Charge Transfer Effects in Naturally Occurring van der Waals Heterostructures $(\mathrm{PbSe}{)}_{1.16}({\mathrm{TiSe}}_2{)}_m$ ($m=1$, 2)

van der Waals heterostructures (VDWHs) exhibit rich properties and thus has potential for applications, and charge transfer between different layers in a heterostructure often dominates its properties and device performance. It is thus critical to reveal and understand the charge transfer effects in VDWHs, for which electronic structure measurements have proven to be effective. Using angle-resolved photoemission spectroscopy, we studied the electronic structures of $(\mathrm{PbSe}{)}_{1.16}({\mathrm{TiSe}}_2{)}_m$ ($m=1$, 2), which are naturally occurring VDWHs, and discovered several striking charge transfer effects. When the thickness of the ${\mathrm{TiSe}}_2$ layers is halved from $m=2$ to $m=1$, the amount of charge transferred increases unexpectedly by more than 250%. This is accompanied by a dramatic drop in the electron-phonon interaction strength far beyond the prediction by first-principles calculations and, consequently, superconductivity only exists in the $m=2$ compound with strong electron-phonon interaction, albeit with lower carrier density. Furthermore, we found that the amount of charge transferred in both compounds is nearly halved when warmed from below 10 K to room temperature, due to the different thermal expansion coefficients of the constituent layers of these misfit compounds. These unprecedentedly large charge transfer effects might widely exist in VDWHs composed of metal-semiconductor contacts; thus, our results provide important insights for further understanding and applications of VDWHs.

Figure 1

(a) Crystal structure of $(\mathrm{PbSe}{)}_{1.16}({\mathrm{TiSe}}_2{)}_m$ ($m=1$, 2). The bottom left depicts the projected 2D Brillouin zones (BZ) of the ${\mathrm{TiSe}}_2$ (blue hexagon) and PbSe layers (red squares). Note that the $\mathrm{\Gamma }$ point of the second PbSe BZ and the $M$ point of the ${\mathrm{TiSe}}_2$ layer coincide. The bottom right shows a comparison of their lattice constants. (b) Schematic diagram of the charge transfer at interfaces. Orange and cyan rectangles represent PbSe and ${\mathrm{TiSe}}_2$ layers, respectively. PbSe layers donate electrons to ${\mathrm{TiSe}}_2$ layers. [(c) and (d)] Photoemission intensity maps of $m1$ and $m2$ at $E_F$, respectively, over the projected 2D BZ. Black dashed ellipses indicate the Fermi pockets and the intensity has been integrated over a window of ($E_F-2.5\mathrm{meV}$, $E_F+2.5\mathrm{meV}$). Data were threefold symmetrized. Photoemission intensity plots (e) and (f) for $m1$ and (g) and (h) for $m2$ are presented near $\mathrm{\Gamma }$ and $M$, respectively. The dashed lines indicate band dispersions obtained from the momentum and energy distribution curves (MDCs and EDCs). All data were taken at 10 K with 80 eV photons.

Figure 2

[(a) and (b)] EDCs along the $\mathrm{\Gamma }\text{−}M$ cuts shown in Figs. 1 and 1 for $m1$ and $m2$, respectively. Spectra around $M$ have been intentionally scaled down by 0.25 to be comparable to those around $\mathrm{\Gamma }$. (c) Comparison of their EDCs at the $M$ point. The line shape (d) for $m1$ can be fitted by a Lorentzian peak, while that (e) for $m2$ is fit best by a Gaussian envelope. (f) The phase diagram of electron-doped ${\mathrm{TiSe}}_2$, whose regime below 0.1 doping is reproduced from that of ${\mathrm{Cu}}_x{\mathrm{TiSe}}_2$ with one Cu ion doping one electron [33], and the overdoped regime is a sketch. $m1$ is located in the heavily overdoped regime with quasiparticlelike spectra, which extends the original phase diagram, while $m2$ is located in the optimally doped regime and its spectra exhibit the typical Franck-Condon broadening of polarons due to strong EPC.

Figure 3

(a) Fermi surfaces of $(\mathrm{PbSe}{)}_{1.16}({\mathrm{TiSe}}_2{)}_m$ ($m=1$, 2). The upper halves are room-temperature photoemission intensity maps of $m1$ and $m2$ integrated over ($E_F-2.5\mathrm{meV}$, $E_F+2.5\mathrm{meV}$). Data were sixfold symmetrized. The lower halves are a quantitative comparison of Fermi pocket size at low (8.5 and 10 K) and room (295 and 312 K) temperatures. (b) Comparisons of photoemission intensity plots around $M$ for $m1$ and $m2$ at low and ambient temperatures. ($c1-c2$) Direct comparisons of the EDCs taken at high and low temperatures for $m1$ and $m2$, respectively. (d) Temperature-dependent EDCs located at $M$ for $m1$ and $m2$, respectively. (e) Temperature dependence of the $\eta$ band bottom energy for $m1$ and $m2$. (f) Temperature dependence of carrier concentrations for $m1$ and $m2$ due to charge transfer.

Figure 4

Band structure comparison of the ${\mathrm{TiSe}}_2$ component in misfit VDWHs at low and room temperatures, as simulated by first-principles calculations based on the thermal expansion of the lattice.