Abstract
Electron–phonon scatterings in solidstate systems are pivotal processes in determining many key physical quantities such as charge carrier mobilities and thermal conductivities. Here, we report direct probing of phonon mode specific electron–phonon scatterings in layered semiconducting transition metal dichalcogenides WSe_{2}, MoSe_{2}, WS_{2}, and MoS_{2} through inelastic electron tunneling spectroscopy measurements, quantum transport simulations, and density functional calculation. We experimentally and theoretically characterize momentumconserving single and twophonon electron–phonon scatterings involving up to as many as eight individual phonon modes in mono and bilayer films, among which transverse, longitudinal acoustic and optical, and flexural optical phonons play significant roles in quantum charge flows. Moreover, the layernumber sensitive higherorder inelastic electron–phonon scatterings, which are confirmed to be generic in all four semiconducting layers, can be attributed to differing electronic structures, symmetry, and quantum interference effects during the scattering processes in the ultrathin semiconducting films.
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Introduction
The collective vibrational modes in atomically arranged structures, namely phonons, and their interactions with charged carriers play crucial roles in determining various properties of condensed matter systems, covering thermal capacity and conductivity, electron mobility, and superconductivity, to name a few^{1,2,3}. Specifically, in twodimensional (2D) van der Waals (vdW) layered materials, electron–phonon interactions have been widely recognized as key elements in characterizing electronic, optical, and quantum properties^{4,5}. Among those, electron–phonon scatterings are considered to determine the intrinsic charge carrier mobility in 2D semiconducting transition metal dichalcogenides (SCTMDs)^{6,7,8,9,10,11}. For instance, as schematically illustrated in Fig. 1a, twophonon modes E″ and A_{2}″ are optically accessible but weakly interact with electrons. In comparison, E′ and A_{1} phonons are Raman active while strongly interacting with electrons. Transverse and longitudinal acoustic phonons have been regarded as the primary factors that limit inplane charge carrier mobilities in 2D vdW SCTMD films^{8,12}. Direct experimental approaches to explore electron–phonon interactions, however, have been largely missing, and most previous reports on phononrelated phenomena have been limited to either one or two isolated phonons and their temporal interactions with optically pumped hot electrons, which would not be relevant in active electronic applications^{13,14}.
Free from stringent optical selection rules, inelastic electron tunneling spectroscopy (IETS) is known for its effectiveness in detecting electron–phonon interactions with a highenergy resolution^{15,16,17,18,19}. Previously, scanning tunneling microscopy (STM) has been used for local IETS measurements of a few phonon excitations in 2D semimetals^{16,17,20,21}. For instance, van Hove singularities of graphene phonon bands and phononmediated inelastic channels to graphene have been observed under an STM probe^{16,17}. When it comes to 2D SCTMDs, however, IETS studies with local probes have been sparse due to weak tunnel signals from the pointlike metallic probe. IETS measurements through the atomically sharp tunnel junctions additionally suffer from the limitation of broad momentum spectra, making it further daunting to isolate phononmode specific electron–phonon scatterings from concerted scattering networks on the Fermi surface of the 2D materials.
In this work, we report IETS measurements with four prototypical typeVI 2D SCTMD films as tunnel media and characterize single and twophonon IETS features involving up to as many as eight distinctive phonon modes in mono and bilayer films. We find out that the momentumconserving electron–phonon scattering processes in 2D semiconductors, reflecting individual phononmode specific electron–phonon coupling strengths, are governed by layernumber dependent electronic structures and inversion symmetry. Moreover, we identify that several twophonon inelastic electron tunneling processes differ between the mono and bilayer SCTMD films. Corroborated with quantum transport simulation and density functional perturbation theory (DFPT), we suggest that the layernumber sensitive electron–phonon scatterings can be understood by a quantum interference effect and symmetryregulated geometric phase in the higherorder scattering processes.
Results
IETS with 2D vdW junctions
A simplified device scheme is illustrated in the inset of Fig. 1g. We implement thin graphite (>5 nm) as source and drain electrodes to preserve the intrinsic physical and electrical properties of the mono and bilayer SCTMDs, while introducing vdW tunnel barriers at the 2D vertical heterojunctions^{22,23,24}. Another advantage of utilizing graphite as contact electrodes is to minimize the momentum mismatch of the electrons tunneling to and from the 2HSCTMDs, which enables efficient monitoring of the electron–phonon scattering processes around the K (Fig. 1b) and Q (Fig. 1c) points, in which the conduction band edges of the hexagonal 2D semiconducting layers are located^{24}. As schematically illustrated in Fig. 1d, electrons injected through a barrier transiently excite to the conduction band edges of the insulator. Although a majority of the electrons elastically tunnel through the insulator while releasing the preborrowed excitation energy (dashed and solid red lines in Fig. 1d), electron–phonon interactions allow some electrons to be scattered off to other electronic states with or without a momentum change (solid blue and green wavy arrows in Fig. 1d, respectively). Accordingly, adjunct transport channels are constructively established in the charge flows through the tunnel junctions, through which inelastic tunneling events are exhibited as conductance modulations (G = dI/dV_{b}, Fig. 1e) or as peaks or dips of the second derivative of tunnel current (dG/dV_{b}, Fig. 1f) depending on sample bias (V_{b}) polarities. During these inelastic electron tunneling processes, momentum conservations limit the accessible phonons to the excitations at specific highsymmetric points, so that phonon excitations probed by our inelastic quantum tunneling measurements can be directly associated with the elemental electron–phonon scattering processes at the highsymmetric points and essentially govern the charge flows through the tunnel media. In that regard, our IETS spectra cannot simply be related to the combined phonon density of states of the SCTMDs, for which the detailed information of phonon momentum is obscured.
Figure 1g–i shows a collection of inelastic electron tunneling spectra from the first set of mono (solid blue lines) and bilayer (dotted red lines) WSe_{2} planar tunnel junctions at T = 5.7 K. We add an AC excitation voltage (V_{pp} = 1 mV, f = 43.33 Hz) to DC V_{b} and simultaneously measure both I–V_{b} (Fig. 1g) and G = dI/dV_{b}–V_{b} (Fig. 1h) with an AC lockin amplifier^{19}. Within the V_{b} range of V_{b} ≤ 100 mV, vertical charge flows through our graphite–WSe_{2}–graphite planar junctions are governed by direct tunneling, which is sensitive to WSe_{2} layer thickness, tunnel junction area, crystallographic misalignment angles between the graphite electrodes and WSe_{2} tunnel insulator, and electron–phonon scatterings. As explained before, weak IETS signals in dI/dV_{b} (Fig. 1e and h) can be better displayed as peaks and valleys in the second derivative of the tunnel current, dG/dV_{b} = d^{2}I/dV_{b}^{2} (Fig. 1f and i), with their symmetric locations around V_{b} = 0 mV representing the characteristic IETS feature linked to electron scatterings with phonons of activation energy eV_{b}^{15}. It is worth pointing out that dG/dV_{b} spectra shapes are sensitive to the tunneljunction parameters, so we limit our discussions to the devices with weak couplings, free from strongly coupled resonance tunneling^{25}. We obtained the dG/dV_{b} spectra by numerically differentiating G = dI/dV_{b}, confirmed to be consistent with data independently measured from an additional AC lockin amplifier synchronized at a frequency of 2f (Supplementary Fig. 1). The conspicuous dG/dV_{b} signals indicate that tunnel electrons heavily interact with WSe_{2} phonons, while the differing dG/dV_{b} values and V_{b} positions between the mono and bilayer devices imply that electron–phonon scatterings in the 2D vdW heterostructures are WSe_{2} layernumber variant. We note that all IETS spectra presented in the manuscript are obtained by numerically averaging out as many as 121 individual dG/dV_{b} spectra, often varying external gate voltage V_{g} applied to the Si/SiO_{2}/hBN back gate (Supplementary Fig. 2). By following this procedure, we can identify V_{g}invariant IETS signals as peaks or dips, while the V_{g}dependent features, such as those relating to defect states and the electronic structures of the SCTMDs and graphite electrodes, can be avoided^{19}.
Singlephonon electron scatterings in mono and bilayer WSe_{2}
Figures 2b and c respectively show comprehensive IETS spectra from the second set of mono and bilayer WSe_{2} devices, measured at T = 0.45 K with an excitation voltage of V_{pp} = 0.3 mV. In total, we are able to identify eight independent IETS features in both mono and bilayer samples within an energy window of eV_{b} ≤ 38 meV and then compare them with DFPTcalculated phonon dispersions of freestanding monolayer WSe_{2} (Fig. 2a) and graphene–WSe_{2}–graphene heterostructures (Supplementary Fig. 3). The V_{b} positions for each IETS feature are assessed through a multipeak Lorentzian fitting (solid grey curves in Fig. 2b), with the collective fitting result (overlaid orange line in Fig. 2b) matching the experimental data very well. Moreover, the open blue squares in Fig. 2b and c respectively indicate the experimental data in negative V_{b} from the mono and bilayer devices, with the dG/dV_{b} dip locations perfectly aligning with the dG/dV_{b} peaks in positive V_{b}. The widths of the ticks (Fig. 2b and c) indicate the intrinsic IETS spectrabroadening in our measurements: FWHM ≈ 0.6 meV ^{26}.
Now we undertake the identification of the phonon modes responsible for each IETS feature, based on theoretical reports on the electron–phonon coupling strengths in 2D semiconductors^{6,7,8,9,10,11}. Since momentumconserving virtual quantum tunneling primarily occurs at the K and Q valleys, highsymmetric phonons connecting the K and Q valleys can be expected to contribute strongly in the electron–phonon scattering processes in monolayer WSe_{2}. First, we mark the dG/dV_{b} peak labeled as P_{2} (8.57 mV ± 0.18 mV) in Fig. 2b is associated with the TAphonon branch, or more specifically, TA(Q) phonon excitation, which is the highsymmetry phonon mode exclusively excited within our measurement uncertainty. Similarly, P_{3} (13.71 mV ± 0.07 mV) in the monolayer junction can be assigned to the LA(Q) phonons, which are predicted to cause strong electron–phonon interactions^{6,7,8,9,10,11}. The next signal, P_{4} (15.95 mV ± 0.05 mV), is within the phonon excitation energies of LA(K) and LA(M). As a note, transverse acoustic (ZA) phonons are expected to deform electrostatic potentials weakly, thus making electron scatterings with ZA phonons irrelevant in our measurements. It is worth mentioning that the IETS features marked with P_{1} in the monolayer (2.36 mV ± 0.12 mV) and bilayer (3.80 mV ± 0.13 mV) can be attributed to a newly excited lattice vibration mode in the graphite–WSe_{2}–graphite heterojunctions. Such lowenergy excitations can be related to the intricate crystallographic arrangements of 2D vdW interfaces^{19}.
Among the other six optical phonon branches of WSe_{2} monolayers, LO_{2}, TO_{2}, and ZO_{1} phonon modes are expected to cause strong electron–phonon scatterings^{6,7,8,9,10,11}. Accordingly, with relative ease, we can assign P_{5} (24.63 mV ± 0.08 mV) in the monolayer to the LO_{2}(K) phonon. Identifying the primary phonon excitations for the next three dG/dV_{b} peaks, however, is not as straightforward as those for the previously assigned lowenergy phonons. For example, P_{6} (27.48 mV ± 0.04 mV) is in close proximity to LO_{2}(M)/TO_{2}(M) and LO_{2}(Q), while P_{7} (31.33 mV ± 0.07 mV) and P_{8} (33.45 mV ± 0.06 mV) are within the energy ranges of the TO_{2} (Γ, K)/ZO_{1}(Γ, K) and ZO_{1}(Q, M) phonon excitations. Here, we point out that identifying the primary optical modes from these energetically closepacked WSe_{2} optical phonons can be possible with higherorder twophonon IETS measurements and quantum transport simulations, as we discuss in detail later.
We find that the IETS spectra from the bilayer device, thus the electron–phonon scattering characteristics in WSe_{2} bilayers, are distinct when compared with their monolayer counterparts, which we relate to the layernumber variant symmetry and the electronic structures around the conducting channels. Inversion symmetry preserved in bilayer 2H SCTMDs renders interlayer tunneling at the K (K′) valley irrelevant because the interlayer couplings at the K (K′) points are weak around the conduction band edges^{27,28,29}. Instead, strong interlayer hybridizations are prompted by the orbitals responsible for the conduction band edges at Q. Therefore, in bilayer WSe_{2}, electrons tunneled into the first layer from the graphite electrode with momentum K (K′) should be scattered off to Q (Q′) through intra or intervalley electron–phonon scatterings (Fig. 1b) before tunneling to the second layer^{27,28}. Accordingly, singlephonon interlayer tunneling assisted by K phonons becomes limited in SCTMD bilayers, leading to diminished inelastic tunnel features with the K phonons. As marked with red inverted triangles in Fig. 2c, the electron–phonon scattering signal with LO_{2}(K) phonons is indeed reduced in intensity in the bilayer (P_{5} in Fig. 2c) when compared with the conspicuous IETS feature for LO_{2}(K) phonons in the monolayer (Fig. 2b). Similarly, the dG/dV_{b} hump marked as P_{4} (15.60 mV ± 0.28 mV) becomes attenuated in intensity, and the moderate undertone of the dG/dV_{b} spectra, P_{7} in the bilayer, could be attributed to quenched TO_{2}(K) and ZO_{1}(K) phonon excitations as well.
Twophonon electron scatterings in mono and bilayer WSe_{2}
Thanks to an excellent tunneljunction stability, we are able to probe highenergy inelastic electron tunneling processes in 2D SCTMDs. Figures 3a and b respectively show dG/dV_{b} spectra from the mono and bilayer WSe_{2} devices up to eV_{b} ≤ 70 meV. Note that no available WSe_{2} phonon modes exist within the energy range 40 meV ≤ eV_{b} ≤ 70 meV, with the majority of phonons associated with the graphite having much higher energies^{19,30}. Interestingly, these highenergy IETS spectra differ by eV_{b} location between the mono and bilayer devices. In the monolayer, for example, a distinct dG/dV_{b} peak is observed at ≈ 59 meV along with a rather broad dG/dV_{b} hump at ≈53 meV. Meanwhile, as shown in Fig. 3b for the bilayer, the strongest IETS signal is formed at ≈42 meV, at which no apparent dG/dV_{b} spectra exist in the monolayer WSe_{2}. In addition, the highenergy spectra in the bilayer (40 meV ≤ eV_{b} ≤ 60 meV) are far stronger in intensity than the IETS signals at low energies (eV_{b}  ≤ 40 meV), which is not the case in the monolayer device.
We accredit the sets of higherenergy layernumberdependent IETS spectra to twophonon electron–phonon scatterings that can be interpreted through quantum interference and the geometric phase in ultrathin WSe_{2} films. Let us begin with an intuitive description of quantum interference and the geometric phase in twophonon electron–phonon scatterings, during which an electron with an initial momentum \({k}_{{{{{{\rm{i}}}}}}}\) is interacting with two respective phonons of momenta \(q\) and \(q{\prime}\) and ends up in a state with a final momentum of \({k}_{{{{{{\rm{f}}}}}}}={k}_{{{{{{\rm{i}}}}}}}qq{\prime}\). In a microscopic view, momentum conservation allows two different electron–phonon inelastic processes with differing scattering orders: emitting the first \(q({q}^{{\prime} })\) phonon and stopping at the intermediate state \({\kappa }_{{{{{{\rm{A}}}}}}}={k}_{{{{{{\rm{i}}}}}}}q({\kappa }_{{{{{{\rm{B}}}}}}}={k}_{{{{{{\rm{i}}}}}}}q{\prime} )\), and arriving at \({\kappa }_{{{{{{\rm{f}}}}}}}\) after scattering off by emitting the second \({q}^{{\prime} }(q)\) phonon. Note that such a pair of distinctive scattering routes form a closed loop in momentum space, and the developed quantum superposition finally determines the inelastic electron tunneling probability that is responsible for the experimentally observable IETS signals in magnitude (insets in Fig. 3c and d). Quite notably, owing to the peculiar electronic structures of the SCTMDs with six distinct Q and K valleys around the conduction band edges, such a quantum interference effect comes into play for various twophonon electron–phonon scattering processes. For instance, when scattered by M and Q phonons such as LA(M) and LO(Q), an electron at the K point is allowed to travel through two intermediate states (\(\kappa _{{{{{\rm{A}}}}}},\kappa_{{{{{\rm{B}}}}}}\)) at Q_{1} and Q_{4} before arriving at the K´ point (inset in Fig. 3d). During these scattering processes, the quantum interference effect becomes prominent since the probability of each scattering route is the same thanks to the identical band structures around the Q_{1} and Q_{4} points. In stark contrast, however, when tunnel electrons are scattered by the phonons at M and K, during which the electrons detour through the intermediate states at the K and Q valleys (inset in Fig. 3c), the quantum interference effect becomes attenuated due to the dissimilar tunneling probabilities resulting from the differing energy gaps at the K and Q valleys.
When a sudden spin change accompanies the course of electrons traveling through a closed loop in momentum space, moreover, the geometric phase can play a pivotal role in determining the quantum interference^{31,32,33,34,35}. In the monolayer SCTMDs, for instance, where timereversal symmetry is preserved but inversion symmetry is not, the additional geometric phase π is added in the twophonon inelastic electron scattering processes with M and Q phonons. On the other hand, the simultaneous presence of timereversal and inversion symmetries in the SCTMD bilayers forces the geometric phase to vanish, and accordingly, the quantum phase around the closed loop becomes equivalently 2π, resulting in constructive quantum interference in the bilayer films (Supplementary Note)^{36,37}. We further note that higherorder electron–phonon scatterings and their experimental realizations in the systems where a spinmomentum locking is absent could be simply related to the joint density of states of interacting phonons. However, in the SCTMDs where the spinmomentum locking is present, the quantum interference and the geometric phase come as major players in the twophonon electron scattering processes (Supplementary Note).
With a rigorous quantum mechanical IETS simulations (see Methods and the Supplementary Note for detailed descriptions), we show that the higherenergy twophonon IETS signals are indeed sensitive to the aforementioned quantum interference and geometric phase. We consider all possible combinations of twophonon inelastic scattering routes out of the experimentally identified eight individual phonons, and confirm that the twophonon IETS signals specifically associated with Q and M phonons are sensitive to the layernumber dependent symmetries and quantum interference. We figure vertical charge flows through the bilayer as interlayer tunneling through two WSe_{2} films with the exclusion of intervalley scattering around the K(K′) in the scattering matrix. Figure 3c and d displays simulated dG/dV_{b} spectra for mono and bilayer WSe_{2} with full consideration of the geometric phase and quantum interference around the closed loop, and the agreement with the experimental data is eminent–in particular, the absence (presence) of dG/dV_{b} signals within 40 meV ≤ eV_{b} ≤ 55 meV in the mono (bi) layer WSe_{2} films. We provide all the theoretically expected positions of IETS features and twophonon inelastic scattering processes exhibiting quantum interference in Supplementary Table 1. It should be pointed out that our transport model for bilayer WSe_{2} has shortcomings to fully analyze the experimental observations. For example, the twophonon inelastic electron scatterings with LA phonons are expected to largely contribute to the vertical charge flows, resulting in higher dG/dV_{b} spectra in value around 25 meV ≤ eV_{b} ≤ 35 meV (dotted orange line in Fig. 3d). Instead, the simulated spectra without considering the double LA phonon scatterings (solid blue line in Fig. 3d) are found to be closer to the experimental observations, calling for further theoretical works to better clarify the phonon interactions with conducting electrons in bilayer WSe_{2}.
Electron–phonon scatterings in MoS_{2}, MoSe_{2}, and WS_{2}
We find out that the key electron–phonon scattering characteristics observed with WSe_{2} films—that single and twophonon electron–phonon scatterings are regulated by layernumber dependent electronic structures and symmetries—are generic to the other typeVI SCTMD films, namely MoS_{2}, MoSe_{2}, and WS_{2}. Figure 4b shows an IETS spectrum from a monolayer MoS_{2} device, measured at T = 0.45 K with an excitation voltage of V_{pp} = 0.5 mV. From the monolayer MoS_{2}, we can identify six distinct IETS features within an energy window of eV_{b} ≤ 55 meV, with each spectrum closely aligned to the TA, LA, LO_{2}, TO_{2}, and ZO_{1} phonon branches (Fig. 4a). Identical to the monolayer WSe_{2}, TA(Q), LA(Q), and LA(M, K) phonons can be marked as the leading acoustic phonon excitations that generate sizable electron–phonon scatterings in monolayer MoS_{2}. Separated by a sizable gap at 30 meV ≤ eV_{b} ≤ 45 meV, three dG/dV_{b} peaks appear close together and can be linked to LO_{2}, TO_{2}, and ZO_{1} optical phonons. As discussed previously, the IETS spectra, thus electron–phonon scatterings in bilayer MoS_{2} films contrast those in monolayer MoS_{2}. Figure 4c shows an IETS spectrum from a bilayer MoS_{2} device, and the IETS feature corresponding to the singlephonon electron scatterings with LA(K) phonons becomes diminished in the bilayer MoS_{2}, as marked with an inverted red triangle in Fig. 4c. Moreover, the highenergy IETS features at 55 meV ≤ eV_{b} ≤ 100 meV, which are attributed to the twophonon inelastic scatterings, are higher in intensity than those for the lowenergy IETS signals. The vertical red tick marks and colored solid and dotted arrows in Fig. 4c indicate various twophonon inelastic electrons scattering processes with Q and M phonons. In comparison, as marked with vertical blue tick marks in Fig. 4b for the monolayer, most highenergy dG/dV_{b} peaks can be explained by the twophonon electron–phonon scatterings, save for the destructive Q and M combinations. Based on these observations, we can infer that the elementary phonon modes in ultrathin MoS_{2} are TA(Q), LA(Q), LA(M), LO_{2}(Q)/LO_{2}(M), TO_{2}(Q)/TO_{2}(M), and ZO_{1}(M) phonons.
Figures 5c and e respectively display IETS measurements from the mono and bilayer MoSe_{2} tunnel devices, and Fig. 5d and f are those from the WS_{2} mono and bilayer devices, along with the DFPTcalculated phonon dispersions and phonon density of states of freestanding monolayer MoSe_{2} (Fig. 5a) and WS_{2} (Fig. 5b). The tunnel spectra observed in MoSe_{2} and WS_{2} are consistent with the previously discussed electron–phonon scattering physics in WSe_{2} and MoS_{2}, in particular, inversion symmetryregulated charged carrier scattering with K phonons: LA(K) as indicated with inverted red triangles in Fig. 5e and f, and geometric phase administered Q and M twophonon inelastic scatterings. Some of the prominent twophonon modes for MoSe_{2} and WS_{2} are marked with colored arrows and their combinations in Fig. 5c–f, with the primary singlephonon excitations identified in our measurements denoted with colored stars in Fig. 5a for MoSe_{2} and Fig. 5b for WS_{2}. It is interesting to point out that, unlike WSe_{2}, MoS_{2}, and MoSe_{2}, the most prominent dG/dV_{b} peak in bilayer WS_{2} is located at low energy ≈32 meV because a sizable phonon gap is formed between the acoustic and optical phonon branches; we can attribute such a strong peak to twophonon electron scatterings with acoustic phonons of TA(Q) + LA(M) and TA(M) + LA(Q). In total, we measured four mono and four bilayer WSe_{2} devices, with all showing consistent single and twophonon electron–phonon scattering features (Supplementary Figs. 4 and 5). Our findings were additionally confirmed with three mono and two bilayer MoSe_{2}, two mono and three bilayer WS_{2}, and one mono and one bilayer MoS_{2} planar tunnel junctions. IETS spectra for the devices not discussed in the main text are presented in Supplementary Figs. 6 and 7.
Lastly, we remark that the experimentally identified ZO_{1} phonons are consistently higher in energy than the theoretically expected freestanding SCTMD phonon excitations, as indicated with red arrows in Fig. 2a (WSe_{2}), Fig. 4a (MoS_{2}), Fig. 5a (MoSe_{2}), and Fig. 5b (WS_{2}), suggesting that flexural motions of chalcogen atoms become hardened in 2D vdW vertical heterostructures by as much as ≈ 3 meV^{19}. Although it is not straightforward to draw the exact phonon dispersions of our graphene–SCTMD–graphene heterojunctions, primarily due to the lattice mismatches, we discover that the assessable ZO phonon density of states indeed shifts to higher energies, even in the simplest graphene(4 × 4)–WSe_{2}(3 × 3) heterostructures (Supplementary Fig. 3).
Discussion
To further support our findings, we prepared another type of graphite–SCTMD–graphite vertical heterostructure: twisted doublelayer WSe_{2} vertical junctions. As shown in the optical image in Supplementary Fig. 8, two monolayer WSe_{2} films are serially transferred on top of the bottom graphite, and the misalignment angle of the double WSe_{2} layers is estimated to be around 13° as judged from the crystallographic directions of each layer. Distinct from Bernal stacked bilayers, the inversion symmetry of the twisted doublelayer WSe_{2} is naturally broken such that the IETS features from the doublelayer device should be quite dissimilar to those from conventional bilayer WSe_{2}. Indeed, we find that the overall IETS signals in the doublelayer device are similar to those from the monolayer films in terms of the excited phonon modes, without noticeable highenergy dG/dV_{b} features that could relate to the Q + M twophonon excitations (Supplementary Fig. 8). Although more indepth experimental works should follow to clarify the compelling electron–phonon scatterings in twisted doublelayer systems, we feel confident that the current data sufficiently support our interpretation made in the current manuscript: layernumber variant electronic structures, symmetry, and quantum interference play important roles in both single and twophonon electron–phonon scattering processes in SCTMD films.
As previously remarked, we implement graphite flakes as the source and drain electrodes in our vertical planar tunnel junctions to preserve the intrinsic electronic properties of the ultrathin SCTMD layers. As electrons tunnel through the graphite–SCTMD vertical junctions, therefore, there is a high chance they will be scattered by graphite phonons as well. From our IETS measurements, we are indeed able to locate several dG/dV_{b} spectra that are likely related to the graphite phonons and the twophonon inelastic electron scatterings with the phonons of the SCTMDs and graphite layers. For example, the dG/dV_{b} spectra at ≈ 66 meV in both mono and bilayer devices, as respectively marked with red arrows and dotted yellow lines in Fig. 6a and b, are from the graphite ZO(K) phonons^{16,18,19}. It is worth mentioning that the graphite ZO(K) signals persist up to T ≥ 100 K, in stark contrast to the temperature sensitive twophonon IETS features discussed above. Moreover, the graphite phonon modes emerge only when the twophonon WSe_{2} electron–phonon scatterings become diminished at elevated temperatures (T > 30 K). We are also able to observe several other graphite and twophonon graphite–SCTMD phonon signatures within the energy range eV_{b} ≤ 300 meV, but detailed analyses of these highenergy spectra are beyond the current study and will be presented elsewhere. Finally, moving beyond bilayer, we find that the IETS signals originating from higherorder electron–phonon scatterings in three and fourlayer SCTMD devices are consistently higher in intensity, as presented in Supplementary Fig. 9, suggesting that charge flows through multilayered SCTMDs become heavily regulated and are often facilitated by multiple electron–phonon scattering processes.
In summary, we spectroscopically characterized phononmode specific electron–phonon scatterings in four prototypical 2D semiconducting films, WSe_{2}, MoS_{2}, WS_{2}, and MoSe_{2}, by IETS measurements, quantum transport simulations, and density functional theory. Thanks to the solid physical and electrical stability of the planar tunnel junctions, we were able to probe several single and twophonon inelastic electron scattering processes that are sensitive to the layernumber dependent electronic structures, symmetry, and geometric phase. From the standpoint of electron–phonon scattering physics in condensed matter systems, our experimental measurements suggest that quantum interference can be a major player in momentumconserving inelastic electron–phonon scatterings and thus charge transport behaviors in 2D SCTMDs. In addition, we demonstrated that our experimental approach, utilizing inelastic tunneling spectroscopy with 2D planar vdW tunnel junctions as a highfidelity material metrology platform, is applicable to a wide range of lowdimensional quantum materials and their unlimited combinations for probing charge carrier interactions with phonons and other intriguing quasiparticles^{38,39}.
Methods
Device fabrication
In our planar vdW heterostructures, preparation of atomically clean interfaces is of critical importance for an accurate and reliable material characterization of the vertical junctions. At first, 60–100 nm thick hBN flakes are mechanically exfoliated on a 90 nm thick SiO_{2} layer on Si substrate. Then, a mechanically isolated graphite flake of thickness 5 nm or more is transferred to a prelocated hBN flake on the SiO_{2}/Si substrate using a dry transfer method. We utilize polymer stacks of PMMA (poly(methyl methacrylate))–PSS (polystyrene sulfonate) layers for such tasks and carefully adjust the thickness of each layer to enhance the optical contrast of the exfoliated ultrathin 2D layered materials. We remove the PMMA film in warm (60 °C) acetone and further anneal the samples at 350 °C for several hours in a mixture of Ar:H_{2} = 9:1 to ensure residuefree graphite surfaces. Next, instead of again using the polymer stacks, we use a GelPak to exfoliate and transfer mono and bilayer SCTMD films on top of the hBN–graphite stack. GelPak residuefree surfaces are confirmed with an atomic force microscope measurement. Finally, a top graphite flake prepared on the PMMA–PSS polymer stack is transferred to form a vertical graphite–SCTMD–graphite planar tunnel device. We note that the crystallographic angles of the graphite electrodes and the SCTMD films are intentionally misaligned, and the thicknesses of the semiconducting layers are confirmed via atomic force microscope. The active junction areas, which are determined by the widths of the top and bottom graphite flakes, are several tenths of a square micrometer. We purchased highpurity (>99.995%) SCTMD crystals from HQ Graphene with no additional dopants added during growth procedures and large size graphenium flakes from NGS Naturgraphit GmbH.
DFPT for calculating phonon dispersion
Phonon dispersions of freestanding SCTMD monolayers and graphene–WSe_{2}–graphene heterostructures are calculated using DFPT, implemented in Vienna Ab initio Simulation Package^{40} within generalized gradient approximation (PBE)^{41}. Projector augmented pseudopotentials are used and the planewave cutoff is set to be 500 eV^{42}. The phonon dispersions of freestranding SCTMD monolayers are calculated with a 3 × 3 supercell and 2 × 2 kpoint mesh. The phonon structures of graphene–WSe_{2}–graphene heterostructures are calculated with a 3 × 3 WSe_{2} supercell and 4 × 4 graphene supercell with 2 × 2 kpoint mesh as well. The lattice constant of WSe_{2} is set to be 3.325 Å in PBE, and the graphene lattices are relaxed by –1% to compensate for any WSe_{2}–graphene lattice mismatch.
Quantum transport simulation
Quantum transport simulations are performed using an electrontunneling scattering matrix with twoparticle Green functions. The twoparticle Green function \({G}_{\kappa \kappa ^{\prime} }(\tau ,s,t)\) determines the transmission probability of the tunnel junctions in the time domain as follows
where \(\tau ,s,t \; > \; 0\). The transmission probability \(T\left({\epsilon }_{{{{{{\rm{f}}}}}}},{\epsilon }_{{{{{{\rm{i}}}}}}}\right)\) is used to calculate the vertical electron tunneling current, \(I\left(V\right)\propto \int d{\epsilon }_{{{{{{\rm{f}}}}}}}d{\epsilon }_{{{{{{\rm{i}}}}}}}T({\epsilon }_{{{{{{\rm{f}}}}}}},{\epsilon }_{{{{{{\rm{i}}}}}}})[{f}_{{{{{{\rm{L}}}}}}}\left({\epsilon }_{{{{{{\rm{i}}}}}}}{eV}\right){f}_{{{{{{\rm{R}}}}}}}\left({\epsilon }_{{{{{{\rm{f}}}}}}}\right)]\). The Green function consists of the product of a probability amplitude and its complex conjugation, which correspond to the propagation of electrons moving forward and backward in the time domain. Although algebraic evaluation of the twoparticle Green function is complicated, Feynman diagrams as provided in Fig. 7 simplify our calculations while providing intuitive understanding. Each vertex represents electron–phonon interaction with coupling strength \({M}_{\kappa ^{\prime} ,\kappa }^{{{{{{\rm{\lambda }}}}}}}\). Here, \({{{{{\rm{\lambda }}}}}}\) denotes a phonon mode that scatters an electron from momentum state \(\kappa\) to \(\kappa ^{\prime}\). When electrons scatter with the phonon modes \({\lambda }_{{{{{{\rm{r}}}}}}}\) and \({\lambda }_{{{{{{\rm{b}}}}}}}\), the momentumconserving twophonon inelastic electron scatterings allow four independent scattering processes, as depicted in the Feynman diagram (Fig. 7). Then, the transmission probability T can be estimated with the absolute square of the sum of the two electron–phonon scattering amplitudes, i.e., T = A+B^{2 }=A^{2}+B^{2}+A(B)*+(A)*B, where the first and second terms represent the first and second Feynman diagrams in Fig. 7. The third and fourth terms, which are responsible for the quantum interference, represent the third and fourth Feynman diagrams, respectively. Detailed evaluations of \({G}_{\kappa {\kappa }^{{\prime} }}\left(\tau ,s,t\right)\), Hamiltonian, and geometric phase are presented in the Supplementary Information.
Data availability
All data supporting the findings of this study are available from the corresponding authors on request.
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Acknowledgements
We thank Y.W.S. and H.S.S. for their careful reading and comments on our manuscript. This work was supported by research grants for basic research (KRISS2020GP20011059) funded by the Korea Research Institute of Standards and Science and the Basic Science Research Program (NRF2019R1A2C2004007) through the National Research Foundation of Korea. This work was also supported by the DFG (SFB1170 “ToCoTronics”), the WűzburgDresden Cluster of Excellence ct.qmat, EXC2147, projectid 39085490.
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S.J. and SJ.C. designed the experiments, and D.H.L and H.K. fabricated the devices and performed the inelastic electron tunneling spectroscopy measurements. SJ.C. carried out the quantum transport simulations and YS.K. performed the DFPT calculations. D.H.L., SJ.C., YS.K., and S.J. analyzed the data and cowrote the paper. All authors contributed to the manuscript.
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Lee, D.H., Choi, SJ., Kim, H. et al. Direct probing of phonon mode specific electron–phonon scatterings in twodimensional semiconductor transition metal dichalcogenides. Nat Commun 12, 4520 (2021). https://doi.org/10.1038/s41467021248752
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DOI: https://doi.org/10.1038/s41467021248752
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