Devil's staircase of incompressible electron states in a nanotube

It is shown that a periodic potential applied to a nanotube can lock electrons into incompressible states. Depending on whether electrons are weakly or tightly bound to the potential, excitation gaps open up either due to the Bragg diffraction enhanced by the Tomonaga - Luttinger correlations, or via pinning of the Wigner crystal. Incompressible states can be detected in a Thouless pump setup, in which a slowly moving periodic potential induces quantized current, with a possibility to pump on average a fraction of an electron per cycle as a result of interactions.Comment: 4 pages, 1 figure, published versio

Rotationally-invariant mapping of scalar and orientational metrics of neuronal microstructure with diffusion MRI

We develop a general analytical and numerical framework for estimating intra- and extra-neurite water fractions and diffusion coefficients, as well as neurite orientational dispersion, in each imaging voxel. By employing a set of rotational invariants and their expansion in the powers of diffusion weighting, we analytically uncover the nontrivial topology of the parameter estimation landscape, showing that multiple branches of parameters describe the measurement almost equally well, with only one of them corresponding to the biophysical reality. A comprehensive acquisition shows that the branch choice varies across the brain. Our framework reveals hidden degeneracies in MRI parameter estimation for neuronal tissue, provides microstructural and orientational maps in the whole brain without constraints or priors, and connects modern biophysical modeling with clinical MRI.Comment: 25 pages, 12 figures, elsarticle two-colum

Hybrid-State Free Precession in Nuclear Magnetic Resonance

The dynamics of large spin-1/2 ensembles in the presence of a varying magnetic field are commonly described by the Bloch equation. Most magnetic field variations result in unintuitive spin dynamics, which are sensitive to small deviations in the driving field. Although simplistic field variations can produce robust dynamics, the captured information content is impoverished. Here, we identify adiabaticity conditions that span a rich experiment design space with tractable dynamics. These adiabaticity conditions trap the spin dynamics in a one-dimensional subspace. Namely, the dynamics is captured by the absolute value of the magnetization, which is in a transient state, while its direction adiabatically follows the steady state. We define the hybrid state as the co-existence of these two states and identify the polar angle as the effective driving force of the spin dynamics. As an example, we optimize this drive for robust and efficient quantification of spin relaxation times and utilize it for magnetic resonance imaging of the human brain

Transport in nanoscale systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2003.Includes bibliographical references.In part I of the Thesis charge ordering and transport in arrays of coated semiconductor nanocrystals (quantum dot arrays) are studied. Charge ordering in dot arrays is considered by mapping the electrons on the dots onto the frustrated spin model on the triangular lattice. A number of phases is identified for this system. Phase diagram is studied by means of the height field order parameter. Novel correlated fluid phase is identified, in which transport of classical charges exhibits correlated behavior. Freezing transitions into commensurate ground state configurations are found to be of the first order. A novel model of transport in disordered systems is proposed to account for experimentally observed current transients in dot arrays at high bias. This transport model yields a non-stationary response in a stationary system. The model proposes a particular power law noise spectrum that is found to be consistent with experiments. In Part II of the Thesis novel effects in Carbon nanotubes are predicted. These effects can be manifest in transport measurements. First, it is shown that a strong electric field applied perpendicularly to the tube axis can fracture the Fermi surface of metallic nanotubes and significantly reduce excitation gap in semiconducting nanotubes. The depolarization problem is linked to the chiral anomaly of 1+1 dimensional Dirac fermions. Second, coupling between a surface acoustic wave and nanotube electrons is proposed as a means to realize an adiabatic charge pump. Incompressible states are identified in the single particle picture, and the corresponding minigaps are found. Conditions for pumping experiment are identified.(cont.) Third, electron properties of a nanotube in a periodic potential are considered. It is shown that when the electron density is commensurate with the potential period, incompressible electron states exist. Electron interactions are treated in the Luttinger liquid framework, and excitation gaps corresponding to incompressible states are found using the phase soliton approach.by Dmitry S. Novikov.Ph.D

Electron properties of carbon nanotubes in a periodic potential

A periodic potential applied to a nanotube is shown to lock electrons into incompressible states that can form a devil's staircase. Electron interactions result in spectral gaps when the electron density (relative to a half-filled Carbon pi-band) is a rational number per potential period, in contrast to the single-particle case where only the integer-density gaps are allowed. When electrons are weakly bound to the potential, incompressible states arise due to Bragg diffraction in the Luttinger liquid. Charge gaps are enhanced due to quantum fluctuations, whereas neutral excitations are governed by an effective SU(4)~O(6) Gross-Neveu Lagrangian. In the opposite limit of the tightly bound electrons, effects of exchange are unimportant, and the system behaves as a single fermion mode that represents a Wigner crystal pinned by the external potential, with the gaps dominated by the Coulomb repulsion. The phase diagram is drawn using the effective spinless Dirac Hamiltonian derived in this limit. Incompressible states can be detected in the adiabatic transport setup realized by a slowly moving potential wave, with electron interactions providing the possibility of pumping of a fraction of an electron per cycle (equivalently, in pumping at a fraction of the base frequency).Comment: 21 pgs, 8 fig