Anisotropic g factor in InAs self-assembled quantum dots

We investigate the wave functions, spectrum, and g-factor anisotropy of low-energy electrons confined to self-assembled, pyramidal InAs quantum dots (QDs) subject to external magnetic and electric fields. We present the construction of trial wave functions for a pyramidal geometry with hard-wall confinement. We explicitly find the ground and first excited states and show the associated probability distributions and energies. Subsequently, we use these wave functions and 8-band $k\cdot p$ theory to derive a Hamiltonian describing the QD states close to the valence band edge. Using a perturbative approach, we find an effective conduction band Hamiltonian describing low-energy electronic states in the QD. From this, we further extract the magnetic field dependent eigenenergies and associated g factors. We examine the g factors regarding anisotropy and behavior under small electric fields. In particular, we find strong anisotropies, with the specific shape depending strongly on the considered QD level. Our results are in good agreement with recent measurements [Takahashi et al., Phys. Rev. B 87, 161302 (2013)] and support the possibility to control a spin qubit by means of g-tensor modulation.Comment: 9 pages, 9 figure

Spin susceptibility of interacting two-dimensional electrons in the presence of spin-orbit coupling

A long-range interaction via virtual particle-hole pairs between Fermi-liquid quasiparticles leads to a nonanalytic behavior of the spin susceptibility $\chi$ as a function of the temperature ($T$), magnetic field ($\mathbf{B}$), and wavenumber. In this paper, we study the effect of the Rashba spin-orbit interaction (SOI) on the nonanalytic behavior of $\chi$ for a two-dimensional electron liquid. Although the SOI breaks the SU(2) symmetry, it does not eliminate nonanalyticity but rather makes it anisotropic: while the linear scaling of $\chi_{zz}$ with $T$ and $|\mathbf{B}|$ saturates at the energy scale set by the SOI, that of $\chi_{xx}$ ($=\chi_{yy}$) continues through this energy scale, until renormalization of the electron-electron interaction in the Cooper channel becomes important. We show that the Renormalization Group flow in the Cooper channel has a non-trivial fixed point, and study the consequences of this fixed point for the nonanalytic behavior of $\chi$. An immediate consequence of SOI-induced anisotropy in the nonanalytic behavior of $\chi$ is a possible instability of a second-order ferromagnetic quantum phase transition with respect to a first-order transition to an XY ferromagnetic state.Comment: 34 pages, 12 figure

Ferromagnetic order of nuclear spins coupled to conduction electrons: a combined effect of the electron-electron and spin-orbit interactions

We analyze the ordered state of nuclear spins embedded in an interacting two-dimensional electron gas (2DEG) with Rashba spin-orbit interaction (SOI). Stability of the ferromagnetic nuclear-spin phase is governed by nonanalytic dependences of the electron spin susceptibility $\chi^{ij}$ on the momentum ($\tilde{\mathbf{q}}$) and on the SOI coupling constant ($\alpha$). The uniform (\tq=0) spin susceptibility is anisotropic (with the out-of-plane component, $\chi^{zz}$, being larger than the in-plane one, $\chi^{xx}$, by a term proportional to $U^2(2k_F)|\alpha|$, where $U(q)$ is the electron-electron interaction). For \tq \leq 2m^*|\alpha|, corrections to the leading, $U^2(2k_F)|\alpha|$, term scale linearly with \tq for $\chi^{xx}$ and are absent for $\chi^{zz}$. This anisotropy has important consequences for the ferromagnetic nuclear-spin phase: $(i)$ the ordered state--if achieved--is of an Ising type and $(ii)$ the spin-wave dispersion is gapped at \tq=0. To second order in $U(q)$, the dispersion a decreasing function of \tq, and anisotropy is not sufficient to stabilize long-range order. However, renormalization in the Cooper channel for \tq\ll2m^*|\alpha| is capable of reversing the sign of the \tq-dependence of $\chi^{xx}$ and thus stabilizing the ordered state. We also show that a combination of the electron-electron and SO interactions leads to a new effect: long-wavelength Friedel oscillations in the spin (but not charge) electron density induced by local magnetic moments. The period of these oscillations is given by the SO length $\pi/m^*|\alpha|$.Comment: 22 pages, 15 figure

Quantum Computing with Electron Spins in Quantum Dots

Several topics on the implementation of spin qubits in quantum dots are reviewed. We first provide an introduction to the standard model of quantum computing and the basic criteria for its realization. Other alternative formulations such as measurement-based and adiabatic quantum computing are briefly discussed. We then focus on spin qubits in single and double GaAs electron quantum dots and review recent experimental achievements with respect to initialization, coherent manipulation and readout of the spin states. We extensively discuss the problem of decoherence in this system, with particular emphasis on its theoretical treatment and possible ways to overcome it.Comment: Lecture notes for Course CLXXI "Quantum Coherence in Solid State Systems" Int. School of Physics "Enrico Fermi", Varenna, July 2008, 61 pages, 20 figure

Cotunneling in the \nu = 5/2 fractional quantum Hall regime

We show that cotunneling in the 5/2 fractional quantum Hall regime allows us to test the Moore-Read wave function, proposed for this regime, and to probe the nature of the fractional charge carriers. We calculate the cotunneling current for electrons that tunnel between two quantum Hall edge states via a quantum dot and for quasiparticles with fractional charges e/4 and e/2 that tunnel via an antidot. While electron cotunneling is strongly suppressed, the quasiparticle tunneling shows signatures characteristic of the Moore-Read state. For comparison, we also consider cotunneling between Laughlin states, and find that electron transport between Moore-Read states and between Laughlin states at filling factor 1/3 have identical voltage dependences

First year Physics labs in a 'suitcase'

Over the past two decades university student demographics have considerably changed. A larger percentage of the population that now attend university come from a variety of teaching and learning cultures and a wide range of socio-economic backgrounds. Under these challenging circumstances, most of the students seem to juggle their time between work, study and family commitments to complete their degree. A survey conducted by Curtin Applied Physics in October 2000 revealed that 58% of the full time students studying physics for their first time work either part time or full time and therefore are time disadvantaged as compared to their full time non-working colleagues. In order to address these issues Physics113/114/115 units were restructured into modular format providing flexible assessment using WebCT. These units have been running for the past three years. Over these years we have found that the flexible module assessment is working well to the satisfaction of the students, but some of the students are still finding it difficult to budget their time to attend laboratories to complete the unit. The laboratory program is an essential part of these units and is thus heavily weighted and requires a considerable time input by the students. At the time when these units were modularised, flexible laboratory program could not be provided due to lack of equipment, funding and staff time constraints

Designing a comprehensive rubric for laboratory report assessment

Assessment moderation processes play a vital role in maintaining quality assurance for university courses. These processes ensure that the assessment is consistent, reproducible and transparent. They also assure students that their work is assessed with fairness and addresses the stated learning outcomes. In line with Curtin's Assessment & Moderation Policy, we applied a moderation process to first-year science enabling units. One of the major assessment components of these units is the laboratory work, which involves taking a wide range of measurements of physical quantities with due regard to measurement uncertainties, analysing the data, calculating the results and interpreting the results. The students then present their work in a formal scientifically written report to their laboratory demonstrator for assessment. The students' reports are assessed using a specific rubric which is available to students and the demonstrators through Blackboard at the beginning of the semester. To gauge any variations in marking, eight demonstrators and two staff members were provided with a set of six de-identified laboratory reports for marking using the current rubric. The results obtained showed that the percentage standard deviation of all the demonstrators varied from 18% to 42% from the mean value. We believe this may be due to a wide range of demonstrators' experience and background knowledge and also whether they have completed the annually run Curtin's Laboratory Demonstrators' Workshop. In consultation with the Office of the Dean of Teaching and Learning, the current rubric was re-designed to show a further breakdown of marks for future use.Following discussion with demonstrators and staff the re-designed rubric was accepted with some modifications. To check the validity and reliability of the new rubric, another set of six reports were marked by the same assessors. In this presentation we will discuss the results of the current and the modified rubric

An index for closed orbits in Beltrami fields

We consider the class of Beltrami fields (eigenfields of the curl operator) on three-dimensional Riemannian solid tori: such vector fields arise as steady incompressible inviscid fluids and plasmas. Using techniques from contact geometry, we construct an integer-valued index for detecting closed orbits in the flow which are topologically inessential (they have winding number zero with respect to the solid torus). This index is independent of the Riemannian structure, and is computable entirely from a C^1 approximation to the vector field on any meridional disc of the solid torus

Interplay of Coulomb blockade and Aharonov-Bohm resonances in a Luttinger liquid

We consider a ring of strongly interacting electrons connected to two external leads by tunnel junctions. By studying the positions of conductance resonances as a function of gate voltage and magnetic flux the interaction parameter $g$ can be determined experimentally. For a finite ring the minimum conductance is strongly influenced by device geometry and electron-electron interactions. In particular, if the tunnel junctions are close to one another the interaction-related orthogonality catastrophe is suppressed and the valley current is unexpectedly large.Comment: 10 page

Decoherence of electron spin qubits in Si-based quantum computers

Direct phonon spin-lattice relaxation of an electron qubit bound by a donor impurity or quantum dot in SiGe heterostructures is investigated. The aim is to evaluate the importance of decoherence from this mechanism in several important solid-state quantum computer designs operating at low temperatures. We calculate the relaxation rate $1/T_1$ as a function of [100] uniaxial strain, temperature, magnetic field, and silicon/germanium content for Si:P bound electrons. The quantum dot potential is much smoother, leading to smaller splittings of the valley degeneracies. We have estimated these splittings in order to obtain upper bounds for the relaxation rate. In general, we find that the relaxation rate is strongly decreased by uniaxial compressive strain in a SiGe-Si-SiGe quantum well, making this strain an important positive design feature. Ge in high concentrations (particularly over 85%) increases the rate, making Si-rich materials preferable. We conclude that SiGe bound electron qubits must meet certain conditions to minimize decoherence but that spin-phonon relaxation does not rule out the solid-state implementation of error-tolerant quantum computing.Comment: 8 figures. To appear in PRB-July 2002. Revisions include: some references added/corrected, several typos fixed, a few things clarified. Nothing dramati