Broken adiabaticity induced by Lifshitz transition in MoS2 and WS2 single layers

Abstract

The breakdown of the adiabatic Born-Oppenheimer approximation is striking dynamical phenomenon, however, it occurs only in a handful of layered materials. Here I show that adiabaticity breaks down in doped single-layer transition metal dichalcogenides in a quite intriguing manner. Namely, significant nonadiabatic coupling, which acts on frequencies of the Raman-active modes, is prompted by a Lifshitz transition due to depopulation and population of multiple valence and conduction valleys, respectively. The outset of the latter event is shown to be dictated by the interplay of highly non-local electron-electron interaction and spin-orbit coupling. In addition, intense electron-hole pair scatterings due to electron-phonon coupling are inducing phonon linewidth modifications as a function of doping. Comprehending these intricate dynamical effects turns out to be a key for mastering characterization of electron doping in two-dimensional nano-devices by means of Raman spectroscopy.The Born-Oppenheimer approximation, which assumes that electrons adiabatically follow the motion of lattice degrees of freedom, is a fundamental starting point in quantum mechanics. Recent studies have, however, shown that striking nonadiabatic (NA) effects visible in vibrational Raman spectra can be found in metallic layered materials, such as graphene [1][2][3], graphite intercalation compounds [4], and magnesium diboride [4,5], as well as in doped semiconductors, such as boron-doped diamond [6]. The strength of this dynamical electronphonon coupling (EPC) can, in fact, be modified as a function of carrier concentration, which makes the Raman spectroscopy a quite powerful tool for characterization of doped two-dimensional and layered materials [7]. However, to make this characterization complete, the precise understanding of the microscopic processes underlying the NA modifications of phonons is needed [1,4,8,9]. Such renormalization of phonons is actually considered quite rare, and apart from these few cases it is not clear in what other two-dimensional materials should adiabaticity break down.Contrary to the aforesaid examples, the vibrational spectra of the single-layer transition metal dichalcogenides (TMDs) under bias voltage is believed to be adiabatic [10,11]. In other words, the gate-induced phonon renormalization can be qualitatively described by means of adiabatic density functional theory (DFT) calculations [11]. Despite this common belief, there are few worthwhile indications that point to the importance of the NA effects in doped TMDs [12][13][14][15]. For instance, recent study on carrier-induced phonon modifications in atomically-thin TMDs had shown that DFT results are largely overestimating the corresponding frequency shifts of the Raman-active modes [12]. Moreover, the theoretical considerations have predicted the importance of the NA coupling in charge transfer dynamics of TMDs heterostructures [13,14] as well as in exciton-mediated Raman scattering of MoS 2 [15]. Additionally, the effect beyond adiabatic approximation, ...

Emergence of large nonadiabatic effects induced by the electron-phonon interaction on the complex vibrational quasiparticle spectrum of doped monolayer MoS2

“…More recently, Raman experiments on the monolayer MoS 2 have revealed strong sensitivity to electron-doping of the optical phonons with a dominant out-of-plane polarization, which exhibit an increasing frequency softening at low carrier concentrations (ρ < 2 × 10 13 cm −2 ) [24]. Although this effect was first understood by means of adiabatic vibrational calculations, several works focussing in the small momen-tum range have pointed out the importance of non-adiabatic corrections when increasing the carrier doping concentration (ρ ∼ 5 × 10 13 cm −2 ) [25,26]. Moreover, the experimentally measured superconductivity [27] and the intricate carrier photoemission spectra [28] at larger doping have been theoretically explained by a considerably large strengthening of the electron-phonon coupling promoted by abrupt changes in the topology of the Fermi surface (FS) [29][30][31].…”

Ultrafast band-gap renormalization and build-up of optical gain in monolayer MoTe2

“…Furthermore, the conduction bands display a spin splitting of −35 meV and side valleys at the Σ/Λ points, that are 97 meV (Σ ↑ /Λ ↓ ) and 82 meV (Λ ↑ /Σ ↓ ) above the respective K/K -valley minima. These values are on the lower end of the range of published values that have been obtained using different functionals for the exchange correlation potential or GW corrections [32][33][34] and sufficiently large to prevent an excitation induced transition from a direct to indirect band gap 35,36 .…”

Strong band-filling-dependence of the scattering lifetime in gated MoS2 nanolayers induced by the opening of intervalley scattering channels

“…It is very important to note that the opening of these intervalley scattering channels has a profound influence not only on the low-T scattering lifetime and mobility, but on several other key properties of gated MoS 2 . Specifically, the availability of these intervalley scattering channels is paramount in optimizing the nesting efficiency of the Fermi surface 65 , thereby allowing to strongly enhance the electron-phonon coupling (EPC) in the system 34,46,[66][67][68][69][70] . This in turn leads to significant changes in the vibrational spectrum 46,66,68 , such as the pronounced doping-dependent phonon softenings which have been observed in ion-gated MoS 2 and other semiconducting TMDs by means of Raman spectroscopy 68,72 .…”