Three mechanisms are known to contribute to second-order nonlinear current: Extrinsic nonlinear Drude, Berry curvature dipole, and intrinsic Berry connection polarizability. Here, we predict an intrinsic contribution to the current related to the quantum metric, a quantum geometric property of the electronic wave function. This contribution manifests in systems that simultaneously break the time-reversal and the inversion symmetry. Interestingly, this contribution is dissipative and contributes to both longitudinal and transverse response. The quantum metric-induced NL current dominates transport in parity-time reversal symmetric systems near the band edges, something we show explicitly for topological antiferromagnets.

Nonlinear responses are actively studied as probes of topology and band geometric properties of solids. Here, we show that second harmonic generation serves as a probe of the Berry curvature, quantum metric, and quantum geometric connection. We generalize the theory of second harmonic generation to include Fermi surface effects in metallic systems, and finite scattering timescale. In doped materials the Fermi surface and Fermi sea cause all second harmonic terms to exhibit resonances, and we identify two novel contributions to the second harmonic signal: a double resonance due to the Fermi surface and a higher-order pole due to the Fermi sea. We discuss experimental observation in the monolayer of time reversal symmetric Weyl semimetal ${\mathrm{WTe}}_2$ and the parity-time reversal symmetric topological antiferromagnet CuMnAs.

We investigate the possibility of band structure engineering in the recently predicted 2D layered form of blue phosphorus via an electric field $\left({\mathrm{E}}_z\right)$ applied perpendicular to the layer(s). Using density functional theory, we study the effect of a transverse electric field in monolayer as well as three differently stacked bilayer structures of blue phosphorus. We find that for ${\mathrm{E}}_z>0.2$ V/Å the direct energy gap at the $\Gamma$ point, which is much larger than the default indirect band gap of mono- and bilayer blue phosphorus, decreases linearly with the increasing electric field, becomes comparable to the default indirect band gap at ${\mathrm{E}}_z\approx 0.45\left(0.35\right)$ V/Å for monolayer (bilayers), and decreases further until the semiconductor to metal transition of 2D blue phosphorus takes place at ${\mathrm{E}}_z\approx 0.7\left(0.5\right)$ V/Å for monolayer (bilayers). Calculated values of the electron and hole effective masses along various high symmetry directions in the reciprocal lattice suggests that the mobility of charge carriers is also influenced by the applied electric field.

Berry curvature in Weyl semimetals leads to intriguing magnetoconductivity and magnetothermal transport properties. Here, we explore the impact of the tilting of the Weyl nodes on the magnetoconductivity of type-I and type-II Weyl semimetals using the Berry-curvature-connected Boltzmann transport formalism. We find that in addition to the quadratic magnetic field ($B$) corrections induced by the tilt, there are also anisotropic and $B$-linear corrections in several elements of the conductivity matrix. For the case of magnetic field applied perpendicular to the tilt direction, we show the existence of previously unexplored $B$-linear transverse conductivity components. For the other case of magnetic field applied parallel to the tilt axis, the $B$-linear corrections appear in the longitudinal conductivity, giving rise to anisotropic magnetoresistance measurements. Our systematic analysis of the full magnetoconductivity matrix predicts several specific experimental signatures related to the tilting of the Weyl nodes in both type-I and type-II Weyl semimetals.

Transition-metal dichalcogenides showing type-II Dirac fermions are emerging as innovative materials for nanoelectronics. However, their excitation spectrum is mostly unexplored yet. By means of high-resolution electron energy loss spectroscopy and density functional theory, here, we identify the collective excitations of type-II Dirac fermions (3D Dirac plasmons) in ${\mathrm{PtTe}}_2$ single crystals. The observed plasmon energy in the long-wavelength limit is $\sim 0.5\mathrm{eV}$, which makes ${\mathrm{PtTe}}_2$ suitable for near-infrared optoelectronic applications. We also demonstrate that interband transitions between the two Dirac bands in ${\mathrm{PtTe}}_2$ give rise to additional excitations at $\sim 1$ and $\sim 1.4\mathrm{eV}$. Our results are crucial to bringing to fruition type-II Dirac semimetals in optoelectronics.