Graphene/MoS 2 heterostructures are formed by combining the nanosheets of graphene and monolayer MoS 2 . The electronic features of both constituent monolayers are rather well-preserved in the resultant heterostructure due to the weak van der Waals interaction between the layers. However, the proximity of MoS 2 induces strong spin orbit coupling effect of strength ∼1 meV in graphene, which is nearly three orders of magnitude larger than the intrinsic spin orbit coupling of pristine graphene. This opens a bandgap in graphene and further causes anticrossings of the spin-nondegenerate bands near the Dirac point. Lattice incommensurate graphene/MoS 2 heterostructure exhibits interesting moiré patterns which have been observed in experiments. The electronic bandstructure of heterostructure is very sensitive to biaxial strain and interlayer twist. Although the Dirac cone of graphene remains intact and no charge-transfer between graphene and MoS 2 layers occurs at ambient conditions, a strain-induced charge-transfer can be realized in graphene/MoS 2 heterostructure. Application of a gate voltage reveals the occurrence of a topological phase transition in graphene/MoS 2 heterostructure. In this chapter, we discuss the crystal structure, interlayer effects, electronic structure, spin states, and effects due to strain and substrate proximity on the electronic properties of graphene/MoS 2 heterostructure. We further present an overview of the distinct topological quantum phases of graphene/MoS 2 heterostructure and review the recent advancements in this field.

Phonon-induced spin relaxation rates and electron g-factor tuning of quantum dots are studied as function of in-plane and perpendicular magnetic fields for different dot sizes. We consider Rashba and Dresselhaus spinorbit mixing in wide and narrow-gap semiconductors, and show how Zeeman sublevels can relax via piezoelectric (GaAs) and deformation (InSb) potential coupling to acoustic phonons. We find that strong confinement may induce minima in the rates at particular values of the magnetic field (due to a magnetic field-induced cancellation of the spin-orbit effects), where spin relaxation times can reach seconds. We also report on g-factor anisotropy. We obtain good agreement with available experimental values.Keywords: g-factor; Phonon-induced spin relaxation; Quantum dotsSince the proposal of a qubit based on the electron spin of quantum dots (QDs) [1], much work has been done to understand the processes that may cause their relaxation, since long coherence times are required. One of those processes is related to the phonon-induced spin-flip rates of Zeeman sublevels in QDs in magnetic fields, where the spin purity of the levels is broken by the spin-orbit (SO) interaction. A recent experiment [2] has shown a spin relaxation time ≈ 0.55 ms at an in-plane field of 10 T in a GaAs QD defined in a 2DEG. In general, SO effects have been considered via perturbation theory [3], although exact treatments have also been presented [4,5]. The perturbative approach, which includes only a few states, has been called into question by the demonstration that a larger basis is needed in order to achieve convergence even for the lowest QD states when the QD vertical width is narrow [4], as a complex interplay between different energy scales can be present [6]. Insights on the purity of the spin degree of freedom of electrons in QDs can also be extracted from measurements of their effective g-factor, e.g., by means of capacitance [7] and energy [8] spectroscopies.In this work we study spin-flip rates and g-factor tuning in QDs under SO influence. Our goal is to compare wide and narrow-gap materials under in-plane and perpendicular magnetic fields, at different QD sizes.The QD is defined by an in-plane parabolic confinement, V (r) = mω 2 0 r 2 /2, where m (ω 0 = E 0 / ) is the electronic effective mass (confinement frequency); the QD lateral length is l 0 = /(mω 0 ). The vertical confinement V (z) is strong enough so that only the state in the first quantum well subband is relevant, and its function is ϕ z (z) = 2/z 0 sin (πz/z 0 ) if a hard wall is assumed, z 0 being the QD vertical well thickness. In a magnetic field B, the unperturbed Hamiltonian, H 0 = 2 k 2 /2m+V (r)+H Z , has the well-known FockDarwin (FD) solution, where H Z = g 0 µ B B · σ/2 is the Zeeman term, g 0 is the bulk g-factor, and k is the kinetic momentum that includes the magnetic vector potential. We include all SO terms in 2D zincblende QDs, namely Rashba * present address: Physics Department, University of Ottawa, Ottawa, Ontario K1N6N5, Canada.and Dresse...

The role of electronic interactions in the level structure of semiconductor quantum dots is analyzed in terms of the correspondence to the integrability of a classical system that models these structures. We find that an otherwise simple system is made strongly non-integrable in the classical regime by the introduction of particle interactions. In particular we present a twoparticle classical system contained in a d-dimensional billiard with hard walls.Similarly, a corresponding two-dimensional quantum dot problem with three particles is shown to have interesting spectral properties as function of the interaction strength and applied magnetic fields.

We study the model of two interacting particles moving in a 1D box, paying main attention to the quantum‐classical correspondence for the average shape of quantum eigenstates and for the local density of states (LDOS). We show that if the classical motion is chaotic, in a deep semi‐classical region of a quantum system, both the shape of eigenstates and of the LDOS coincide with their classical analogs, on average. However, individual eigenstates exhibit quite large fluctuations which may not be treated as statistical ones. Thus, comparison of quantum quantities to the classical ones allows one to detect quantum effects of localization which for conservative systems emerge in the energy space.

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