arXiv subjects

Vincent E. Sacksteder IV

Publications and source records attributed to Vincent E. Sacksteder IV.

13 recordsLinked to original sources

arXiv2021

Existence of a Phase with Finite Localization Length in the Double Scaling Limit of N-Orbital Models

Among the models of disordered conduction and localization, models with $N$ orbitals per site are attractive both for their mathematical tractability and for their physical realization in coupled disordered grains. However Wegner proved that there is no Anderson transition and no localized phase in the $N \rightarrow \infty$ limit, if the hopping constant $K$ is kept fixed. Here we show that the localized phase is preserved in a different limit where $N$ is taken to infinity and the hopping $K$ is simultaneously adjusted to keep $N \, K$ constant. We support this conclusion with two arguments. The first is numerical computations of the localization length showing that in the $N \rightarrow \infty$ limit the site-diagonal-disorder model possesses a localized phase if $N\,K$ is kept constant, but does not possess that phase if $K$ is fixed. The second argument is a detailed analysis of the energy and length scales in a functional integral representation of the gauge invariant model. The analysis shows that in the $K$ fixed limit the functional integral's spins do not exhibit long distance fluctuations, i.e. such fluctuations are massive and therefore decay exponentially, which signals conduction. In contrast the $N\,K$ fixed limit preserves the massless character of certain spin fluctuations, allowing them to fluctuate over long distance scales and cause Anderson localization.

cond-mat.dis-nn↗

arXiv2020

Indications for Topological Physics in High-$T_c$ Materials

Research on high-$T_c$ superconductors has generally not focused on analysis of the topological structure of electronic bands in these materials. In this article we collate and discuss several well-known experimental observables that signal that certain signatures of topology may be present. The topological signatures suggested by experiment include dimensional reduction, electronic transport determined by loop statistics, a winding number, Weyl fermions, and others. We suggest that topology, in a wider sense than band topology, may be key to the mechanism of high-$T_c$ superconductivity.

cond-mat.supr-con↗

arXiv2020

Electronic Conduction in Disordered Materials: Wave-like or Particle-like?

When materials are in the diffusive regime, i.e. when the scattering length is less than the sample size, charge transport is mediated by diffusons and cooperons. We argue that these charge carriers are not always spread out throughout the sample, like waves. When the scattering length is smaller than the sample size, diffusons and cooperons follow trajectories inside the sample which have an effective width determined by the scattering length. The net effect is particle-like motion. We discuss three experiments whose results confirm the existence of cooperons following particle-like trajectories. One experiment, with magnetic field perpendicular to a topological insulator surface, resolved and measured the areas of Cooperon loops. The other two experiments, with magnetic field parallel to wires where conduction occurred on the wire surface, measured the number of times that a Cooperon trajectory wound around the wire.

cond-mat.mes-hall↗

arXiv2019

Phase-coherent loops in selectively-grown topological insulator nanoribbons

Universal conductance fluctuations and the weak antilocalization effect are defect structure specific fingerprints in the magnetoconductance that are caused by electron interference. Experimental evidence is presented that the conductance fluctuations in the present topological insulator (Bi$_{0.57}$Sb$_{0.43}$)$_2$Te$_3$ nanoribbons which are selectively grown by molecular beam epitaxy are caused by well-defined and sharply resolved phase-coherent loops. From measurements at different magnetic field tilt angles we deduced that these loops are preferentially oriented parallel to the quintuple layers of the topological insulator material. Both from a theoretical analysis of universal conductance fluctuations and from weak antilocalization measured at low temperature the electronic phase-coherence lengths $l_ϕ$ are extracted, which is found to be larger in the former case. Possible reasons for this deviation are discussed.

cond-mat.mes-hall↗

arXiv2016

Quantum Interference Effects in Topological Nanowires In a Longitudinal Magnetic Field

We study the magnetoconductance of topological insulator nanowires in a longitudinal magnetic field, including Aharonov-Bohm, Altshuler-Aronov-Spivak, perfectly conducting channel, and universal conductance fluctuation effects. Our focus is on predicting experimental behavior in single wires in the quantum limit where temperature is reduced to zero. We show that changing the Fermi energy $E_F$ can tune a wire from from ballistic to diffusive conduction and to localization. In both ballistic and diffusive single wires we find both Aharonov-Bohm and Altshuler-Aronov-Spivak oscillations with similar strengths, accompanied by quite strong universal conductance fluctuations (UCFs), all with amplitudes between $0.3 \, G_0$ and $1\,G_0$. This contrasts strongly with the average behavior of many wires, which shows Aharonov-Bohm oscillations in the ballistic regime and Altshuler-Aronov-Spivak oscillations in the diffusive regime, with both oscillations substantially larger than the conductance fluctuations. In single wires the ballistic and diffusive regimes can be distinguished by varying $E_F$ and studying the sign of the AB signal, which depends periodically on $E_F$ in ballistic wires and randomly on $E_F$ in diffusive wires. We also show that in long wires the perfectly conducting channel is visible at a wide range of energies within the bulk gap. We present typical conductance profiles at several wire lengths, showing that conductance fluctuations can dominate the average signal. Similar behavior will be found in carbon nanotubes.

cond-mat.mes-hall↗

arXiv2014

Topological Effects on the Magnetoconductivity in Topological Insulators

Three-dimensional strong topological insulators (TIs) guarantee the existence of a 2-D conducting surface state which completely covers the surface of the TI. The TI surface state necessarily wraps around the TI's top, bottom, and two sidewalls, and is therefore topologically distinct from ordinary 2-D electron gases (2DEGs) which are planar. This has several consequences for the magnetoconductivity $Δσ$, a frequently studied measure of weak antilocalization which is sensitive to the quantum coherence time $τ_ϕ$ and to temperature. We show that conduction on the TI sidewalls systematically reduces $Δσ$, multiplying it by a factor which is always less than one and decreases in thicker samples. In addition, we present both an analytical formula and numerical results for the tilted-field magnetoconductivity which has been measured in several experiments. Lastly, we predict that as the temperature is reduced $Δσ$ will enter a wrapped regime where it is sensitive to diffusion processes which make one or more circuits around the TI. In this wrapped regime the magnetoconductivity's dependence on temperature, typically $1/T^2$ in 2DEGs, disappears. We present numerical and analytical predictions for the wrapped regime at both small and large field strengths. The wrapped regime and topological signatures discussed here should be visible in the same samples and at the same temperatures where the Altshuler-Aronov-Spivak (AAS) effect has already been observed, when the measurements are repeated with the magnetic field pointed perpendicularly to the TI's top face.

cond-mat.mes-hall↗

arXiv2014

Hole Spin Helix: Anomalous Spin Diffusion in Anisotropic Strained Hole Quantum Wells

We obtain the spin-orbit interaction and spin-charge coupled transport equations of a two-dimensional heavy hole gas under the influence of strain and anisotropy. We show that a simple two-band Hamiltonian can be used to describe the holes. In addition to the well-known cubic hole spin-orbit interaction, anisotropy causes a Dresselhaus-like term, and strain causes a Rashba term. We discover that strain can cause a shifting symmetry of the Fermi surfaces for spin up and down holes. We predict an enhanced spin lifetime associated with a spin helix standing wave similar to the Persistent Spin Helix which exists in the two-dimensional electron gas with equal Rashba and Dresselhaus spin-orbit interactions. These results may be useful both for spin-based experimental determination of the Luttinger parameters of the valence band Hamiltonian and for creating long-lived spin excitations.

cond-mat.mes-hall↗

arXiv2013

Robust topological insulator surface conduction under strong surface disorder

Topological insulators are characterized by specially protected conduction on their outer boundaries. We show that the protected edge conduction exhibited by 2-D topological insulators (and also Chern insulators) is independent of non-magnetic boundary disorder. In particular, the edge states residing inside the bulk gap remain conducting even when edge state inhomogeneities destroy the characteristic linear Dirac relation between energy and momentum. The main effects of boundary disorder on the in-gap states are to decrease the Fermi velocity, increase the density of states, pull the states into the disordered region if spin is conserved, and at very large disorder shift the states to the boundary between the disordered edge and the clean bulk. These effects, which may be useful for device engineering, are controlled by a resonance between the disordered edge and the bulk bands. The resonance's energy is set by the bulk band width; protection of the in-gap edge states' plane-wave character is controlled by the bulk band width, not the bulk band gap.

cond-mat.mes-hall↗

arXiv2012

Spin Conduction in Anisotropic 3-D Topological Insulators

When topological insulators possess rotational symmetry their spin lifetime is tied to the scattering time. We show that in anisotropic TIs this tie can be broken and the spin lifetime can be very large. Two different mechanisms can obtain spin conduction over long distances. The first is tuning the Hamiltonian to conserve a spin operator $\cos ϕ\, σ_x + \sin ϕ\, σ_y$, while the second is tuning the Fermi energy to be near a local extremum of the energy dispersion. Both mechanisms can produce persistent spin helices. We report spin lifetimes and spin diffusion equations.

cond-mat.mes-hall↗

arXiv2009

The Mechanism of Localization in Weakly Coupled Disordered Grains

It is shown that the Wegner model of disorder contains a system of constraints which is important whenever the disorder is not weak and which is responsible for localization in D > 2 dimensions. When the disorder is strong the constraints divide the phase space into an exponentially large number of domains; the localized phase is a glass. This work is based on recently developed field theories which are exactly equivalent to the Wegner model and to an easier variant.

cond-mat.dis-nn↗

arXiv2009

A Mathematically Controlled Alternative to the Supersymmetric Sigma Model of Disorder

This paper shows how to obtain non-rigorous mathematical control over models of loosely coupled disordered grains; it provides new information about saddle point structure and perturbative corrections. Both the Wegner model and a variant due to Disertori are transformed to matrix models which are similar to the supersymmetric model of disorder, having two matrices $Q^f$ and $Q^b$ which correspond to the two bosonic sectors of the SUSY matrix. However the Grassman (fermionic) sector of the SUSY matrix is omitted, and compensated by a spectral determinant. The transformation is exact for Disertori's model, while for the Wegner model it involves an integral which can be approximated while maintaining mathematical control. Previous derivations of sigma models of disorder assumed a spatially uniform saddle point independent of the Goldstone bosons and found that corrections are well controlled in the large $N$ limit. This paper takes into account spatial fluctuations of the Goldstone bosons and finds that corrections to the sigma model approximation in extended systems are controlled by powers of the inverse conductance $1/g$. In the weak localization regime Disertori's model exhibits remarkable simplifications and is completely controlled by perturbative expansions in various small parameters. The Wegner model might also be controlled. The standard weak localization results of the supersymmetric sigma model, including anomalously localized states, are reproduced and extended.

cond-mat.dis-nn↗

arXiv2007

Sums over geometries and improvements on the mean field approximation

The saddle points of a Lagrangian due to Efetov are analyzed. This Lagrangian was originally proposed as a tool for calculating systematic corrections to the Bethe approximation, a mean-field approximation which is important in statistical mechanics, glasses, coding theory, and combinatorial optimization. Detailed analysis shows that the trivial saddle point generates a sum over geometries reminiscent of dynamically triangulated quantum gravity, which suggests new possibilities to design sums over geometries for the specific purpose of obtaining improved mean field approximations to $D$-dimensional theories. In the case of the Efetov theory, the dominant geometries are locally tree-like, and the sum over geometries diverges in a way that is similar to quantum gravity's divergence when all topologies are included. Expertise from the field of dynamically triangulated quantum gravity about sums over geometries may be able to remedy these defects and fulfill the Efetov theory's original promise. The other saddle points of the Efetov Lagrangian are also analyzed; the Hessian at these points is nonnormal and pseudo-Hermitian, which is unusual for bosonic theories. The standard formula for Gaussian integrals is generalized to nonnormal kernels.

hep-th↗

arXiv2004

Linear Algebra with Disordered Sparse Matrices that have Spatial Structure: Theory and Computation

This Ph.D. thesis contains original contributions to several areas within the disciplines of disordered systems, numerical linear algebra, and scientific computing: (1) Theoretical and numerical study of the errors caused by using certain O(N) algorithms for evaluating matrix functions. (2) Numerical results on the localization of matrix functions, and on the length scales of eigenfunctions. (3) A simple model which generalizes Berry's model of wavefunctions in chaotic systems to include both localization and multifractality. (4) A proposal of a new sigma model for disordered systems which does not involve graded matrixes but should reproduce the same results as the supersymmetric sigma model. A detailed derivation of the new sigma model is provided. (5) Proposals for many new O(N) algorithms, and for many O(N log N) algorithms suitable to systems with many length scales. (6) A review of the problems which computing can cause for the physics community, and of the physics community's current efforts to handle those problems. Following this review is a set of recommendations for better managing these problems.

cond-mat.mes-hall↗