Excellent thermoelectric performance in the out-of-layer $n$-doped SnSe has been observed experimentally [Chang et al., Science 360, 778 (2018)]. However, a first-principles investigation of the dominant scattering mechanisms governing all thermoelectric transport properties is lacking. In the present paper, by applying extensive first-principles calculations of electron-phonon coupling associated with parameterized calculation of the scattering by ionized impurities, we investigate the reasons behind the superior figure of merit as well as the enhancement of $zT$ above 600 K in $n$-doped out-of-layer SnSe, as compared to $p$-doped SnSe with similar carrier densities. For the $n$-doped case, the relaxation time is dominated by ionized impurity scattering and increases with temperature, a feature that maintains the power factor at high values at higher temperatures and simultaneously causes the carrier thermal conductivity at zero electric current $\left({\kappa }_{\mathrm{el}}\right)$ to decrease faster for higher temperatures, leading to an ultrahigh-$zT=3.1$ at 807 K. We rationalize the roles played by ${\kappa }_{\mathrm{el}}$ and ${\kappa }^0$ (the thermal conductivity due to carrier transport under isoelectrochemical conditions) in the determination of $zT$. Our results show the ratio between ${\kappa }^0$ and the lattice thermal conductivity indeed corresponds to the upper limit for $zT$, whereas the difference between calculated $zT$ and the upper limit is proportional to ${\kappa }_{\mathrm{el}}$.

The interlayer coupling in van der Waals heterostructures governs a variety of optical and electronic properties. The intrinsic dipole moment of Janus transition metal dichalcogenides (TMDs) offers a simple and versatile approach to tune the interlayer interactions. In this work, we demonstrate how the van der Waals interlayer coupling and charge transfer of Janus MoSSe/MoS₂ heterobilayers can be tuned by the twist angle and interface composition. Specifically, the Janus heterostructures with a sulfur/sulfur (S/S) interface display stronger interlayer coupling than the heterostructures with a selenium/sulfur (Se/S) interface as shown by the low-frequency Raman modes. The differences in interlayer interactions are explained by the interlayer distance computed by density-functional theory (DFT). More intriguingly, the built-in electric field contributed by the charge density redistribution and interlayer coupling also play important roles in the interfacial charge transfer. Namely, the S/S and Se/S interfaces exhibit different levels of photoluminescence (PL) quenching of MoS₂ A exciton, suggesting enhanced and reduced charge transfer at the S/S and Se/S interface, respectively. Our work demonstrates how the asymmetry of Janus TMDs can be used to tailor the interfacial interactions in van der Waals heterostructures.

The coupling between electrons and phonons in solids plays a central role in describing many phenomena, including superconductivity and thermoelecric transport. Calculations of this coupling are exceedingly demanding as they necessitate integrations over both the electron and phonon momenta, both of which span the Brillouin zone of the crystal, independently. We present here an ab initio method for efficiently calculating electron-phonon mediated transport properties by dramatically accelerating the computation of the double integrals with a dual interpolation technique that combines maximally localized Wannier functions with symmetry-adapted plane waves. The performance gain in relation to the current state-of-the-art Wannier-Fourier interpolation is approximately \(2n_s \times M\) , where \(n_s \) is the number of crystal symmetry operations and \(M\), a number in the range 5 - 60, governs the expansion in star functions. We demonstrate with several examples how our method performs some ab initio calculations involving electron-phonon interactions.

The Kondo insulator SmB₆ has emerged as a primary candidate for exotic quantum phases, due to the predicted formation of strongly correlated, low-velocity topological surface states and corresponding high Fermi-level density of states. However, measurements of the surface-state velocity in SmB₆ differ by orders of magnitude, depending on the experimental technique used. Here we reconcile two techniques, scanning tunneling microscopy (STM) and angle-resolved photoemission spectroscopy (ARPES), by accounting for surface band bending on polar terminations. Using spatially resolved scanning tunneling spectroscopy, we measure a band shift of ∼20 meV between full-Sm and half-Sm terminations, in qualitative agreement with our density-functional theory calculations of the surface charge density. Furthermore, we reproduce the apparent high-velocity surface states reported by ARPES by simulating their observed spectral function as an equal-weight average over the two band-shifted domains that we image by STM. Our results highlight the necessity of local measurements to address inhomogeneously terminated surfaces or fabrication techniques to achieve uniform termination for meaningful large-area surface measurements of polar crystals such as SmB₆.

Quantum confinement endows two-dimensional (2D) layered materials with exceptional physics and novel properties compared to their bulk counterparts. Although certain two- and few-layer configurations of graphene have been realized and studied, a systematic investigation of the properties of arbitrarily layered graphene assemblies is still lacking. We introduce theoretical concepts and methods for the processing of materials information, and as a case study, apply them to investigate the electronic structure of multi-layer graphene-based assemblies in a high-throughput fashion. We provide a critical discussion of patterns and trends in tight binding band structures and we identify specific layered assemblies using low-dispersion electronic bands as indicators of potentially interesting physics like strongly correlated behavior. A combination of data-driven models for visualization and prediction is used to intelligently explore the materials space. This work more generally aims to increase confidence in the combined use of physics-based and data-driven modeling for the systematic refinement of knowledge about 2D layered materials, with implications for the development of novel quantum devices.

Intercalation of lithium atoms between layers of 2D materials can alter their atomic and electronic structure. We investigate effects of Li intercalation in twisted bilayers of the transition metal dichalcogenide MoS₂ through first-principles calculations, tight-binding parameterization based on the Wannier transformation, and analysis of moiré band structures through an effective continuum model. The energetic stability of different intercalation sites for Li between layers of MoS₂ are classified according to the local coordination type and the number of vertically aligned Mo atoms, suggesting that the Li atoms will cluster in certain regions of the moiré superlattice. The proximity of a Li atom has a dramatic influence on the interlayer interaction between sulfur atoms, deepening the moiré potential well and leading to better isolation of the flat bands in the energy spectrum. These results point to the usefulness for the use of chemical intercalation as a powerful means for controlling moiré flat-band physics in 2D semiconductors.

We investigate the effects of lithium intercalation in twisted bilayers of graphene, using first-principles electronic structure calculations. To model this system we employ commensurate supercells that correspond to twist angles of $7.{34}^{\circ }$ and $2.{45}^{\circ }$. From the energetics of lithium absorption we demonstrate that for low Li concentration the intercalants cluster in the AA regions with double the density of a uniform distribution. The charge donated by the Li atoms to the graphene layers results in modifications to the band structure that can be qualitatively captured using a continuum model with modified interlayer couplings in a region of parameter space that has yet to be explored either experimentally or theoretically. Thus, the combination of intercalation and twisted layers simultaneously provides the means for spatial control over material properties and an additional knob with which to tune moiré physics in twisted bilayers of graphene, with potential applications ranging from energy storage and conversion to quantum information.

Single-layer transition metal dichalcogenides (TMDCs) can adopt two distinct structures corresponding to different coordination of the metal atoms. TMDCs adopting the T-type structure exhibit a rich and diverse set of phenomena, including charge density waves (CDWs) in a √13 × √13 supercell pattern in TaS₂ and TaSe₂, and a possible excitonic insulating phase in TiSe₂ . These properties make the T-TMDCs desirable components of layered heterostructure devices. In order to predict the emergent properties of combinations of different layered materials, one needs simple and accurate models for the constituent layers which can take into account potential effects of lattice mismatch, relaxation, strain, and structural distortion. Previous studies have developed ab initio tight-binding Hamiltonians for H-type TMDCs [S. Fang et al., Phys. Rev. B 98, 075106
(2018)]. Here we extend this work to include T-type TMDCs. We demonstrate the capabilities and limitations of our model using three example systems: a one-dimensional sinusoidal ripple, which represents a longitudinal acoustic phonon; the 2 × 2 CDW in TiSe₂; and the √13 × √13 CDW in TaS₂. Using the technique of band unfolding we compare the electronic structure of the distorted crystals to the pristine band structure and find our tight-binding model reproduces many features revealed by direct density functional theory calculations, provided the magnitude of the distortions remains in the linear regime. This model of the strain response of single layers is a necessary ingredient for the construction of models of van der Waals heterostructures with multiple layers, because the deformation and strain from mechanical relaxations in a twisted bilayer have important effects on the
electronic structure.

Following the recent isolation of monolayer CrI3 (ref. 1), many more two-dimensional van der Waals magnetic materials have been isolated2,3,4,5,6,7,8,9,10,11,12. Their incorporation in van der Waals heterostructures offers a new platform for spintronics5,6,7,8,9, proximity magnetism13 and quantum spin liquids14. A primary question in this field is how exfoliating crystals to the few-layer limit influences their magnetism. Studies of CrI3 have shown a different magnetic ground state for ultrathin exfoliated films1,5,6 compared with the bulk, but the origin is not yet understood. Here, we use electron tunnelling through few-layer crystals of the layered antiferromagnetic insulator CrCl3 to probe its magnetic order and find a tenfold enhancement of the interlayer exchange compared with bulk crystals. Moreover, temperature- and polarization-dependent Raman spectroscopy reveals that the crystallographic phase transition of bulk crystals does not occur in exfoliated films. This results in a different low-temperature stacking order and, we hypothesize, increased interlayer exchange. Our study provides insight into the connection between stacking order and interlayer interactions in two-dimensional magnets, which may be relevant for correlating stacking faults and mechanical deformations with the magnetic ground states of other more exotic layered magnets such as RuCl3 (ref. 14).

Molecular-scale manipulation of electronic and ionic charge accumulation in materials is the backbone of electrochemical energy storage^1,2,3,4. Layered van der Waals (vdW) crystals are a diverse family of materials into which mobile ions can electrochemically intercalate into the interlamellar gaps of the host atomic lattice^5,6. The structural diversity of such materials enables the interfacial properties of composites to be optimized to improve ion intercalation for energy storage and electronic devices^{7,8,9,10,11,12}. However, the ability of heterolayers to modify intercalation reactions, and their role at the atomic level, are yet to be elucidated. Here we demonstrate the electrointercalation of lithium at the level of individual atomic interfaces of dissimilar vdW layers. Electrochemical devices based on vdW heterostructures¹³ of stacked hexagonal boron nitride, graphene and molybdenum dichalcogenide (MoX₂; X = S, Se) layers are constructed. We use transmission electron microscopy, in situ magnetoresistance and optical spectroscopy techniques, as well as low-temperature quantum magneto-oscillation measurements and ab initio calculations, to resolve the intermediate stages of lithium intercalation at heterointerfaces. The formation of vdW heterointerfaces between graphene and MoX₂ results in a more than tenfold greater accumulation of charge in MoX₂ when compared to MoX₂/MoX₂ homointerfaces, while enforcing a more negative intercalation potential than that of bulk MoX₂ by at least 0.5 V. Beyond energy storage, our combined experimental and computational methodology for manipulating and characterizing the electrochemical behaviour of layered systems opens new pathways to control the charge density in two-dimensional electronic and optoelectronic devices.