Understanding the dynamics of excitons in two dimensional semiconductors requires a theory that incorporates the essential physics distinct from their three-dimensional counterparts. In addition to the modified dielectric environment, single-particle states with strongly non-parabolic dispersion appear in many two-dimensional band structures, so that "effective mass" is ill-defined. Focusing on electrostatically-biased bilayer graphene as an example where quartic (and higher) dispersion terms are necessary, we present a semi-analytic theory used to investigate the properties of ground and excited excitonic states. This includes determination of relative oscillator strengths and magnetic moments (g-factors) which can be directly compared to recent experimental measurements.

Using a tight-binding description, we show how the zero-dimensional state bound to the edge of a single one-dimensional helical chain of tellurium atoms evolves into two-dimensional states on the c-axis surface of the three-dimensional trigonal bulk. We give an effective Hamiltonian description of its dispersion in k-space by exploiting confinement to a virtual bilayer, and elaborate on the diminished role of spin-orbit coupling. These previously-unidentified intrinsic gap-penetrating surface bands were neglected in the interpretation of seminal experiments, where two-dimensional transport was otherwise attributed to extrinsic accumulation layers.

The combination of space inversion and time reversal symmetries result in doubly-degenerate Bloch states with opposite spin. Many lattices with these symmetries can be constructed by combining a noncentrosymmetric potential (lacking this degeneracy) with its inverted copy. Using simple models, we unravel the evolution of local spin-splitting during this process of inversion symmetry restoration, in the presence of spin-orbit interaction and sublattice coupling. Importantly, through an analysis of quantum mechanical commutativity, we examine the difficulty of identifying states that are simultaneously spatially segregated and spin polarized. We also explain how experimental probes (such as angle-resolved photoemission spectroscopy, or ARPES) of `hidden spin polarization' in layered materials are susceptible to unrelated spin splitting intrinsically induced by broken inversion symmetry at the surface.

Atomic-scale helices exist as motifs for several material lattices. We examine a tight-binding model for a single one-dimensional monatomic chain with a p-orbital basis coiled into a helix. A topologically nontrivial phase emerging from this model supports a chiral symmetry-protected zero-energy mode localized to a boundary, always embedded within a continuum band, regardless of termination site. We identify a topological invariant for this phase that is related to the number of zero energy end modes by means of the bulk-boundary correspondence, and give strict conditions for the existence of the bound state. An additional class of gapped edge modes in the model spectrum has practical consequences for surface states in, e.g., trigonal tellurium and selenium and other van der Waals-bonded one-dimensional semiconductors.

Bandedge states in the indirect-gap group-IV metal monochalcogenide monolayers ('four-six-enes' such as SnS, GeTe, etc.) inherit the properties of nearby reciprocal space points of high symmetry at the Brillouin zone edge. We employ group theory and the method of invariants to capture these essential symmetries in effective Hamiltonians including spin-orbit coupling, and use perturbation theory to shed light on the nature of the bandedge states. In particular, we show how the structure of derived wavefunctions leads to specific dominant momentum and spin scattering mechanisms for both valence holes and conduction electrons, we analyze the direct optical transitions across the bandgap, and expose the interactions responsible for subtle features of the local dispersion relations.

Long carrier spin lifetimes are a double-edged sword for the prospect of constructing "spintronic" logic devices: Preservation of the logic variable within the transport channel or interconnect is essential to successful completion of the logic operation, but any spins remaining past this event will pollute the environment for subsequent clock cycles. Electric fields can be used to manipulate these spins on a fast time scale by careful interplay of spin-orbit effects, but efficient controlled depolarization can only be completely achieved with amenable materials properties. Taking III-VI monochalcogenide monolayers as an example 2D semiconductor, we use symmetry analysis, perturbation theory, and ensemble calculation to show how this longstanding problem can be solved by suitable manipulation of conduction electrons.

Several recent measurements of magnetoresistance in ferromagnet/insulator/semiconductor tunnel junctions have led to controversial claims of spin accumulation, where the signal amplitude and derived spin relaxation time often deviates from theoretically calculated and experimentally confirmed values by several orders of magnitude. These discrepancies cast doubt on the physical origin of the measured magnetoresistance, which was initially attributed to spin precession and dephasing in the semiconductor. More recently, models incorporating transport through localized defects have shown that they can account for device behavior, without any spin accumulation. To directly investigate the role of localized states in this signal, we subject CoFe/SiO2/n-Si junctions to varying doses of proton irradiation. Weak radiation doses not only have little effect on the electrical current-voltage relationship of the junction but also modify the magnetoresistance substantially. Our interpretation of this phenomenon involves the hydrogen passivation of defects within the tunnel barrier, and is consistent with the emerging consensus that defects within the barrier play a crucial role in the physical mechanism behind junction magnetoresistance in this class of devices.

Several recent experiments on three-dimensional topological insulators claim to observe a large charge current-induced nonequilibrium ensemble spin polarization of electrons in the helical surface state. We present a comprehensive criticism of such claims, using both theory and experiment: First, we clarify the interpretation of quantities extracted from these measurements by deriving standard expressions from a Boltzmann transport equation approach in the relaxation-time approximation at zero and finite temperature to emphasize our assertion that, despite high in-plane spin projection, obtainable current-induced ensemble spin polarization is minuscule. Second, we use a simple experiment to demonstrate that magnetic field-dependent open-circuit voltage hysteresis (identical to those attributed to current-induced spin polarization in topological insulator surface states) can be generated in analogous devices where current is driven through thin films of a topologically trivial metal. This result ipso facto discredits the naive interpretation of previous experiments with TIs, which were used to claim observation of helicity, i.e., spin-momentum locking in the topologically protected surface state.

The electronic structure of (group-III) metal-monochalcogenide monolayers exhibits many unusual features. Some, such as the unusually distorted upper valence band dispersion we describe as a 'caldera', are primarily the result of purely orbital interactions. Others, including spin splitting and wavefunction spin-mixing, are directly driven by spin-orbit coupling. We employ elementary group theory to explain the origins of these properties, and use a tight-binding model to calculate the phenomena enabled by them, such as band-edge carrier effective g-factors, optical absorption spectrum, conduction electron spin orientation, and a relaxation-induced upper valence band population inversion and spin polarization mechanism.

The electron number-parity of the ground state of a semiconductor narowire proximity-coupled to a bulk superconductor can alternate between the quantised values $\pm 1$ if parameters such as the wire length $L$, the chemical potential $\mu$ or the magnetic field $B$ are varied inside the topological superconductor phase. % The parity jumps, which may be interpreted as changes in the occupancy of the fermion state formed from the pair of Majorana modes at opposite ends of the wire, are accompanied by jumps $\delta N$ in the charge of the nanowire, whose values decrease exponentially with the wire length. % We study theoretically the dependence of $\delta N$ on system parameters, and compare the locations in the $\mu$-$B$ plane of parity jumps when the nanowire is or is not proximity-coupled to a bulk superconductor. % We show that, despite the fact that the wave functions of the Majorana modes are localised near the two ends of the wire, the charge-density jumps have spatial distributions that are essentially uniform along the wire length, being proportional to the product of the two Majorana wave functions. % We explain how charge measurements, say by an external single-electron transistor, could reveal these effects. % Whereas existing experimental methods require direct contact to the wire for tunneling measurements, charge sensing avoids this issue and provides an orthogonal measurement to confirm recent experimental developments. % Furthermore, by comparing density of states measurements which show Majorana features at the wire ends with the uniformly-distributed charge measurements, one can rule out alternative explanations for earlier results. % We shed light on a new parameter regime for these wire-superconductor hybrid systems, and propose a related experiment to measure spin density.

At low temperatures, electrons in semiconductors are bound to shallow donor impurity ions, neutralizing their charge in equilibrium. Inelastic scattering of other externally-injected conduction electrons accelerated by electric fields can excite transitions within the manifold of these localized states. Promotion of the bound electron into highly spin-orbit-mixed excited states drives a strong spin relaxation of the conduction electrons via exchange interactions, reminiscent of the Bir-Aronov-Pikus process where exchange occurs with valence band hole states. Through low-temperature experiments with silicon spin transport devices and complementary theory, we reveal the consequences of this previously unknown spin depolarization mechanism both below and above the impact ionization threshold.