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.

Operation speed and coherence time are two core measures for the viability of a qubit. Strong spin-orbit interaction (SOI) and relatively weak hyperfine interaction make holes in germanium (Ge) intriguing candidates for spin qubits with rapid, all-electrical coherent control. Here we report ultrafast single-spin manipulation in a hole-based double quantum dot in a germanium hut wire (GHW). Mediated by the strong SOI, a Rabi frequency exceeding 540 MHz is observed at a magnetic field of 100 mT, setting a record for ultrafast spin qubit control in semiconductor systems. We demonstrate that the strong SOI of heavy holes (HHs) in our GHW, characterized by a very short spin-orbit length of 1.5 nm, enables the rapid gate operations we accomplish. Our results demonstrate the potential of ultrafast coherent control of hole spin qubits to meet the requirement of DiVincenzo’s criteria for a scalable quantum information processor.

The observation of an antisymmetric magnetoresistance in a trilayer van der Waals heterostructure Fe ₃ GeTe ₂ /graphite/Fe ₃ GeTe ₂ .

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 review theoretical and experimental highlights in transport in two-dimensional topological materials over the last five years. Topological materials comprise topological insulators, Weyl semimetals and topological superconductors. This review focuses on key developments in the understanding of transport phenomena involving surfaces and interfaces of two-dimensional topological materials that have not been covered elsewhere. The review is structured around the following general topics: (i) topological insulators are finding applications in magnetic devices, while controversy continues to surround Hall transport in doped samples and the general issue of topological protection; (ii) state-of-the-art experiments on transition metal dichalcogenides have revealed new valley-dependent electrical and optical phenomena which have spin-dependent counterparts in topological insulators; (iii) in Weyl semimetals the manifestations of Fermi arcs in transport are actively investigated as well as controversial; (iv) a new and growing field centres on the non-linear electrical and optical responses of topological materials, where fundamental questions emerge about the interplay of the Berry curvature and disorder scattering; and (v) topological superconductor research is dominated by the quest for chiral superconductivity, Majorana fermions and topological quantum computing. Prospects for future research in this vast field are outlined in the closing section.

Silicon quantum dot spin qubits provide a promising platform for large-scale quantum computation because of their compatibility with conventional CMOS manufacturing and the long coherence times accessible using ²⁸Si enriched material. A scalable error-corrected quantum processor, however, will require control of many qubits in parallel, while performing error detection across the constituent qubits. Spin resonance techniques are a convenient path to parallel two-axis control, while Pauli spin blockade can be used to realize local parity measurements for error detection. Despite this, silicon qubit implementations have so far focused on either single-spin resonance control, or control and measurement via voltage-pulse detuning in the two-spin singlet–triplet basis, but not both simultaneously. Here, we demonstrate an integrated device platform incorporating a silicon metal-oxide-semiconductor double quantum dot that is capable of single-spin addressing and control via electron spin resonance, combined with high-fidelity spin readout in the singlet-triplet basis.