Phonon‐Induced Markovian and Non‐Markovian Effects on Absorption Spectra of Moiré Excitons in Twisted Transition Metal Dichalcogenide Bilayers

Moiré is More: Access to New Properties of Two-Dimensional Layered Materials

Excitons in twisted bilayers of transition metal dichalcogenides have strongly modified dispersion relations due to the formation of periodic moiré potentials. The strong coupling to a light field in an optical cavity leads to the appearance of moiré polaritons. In this paper, we derive a theoretical model for the linear absorption spectrum of the coupled moiré polariton–phonon system based on the time-convolutionless (TCL) approach. Results obtained by numerically solving the TCL equation are compared to those obtained in the Markovian limit and from a perturbative treatment of non-Markovian corrections. A key quantity for the interpretation of the findings is the generalized phonon spectral density. We discuss the phonon impact on the spectrum for realistic moiré exciton dispersions by varying twist angle and temperature. Key features introduced by the coupling to phonons are broadenings and energy shifts of the upper and lower polariton peak and the appearance of phonon sidebands between them. We analyze these features with respect to the role of Markovian and non-Markovian effects and find that they strongly depend on the twist angle. We can distinguish between the regimes of large, small, and intermediate twist angles. In the latter phonon effects are particularly pronounced due to dominating phonon transitions into regions which are characterized by van Hove singularities in the density of states.

Moiré superlattices (MSLs) in twisted two-dimensional van der Waals materials feature twist-angle-dependent crystal symmetry and strong optical nonlinearities. By adjusting the twist angle in bilayer van der Waals materials, the second-harmonic generation (SHG) can be controlled. Here, we focus on exploring the electronic and SHG properties of MSLs in 2D bilayer transition metal dichalcogenides (TMDs) with different twist angles through first-principles calculations. We constructed MSL structures of five TMD materials, including three single-phase materials (MoS2, WS2, and MoSe2) and two heterojunctions (MoS2/MoSe2 and MoS2/WS2) with twist angles of 9.4°, 13.2°, 21.8°, 32.2°, and 42.1° without lattice mismatch. Our findings demonstrate a consistent variation in the SHG susceptibility among different TMD MSLs as a response to twist-angle changes. The underlying reason for the twist-angle dependence of SHG is that the twist angle regulates the interlayer coupling strength, affecting the optical band gap of MSLs and subsequently tuning the SHG susceptibility. Through a comparison of the static SHG susceptibility values, we identified the twist angle of 9.4° as the configuration that yields the highest SHG susceptibility (e.g. 358.5 pm V-1 for the 9.4° MoSe2 MSL). This value is even twice that of the monolayer (173.3 pm V-1 for monolayer MoSe2) and AA'-stacked bilayer structures (139.8 pm V-1 for AA' MoSe2). This high SHG susceptibility is attributed to the strong interlayer coupling in the 9.4° MSL, which enhances the valence band energy (contributed by the antibonding orbitals of chalcogen-pz and transition metal-dz2) and consequently leads to a small optical band gap, thus improving the optical transitions. The findings of this study provide a straightforward way to improve the SHG performance of bilayer TMDs and also throw light on the sensitive relationship between the twist angle, band structure and SHG properties of TMD MSLs.

Layered two-dimensional (2D) materials exhibit unique properties not found in their individual forms, opening new avenues for material exploration. This study examines MX2 transition metal dichalcogenides (TMDCs), where M is Mo or W, and X is S, Se or Te. These materials are foundational for the creation of hetero- and homo-bilayers with various stacking configurations. Recent interest has focused on twisted homogeneous bilayers, as critical twist angles can significantly alter material properties. This work highlights MX2 TMDC bilayers with twisted angles that form Moiré patterns, essential to understanding the behaviors of these materials. We performed first-principles calculations using Density Functional Theory (DFT) with range-separated hybrid functionals on 30 combinations of six MX2 materials with two stacking configurations, revealing that the building blocks and stacking arrangements influence the stability of the heterostructure and the band gap energy (E g). In particular, the MoTe2/WSe2 heterostructure, shifted by 60°, exhibits a direct band gap, indicating potential for novel applications. Our investigation of homobilayers included fully relaxed and low-strain scenarios, examining various stacking styles and twisting angles. Under low-strain conditions, MoS2, WS2, and WSe2 can exhibit direct or indirect band gaps at specific twist angles. Additionally, MoS2 can transition between semiconductor and conductor states, showcasing diverse electronic properties. Critical twist angles, specifically 17.9° and its corresponding angles (42.1°, 77.9° and 102.1°), in twisted WS2 and WSe2 bilayers create symmetric Moiré patterns, leading to direct band gaps. The magnitude of the band gap energy can be tuned by varying the twist angles, which also affect the flatness of the electronic band. Like conventional stacking, most twisted TMDC bilayers exhibit favorable interlayer interactions but with more tailorable characteristics. Using heterostructures and controlled twist angles is a powerful approach in material engineering, enabling the manipulation of various electronic behaviors in advanced materials.

Twisted bilayers of transition metal dichalcogenides (TMDC) form moiré superlattices hosting localized excitons and enabling access to Mott-Hubbard physics by the formation of moiré minibands. However, their electronic properties are highly sensitive to twist angle fluctuations, disorder, and lattice reconstructions, making fast and noninvasive local characterization challenging. Here, we correlate twist angle variations in twisted WSe2 bilayers across micrometer length scales using lateral force microscopy (LFM) and micro-Raman spectroscopy. We reveal twist angle variations exceeding 1° across optically and transport-relevant length scales. For twist angles in the range 3° < α < 12°, distinct Raman signatures from optical moiré phonons enable high-precision twist angle determination with sub-micrometer spatial resolution under ambient conditions. Our approach achieves a precision better than ± 0.3° particularly in the low-twist angle regime relevant for correlation physics and is applicable to hBN-encapsulated heterostructures, establishing micro-Raman spectroscopy as a rapid, noninvasive tool for twist angle screening.

The twist angle in transition metal dichalcogenide heterobilayers is a compelling degree of freedom that determines electron correlations and the period of lateral confinement of moir\'e excitons. Here we perform polarization-resolved second harmonic generation (SHG) spectroscopy of $\mathrm{Mo}{\mathrm{S}}_{2}/\mathrm{W}{\mathrm{Se}}_{2}$ heterostructures. We demonstrate that by choosing suitable laser energies the twist angle between two monolayers can be measured directly on the assembled heterostructure. We show that the amplitude and polarization of the SHG signal from the heterostructure are determined by the twist angle between the layers and exciton resonances at the SH energy. For heterostructures with close to zero twist angle, we observe changes of exciton resonance energies and the appearance of new resonances in the linear and nonlinear susceptibilities.

Doping in transition metal dichalcogenide (TMD) has received extensive attention for its prospect in the application of photoelectric devices. Currently researchers focus on the doping ability and doping distribution in monolayer TMD and have obtained a series of achievements. Bilayer TMD has more excellent properties compared with monolayer TMD. Moreover, bilayer TMD with different stacking structures presents varying performance due to the difference in interlayer coupling. Herein, this work focuses on doping ability of dopants in different bilayer stacking structures that has not been studied yet. Results of this work show that the doping ability of V atoms in bilayer AA' and AB stacked WS2 is different, and the doping concentration of V atoms in AB stacked WS2 is higher than in AA' stacked WS2. Moreover, dopants from top and bottom layer can be distinguished by scanning transmission electron microscopy (STEM)image. Density functional theory (DFT) calculation further confirms the doping rule. This study reveals the mechanism of the different doping ability caused by stacking structures in bilayer TMD and lays a foundation for further preparation of controllable-doping bilayer TMD materials.

The electron-electron interaction is the origin of many interesting phenomena in condensed matter. These phenomena post challenges to theoretical physics and can lead to important future applications. Transition metal dichalcogenide heterostructures provide excellent platforms to study these phenomena because of the two-dimensional nature, large effective mass and tunable bandwidth with moiré potential. As electron bands become narrower such that the Coulomb interaction energy becomes comparable to the bandwidth, interactions can drive new quantum phases. This dissertation describes the realization of this platform and probing of correlated phenomena with low- temperature transport measurements.\n\n As the first step, the electrical contact problem of few-layer transition metal dichalcogenides, which prohibits low-temperature transport measurements, needs to be solved. Two different contact schemes have been used to attack this problem. For p-type transition metal dichalcogenide, prepatterned platinum is used to bottom contact transition metal dichalcogenides. This method prevents channel from deterioration due to electron beam evaporation and the high workfunction platinum can place the Fermi level underneath the material valence band. Alternatively, for n-type transition metal dichalcogenides, a single layer of boron nitride is put on transition metal dichalcogenide before cobalt evaporation. This way, the boron nitride layer protects the transition metal dichalcogenide from the process of evaporation and can decrease the work function of cobalt thus putting Fermi level above the conduction band. With these contact methods, Ohmic contacts can be achieved at cryogenic temperature and probing the transition metal dichalcogenide heterostructures with transport measurements become accessible.\n\n Then, the magnetotransport properties of monolayer molybdenum disulphide and bilayer tungsten diselenide encapsulated with boron nitride with graphite dual-gate were measured. There are three unique features underlie this two dimensional electron gas system. First, the system is strong correlated. The Landau level spectrum reveals strong correlated signatures, such as enhanced spin-orbit coupling splitting and enhanced effective g-factor. Second, the longitudinal resistance/conductance at half-filling of Landau levels are found to depend on the spin orientation. The minority spin Landau level become totally localized at higher magnetic field. Third, in bilayer device the two layers are weak coupled and can be independently controlled by two gates. All this features establish transition metal dichalcogenide a unique platform for studying correlated physics.\n\n Finally, to achieve higher level of correlation, two layers of tungsten diselenide are stacked together with a small twist angle. With the help of moiré potential and layer hybridization, the bandwidth can be continuously tuned by the twist angle. In the range of 3 degree to 5.1degree, with moderate correlation strength, correlated insulating states are shown at half-filled flatband and are highly tunable with vertical electric field.

Twisted 2D bilayer transition metal dichalcogenides (TMDs) heterostructures exhibit rich physical properties due to the interaction of interlayer coupling and moiré superlattice effects. However, the influence of interlayer coupling changes induced by the twist angle on various TMDs properties still requires further exploration. To systematically investigate how the twist angle influences the structural, electronic and optical properties of TMDs, density functional theory (DFT) is used to examine MoS2/WS2 superlattice heterostructures. Compared with that of the 2H stack, the interlayer coupling effect is weakened in the 21.79° and particularly 38.21° stacked heterostructures. A larger twist angle promotes an indirect‐to‐direct bandgap transition trend. Additionally, the twist angle can cause interlayer charge redistribution, which varies with the moiré pattern. Moreover, spin‒orbit coupling (SOC) causes a redshift by reducing the bandgap in the absorption spectra, and the twist angle suppresses interlayer direct transitions in the 𝜥 valley and alters the Raman and infrared spectra, with low‐frequency Raman modes providing a powerful tool for characterizing changes in interlayer coupling. These findings highlight the critical role of the twist angle in tuning the properties of TMDs heterostructures, with promising implications for optoelectronic and valleytronic applications.

Overlaying two two-dimensional (2D) lattices with different periodicities or a relative twist angle gives rise to a larger (quasi-) periodic lattice called a moiré pattern. In van der Waals (vdW) heterostructures, the moiré pattern has recently been shown to display interesting novel physical phenomena. For instance, twisted bilayer graphene near the “magic angle” of 1.1° hosts flat electronic bands and strongly correlated states such as unconventional superconductivity [1, 2]. On the other hand, the moiré pattern has been found to both localize and tune interlayer excitons in transition metal dichalcogenides (TMDCs) heterostructures with small twist angle [3-5]. Such moiré heterostructures are generally produced by mechanical exfoliation and stacking to precisely control the twist angle and moiré periodicity. However, this laborious method leads to interfacial contamination and twist angle inhomogeneities and is inherently not scalable. In principle, direct growth of van der Waals heterostructures can overcome these limitations. However, due to energetic considerations, control over the twist angle, and therefore the moiré lattice, has not yet been achieved. Herein, using TMDCs as a model system, we demonstrate the scalable growth of moiré heterostructures with continuously tunable periodicity. By controlling the substitutional alloying of larger atoms within the same group of the periodic table (S, Se), we precisely engineer the lattice parameters of the 2D layers and the moiré period. The grown moiré heterostructures have lateral size up to 200 μm and are shown to host moiré excitons. These results lay the groundwork for the integration of moiré heterostructures in emerging quantum technologies.[1] Cao, Y.; Fatemi, V.; Fang, S.; Watanabe, K.; Taniguchi, T.; Kaxiras, E.; Jarillo-Herrero, P. Nature 2018, 556 (7699), 43-50.[2] Cao, Y., Fatemi, V., Demir, A., Fang, S., Tomarken, S. L., Luo, J. Y., ... & Jarillo-Herrero, P. 2018. Nature, 556 (7699), 80-84.[3] Yu, H.; Liu, G.-B.; Tang, J.; Xu, X.; Yao, W. (2017). Science Advances 2017. 3 (11), e1701696.[4] Seyler, K. L.; Rivera, P.; Yu, H.; Wilson, N. P.; Ray, E. L.; Mandrus, D. G.; Yan, J.; Yao, W.; Xu, X. Nature 2019, 567 (7746), 66.[5] Jin, C.; Regan, E. C.; Yan, A.; Utama, M. I. B.; Wang, D.; Zhao, S.; Qin, Y.; Yang, S.; Zheng, Z.; Shi, S.; et al. Nature 2019, 567 (7746), 76.

This letter evaluates and analyzes the impacts of random variations on cell stability and write-ability of low-voltage SRAMs using monolayer and bilayer transition metal dichalcogenide (TMD) devices based on ITRS 2028 (5.9 nm) node with the aid of atomistic TCAD mixed-mode simulations. Our study indicates that, for 6T SRAM, the monolayer/bilayer TMD devices may fail to provide the $6\sigma $ yield requirement for read static noise margin (RSNM) due to severe metal-gate work function variation in spite of their excellent electrostatics, and hence circuit techniques, such as bootstrapped dynamic power rails or the standard 8T cell, are needed. Besides, $R_{\mathrm {SD}}$ as a major concern of TMDs should be less of an issue for near-/sub-threshold SRAMs for ultra low-power applications. For the standard 8T cell structure, the RSNMs of both monolayer and bilayer 8T SRAMs improve significantly, and the bilayer 8T SRAM exhibits better write static noise margin (WSNM). In addition, write-assist techniques (including negative bit-line, boosted word-line, and lower cell supply) for improving WSNM are examined and shown to be more effective for monolayer 8T SRAMs than the bilayer counterparts.

Several numerical studies have shown that the electronic properties of twisted bilayers of graphene (TBLG) and transition metal dichalcogenides (TMDs) are tunable by strain engineering of the stacking layers. In particular, the flatness of the low-energy moir\'e bands of the rigid and the relaxed TBLG was found to be, substantially, sensitive to the strain. However, to the best of our knowledge, there are no full analytical calculations of the effect of strain on such bands. We derive, based on the continuum model of moir\'e flat bands, the low-energy Hamiltonian of twisted homobilayers of graphene and TMDs under strain at small twist angles. We obtain the analytical expressions of the strain-renormalized Dirac velocities and explain the role of strain in the emergence of the flat bands. We discuss how strain could correct the twist angles and bring them closer to the magic angle ${\ensuremath{\theta}}_{m}=1.{05}^{\ensuremath{\circ}}$ of TBLG and how it may reduce the widths of the lowest-energy bands at charge neutrality of the twisted homobilayer of TMDs. The analytical results are compared with numerical and experimental findings and also with our numerical calculations based on the continuum model.

Twistronic van der Waals heterostrutures offer exciting opportunities for engineering optoelectronic properties of nanomaterials, in particular, due to the formation of moiré superlattice structures. In twisted bilayers of transition metal dichalcogenides moiré superlattice effects are additionally enriched by the lack of inversion symmetry in each monolayer unit cell. Here, we use multiscale modelling to establish a rich variety of confinement conditions for electrons, holes and layer-indirect excitons in twistronic WX2/MoX2 bilayers (X = S,Se). Such trapping of charge carriers and excitons is caused by ferroelectric (interlayer) polarisation and piezoelectric effects generated by the reconstruction of twistronic bilayers into preferential stacking domains separated by domain wall networks. For almost aligned bilayers with anti-parallel (AP) orientation of WX2 and MoX2 unit cells, we find that upon lattice relaxation piezoelectric potential modulation traps holes and electrons in the opposite corners—WMo and XX (tungsten over molybdenum versus overlaying chalcogens)—of hexagonal-shaped 2H (simultaneously WX and XMo) stacking domains, swapping their positions at a twist angle 0.2∘. This crossover happens at such small angles (set by a very small lattice mismatch between WX2 and MoX2) that would impose an alignment accuracy and homogeneity better than 0.1∘ for achieving reproducibility of electronic characteristics of such heterostructures. At the same time, for all angles, XX corners provide 30 meV deep traps for the interlayer excitons. In bilayers with parallel (P) orientation of WX2 and MoX2 unit cells, band edges for both electrons and holes appear in triangular domains, where WX2 chalcogens set over MoX2 molybdenums. We find that, due to a weak ferroelectric polarisation, these triangular domains act as 130 meV deep quantum boxes for interlayer excitons for twist angles , shifting towards XX stacking sites of the domain wall network at larger twist angles.

Many of the intriguing properties of bilayer graphene (BLG) are related to interlayer electronic coupling. Since this coupling is sensitive to an applied electric field perpendicular to the layers, we develop a strategy for determining interlayer coupling by decomposing the total electric dipole polarizability, which measures the response of electrons to applied fields, into site-specific contributions and consequently the intralayer and interlayer components. The interlayer polarizability is evaluated from field-induced electron density variations computed with a first-principles approach for twisted BLG quantum dots (QDs). Changes in interlayer polarizability dominate the polarizability variation with twist angle. In addition to the well-recognized strong coupling in the Bernal stackings, enhanced coupling is revealed for the structures at small and size-dependent twist angles when AB stacking first appears in the outermost shell of the QD. The values of these magic angles depend on the QD size. This paper not only provides an approach for measuring interlayer coupling strength but also indicates the existence of strong interlayer coupling even at small twist angles, which could be important for understanding the properties of twisted BLG.

We study the optical transport properties of the monolayer transition metal dichalcogenides (TMDCs) such as ${\mathrm{MoS}}_{2}$, ${\mathrm{WS}}_{2}$, ${\mathrm{MoSe}}_{2}$, and ${\mathrm{WSe}}_{2}$ in the presence of a magnetic field. The TMDCs band structures are obtained and discussed by using the effective massive Dirac model, in which the spin and valley Zeeman effects as well as an external electric field are included. The magneto-optical absorption coefficient (MOAC) is derived as a function of absorbed photon energy when the carriers are scattered by random impurities combined with the intrinsic acoustic and optical phonons in TMDCs and the surface optical (SO) phonons of substrates. Our result shows that the spin-splitting feature appeared in all four TMDC materials. The combination of strong spin-orbit coupling (SOC) and Zeeman fields has doubled the Landau levels but has not changed the energy gap of the TMDCs monolayer, which can be controlled by the electric field. Because of their strong SOC effect, the absorption spectrum in monolayer TMDCs is separated into two separate peaks caused by spin up and down. At the low temperature, the MOAC intensity via impurity scattering is the biggest followed by that of the SO phonons while the intrinsic acoustic and optical phonon scatterings display the smallest. For the monolayer TMDCs on substrates, ${\mathrm{SiO}}_{2}$ always shows its superiority in comparison with the others. Among the four TMDC materials, ${\mathrm{MoSe}}_{2}$ shows the biggest MOAC intensity, while ${\mathrm{WS}}_{2}$ has the biggest value of the absorbed photon energy. The full-width at half-maximum (FWHM) via impurity scattering achieves its highest value in ${\mathrm{WS}}_{2}$, while this occurs in ${\mathrm{MoSe}}_{2}$ and ${\mathrm{MoS}}_{2}$ via intrinsic acoustic and optical phonon scatterings, respectively. Our estimation of mobility from FWHM gives good agreement with the experimental results in ${\mathrm{WS}}_{2}$.