Nanoscale Conductivity Imaging of Correlated Electronic States in WSe_{2}/WS_{2} Moiré Superlattices

Gold-Template-Assisted Mechanical Exfoliation of Large-Area 2D Layers Enables Efficient and Precise Construction of Moiré Superlattices

Moiré superlattices, consisting of rotationally aligned 2D atomically thin layers, provide a highly novel platform for the study of correlated quantum phenomena. However, reliable and efficient construction of moiré superlattices is challenging because of difficulties to accurately angle-align small exfoliated 2D layers and the need to shun wet-transfer processes. Here, efficient and precise construction of various moiré superlattices is demonstrated by picking up and stacking large-area 2D mono- or few-layer crystals with predetermined crystal axes, made possible by a gold-template-assisted mechanical exfoliation method. The exfoliated 2D layers are semiconductors, superconductors, or magnets and their high quality is confirmed by photoluminescence and Raman spectra and by electrical transport measurements of fabricated field-effect transistors and Hall devices. Twisted homobilayers with angle-twisting accuracy of ≈0.3°, twisted heterobilayers with sub-degree angle-alignment accuracy, and multilayer superlattices are precisely constructed and characterized by their moiré patterns, interlayer excitons, and second harmonic generation. The present study paves the way for exploring emergent phenomena in moiré superlattices.

Unraveling the strain tuning mechanism of interlayer excitons in WSe2/MoSe2heterostructure

Atomically thin transition metal dichalcogenides (TMDs) exhibit rich excitonic physics, due to reduced dielectric screening and strong Coulomb interactions. Especially, some attractive topics in modern condensed matter physics, such as correlated insulator, superconductivity, topological excitons bands, are recently reported in stacking two monolayer (ML) TMDs. Here, we clearly reveal the tuning mechanism of tensile strain on interlayer excitons (IEXs) and intralayer excitons (IAXs) in WSe2/MoSe2heterostructure (HS) at low temperature. We utilize the cryogenic tensile strain platform to stretch the HS, and measure by micro-photoluminescence (μ-PL). The PL peaks redshifts of IEXs and IAXs in WSe2/MoSe2HS under tensile strain are well observed. The first-principles calculations by using density functional theory reveals the PL peaks redshifts of IEXs and IAXs origin from bandgap shrinkage. The calculation results also show the Mo-4d states dominating conduction band minimum shifts of the ML MoSe2plays a dominant role in the redshifts of IEXs. This work provides new insights into understanding the tuning mechanism of tensile strain on IEXs and IAXs in two-dimensional (2D) HS, and paves a way to the development of flexible optoelectronic devices based on 2D materials.

Anisotropic Interlayer Force Field for Group-VI Transition Metal Dichalcogenides

An anisotropic interlayer force field that describes the interlayer interactions in homogeneous and heterogeneous interfaces of group-VI transition metal dichalcogenides (MX2, where M = Mo, W, and X = S, Se) is presented. The force field is benchmarked against density functional theory calculations for bilayer systems within the Heyd-Scuseria-Ernzerhof hybrid density functional approximation, augmented by a nonlocal many-body dispersion treatment of long-range correlation. The parametrization yields good agreement with the reference calculations of binding energy curves and sliding potential energy surfaces. It is found to be transferable to transition metal dichalcogenide (TMD) junctions outside of the training set that contain the same atom types. Calculated bulk moduli agree with most previous dispersion-corrected density functional theory predictions, which underestimate the available experimental values. Calculated phonon spectra of the various junctions under consideration demonstrate the importance of appropriately treating the anisotropic nature of the layered interfaces. Considering our previous parametrization for MoS2, the anisotropic interlayer potential enables accurate and efficient large-scale simulations of the dynamical, tribological, and thermal transport properties of a large set of homogeneous and heterogeneous TMD interfaces.

Electronic Kapitza conductance and related kinetic coefficients at an interface between n-type semiconductors

We calculate the Kapitza conductance, which is the proportionality coefficient between heat flux and temperature jump at the interface, for the case of two conducting solids separated by the interface. We show that for conducting solids in a non-equilibrium state, there should also arise the electrochemical potential jump at the interface. Hence to describe linear transport at the interface we need three kinetic coefficients: interfacial analogs of electric and heat conductances and interfacial analog of the Seebeck coefficient. We calculate these coefficients for the case of an interface between n-type semiconductors. We perform calculations in the framework of Boltzmann transport theory. We have found out that the interfacial analog of the Seebeck coefficient for some range of parameters of the considered semiconductors, has a high value of about 10-3V K-1. Thus this effect has the potential to be used for the synthesis of effective thermoelectric materials.

Interlayer donor-acceptor pair excitons in MoSe2/WSe2 moiré heterobilayer

Localized interlayer excitons (LIXs) in two-dimensional moiré superlattices exhibit sharp and dense emission peaks, making them promising as highly tunable single-photon sources. However, the fundamental nature of these LIXs is still elusive. Here, we show the donor-acceptor pair (DAP) mechanism as one of the origins of these excitonic peaks. Numerical simulation results of the DAP model agree with the experimental photoluminescence spectra of LIX in the moiré MoSe2/WSe2 heterobilayer. In particular, we find that the emission energy-lifetime correlation and the nonmonotonic power dependence of the lifetime agree well with the DAP IX model. Our results provide insight into the physical mechanism of LIX formation in moiré heterostructures and pave new directions for engineering interlayer exciton properties in moiré superlattices.

MilliKelvin microwave impedance microscopy in a dry dilution refrigerator

Microwave impedance microscopy (MIM) is a near-field imaging technique that has been used to visualize the local conductivity of materials with nanoscale resolution across the GHz regime. In recent years, MIM has shown great promise for the investigation of topological states of matter, correlated electronic states, and emergent phenomena in quantum materials. To explore these low-energy phenomena, many of which are only detectable in the milliKelvin regime, we have developed a novel low-temperature MIM incorporated into a dilution refrigerator. This setup, which consists of a tuning-fork-based atomic force microscope with microwave reflectometry capabilities, is capable of reaching temperatures down to 70 mK during imaging and magnetic fields up to 9 T. To test the performance of this microscope, we demonstrate microwave imaging of the conductivity contrast between graphite and silicon dioxide at cryogenic temperatures and discuss the resolution and noise observed in these results. We extend this methodology to visualize edge conduction in Dirac semi-metal cadmium arsenide in the quantum Hall regime.

Tunable spin and valley excitations of correlated insulators in Γ-valley moiré bands

Moiré superlattices formed from transition metal dichalcogenides support a variety of quantum electronic phases that are highly tunable using applied electromagnetic fields. While the valley degree of freedom affects optoelectronic properties in the constituent transition metal dichalcogenides, it has yet to be fully explored in moiré systems. Here we establish twisted double-bilayer WSe₂ as an experimental platform to study electronic correlations within Γ-valley moiré bands. Through local and global electronic compressibility measurements, we identify charge-ordered phases at multiple integer and fractional moiré fillings. By measuring the magnetic field dependence of their energy gaps and the chemical potential upon doping, we reveal spin-polarized ground states with spin-polaron quasiparticle excitations. In addition, an applied displacement field induces a metal-insulator transition driven by tuning between Γ- and K-valley moiré bands. Our results demonstrate control over the spin and valley character of the correlated ground and excited states in this system.

Implementing microwave impedance microscopy in a dilution refrigerator

We report the implementation of a dilution refrigerator-based scanning microwave impedance microscope with a base temperature of ∼100 mK. The vibration noise of our apparatus with tuning-fork feedback control is as low as 1 nm. Using this setup, we have demonstrated the imaging of quantum anomalous Hall states in magnetically (Cr and V) doped (Bi, Sb)2Te3 thin films grown on mica substrates. Both the conductive edge modes and topological phase transitions near the coercive fields of Cr- and V-doped layers are visualized in the field-dependent results. Our study establishes the experimental platform for investigating nanoscale quantum phenomena at ultralow temperatures.

Layer-dependent correlated phases in WSe2/MoS2 moiré superlattice

Electron correlation plays an essential role in the macroscopic quantum phenomena in the moiré heterostructure, such as antiferromagnetism and correlated insulating phases. Unlike the phenomena where the interaction involves only electrons in one layer, the interaction of distinct phases in two or more layers represents a new horizon forward, such as the one in the Kondo lattice model. Here, using interlayer excitons as a probe, we show that the interlayer interactions in heterobilayers of tungsten diselenide and molybdenum disulfide (WSe₂/MoS₂) can be electrically switched on and off, resulting in a layer-dependent correlated phase diagram, including single-layer, layer-selective, excitonic-insulator and layer-hybridized regions. We demonstrate that these correlated phases affect the interlayer exciton non-radiative decay pathways. These results reveal the role of strong correlation on interlayer exciton dynamics and pave the way for studying the layer-resolved strong correlation behaviour in moiré heterostructures.

Moiré Potential, Lattice Relaxation, and Layer Polarization in Marginally Twisted MoS2 Bilayers

Artificially twisted heterostructures of semiconducting transition-metal dichalcogenides (TMDs) offer unprecedented control over their electronic and optical properties via the spatial modulation of interlayer interactions and structural reconstruction. Here we study twisted MoS₂ bilayers in a wide range of twist angles near 0° using scanning tunneling microscopy/spectroscopy. We investigate the twist angle dependence of the moiré pattern, which is dominated by lattice reconstruction for small angles (<2°), leading to large triangular domains with rhombohedral stacking. Local spectroscopy measurements reveal a large moiré-potential strength of 100-200 meV for angles <3°. In reconstructed regions, we see a bias-dependent asymmetry between neighboring triangular domains, which we relate to the vertical polarization that is intrinsic to rhombohedral stacked TMDs. This viewpoint is further supported by spectroscopy maps and ambient piezoresponse measurements. Our results provide a microscopic perspective of this new class of interfacial ferroelectrics and can offer clues for designing novel heterostructures that harness this effect.

Tuning moiré excitons and correlated electronic states through layer degree of freedom

Moiré coupling in transition metal dichalcogenides (TMDCs) superlattices introduces flat minibands that enable strong electronic correlation and fascinating correlated states, and it also modifies the strong Coulomb-interaction-driven excitons and gives rise to moiré excitons. Here, we introduce the layer degree of freedom to the WSe₂/WS₂ moiré superlattice by changing WSe₂ from monolayer to bilayer and trilayer. We observe systematic changes of optical spectra of the moiré excitons, which directly confirm the highly interfacial nature of moiré coupling at the WSe₂/WS₂ interface. In addition, the energy resonances of moiré excitons are strongly modified, with their separation significantly increased in multilayer WSe₂/monolayer WS₂ moiré superlattice. The additional WSe₂ layers also modulate the strong electronic correlation strength, evidenced by the reduced Mott transition temperature with added WSe₂ layer(s). The layer dependence of both moiré excitons and correlated electronic states can be well described by our theoretical model. Our study presents a new method to tune the strong electronic correlation and moiré exciton bands in the TMDCs moiré superlattices, ushering in an exciting platform to engineer quantum phenomena stemming from strong correlation and Coulomb interaction.

Twisted heterostructures of transition metal dichalcogenides host the so-called moiré excitons, or intralayer excitons modified by the moiré potential. Here the authors show tunability of the moiré excitons and the coexisting correlated electronic states in WSe₂/WS₂ superlattices with varying WSe₂ layer thickness

Morphology Deformation and Giant Electronic Band Modulation in Long-Wavelength WS2 Moiré Superlattices

As a lattice interference effect, moiré superlattices feature a magnification effect that they respond sensitively to both the extrinsic mechanical perturbations and intrinsic atomic reconstructions. Here, using scanning tunneling microscopy and spectroscopy, we observe that long-wavelength WS₂ superlattices are reconstructed into various moiré morphologies, ranging from regular hexagons to heavily deformed ones. We show that a dedicated interplay between the extrinsic nonuniform heterostrain and the intrinsic atomic reconstruction is responsible for this interesting moiré structure evolution. Importantly, the interplay between these two factors also introduces a local inhomogeneous intralayer strain within a moiré. Contrary to the commonly reported electronic modulation that occurred at the valence band edge due to interlayer hybridization, we find that this local intralayer strain induces a strong modulation at K point of the conduction band, reaching up to 300 meV in the heavily deformed moiré. Our microscopic explorations provide valuable information in understanding the intriguing physics in TMD moirés.

Excitons in semiconductor moiré superlattices

Semiconductor moiré superlattices represent a rapidly developing area of engineered photonic materials and a new platform to explore correlated electron states and quantum simulation. In this Review, we briefly introduce early experiments that identified new exciton resonances in transition metal dichalcogenide heterobilayers and discuss several topics including two types of transition metal dichalcogenide moiré superlattice, new optical selection rules, early evidence of moiré excitons, and how the resonant energy, dynamics and diffusion properties of moiré excitons can be controlled via the twist angle. To interpret optical spectra, it is important to measure the energy modulation within a moiré supercell. In this context, we describe a few scanning tunnelling microscopy experiments that measure the moiré potential landscape directly. Finally, we review a few recent experiments that applied excitonic optical spectroscopy to probe correlated electron phenomena in transition metal dichalcogenide moiré superlattices.

Anisotropic Interlayer Force Field for Transition Metal Dichalcogenides: The Case of Molybdenum Disulfide

An anisotropic interlayer force field that describes the interlayer interactions in molybdenum disulfide (MoS2) is presented. The force field is benchmarked against density functional theory calculations for both bilayer and bulk systems within the Heyd-Scuseria-Ernzerhof hybrid density functional approximation, augmented by a nonlocal many-body dispersion treatment of long-range correlation. The parametrization yields good agreement with the reference calculations of binding energy curves and sliding potential energy surfaces for both bilayer and bulk configurations. Benchmark calculations for the phonon spectra of bulk MoS2 provide good agreement with experimental data, and the calculated bulk modulus falls in the lower part of experimentally measured values. This indicates the accuracy of the interlayer force field near equilibrium. Under external pressures up to 20 GPa, the developed force field provides a good description of compression curves. At higher pressures, deviations from experimental data grow, signifying the validity range of the developed force field.

Charge-order-enhanced capacitance in semiconductor moiré superlattices

Van der Waals moiré materials have emerged as a highly controllable platform to study electronic correlation phenomena^1-17. Robust correlated insulating states have recently been discovered at both integer and fractional filling factors of semiconductor moiré systems^10-17. In this study we explored the thermodynamic properties of these states by measuring the gate capacitance of MoSe₂/WS₂ moiré superlattices. We observed a series of incompressible states for filling factors 0-8 and anomalously large capacitance in the intervening compressible regions. The anomalously large capacitance, which was nearly 60% above the device's geometrical capacitance, was most pronounced at small filling factors, below the melting temperature of the charge-ordered states, and for small sample-gate separation. It is a manifestation of the device-geometry-dependent Coulomb interaction between electrons and phase mixing of the charge-ordered states. Based on these results, we were able to extract the thermodynamic gap of the correlated insulating states and the device's electronic entropy and specific heat capacity. Our findings establish capacitance as a powerful probe of the correlated states in semiconductor moiré systems and demonstrate control of these states via sample-gate coupling.

Excitonic and Valley-Polarization Signatures of Fractional Correlated Electronic Phases in a WSe_{2}/WS_{2} Moiré Superlattice

We have measured the reflectance contrast, photoluminescence, and valley polarization of a WSe_{2}/WS_{2} heterobilayer moiré superlattice at gate-tunable charge density. We observe absorption modulation of three intralayer moiré excitons at filling factors ν=1/3 and 2/3. We also observe luminescence modulation of interlayer trions at around a dozen fractional filling factors, including ν=-3/2, 1/4, 1/3, 2/5, 2/3, 6/7, 5/3. Remarkably, the valley polarization of interlayer trions is suppressed at some fractional fillings. These results demonstrate that electron crystallization can modulate the absorption, emission, and valley dynamics of the excitonic states in a moiré superlattice.

Strong interaction between interlayer excitons and correlated electrons in WSe2/WS2 moiré superlattice

Heterobilayers of transition metal dichalcogenides (TMDCs) can form a moiré superlattice with flat minibands, which enables strong electron interaction and leads to various fascinating correlated states. These heterobilayers also host interlayer excitons in a type-II band alignment, in which optically excited electrons and holes reside on different layers but remain bound by the Coulomb interaction. Here we explore the unique setting of interlayer excitons interacting with strongly correlated electrons, and we show that the photoluminescence (PL) of interlayer excitons sensitively signals the onset of various correlated insulating states as the band filling is varied. When the system is in one of such states, the PL of interlayer excitons is relatively amplified at increased optical excitation power due to reduced mobility, and the valley polarization of interlayer excitons is enhanced. The moiré superlattice of the TMDC heterobilayer presents an exciting platform to engineer interlayer excitons through the periodic correlated electron states.

Imaging Dual-Moiré Lattices in Twisted Bilayer Graphene Aligned on Hexagonal Boron Nitride Using Microwave Impedance Microscopy

Moiré superlattices (MSLs) formed in van der Waals materials have become a promising platform to realize novel two-dimensional electronic states. Angle-aligned trilayer structures can form two sets of MSLs which could potentially interfere. In this work, we directly image the moiré patterns in both monolayer and twisted bilayer graphene aligned on hexagonal boron nitride (hBN), using combined scanning microwave impedance microscopy and conductive atomic force microscopy. Correlation of the two techniques reveals the contrast mechanism for the achieved ultrahigh spatial resolution (<2 nm). We observe two sets of MSLs with different periodicities in the trilayer stack. The smaller MSL breaks the 6-fold rotational symmetry and exhibits abrupt discontinuities at the boundaries of the larger MSL. Using a rigid atomic-stacking model, we demonstrate that the hBN layer considerably modifies the MSL of twisted bilayer graphene. We further analyze its effect on the reciprocal space spectrum of the dual-moiré system.

Ultrahigh-resolution scanning microwave impedance microscopy of moiré lattices and superstructures

Two-dimensional heterostructures composed of layers with slightly different lattice vectors exhibit new periodic structure known as moiré lattices, which, in turn, can support novel correlated and topological phenomena. Moreover, moiré superstructures can emerge from multiple misaligned moiré lattices or inhomogeneous strain distributions, offering additional degrees of freedom in tailoring electronic structure. High-resolution imaging of the moiré lattices and superstructures is critical for understanding the emerging physics. Here, we report the imaging of moiré lattices and superstructures in graphene-based samples under ambient conditions using an ultrahigh-resolution implementation of scanning microwave impedance microscopy. Although the probe tip has a gross radius of ~100 nm, spatial resolution better than 5 nm is achieved, which allows direct visualization of the structural details in moiré lattices and the composite super-moiré. We also demonstrate artificial synthesis of novel superstructures, including the Kagome moiré arising from the interplay between different layers.