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Related publication: Kang M., Jung S. W., Shin W. J., Sohn Y., Ryu S. H., Kim T. K., Hoesch M. & Kim K. S. Holstein polaron in a valleydegenerate two-dimensional semiconductor. Nat. Mater. 17, 676–680 (2018). DOI: 10.1038/s41563-018-0092-7
If you imagine a solid bead rolling on a soft cushion, it leaves distortions in the cushion in its wake. Transfer this analogy to the quantum-mechanical realm, and the condensed matter physics version of the rolling bead is a polaron.
In nature, one can often find an entity strongly interacting with its surrounding environments. A familiar example is a solid bead rolling on a soft cushion, which is accompanied by some distortions left along the moving path. The quantum-mechanical version of this rolling bead in condensed-matter physics is a composite particle called the polaron. The theoretical basis of polarons was founded by Soviet Physicist Landau back in the early 1930s. An electron residing in an ionic crystal would attract the positively charged ions towards it and push the negatively charged ions away from it by electric forces. This can be viewed as a composite particle of an electron dragging a cloud of lattice distortions (or phonons) with it (Fig. 1). This electron-phonon interaction can be approximately described by two standard models, one is the Fröhlich-type and the other is the Holstein-type1. The Holstein-type polaron is the lattice model that has been widely employed to describe the mechanism of high-temperature superconductivity and the limiting factor of carrier mobility in solar-cell devices. Despite such potential importance in both fundamental physics and device applications, the Holstein polaron has remained elusive, because it is extremely difficult to solve analytically. Only recently, the energy spectrum of Holstein polarons, which is key to understanding their fundamental properties, was successfully calculated owing to the recent advances in theoretical models and computational techniques2. These theoretical predictions laid a ground for experimentalists to hunt for the energy spectrum of Holstein polarons that have remained undiscovered for more than 50 years.
The electron density of 1014 cm–2 was achieved by ionic liquid gating3, where the spatial separation of positively charged and negatively charged ions forms an electric double layer in the surface of multilayer MoS2. The similar atomic-scale dipole layer can also be formed by the deposition of alkali-metal (Rb) atoms that donate electrons to MoS2 and become positively charged ions4. This surface chemical doping was employed in our study to experimentally explore a signature of Holstein polarons in the superconducting regime of MoS2. The energy spectrum of Holstein polarons can be detected by an experimental technique called ARPES5. The high-flux photons generated by the synchrotron radiation is incident on the samples, and photoelectrons are generated leaving photoholes behind (Fig. 2a). By recording the energy and angle of the emitted photoelectrons by an electron spectrometer, one can learn about the energy-momentum relation of initial-state electrons in the samples. This process is basically a quantum-mechanical transition, and information on the interaction of photoholes left in the samples to other degrees of freedom, such as phonons, is recorded together in the energy-momentum relation measured by ARPES. The strong interaction of electrons to phonons (polarons) appears as a series of abrupt changes in the energy-momentum spectrum (Fig. 2b). The typical energy scale of electron-phonon coupling is in the order of a few tens of milli-electronvolts, which is comparable to the energy resolution of ARPES. In this respect, the energy resolution was expected to be critical in resolving the signature of Holstein polarons, and our first choice of beamline was I05 at Diamond.
Our team had tried with help from the beamline scientists at I05 to find a signature of electron-phonon interactions in MoS2 doped by Rb atoms up to the carrier density at which the superconducting dome was observed. The energy-momentum spectrum of doped electrons in MoS2 shown below the Fermi energy by surface doping and measured by ARPES was overall parabolic. At that time, the yield of photoelectrons was anomalously high with the photon energy of 50–60 eV. At beamline I05, there is a safety rule that one has to keep the number of photoelectrons below a certain limit to prevent the detector from being burned out. As restricted by this safety rule, we had to reduce the number of photoelectrons at detector by narrowing the slit of the electron analyser (the narrower the slit is the better the energy resolution, but usually not used for poor yield of photoelectrons). With the narrowest slit (the best energy-resolution condition), we found something totally unexpected in the energy-momentum spectrum of MoS2. That is, we could observe a subtle signature of abrupt kinks (indicated by arrows in (Fig. 2c)) which is collectively identified as a hitherto unobserved energy spectrum of Holstein polarons predicted in theory2. To the best of our knowledge, this is the first experimental observation of the spectral function of Holstein polarons, which would not be possible without the superior energy resolution of beamline I05.
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