrate high-spatial-resolution magnetic field imaging with a boron vacancy (V$_\text{B}^-$) defects array in hexagonal boron nitride with a few 10 nm thickness. V$_\text{B}^-$ sensor spots with a size of (100 nm)$^2$ are arranged periodically with nanoscale precision using a helium ion microscope and attached tightly to a gold wire. The sensor array allows us to visualize the magnetic field induced by the current in the wire with a spatial resolution beyond the diffraction limit. Each sensor exhibits a practical sensitivity of $73.6~\mu\text{T/Hz}^{0.5}$, suitable for quantum materials research. Our technique of arranging V$_\text{B}^-$ quantum sensors periodically and tightly on measurement targets will maximize their potential., Comment: 6 pages, 4 figures

Fermi liquids respond differently to perturbations depending on whether their frequency is larger (collisionless regime) or smaller (hydrodynamic regime) than the inter-particle collision rate. This results in a different phase velocity between the collisionless zero sound and hydrodynamic first sound. We performed terahertz photocurrent nanoscopy measurements on graphene devices, with a metallic gate in close proximity to the sample, to probe the dispersion of propagating acoustic plasmons, the counterpart of sound modes in electronic Fermi liquids. We report the observation of a change in the plasmon phase velocity when the excitation frequency approaches the electron-electron collision rate. This first observation of the first sound mode in an electronic Fermi liquid is of fundamental interest and can enable novel terahertz emitter and detection implementations.

Rhombohedral stacked multilayer graphene is an ideal platform to search for correlated electron phenomena, due to its pair of flat bands touching at zero energy and further tunability by an electric field. Furthermore, its valley-dependent Berry phase at zero energy points to possible topological states when the pseudospin symmetry is broken by electron correlation. However, experimental explorations of these opportunities are very limited so far, due to a lack of devices with optimized layer numbers and configurations. Here we present electron transport measurements of hBN-encapsulated pentalayer graphene at down to 100 milli-Kelvin. We observed a correlated insulating state with >MOhm resistance at zero charge density and zero displacement field, where the tight-binding calculation predicts a metallic ground state. By increasing the displacement field, we observed a Chern insulator state with C = -5 and two other states with C = -3 at a low magnetic field of ~1 Tesla. At high displacement fields and charge densities, we observed isospin-polarized quarter- and half-metals. Therefore, rhombohedral-stacked pentalayer graphene is the first graphene system to exhibit two different types of Fermi-surface instabilities: driven by a pair of flat bands touching at zero energy, and by the Stoner mechanism in a single flat band. Our results demonstrate a new direction to explore intertwined electron correlation and topology phenomena in natural graphitic materials without the need of moiré superlattice engineering.

The supermoiré lattice, built by stacking two moiré patterns, provides a platform for creating flat mini-bands and studying electron correlations. An ultimate challenge in assembling a graphene supermoiré lattice is in the deterministic control of its rotational alignment, which is made highly aleatory due to the random nature of the edge chirality and crystal symmetry of each component layer. Employing the so-called golden rule of three, here we present an experimental strategy to overcome this challenge and realize the controlled alignment of double-aligned hBN/graphene/hBN supermoiré lattice, where graphene is precisely aligned with both top hBN and bottom hBN. Remarkably, we find that the crystallographic edge of neighboring graphite can be used to better guide the stacking alignment, as demonstrated by the controlled production of 20 moiré samples with an accuracy better than 0.2 degree. Finally, we extend our technique to other strongly correlated electron systems, such as low-angle twisted bilayer graphene and ABC-stacked trilayer graphene, providing a strategy for flat-band engineering in these moiré materials., 20 pages, 4 figures

The interaction mechanisms of water with nanoscale geometries remain poorly understood. This study focuses on behaviour of water clusters under varying external electric fields with a particular focus on molecular ferroelectric devices. We employ a two-fold approach, combining experiments with large-scale molecular dynamics simulations on graphene nanoribbon field effect transistors. We show that bilayer graphene nanoribbons provide stable anchoring of water clusters on the oxygenated edges, resulting in a ferroelectric effect. A molecular dynamics model is then used to investigate water cluster behaviour under varying external electric fields. Finally, we show that these nanoribbons exhibit significant and persistent remanent fields that can be employed in ferroelectric heterostructures and neuromorphic circuits.

The energy landscape of optical excitations in mono- and few-layer transition metal dichalcogenides (TMDs) is dominated by optically bright and dark excitons. These excitons can be fully localized within a single TMD layer, or the electron- and the hole-component of the exciton can be charge-separated over multiple TMD layers. Such intra- or interlayer excitons have been characterized in detail using all-optical spectroscopies, and, more recently, photoemission spectroscopy. In addition, there are so-called hybrid excitons whose electron- and/or hole-component are delocalized over two or more TMD layers, and therefore provide a promising pathway to mediate charge-transfer processes across the TMD interface. Hence, an in-situ characterization of their energy landscape and dynamics is of vital interest. In this work, using femtosecond momentum microscopy combined with many-particle modeling, we quantitatively compare the dynamics of momentum-indirect intralayer excitons in monolayer WSe$_2$ with the dynamics of momentum-indirect hybrid excitons in heterobilayer WSe$_2$/MoS$_2$, and draw three key conclusions: First, we find that the energy of hybrid excitons is reduced when compared to excitons with pure intralayer character. Second, we show that the momentum-indirect intralayer and hybrid excitons are formed via exciton-phonon scattering from optically excited bright excitons. And third, we demonstrate that the efficiency for phonon absorption and emission processes in the mono- and the heterobilayer is strongly dependent on the energy alignment of the intralayer and hybrid excitons with respect to the optically excited bright exciton. Overall, our work provides microscopic insights into exciton dynamics in TMD mono- and bilayers., Comment: 27 pages, 5 figures

Moiré superlattices provide a highly tunable and versatile platform to explore novel quantum phases and exotic excited states ranging from correlated insulators1-17 to moiré excitons7-10,18. Scanning tunneling microscopy has played a key role in probing microscopic behaviors of the moiré correlated ground states at the atomic scale1,11-15,19. Atomic-resolution imaging of quantum excited state in moiré heterostructures, however, has been an outstanding experimental challenge. Here we develop a novel photocurrent tunneling microscopy by combining laser excitation and scanning tunneling spectroscopy (laser-STM) to directly visualize the electron and hole distribution within the photoexcited moiré exciton in a twisted bilayer WS2 (t-WS2). We observe that the tunneling photocurrent alternates between positive and negative polarities at different locations within a single moiré unit cell. This alternating photocurrent originates from the exotic in-plane charge-transfer (ICT) moiré exciton in the t-WS2 that emerges from the competition between the electron-hole Coulomb interaction and the moiré potential landscape. Our photocurrent maps are in excellent agreement with our GW-BSE calculations for excitonic states in t-WS2. The photocurrent tunneling microscopy creates new opportunities for exploring photoexcited non-equilibrium moiré phenomena at the atomic scale.

Wigner crystals are predicted as the crystallization of the dilute electron gas moving in a uniform background when the electron-electron Coulomb energy dominates the kinetic energy. The Wigner crystal has previously been observed in the ultraclean two-dimensional electron gas (2DEG) present on the surface of liquid helium and in semiconductor quantum wells at high magnetic field. More recently, Wigner crystals have also been reported in WS2/WSe2 moiré heterostructures. ABC-stacked trilayer graphene on boron nitride (ABC-TLG/hBN) moiré superlattices provide a unique tunable platform to explore Wigner crystal states where the electron correlation can be controlled by electric and magnetic field. Here we report the observation of magnetic field stabilized Wigner crystal states in a ABC-TLG/hBN moiré superlattice. We show that correlated insulating states emerge at multiple fractional and integer fillings corresponding to v = 1/3, 2/3, 1, 4/3, 5/3 and 2 electrons per moiré lattice site under a magnetic field. These correlated insulating states can be attributed to generalized Mott states for the integer fillings (v = 1, 2) and generalized Wigner crystal states for the fractional fillings (v = 1/3, 2/3, 4/3, 5/3). The generalized Wigner crystal states are stabilized by a vertical magnetic field, and they are strongest at one magnetic flux quantum per three moiré superlattices. The correlated insulating states at v = 2 persists up to 30 Tesla, which can be described by a Mott-Hofstadter transition at high magnetic field. The tunable Mott and Wigner crystal states in the ABC-TLG/hBN highlight the opportunities to discover new correlated quantum phases due to the interplay between the magnetic field and moiré flatbands., 19 pages, 6 figures

The superconductor to insulator or metal transition in two dimensions (2D) provides a valuable platform for studying continuous quantum phase transitions (QPTs) and critical phenomena. Distinct theoretical models, including both fermionic and bosonic localization scenarios, have been developed, but many questions remain unsettled despite decades of research. Extending Nernst experiments down to millikelvin temperatures, we uncover anomalous quantum fluctuations and identify an unconventional superconducting quantum critical point (QCP) in a gate-tuned excitonic quantum spin Hall insulator (QSHI), the monolayer tungsten ditelluride (WTe2). The observed vortex Nernst effect reveals singular superconducting fluctuations in the resistive normal state induced by magnetic fields or temperature, even well above the transition. Near the doping-induced QCP, the Nernst signal driven by quantum fluctuations is exceptionally large in the millikelvin regime, with a coefficient of ~ 4,100 uV/KT at zero magnetic field, an indication of the proliferation of vortices. Surprisingly, the Nernst signal abruptly disappears when the doping falls below the critical value, in striking conflict with conventional expectations. This series of phenomena, which have no prior analogue, call for careful examinations of the mechanism of the QCP, including the possibility of a continuous QPT between two distinct ordered phases in the monolayer. Our experiments open a new avenue for studying unconventional QPTs and quantum critical matter.

At partial fillings of its flat electronic bands, magic-angle twisted bilayer graphene (MATBG) hosts a rich variety of competing correlated phases that show sample to sample variations. Divergent phase diagrams in MATBG are often attributed to the sublattice polarization energy scale, tuned by the degree of alignment of the hexagonal boron nitride (hBN) substrates typically used in van der Waals devices. Unaligned MATBG exhibits unconventional superconductivity and correlated insulating phases, while nearly perfectly aligned MATBG/hBN exhibits zero-field Chern insulating phases and lacks superconductivity. Here we use scanning tunneling microscopy and spectroscopy (STM/STS) to observe gapped phases at partial fillings of the flat bands of MATBG in a new intermediate regime of sublattice polarization, observed when MATBG is only partially aligned ($\theta_{Gr-hBN}$ $\approx$ 1.65$^\circ$) to the underlying hBN substrate. Under this condition, MATBG hosts not only phenomena that naturally interpolate between the two sublattice potential limits, but also unexpected gapped phases absent in either of these limits. At charge neutrality, we observe an insulating phase with a small energy gap ($\Delta$ < 5 meV) likely related to weak sublattice symmetry breaking from the hBN substrate. In addition, we observe new gapped phases near fractional fillings $\nu$ = $\pm 1/3$ and $\nu$ = $\pm 1/6$, which have not been previously observed in MATBG. Importantly, energy-resolved STS unambiguously identifies these fractional filling states to be of single-particle origin, possibly a result of the super-superlattice formed by two moir\'e superlattices. Our observations emphasize the power of STS in distinguishing single-particle gapped phases from many-body gapped phases in situations that could be easily confused in electrical transport measurements., Comment: 4 figures

The coherent dynamics of a quantum mechanical two-level system passing through an anti-crossing of two energy levels can give rise to Landau-Zener-St\"uckelberg (LZS) interference. LZS interference spectroscopy has proven to be a fruitful tool to investigate charge noise and charge decoherence in semiconductor quantum dots (QDs). Recently, bilayer graphene has developed as a promising platform to host highly tunable QDs potentially useful for hosting spin and valley qubits. So far, in this system no coherent oscillations have been observed and little is known about charge noise in this material. Here, we report coherent charge oscillations and $T_2^*$ charge decoherence times in a bilayer graphene double QD. The charge decoherence times are measured independently using LZS interference and photon assisted tunneling. Both techniques yield $T_2^*$ average values in the range of 400 to 500~ps. The observation of charge coherence allows to study the origin and spectral distribution of charge noise in future experiments., Comment: Article: 9 pages, 5 figures; Supplementary Information: 8 pages, 7 figures

Coherent optical manipulation of electronic bandstructures via Floquet Engineering is a promising means to control quantum systems on an ultrafast timescale. However, the ultrafast switching on/off of the driving field comes with questions regarding the limits of validity of the Floquet formalism, which is defined for an infinite periodic drive, and to what extent the transient changes can be driven adibatically. Experimentally addressing these questions has been difficult, in large part due to the absence of an established technique to measure coherent dynamics through the duration of the pulse. Here, using multidimensional coherent spectroscopy we explicitly excite, control, and probe a coherent superposition of excitons in the $K$ and $K^\prime$ valleys in monolayer WS$_2$. With a circularly polarized, red-detuned, pump pulse, the degeneracy of the $K$ and $K^\prime$ excitons can be lifted and the phase of the coherence rotated. We demonstrate phase rotations during the 100 fs driving pulse that exceed $\pi$, and show that this can be described by a combination of the AC-Stark shift of excitons in one valley and Bloch-Siegert shift of excitons in the opposite valley. Despite showing a smooth evolution of the phase that directly follows the intensity envelope of the pump pulse, the process is not perfectly adiabatic. By measuring the magnitude of the macroscopic coherence as it evolves before, during, and after the pump pulse we show that there is additional decoherence caused by power broadening in the presence of the pump. This non-adiabaticity may be a problem for many applications, such as manipulating q-bits in quantum information processing, however these measurements also suggest ways such effects can be minimised or eliminated.

The role and impact of spatial heterogeneity in two-dimensional quantum materials represents one of the major research quests regarding the future application of these materials in optoelectronics and quantum information science. In the case of transition-metal dichalcogenide heterostructures, in particular, direct access to heterogeneities in the dark-exciton landscape with nanometer spatial and ultrafast time resolution is highly desired, but remains largely elusive. Here, we introduce ultrafast dark field momentum microscopy to spatio-temporally resolve dark exciton formation dynamics in a twisted WSe$_2$/MoS$_2$ heterostructure with 55 femtosecond time- and 500~nm spatial resolution. This allows us to directly map spatial heterogeneity in the electronic and excitonic structure, and to correlate these with the dark exciton formation and relaxation dynamics. The benefits of simultaneous ultrafast nanoscale dark-field momentum microscopy and spectroscopy is groundbreaking for the present study, and opens the door to new types of experiments with unprecedented spectroscopic and spatiotemporal capabilities., Comment: 39 pages, 4 main figures, 8 supplemental figures

Semiconductor moir\'e superlattices have been shown to host a wide array of interaction-driven ground states. However, twisted homobilayers have been difficult to study in the limit of large moir\'e wavelength, where interactions are most dominant, and despite numerous predictions of nontrivial topology in these homobilayers, experimental evidence has remained elusive. Here, we conduct local electronic compressibility measurements of twisted bilayer WSe$_2$ at small twist angles. We demonstrate multiple topological bands which host a series of Chern insulators at zero magnetic field near a 'magic angle' around $1.23^\circ$. Using a locally applied electric field, we induce a topological quantum phase transition at one hole per moir\'e unit cell. Furthermore, by measuring at a variety of local twist angles, we characterize how the interacting ground states of the underlying honeycomb superlattice depend on the size of the moir\'e unit cell. Our work establishes the topological phase diagram of a generalized Kane-Mele-Hubbard model in tWSe$_2$, demonstrating a tunable platform for strongly correlated topological phases.

Second-order superlattices form when moiré superlattices of similar dimensions interfere with each other, leading to even larger superlattice periodicities. These crystalline structures have been engineered utilizing two-dimensional (2D) materials such as graphene and hexagonal boron nitride (hBN) under specific alignment conditions. Such specific alignment has shown to play a crucial role in facilitating correlation-driven topological phases featuring the quantized anomalous Hall effect. While signatures of second-order superlattices have been found in transport experiments, any real-space visualization is lacking to date. In this work, we present cryogenic nanoscale photovoltage (PV) measurements that reveal a second-order superlattice in magic-angle twisted bilayer graphene (MATBG) closely aligned to hBN. This is evidenced by long-range periodic photovoltage modulations across the entire sample backed by corresponding electronic transport features. Our theoretical framework shows that small strain- or twist-angle variations can lead to a drastic shift between a local one-dimensional, square or triangular superlattices. Our real-space observations shed new light on the mechanisms responsible for breaking spatial symmetries in TBG and pave an avenue to engineer long-range superlattice structures in 2D materials., 15 pages, 12 figures

The interplay of charge, spin, lattice, and orbital degrees of freedom leads to a wide range of emergent phenomena in strongly correlated systems. In heterobilayer transition metal dichalcogenide moiré systems, recent observations of Mott insulators and generalized Wigner crystals are well described by triangular lattice single-orbital Hubbard models based on K-valley derived moiré bands. Richer phase diagrams, mapped onto multi-orbital Hubbard models, are possible with hexagonal lattices in $Γ$-valley derived moiré bands and additional layer degrees of freedom. Here we report the tunable interaction between strongly correlated hole states hosted by $Γ$- and K-derived moiré bands in a monolayer MoSe$_2$ / natural WSe$_2$ bilayer device. To precisely probe the nature of the correlated states, we optically characterise the behaviour of exciton-polarons and distinguish the layer and valley degrees of freedom. We find that the honeycomb $Γ$-band gives rise to a charge-transfer insulator described by a two-orbital Hubbard model with inequivalent $Γ_\mathrm{A}$ and $Γ_\mathrm{B}$ orbitals. With an out-of-plane electric field, we re-order the $Γ_\mathrm{B}$- and K-derived bands energetically, driving an abrupt redistribution of carriers to the layer-polarized K orbital where new correlated states are observed. Finally, by fine-tuning the band-alignment, we obtain degeneracy of the $Γ_\mathrm{B}$ and K orbitals at the Fermi level. In this critical condition, stable Wigner crystals with carriers distributed across the two orbitals are observed until the Fermi-level reaches one hole per lattice site, whereupon the system collapses into a filled $Γ_\mathrm{B}$ orbital. Our results establish a platform to investigate the interplay of charge, spin, lattice, and layer geometry in multi-orbital Hubbard model Hamiltonians., 14 pages, 5 figures