A short proof of the surjectivity of the period map on K3 manifolds

In this note, we give a simple proof of the Todorov's surjectivity result on the period map of K3 surfaces in a differential geometric setting. Our proof makes use of collasping geometry of hyperk\"{a}hler 4-manifolds developped by Sun-Zhang, and does not rely on the solution to the Calabi conjecture

Weak Localization and Antilocalization in Twisted Bilayer Graphene

We theoretically study the weak localization (WL) and weak antilocalization (WAL) effects in twisted bilayer graphene that placed in alignment on a hexagonal boron nitride substrate. The low-energy band of the top layer exhibits a Dirac cone with a negligible gap, while the bottom layer has a relatively large band gap. The system features a low concentration of impurities, and the quantum correction to the conductivity arises from the quantum interference between two time-reversed impurity scattering trajectories. Through bias voltage tuning, we find that inter-layer scattering significantly contributes to the conductivity correction when the Fermi surface areas of the two valleys at low energy are comparable. We observe a double crossover from WL to WAL and back to WL at a specific range of Fermi energy, which is a particularly intriguing phenomenon.Comment: 10 pages,4 figure

Moir\'e excitons: from programmable quantum emitter arrays to spin-orbit coupled artificial lattices

Highly uniform and ordered nanodot arrays are crucial for high performance quantum optoelectronics including new semiconductor lasers and single photon emitters, and for synthesizing artificial lattices of interacting quasiparticles towards quantum information processing and simulation of many-body physics. Van der Waals heterostructures of 2D semiconductors are naturally endowed with an ordered nanoscale landscape, i.e. the moir\'e pattern that laterally modulates electronic and topographic structures. Here we find these moir\'e effects realize superstructures of nanodot confinements for long-lived interlayer excitons, which can be either electrically or strain tuned from perfect arrays of quantum emitters to excitonic superlattices with giant spin-orbit coupling (SOC). Besides the wide range tuning of emission wavelength, the electric field can also invert the spin optical selection rule of the emitter arrays. This unprecedented control arises from the gauge structure imprinted on exciton wavefunctions by the moir\'e, which underlies the SOC when hopping couples nanodots into superlattices. We show that the moir\'e hosts complex-hopping honeycomb superlattices, where exciton bands feature a Dirac node and two Weyl nodes, connected by spin-momentum locked topological edge modes.Comment: To appear in Science Advance

Spin-valley qubit in nanostructures of monolayer semiconductors: Optical control and hyperfine interaction

We investigate the optical control possibilities of spin-valley qubit carried by single electrons localized in nanostructures of monolayer TMDs, including small quantum dots formed by lateral heterojunction and charged impurities. The quantum controls are discussed when the confinement induces valley hybridization and when the valley hybridization is absent. We show that the bulk valley and spin optical selection rules can be inherited in different forms in the two scenarios, both of which allow the definition of spin-valley qubit with desired optical controllability. We also investigate nuclear spin induced decoherence and quantum control of electron-nuclear spin entanglement via intervalley terms of the hyperfine interaction. Optically controlled two-qubit operations in a single quantum dot are discussed.Comment: 17pages, 10 figure