Phonon softening is a ubiquitous phenomenon in condensed matter systems which is usually associated with charge density wave (CDW) instabilities and anharmonicity. The interplay between phonon softening, CDW and superconductivity is a topic of intense debate. In this work, the effects of anomalous soft phonon instabilities on superconductivity are studied based on a recently developed theoretical framework that accounts for phonon damping and softening within the Migdal-Eliashberg theory. Model calculations show that the phonon softening in the form of a sharp dip in the phonon dispersion relation, either acoustic or optical (including the case of Kohn-type anomalies typically associated with CDW), can cause a manifold increase of the electron-phonon coupling constant λ. This, under certain conditions, which are consistent with the concept of optimal frequency introduced by Bergmann and Rainer, can produce a large increase of the superconducting transition temperature Tc. In summary, our results suggest the possibility of reaching high-temperature superconductivity by exploiting soft phonon anomalies restricted in momentum space.

The uniaxial strain is an effective way to change the symmetry of a crystal and thus tuning their electronic properties. In the present work, we elucidate the physical mechanism of the symmetry-broken-induced energy valleys drift in monolayer molybdenum disulfide. When the uniaxial strain reduces the rotational symmetry of valleys from C 3 to C 1 and an in-plane electric field breaks the balance of electron distribution of valleys, the valley dipole can survive readily and quantum nonlinear Hall effect might be realized. Our work offers key insights for understanding the uniaxial strain induced valleys drift in monolayer MoS2, which is critical to precisely control the valleytronics properties of two-dimensional materials.

Two-dimensional, honeycomb, and sandwich-structured transition metal dichalcogenides (TMDs) have two nonequivalent energy valleys at the six corners of the hexagonal first Brillouin zone, resulting in promising applications in valleytronics. Here, based on the WSe2/CrSe2 heterojunction, biaxial and uniaxial tensile strains with magnitudes of 0%–6% are demonstrated to have a similar effect on magnetism-induced valley splitting in the lowest conduction band of WSe2. However, at larger magnitudes of 6%–10%, uniaxial strain dramatically decreases the valley splitting. This decrease in valley splitting can be understood by the spin-orbit coupling induced different spin splitting between the two valleys. The findings provide valuable guidance for the valleytronic applications of TMDs.

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