Nonlinear optical processes, such as harmonic generation, are of great interest for various applications, e.g., microscopy, therapy, and frequency conversion. However, high-order harmonic conversion is typically much less efficient than low-order, due to the weak intrinsic response of the higher-order nonlinear processes. Here we report ultra-strong optical nonlinearities in monolayer MoS₂ (1L-MoS₂): the third harmonic is 30 times stronger than the second, and the fourth is comparable to the second. The third harmonic generation efficiency for 1L-MoS₂ is approximately three times higher than that for graphene, which was reported to have a large χ⁽³⁾. We explain this by calculating the nonlinear response functions of 1L-MoS₂ with a continuum-model Hamiltonian and quantum mechanical diagrammatic perturbation theory, highlighting the role of trigonal warping. A similar effect is expected in all other transition-metal dichalcogenides. Our results pave the way for efficient harmonic generation based on layered materials for applications such as microscopy and imaging.

We propose an effective lattice Hamiltonian for monolayer MoS${}_2$ in order to describe the low-energy band structure and investigate the effect of perpendicular electric and magnetic fields on its electronic structure. We derive a tight-binding model based on the hybridization of the $d$ orbitals of molybdenum and $p$ orbitals of sulfur atoms and then introduce a modified two-band continuum model of monolayer MoS${}_2$ by exploiting the quasidegenerate partitioning method. Our theory proves that the low-energy excitations of the system are no longer massive Dirac fermions. It reveals a difference between electron and hole masses and provides trigonal warping effects. Furthermore, we predict a valley-degeneracy-breaking effect in the Landau levels. In addition, we also show that applying a gate voltage perpendicular to the monolayer modifies the electronic structure, including the band gap and effective masses.

Strain engineering has emerged as a powerful tool to modify the optical and electronic properties of two-dimensional crystals. Here we perform a systematic study of strained semiconducting transition metal dichalcogenides. The effect of strain is considered within a full Slater-Koster tight-binding model, which provides us with the band structure in the whole Brillouin zone (BZ). From this, we derive an effective low-energy model valid around the $K$ point of the BZ, which includes terms up to second order in momentum and strain. For a generic profile of strain, we show that the solutions for this model can be expressed in terms of the harmonic oscillator and double quantum well models, for the valence and conduction bands respectively. We further study the shift of the position of the electron and hole band edges due to uniform strain. Finally, we discuss the importance of spin-strain coupling in these 2D semiconducting materials.

We study the second-order nonlinear optical response of a Weyl semimetal (WSM), i.e., a three-dimensional metal with linear band touchings acting as pointlike sources of Berry curvature in momentum space, termed “Weyl-Berry monopoles.” We first show that the anomalous second-order photocurrent of WSMs can be elegantly parametrized in terms of Weyl-Berry dipole and quadrupole moments. We then calculate the corresponding charge and node conductivities of WSMs with either broken time-reversal invariance or inversion symmetry. In particular, we predict a dissipationless second-order anomalous node conductivity for WSMs belonging to the TaAs family.

We study the effect of a perpendicular magnetic field on the electronic structure and charge transport of a monolayer ${\text{MoS}}_{2}$ nanoribbon at zero temperature. We particularly explore the induced valley Zeeman effect through the coupling between the magnetic field $B$ and the orbital magnetic moment. We show that the effective two-band Hamiltonian provides a mismatch between the valley Zeeman coupling in the conduction and valence bands due to the effective mass asymmetry and it is proportional to ${B}^{2}$ similar to the diamagnetic shift of exciton binding energies. However, the dominant term which evolves with $B$ linearly, originates from the multiorbital and multiband structures of the system. Besides, we investigate the transport properties of the system by calculating the spin-valley resolved conductance and show that, in a low-hole doped case, the transport channels at the edges are chiral for one of the spin components. This leads to a localization of the nonchiral spin component in the presence of disorder and thus provides a spin-valley polarized transport induced by disorder.