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Register a new userHybrid k$cdot$p tight-binding model for subbands and infrared intersubband optics in few-layer films of transition-metal dichalcogenides: MoS$_2$, MoSe$_2$, WS$_2$ and WSe${}_2$
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David Ruiz-Tijerina
Publication date
2018
fields
Physics
and research's language is
English
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We present a density functional theory parametrized hybrid k$cdot$p tight binding model for electronic properties of atomically thin films of transition-metal dichalcogenides, 2H-$MX_2$ ($M$=Mo, W; $X$=S, Se). We use this model to analyze intersubband transitions in $p$- and $n$-doped $2{rm H}-MX_2$ films and predict the line shapes of the intersubband excitations, determined by the subband-dependent two-dimensional electron and hole masses, as well as excitation lifetimes due to emission and absorption of optical phonons. We find that the intersubband spectra of atomically thin films of the 2H-${MX_2}$ family with thicknesses of $N=2$ to $7$ layers densely cover the infrared spectral range of wavelengths between $2$ and $30 {rm mu m}$. The detailed analysis presented in this paper shows that for thin $n$-doped films, the electronic dispersion and spin-valley degeneracy of the lowest-energy subbands oscillate between odd and even number of layers, which may also offer interesting opportunities for quantum Hall effect studies in these systems.
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Accurately described excitonic properties of transition metal dichalcogenide heterobilayers (HBLs) are crucial to comprehend the optical response and the charge carrier dynamics of them. Excitons in multilayer systems posses inter or intralayer character whose spectral positions depend on their binding energy and the band alignment of the constituent single-layers. In this study, we report the electronic structure and the absorption spectra of MoS$_2$/WS$_2$ and MoSe$_2$/WSe$_2$ HBLs from first-principles calculations. We explore the spectral positions, binding energies and the origins of inter and intralayer excitons and compare our results with experimental observations. The absorption spectra of the systems are obtained by solving the Bethe-Salpeter equation on top of a G$_0$W$_0$ calculation which corrects the independent particle eigenvalues obtained from density functional theory calculations. Our calculations reveal that the lowest energy exciton in both HBLs possesses interlayer character which is decisive regarding their possible device applications. Due to the spatially separated nature of the charge carriers, the binding energy of inter-layer excitons might be expected to be considerably smaller than that of intra-layer ones. However, according to our calculations the binding energy of lowest energy interlayer excitons is only $sim$ 20% lower due to the weaker screening of the Coulomb interaction between layers of the HBLs. Therefore, it can be deduced that the spectral positions of the interlayer excitons with respect to intralayer ones are mostly determined by the band offset of the constituent single-layers. By comparing oscillator strengths and thermal occupation factors, we show that in luminescence at low temperature, the interlayer exciton peak becomes dominant, while in absorption it is almost invisible.
Twistronic van der Waals heterostrutures offer exciting opportunities for engineering optoelectronic properties of nanomaterials. Here, we use multiscale modeling to study trapping of charge carriers and excitons by ferroelectric polarisation and piezoelectric charges by domain structures in twistronic WX$_2$/MoX$_2$ bilayers (X=S,Se). For almost aligned 2H-type bilayers, we find that holes and electrons are trapped in the opposite -- WMo and XX (tungsten over molybdenum {it versus} overlaying chalcogens) -- corners of the honeycomb domain wall network, swapping their position at a twist angle $0.2^{circ}$, with XX corners providing $30$,meV deep traps for the interlayer excitons for all angles. In 3R-type bilayers, both electrons and holes are trapped in triangular 3R stacking domains, where WX$_2$ chalcogens set over MoX$_2$ molybdenums, which act as $130$,meV deep quantum boxes for interlayer excitons for twist angles $lesssim 1^{circ}$, for larger angles shifting towards domain wall network XX stacking sites.
Twisted bilayers of two-dimensional materials, such as twisted bilayer graphene, often feature flat electronic bands that enable the observation of electron correlation effects. In this work, we study the electronic structure of twisted transition metal dichalcogenide (TMD) homo- and heterobilayers that are obtained by combining MoS$_2$, WS$_2$, MoSe$_2$ and WSe$_2$ monolayers, and show how flat band properties depend on the chemical composition of the bilayer as well as its twist angle. We determine the relaxed atomic structure of the twisted bilayers using classical force fields and calculate the electronic band structure using a tight-binding model parametrized from first-principles density-functional theory. We find that the highest valence bands in these systems can derive either from $Gamma$-point or $K$/$K$-point states of the constituent monolayers. For homobilayers, the two highest valence bands are composed of monolayer $Gamma$-point states, exhibit a graphene-like dispersion and become flat as the twist angle is reduced. The situation is more complicated for heterobilayers where the ordering of $Gamma$-derived and $K$/$K$-derived states depends both on the material composition and also the twist angle. In all systems, qualitatively different band structures are obtained when atomic relaxations are neglected.
The optical spectra of vertically stacked MoSe$_2$/WSe$_2$ heterostructures contain additional interlayer excitonic peaks that are absent in the individual monolayer materials and exhibit a significant spatial charge separation in out-of-plane direction. Extending on a previous study, we used a many-body perturbation theory approach to simulate and analyse the excitonic spectra of MoSe$_2$/WSe$_2$ heterobilayers with three stacking orders, considering both momentum-direct and momentum-indirect excitons. We find that the small oscillator strengths and corresponding optical responses of the interlayer excitons are significantly stacking-dependent and give rise to high radiative lifetimes in the range of 5-200,ns (at T=4,K) for the bright interlayer excitons. Solving the finite-momentum Bethe-Salpeter Equation, we predict that the lowest-energy excitation should be an indirect exciton over the fundamental indirect band gap (K$rightarrow$Q), with a binding energy of 220,meV. However, in agreement with recent magneto-optics experiments and previous theoretical studies, our simulations of the effective excitonic Lande g-factors suggest that the low-energy momentum-indirect excitons are not experimentally observed for MoSe$_2$/WSe$_2$ heterostructures. We further reveal the existence of interlayer C excitons with significant exciton binding energies and optical oscillator strengths, which are analogous to the prominent band nesting excitons in mono- and few-layer transition-metal dichalcogenides.
Interlayer excitons in layered materials constitute a novel platform to study many-body phenomena arising from long-range interactions between quantum particles. The ability to localise individual interlayer excitons in potential energy traps is a key step towards simulating Hubbard physics in artificial lattices. Here, we demonstrate spatial localisation of long-lived interlayer excitons in a strongly confining trap array using a WS$_{2}$/WSe$_{2}$ heterostructure on a nanopatterned substrate. We detect long-lived interlayer excitons with lifetime approaching 0.2 ms and show that their confinement results in a reduced lifetime in the microsecond range and stronger emission rate with sustained optical selection rules. The combination of a permanent dipole moment, spatial confinement and long lifetime places interlayer excitons in a regime that satisfies one of the requirements for observing long-range dynamics in an optically resolvable trap lattice.
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