Photo-induced spin filtering in a double quantum dot

We investigate the spin-resolved electron dynamics in a double quantum dot driven by ultrafast asymmetric electromagnetic pulses. Using a analytical model we show that applying an appropriate pulse sequence allows to control coherently the spin degree of freedom on the femtosecond time scale. It can be achieved that the spin-up state is localized in a selected quantum dot while the spin-down state remains in the other dot. We show that this photo-induced spin-dependent separation can be maintained for a desired period of time.Comment: shortened, revised version 2 article published at Appl. Phys. Let

Confinement-induced Berry phase and helicity-dependent photocurrents

The photocurrent in an optically active metal is known to contain a component that switches sign with the helicity of the incident radiation. At low frequencies, this current depends on the orbital Berry phase of the Bloch electrons via the "anomalous velocity" of Karplus and Luttinger. We consider quantum wells in which the parent material, such as GaAs, is not optically active and the relevant Berry phase only arises as a result of quantum confinement. Using an envelope approximation that is supported by numerical tight-binding results, it is shown that the Berry phase contribution is determined for realistic wells by a cubic Berry phase intrinsic to the bulk material, the well width, and the well direction. These results for the magnitude of the Berry-phase effect suggest that it may already have been observed in quantum well experiments.Comment: 4 pages, 2 figure

Interface roughness, valley-orbit coupling and valley manipulation in quantum dots

We present a systematic study of interface roughness and its effect on coherent dynamical processes in quantum dots. The potential due to a sharp, flat interface lifts the degeneracy of the lowest energy valleys and yields a set of valley eigenstates. Interface roughness is characterized by fluctuations in the location of the interface and in the magnitude of the potential step. Variations in the position of the interface, which are expected to occur on the length scale of the lattice constant, reduce the magnitude of the valley-orbit coupling. Variations in the size of the interface potential step alter the magnitude of the valley-orbit coupling and induce transitions between different valley eigenstates in dynamics involving two (or more) dots. Such transitions can be studied experimentally by manipulating the bias between two dots and can be detected by charge sensing. However, if the random variable characterizing the position of the interface is correlated over distances of the order of a quantum dot, which is unlikely but possible, the phase of the valley-orbit coupling may be different in adjacent dots. In this case tunneling between like and opposite valley eigenstates is in effect a random variable and cannot be controlled. We suggest a resonant tunneling experiment that can identify the matrix elements for tunneling between like and opposite valley eigenstates.Comment: 18 pages, 6 figure

Dirac and Klein-Gordon particles in one-dimensional periodic potentials

We evaluate the dispersion relation for massless fermions, described by the Dirac equation, and for zero-spin bosons, described by the Klein-Gordon equation, moving in two dimensions and in the presence of a one-dimensional periodic potential. For massless fermions the dispersion relation shows a zero gap for carriers with zero momentum in the direction parallel to the barriers in agreement with the well-known "Klein paradox". Numerical results for the energy spectrum and the density of states are presented. Those for fermions are appropriate to graphene in which carriers behave relativistically with the "light speed" replaced by the Fermi velocity. In addition, we evaluate the transmission through a finite number of barriers for fermions and zero-spin bosons and relate it with that through a superlattice.Comment: 9 pages, 12 figure

Choosing a basis that eliminates spurious solutions in k.p theory

A small change of basis in k.p theory yields a Kane-like Hamiltonian for the conduction and valence bands of narrow-gap semiconductors that has no spurious solutions, yet provides an accurate fit to all effective masses. The theory is shown to work in superlattices by direct comparison with first-principles density-functional calculations of the valence subband structure. A reinterpretation of the standard data-fitting procedures used in k.p theory is also proposed.Comment: 15 pages, 2 figures; v3: expanded with much new materia

Static polarizability of two-dimensional hole gases

We have calculated the density-density (Lindhard) response function of a homogeneous two-dimensional (2D) hole gas in the static (omega=0) limit. The bulk valence-band structure comprising heavy-hole (HH) and light-hole (LH) states is modeled using Luttinger's kdotp approach within the axial approximation. We elucidate how, in contrast to the case of conduction electrons, the Lindhard function of 2D holes exhibits unique features associated with (i) the confinement-induced HH-LH energy splitting and (ii) the HH-LH mixing arising from the charge carriers' in-plane motion. Implications for the dielectric response and related physical observables are discussed.Comment: 11 pages, 3 figures, IOP latex style, v2: minor changes, to appear in NJ

Binding energy of shallow donors in a quantum well in the presence of a tilted magnetic field

We present results of variational calculations of the binding energy of a neutral donor in a quantum well in the presence of a magnetic field tilted relative to the QW plane. Assuming that the donor is located in the center of the QW, we perform calculations for parameters typical of a II-VI wide-gap semiconductor heterostructure, using as an example the case of a rectangular CdTe quantum well with CdMgTe barriers. We present the dependence of the binding energy of a neutral donor on the tilt angle and on the magnitude of the applied magnetic filed. As a key result, we show that measurement of the binding energy of a donor at two angles of the magnetic field with respect to the quantum well plane can be used to unambiguously determined the conduction band offset of the materials building up heterostructure.Comment: 6 pages, 5 figure

Energy spectra for quantum wires and 2DEGs in magnetic fields with Rashba and Dresselhaus spin-orbit interactions

We introduce an analytical approximation scheme to diagonalize parabolically confined two dimensional electron systems with both the Rashba and Dresselhaus spin-orbit interactions. The starting point of our perturbative expansion is a zeroth-order Hamiltonian for an electron confined in a quantum wire with an effective spin-orbit induced magnetic field along the wire, obtained by properly rotating the usual spin-orbit Hamiltonian. We find that the spin-orbit-related transverse coupling terms can be recast into two parts W and V, which couple crossing and non-crossing adjacent transverse modes, respectively. Interestingly, the zeroth-order Hamiltonian together with W can be solved exactly, as it maps onto the Jaynes-Cummings model of quantum optics. We treat the V coupling by performing a Schrieffer-Wolff transformation. This allows us to obtain an effective Hamiltonian to third order in the coupling strength k_Rl of V, which can be straightforwardly diagonalized via an additional unitary transformation. We also apply our approach to other types of effective parabolic confinement, e.g., 2D electrons in a perpendicular magnetic field. To demonstrate the usefulness of our approximate eigensolutions, we obtain analytical expressions for the n^th Landau-level g_n-factors in the presence of both Rashba and Dresselhaus couplings. For small values of the bulk g-factors, we find that spin-orbit effects cancel out entirely for particular values of the spin-orbit couplings. By solving simple transcendental equations we also obtain the band minima of a Rashba-coupled quantum wire as a function of an external magnetic field. These can be used to describe Shubnikov-de Haas oscillations. This procedure makes it easier to extract the strength of the spin-orbit interaction in these systems via proper fitting of the data.Comment: 13 pages, 11 figure

Theory of valley-orbit coupling in a Si/SiGe quantum dot

Electron states are studied for quantum dots in a strained Si quantum well, taking into account both valley and orbital physics. Realistic geometries are considered, including circular and elliptical dot shapes, parallel and perpendicular magnetic fields, and (most importantly for valley coupling) the small local tilt of the quantum well interface away from the crystallographic axes. In absence of a tilt, valley splitting occurs only between pairs of states with the same orbital quantum numbers. However, tilting is ubiquitous in conventional silicon heterostructures, leading to valley-orbit coupling. In this context, "valley splitting" is no longer a well defined concept, and the quantity of merit for qubit applications becomes the ground state gap. For typical dots used as qubits, a rich energy spectrum emerges, as a function of magnetic field, tilt angle, and orbital quantum number. Numerical and analytical solutions are obtained for the ground state gap and for the mixing fraction between the ground and excited states. This mixing can lead to valley scattering, decoherence, and leakage for Si spin qubits.Comment: 18 pages, including 4 figure

Lande-like formula for the g factors of hole-nanowire subband edges

We have analyzed theoretically the Zeeman splitting of hole-quantum-wire subband edges. As is typical for any bound state, their g factor depends on both an intrinsic g factor of the material and an additional contribution arising from a finite bound-state orbital angular momentum. We discuss the quantum-confinement-induced interplay between bulk-material and orbital effects, which is nontrivial due to the presence of strong spin-orbit coupling. A compact analytical formula is provided that elucidates this interplay and can be useful for predicting Zeeman splitting in generic hole-wire geometries.Comment: 4 pages, 2 figure