Structure Adaptive Lasso

Lasso is of fundamental importance in high-dimensional statistics and has been routinely used to regress a response on a high-dimensional set of predictors. In many scientific applications, there exists external information that encodes the predictive power and sparsity structure of the predictors. In this article, we develop a new method, called the Structure Adaptive Lasso (SA-Lasso), to incorporate these potentially useful side information into a penalized regression. The basic idea is to translate the external information into different penalization strengths for the regression coefficients. We study the risk properties of the resulting estimator. In particular, we generalize the state evolution framework recently introduced for the analysis of the approximate message-passing algorithm to the SA-Lasso setting. We show that the finite sample risk of the SA-Lasso estimator is consistent with the theoretical risk predicted by the state evolution equation. Our theory suggests that the SA-Lasso with an informative group or covariate structure can significantly outperform the Lasso, Adaptive Lasso, and Sparse Group Lasso. This evidence is further confirmed in our numerical studies. We also demonstrate the usefulness and the superiority of our method in a real data application.Comment: 42 pages, 24 figure

Spin Polarized Transport in Nanoscale Devices

The ultimate goal in the rapidly burgeoning field of spintronics is to realize semiconductor-based devices that utilize the spin degree of freedom of a single charge carrier (electron or hole) or an ensemble of such carriers to achieve novel and/or enhanced device functionalities such as spin based light emitting devices, spin transistors and femto-Tesla magnetic field sensors. These devices share a common feature: they all rely on controlled transport of spins in semiconductors. A prototypical spintronic device has a transistor-like configuration in which a semiconducting channel is sandwiched between two contacts (source and drain) with a gate electrode sitting on top of the channel. Unlike conventional charge-based transistors, the source electrode of a spin transistor is a ferromagnetic (or half-metallic) material which injects spin polarized electrons in the channel. During transit, the spin polarizations of the electrons are controllably rotated by a gate electric field mediated spin-orbit coupling effect. The drain contact is ferromagnetic (or half-metallic) as well and the transmission probability of an electron through this drain electrode depends on the relative orientation of electron spin polarization and the (fixed) magnetization of the drain. When the spins of the electrons are parallel to the drain magnetization, they are transmitted by the drain resulting in a large device current (ON state of spin FET). However, these electrons will be completely blocked if their spins are antiparallel to the drain magnetization, and ideally, in this situation device current will be zero (OFF state of spinFET). Thus, if we vary the gate voltage, we can modulate the channel current by controlling the spin orientations of the electrons with respect to the drain magnetization. This is how transistor action is realized (Datta-Das model). However, during transport, electrons\u27 velocities change randomly with time due to scattering and hence different electrons experience different spin-orbit magnetic fields. As a result, even though all electrons start their journey with identical spin orientations, soon after injection spins of different electrons point along different directions in space. This randomization of initial spin polarization is referred to as spin relaxation and this is detrimental to the spintronic devices. In particular, for Datta-Das transistor, this will lead to inefficient gate control and large leakage current in the OFF state of the spinFET. The aim of this work is to understand various spin relaxation processes that are operative in semiconductor nanostructures and to indicate possible ways of minimizing them. The theoretical aspect of this work (Chapters 2-5) focuses on the D\u27yakonov-Perel\u27 process of spin relaxation in a semiconductor quantum wire. This process of spin relaxation occurs because during transport electron spin precesses like a spinning top about the spin-orbit magnetic field. We show that the conventional drift-diffusion model of spin transport, which has been used extensively in literature, completely breaks down in case of a quantum confined system (e.g. a quantum wire). Our approach employs a semi-classical model which couples the spin density matrix evolution with the Boltzmann transport equation. Using this model we have thoroughly studied spin relaxation in a semiconductor quantum wire and identified several inconsistencies of the drift-diffusion formalism.The experimental side of this work (Chapters 6-8) deals with two different issues: (a) performing spin transport experiments in order to extract spin relaxation length and time in various materials (e.g. Cu, Alq3) under one-dimensional confinement, and (b) measurement of the ensemble spin dephasing time in self-assembled cadmium sulfide quantum dots using electron spin resonance technique. The spin transport experiment, as described in Chapter 7 of this dissertation, shows that the spin relaxation time in organic semiconductor (Alq3) is extremely long, approaching a few seconds at low temperatures. Alq3 is the chemical formula of tris- 8 hydroxy-quinoline aluminum, which is a small molecular weight organic semiconductor. This material is extensively used in organic display industry as the electron transport and emission layer in green organic light emitting diodes. The long spin relaxation time in Alq3 makes it an ideal platform for spintronics. This also indicates that it may be possible to realize spin based organic light emitting diodes which will have much higher internal quantum efficiency than their conventional non-spin counterparts. From spin transport experiments mentioned above we have also identified Elliott-Yafet mode as the dominant spin relaxation mechanism operative in organic semiconductors. Electron spin resonance experiment performed on self-assembled quantum dots (Chapter 8) allows us to determine the ensemble spin dephasing time (or transverse spin relaxation time) of electrons confined in these systems. In quantum dots electrons are strongly localized in space. Surprisingly, the ensemble spin dephasing time shows an increasing trend as we increase temperature. The most likely explanation for this phenomenon is that spin dephasing in quantum dots (unlike quantum wells and wires) is dominated by nuclear hyperfine interaction, which weakens progressively with temperature. We hope that our work, which elaborates on all of the above mentioned topics in great detail, will be a significant contribution towards the current state of knowledge of subtle spin-based issues operative in nanoscale device structures, and will ultimately lead to realization of novel nano-spintronic devices

Energy dispersion relations of spin-split subbands in a quantum wire and electrostatic modulation of carrier spin polarization

We numerically calculate the energy dispersion relations of the spin-split subbands in a quantum wire subjected to a transverse magnetic field in the presence of Rashba and Dresselhaus spin-orbit interactions. The spin splitting energy at zero wave vector is found to be neither equal to the bare Zeeman splitting nor linear in the magnetic field in any subband. This happens because the expectation value of the spin angular momentum operator varies along the width of the wire, causing a spatial modulation of the spin density. We also show that spin splitting energy is subband dependent and has a complex dependence on the external magnetic field. In some subbands, it can vanish entirely at nonzero values of the external magnetic field. The effective spin polarization of carriers in any subband can be changed in both magnitude and sign with an external electrostatic potential, applied, for example, via a gate terminal. This has practical applications in quantum computing and other areas