Indirect bandgap of hBN-encapsulated monolayer MoS2

We present measurements of temperature dependence of photoluminescence intensity from monolayer MoS2 encapsulated by hexagonal boron nitride (hBN) flakes. The obtained temperature dependence shows an opposite trend to that of previously observed in a monolayer MoS2 on a SiO2 substrate. Ab-initio bandstructure calculations have revealed that monolayer MoS2 encapsulated by hBN flakes have no longer a direct-gap semiconductor but an indirect-gap semiconductor. This is caused by orbital hybridization between MoS2 and hBN, which leads to upward shift of gamma-valley of MoS2. This work shows an important implication that the hBN-encapsulated structures used to address intrinsic properties of two-dimensional crystals can alter basic properties encapsulated materials.

Recently appearing two-dimensional (2D) materials, including graphene, phosphorene, transition metal dichalcogenides (TMDs), etc., have opened up a new field in the science of low-dimensional materials [1][2][3][4][5][6] . TMDs, in particular, provide a wide variety of 2D layered materials with various compositions and electronic structures, giving us a widespread and excellent field for exploration of physics in the realm of the 2D world. In contrast to graphene, semiconducting 2D-TMDs can have a sizable bandgap up to ~2 eV, which offers an opportunity to explore optical responses at the 2D limit and develop TMD-based nanoelectronic devices 5,7,8 .
Furthermore, 2D-TMDs afford vertical or lateral heterostructures, whose electronic structure and physical properties can be tuned through selecting the combination and stacking angles of each layer. Coupled with the possibility arising from the valley degree of freedom 9,10 , TMDs have been yielding new perspectives and attracting a wide range of research interests.
For exploration of the fascinating opportunities, one of the important things is to address intrinsic properties of TMDs. For this purpose, TMDs encapsulated by hexagonal boron nitride (hBN), hBN/TMD/hBN, have been widely used [11][12][13][14] .
2D-TMDs are very sensitive to the external environment, such as substrates and adsorbents, because almost all atoms in a 2D-TMD locate at the surface. SiO2/Si usually used as a substrate has a rough surface with dangling bonds, low-energy optical phonons, and charged impurities, which can significantly degrade the quality of samples 15 . In contrast, hBN, a graphene analogue insulator (bandgap ~ 6 eV), is free from these degradation factors, providing an ideal environment to address intrinsic properties of 2D-TMDs.
Up to now, quite a few studies have been done with hBN/TMD/hBN to investigate intrinsic properties of 2D-TMDs. For example, high-mobility devices with hBN-encapsulated structures have been reported, showing carrier mobility of 19-94 cm 2 /Vs at room temperature in a monolayer MoS2 (ML-MoS2) encapsulated by hBN flakes; typical mobilities of ML-MoS2 on silicon substrates range from 1 to 10 cm 2 /Vs 16,17 . The enhancement in carrier mobility arises from suppression of the extrinsic carrier scatterings in hBN-encapsulated samples. The high quality of hBN-encapsulated samples has also been observed in optical measurements.
Photoluminescence (PL) spectra of a ML-TMD on a silicon substrate each show a relatively broad peak arising from radiative recombination of excitons; for example, monolayer WS2 on a silicon substrate shows a PL peak whose full width at half maximum (FWHM) is typically 50-55 or 75 meV. In contrast, the PL spectrum of a hBN/WS2/hBN shows a corresponding PL peak with a much smaller FWHM of ~26 meV, and this small FWHM mainly results from suppression of inhomogeneous broadening arising from substrates [18][19][20] . These results strongly indicate that hBN-encapsulated samples are essential to address intrinsic properties of 2D-TMDs.
In this work, we have focused on the electronic structure of one of the most popular TMDs, ML-MoS2, encapsulated by hBN, hBN/MoS2/hBN. As discussed above, hBN-encapsulated structures are probably the best structure for investigations of intrinsic properties of TMDs, but a question here is "does the hBN-encapsulation really preserve the original electronic structure of a 2D-TMD or not?" In multi-layer systems assembled through van der Waals (vdW) interaction, it has been reported that the band structure of vdW stacks can be modulated by inter-layer interaction. Bilayer graphenes are one of the most significant examples.
A recent work has revealed that interlayer interaction causes a flat band in a bilayer graphene, which leads to the Mott insulating state and even superconductivity at low temperature. Interlayer interaction in hBN/TMD/hBN, at first sight, is not the case, because hBN have a large bandgap of ~6 eV and the valence band maximum (VBM) and conduction band minimum (CBM) of TMD locate away from those of hBN, but is this really the case?
In this paper, we show that modification of the band structure of ML-MoS2 occurs through interlayer interaction between ML-MoS2 and hBN flakes. Through detailed PL measurements and first-principles band-structure calculations, we have found   Figure 1). The FWHM of the exciton PL peak is 39 meV, which is much smaller than those of samples on silicon substrates (typically ~70 or 56 meV) 22,23 . Figure 2(b) shows a PL image of the sample, where the red-dashed rectangle corresponds to the place cleaned by the nano-"squeegee" technique. The PL image, in particular at the red rectangle, clearly shows uniform PL, which represents a high-quality clean interface between ML-MoS2 and hBN. The brighter PL at the cleaned place indicates that non-radiative decay, which is caused by contaminants, is suppressed 19,24,25 .
Figure 3(a) shows PL spectra measured at temperatures ranging from 220 to 320 K. PL peaks arising from radiative recombination of excitons show blue shift as temperature decreases, which originates from bandgap widening caused by the electron-phonon interaction. The temperature dependence is well described by Varshni's equation, which is shown in Supplementary Figure 2; the obtained parameters are consistent with previously reported values. As you can clearly see, intensities of the PL peaks become weak as temperature decreases. To evaluate the intensity decrease precisely, we measured PL intensity from the red rectangular regions in PL images; PL intensities are averaged over the area to minimize the position-dependent fluctuation. As clearly seen in Figure 3(b), PL intensity monotonically decreases as temperature decreases, and PL intensity at 260 K is two-thirds of that at 320 K.
In a previous report, PL intensity of ML-MoS2 on a silicon substrate increased as temperature decreased 26 . Ab-initio band structure calculation tells us that ML-MoS2 is a direct-gap semiconductor, and bright excitons might be the lowest-energy excited state. This is consistent with the previously reported temperature dependence of PL intensity because the population of bright excitons is expected to increase as temperature decreases if the bright state is the lowest-energy state. A recent theoretical investigation, however, has suggested that lower-energy dark excitons can exist in a ML-MoS2, which dark excitons correspond to holes located at   showing exponential decay against the interlayer distance ( Supplementary Fig. S4).
This strong interlayer dependence indicates that the upward shift in the VBM at the -valley originates not from long-range interaction, such as electrostatic interaction, but from orbital hybridization arising from overlap in wave functions between MoS2 and hBN. It should be noted that accurate estimation of interlayer distance based on DFT is not straight forward and the degree of the upward shift should be influenced by the accuracy.