arXiv subjects

Emil Prodan

Publications and source records attributed to Emil Prodan.

At least 91 records · Page 5Linked to original sources

arXiv2012

Quantum transport in disordered systems under magnetic fields: A study based on operator algebras

The linear conductivity tensor for generic homogeneous, microscopic quantum models was formulated as a noncommutative Kubo formula in Refs. \cite{BELLISSARD:1994xj,Schulz-Baldes:1998vm,Schulz-Baldes:1998oq}. This formula was derived directly in the thermodynamic limit, within the framework of $C^*$-algebras and noncommutative calculi defined over infinite spaces. As such, the numerical implementation of the formalism encountered fundamental obstacles. The present work defines a $C^*$-algebra and an approximate noncommutative calculus over a finite real-space torus, which naturally leads to an approximate finite-volume noncommutative Kubo formula, amenable on a computer. For finite temperatures and dissipation, it is shown that this approximate formula converges exponentially fast to its thermodynamic limit, which is the exact noncommutative Kubo formula. The approximate noncommutative Kubo formula is then deconstructed to a form that is implementable on a computer and simulations of the quantum transport in a 2-dimensional disordered lattice gas in a magnetic field are presented.

cond-mat.dis-nn↗

arXiv2012

The noncommutative Kubo Formula: Applications to Transport in Disordered Topological Insulators with and without Magnetic Fields

The non-commutative theory of charge transport in mesoscopic aperiodic systems under magnetic fields, developed by Bellissard, Shulz-Baldes and collaborators in the 90's, is complemented with a practical numerical implementation. The scheme, which is developed within a $C^*$-algebraic framework, enable efficient evaluations of the non-commutative Kubo formula, with errors that vanish exponentially fast in the thermodynamic limit. Applications to a model of a 2-dimensional Quantum spin-Hall insulator are given. The conductivity tensor is mapped as function of Fermi level, disorder strength and temperature and the phase diagram in the plane of Fermi level and disorder strength is quantitatively derived from the transport simulations. Simulations at finite magnetic field strength are also presented.

cond-mat.stat-mech↗

arXiv2012

Effect of Strong Disorder in a 3-Dimensional Topological Insulator: Phase Diagram and Maps of the Z2 Invariant

We study the effect of strong disorder in a 3-dimensional topological insulators with time-reversal symmetry and broken inversion symmetry. Firstly, using level statistics analysis, we demonstrate the persistence of delocalized bulk states even at large disorder. The delocalized spectrum is seen to display the levitation and pair annihilation effect, indicating that the delocalized states continue to carry the Z2 invariant after the onset of disorder. Secondly, the Z2 invariant is computed via twisted boundary conditions using an efficient numerical algorithm. We demonstrate that the Z2 invariant remains quantized and non-fluctuating even after the spectral gap becomes filled with dense localized states. In fact, our results indicate that the Z2 invariant remains quantized until the mobility gap closes or until the Fermi level touches the mobility edges. Based on such data, we compute the phase diagram of the Bi2Se3 topological material as function of disorder strength and position of the Fermi level.

cond-mat.dis-nn↗

arXiv2011

Topologically Protected Extended States in Disordered Quantum Spin-Hall Systems without Time-Reversal Symmetry

We demonstrate the existence of robust bulk extended states in the disordered Kane-Mele model with vertical and horizontal Zeeman fields, in the presence of a large Rashba coupling. The phase diagrams are mapped out by using level statistics analysis and computations of the localization length and spin-Chern numbers $C_\pm$. $C_\pm$ are protected by the finite energy and spin mobility gaps. The latter is shown to stay open for arbitrarily large vertical Zeeman fields, or for horizontal Zeeman fields below a critical strength or at moderate disorder. In such cases, a change of $C_\pm$ is necessarily accompanied by the closing of the mobility gap at the Fermi level. The numerical simulations reveal sharp changes in the quantized values of $C_\pm$ when crossing the regions of bulk extended states, indicating that the topological nature of the extended states is indeed linked to the spin-Chern numbers. For large horizontal Zeeman fields, the spin-gap closes at strong disorder prompting a change in the quantized spin-Chern numbers without a closing of the energy mobility gap.

cond-mat.mes-hall↗

arXiv2011

Manifestly gauge independent formulations of the Z2 invariants

We use a "monodromy" argument to derive new expressions for the ${\bm Z}_2$ invariants of topological insulators with time-reversal symmetry in 2 and 3 dimensions. The derivations and the final expressions do not require any gauge choice and the calculation of the invariants is based entirely on the projectors onto the occupied states. Explicit numerical tests for tight-binding models with strongly broken inversion symmetry are presented in 2 and 3-dimensions.

cond-mat.mtrl-sci↗

arXiv2011

Three-dimensional phase diagram of disordered HgTe/CdTe Quantum spin-Hall wells

We compute the phase diagram of the HgTe/CdTe quantum wells in the 3 dimensional (3D) parameter space of Dirac mass, Fermi level and disorder strength. The phase diagram reveals the Quantum spin-Hall, the metallic and the normal insulating phases. The phase boundary of the Quantum spin-Hall state is shown to be strongly deformed by the disorder. Taking specific cuts into this 3D phase diagram, we recover the so called topological Anderson insulator (TAI) phase, but now we can demonstrate explicitly that TAI is not a distinct phase and instead it is part of the Quantum spin-Hall phase. The calculations are performed with $S_z$-conserving and $S_z$-nonconserving Hamiltonians.

cond-mat.dis-nn↗

arXiv2011

Topological phonon modes in filamentous structures

Topological phonon modes are robust vibrations localized at the edges of special structures. Their existence is determined by the bulk properties of the structures and, as such, the topological phonon modes are stable to changes occurring at the edges. The first class of topological phonons was recently found in 2-dimensional structures similar to that of Microtubules. The present work introduces another class of topological phonons, this time occurring in quasi one-dimensional filamentous structures with inversion symmetry. The phenomenon is exemplified using a structure inspired from that of actin Microfilaments, present in most live cells. The system discussed here is probably the simplest structure that supports topological phonon modes, a fact that allows detailed analysis in both time and frequency domains. We advance the hypothesis that the topological phonon modes are ubiquitous in the biological world and that living organisms make use of them during various processes.

cond-mat.soft↗

arXiv2010

Disordered Topological Insulators: A Non-Commutative Geometry Perspective

This review deals with strongly disordered topological insulators and covers some recent applications of a well established analytic theory based on the methods of Non-Commutative Geometry (NCG) and developed for the Integer Quantum Hall-Effect. Our main goal is to exemplify how this theory can be used to define topological invariants in the presence of strong disorder, other than the Chern number, and to discuss the physical properties protected by these invariants. Working with two explicit 2-dimensional models, one for a Chern insulator and one for a Quantum spin-Hall insulator, we first give an in-depth account of the key bulk properties of these topological insulators in the clean and disordered regimes. Extensive numerical simulations are employed here. A brisk but self-contained presentation of the non-commutative theory of the Chern number is given and a novel numerical technique to evaluate the non-commutative Chern number is presented. The non-commutative spin-Chern number is defined and the analytic theory together with the explicit calculation of the topological invariants in the presence of strong disorder are used to explain the key bulk properties seen in the numerical experiments presented in the first part of the review.

cond-mat.dis-nn↗

arXiv2010

Robust extended states in a topological bulk model with even spin-Chern invariant

This paper demonstrates the existence of topological models with gapped edge states but protected extended bulk states against disorder. Such systems will be labeled as trivial by the current classification of topological insulators. Our finding calls for a re-examination of the definition of a topological insulator. The analysis is supported by extensive numerical data for a model of non-interacting electrons in the presence of strong disorder. In the clean limit, the model displays a topological insulating phase with spin-Chern number $C_s$=2 and gapped edge states. In the presence of disorder, level statistics on energy spectrum reveals regions of extended states displaying levitation and pair annihilation. Therefore, the extended states carry a topological invariant robust against disorder. By driving the Fermi level over the mobility edges, it is shown that this invariant is precisely the spin-Chern number. The protection mechanism for the extended state is explained.

cond-mat.dis-nn↗

arXiv2010

Inversion Symmetric Topological Insulators

We study translationally-invariant insulators with inversion symmetry that fall outside the established classification of topological insulators. These insulators are not required to have gapless boundary modes in the energy spectrum. However, they do exhibit protected modes in the entanglement spectrum localized on the cut between two entangled regions. Their entanglement entropy cannot be made to vanish adiabatically, and hence the insulators can be called topological. There is a direct connection between the inversion eigenvalues of the band structure and the mid-gap states in the entanglement spectrum. The classification of protected entanglement levels is given by an integer $n\in Z$, which is the difference between the negative inversion eigenvalues at inversion symmetric points in the Brillouin zone, taken in sets of two. When the Hamiltonian describes a Chern insulator or a non-trivial T-invariant topological insulator, the entanglement spectrum exhibits spectral flow. If the Chern number is zero for the former, or T is broken in the latter, the entanglement spectrum does \emph{not} have spectral flow, but, depending on the inversion eigenvalues, can still have protected midgap bands. Although spectral flow is broken, the mid-gap entanglement bands cannot be adiabatically removed, and the insulator is `topological.' In 1D, we establish a link between the product of the inversion eigenvalues of all occupied bands at all inversion momenta and charge polarization. In 2D, we prove a link between the product of the inversion eigenvalues and the parity of the Chern number. In 3D, we find a topological constraint on the product of the inversion eigenvalues indicating that some 3D materials are topological metals, and we show the link between the inversion eigenvalues and the 3D Quantum Hall Effect and the magnetoelectric polarization in the absence of T-symmetry.

cond-mat.mes-hall↗

arXiv2010

Entanglement Spectrum of a Disordered Topological Chern Insulator

How much information is stored in the ground-state of a system without \emph{any symmetry} and how can we extract it? This question is investigated by analyzing the behavior of a topological Chern Insulator (CI) in the presence of disorder, with a focus on its entanglement spectrum (EtS) constructed from the ground state. For systems with symmetries, the EtS was shown to contain explicit information revealed by sorting the EtS against the conserved quantum numbers. In the absence of any symmetry, we demonstrate that statistical methods such as the level statistics of the EtS can be equally insightful, allowing us to distinguish when an insulator is in a topological or trivial phase and to map the boundary between the two phases, where EtS becomes entirely delocalized. The phase diagram of a CI is explicitly computed as function of Fermi level ($E_F$) and disorder strength using the level statistics of the EtS and energy spectrum (EnS), together with a computation of the Chern number via an efficient real-space formula.

cond-mat.mes-hall↗

arXiv2010

Tunneling transport in devices with semiconducting leads

This paper extends the modern theory of tunneling transport to finite temperatures. The extension enables applications to molecular electronic devices connected to semiconducting leads. The paper presents an application of the theory to molecular devices made of alkyl chains connected to silicon nano-wires, mapping their transport characteristics as functions of temperature and alkyl chain's length. Based on these calculations and on the analytic theory, it is found that the tunneling decay constant is determined not by the Fermi level, but by the edge of the valence or conductance band, whichever is closer to the Fermi level. Further insight is provided by mapping the evanescent transport channels of the alkyl chains and few other physical quantities appearing in the analytic formula for conductance. A good qualitative agreement with the experimental data is obtained.

cond-mat.mes-hall↗

arXiv2010

Mapping the braiding properties of the Moore-Read state

In this paper we explore the braiding properties of the Moore-Read fractional Hall sequence, which amounts to computing the adiabatic evolution of the Hall liquid when the anyons are moved along various trajectories. In this work, the anyons are pinned to precise spatial configurations by using specific external potentials. Such external potentials break the translational symmetry and it appears that one will be forced to simulate the braidings on the entire many-body Hilbert space, an absolutely prohibitive scenario. We demonstrate how to overcome this difficulty and obtain the exact braidings for fairly large Hall systems. For this, we show that the incompressible state of a general $(k,m)$ fractional Hall sequence can be viewed as the unique zero mode of a specific Hamiltonian $H^{(k,m)}$, whose form is explicitly derived by using k-particles creation operators. The compressible Hall states corresponding to $n$$\times$$k$ anyons fixed at $w_1$,...,$w_{nk}$ are shown to be the zero modes of a pinning Hamiltonian $H^{(k,m)}_{w_1,...,w_{nk}}$, which is also explicitly derived. The zero modes of $H^{(k,m)}_{w_1,...,w_{nk}}$ are shown to be contained in the space of the zero modes of $H^{(k,m)}$. Therefore, the computation of the braidings can be done entirely within this space, which we map out for a number of Hall systems. Using this efficient computational method, we study various properties of the Moore-Read states. In particular, we give direct confirmation of their topological and non-abelian properties that were previously implied from the underlying Conformal Field Theory (CFT) structure of the Moore-Read state.

cond-mat.str-el↗

arXiv2009

Non-Commutative Tools for Topological Insulators

This paper reviews several analytic tools for the field of topological insulators, developed with the aid of non-commutative calculus and geometry. The set of tools includes bulk topological invariants defined directly in the thermodynamic limit and in the presence of disorder, whose robustness is shown to have non-trivial physical consequences for the bulk states. The set of tools also includes a general relation between the current of an observable and its edge index, relation that can be used to investigate the robustness of the edge states against disorder. The paper focuses on the motivations behind creating such tools and on how to use them.

cond-mat.stat-mech↗

arXiv2009

Topological phonon modes and their role in dynamic instability of microtubules

Microtubules (MTs) are self-assembled hollow protein tubes playing important functions in live cells. Their building block is a protein called tubulin, which self-assembles in a particulate 2 dimensional lattice. We study the vibrational modes of this lattice and find Dirac points in the phonon spectrum. We discuss a splitting of the Dirac points that leads to phonon bands with nonzero Chern numbers, signaling the existence of topological vibrational modes localized at MTs edges, which we indeed observe after explicit calculations. Since these modes are robust against the large changes occurring at the edges during the dynamic cycle of the MTs, we can build a simple mechanical model to illustrate how they would participate in this phenomenon.

cond-mat.soft↗

arXiv2009

Symmetry breaking in self-consistent models: Lessons from an exactly solvable many-fermion model

This work presents a many-fermion Hamiltonian with the following properties: 1) is exactly solvable, 2) has a second order insulator-metal quantum phase transition, 3) has a well defined mean field approximation and 4) its mean-field ground state displays a liquid-solid transition. The phenomenon of symmetry breaking in fermionic self-consistent models is discussed in the light of these remarkable properties of the many-body model.

cond-mat.quant-gas↗

arXiv2009

Robustness of the Spin-Chern number

The Spin-Chern ($C_s$) was originally introduced on finite samples by imposing spin boundary conditions at the edges. This definition lead to confusing and contradictory statements. On one hand the original paper by Sheng and collaborators revealed robust properties of $C_s$ against disorder and certain deformations of the model and, on the other hand, several people pointed out that $C_s$ can change sign under special deformations that keep the bulk Hamiltonian gap open. Because of the later findings, the Spin-Chern number was dismissed as a true bulk topological invariant and now is viewed as something that describes the edge where the spin boundary conditions are imposed. In this paper, we define the Spin-Chern number directly in the thermodynamic limit, without using any boundary conditions. We demonstrate its quantization in the presence of strong disorder and we argue that $C_s$ is a true bulk topological invariant whose robustness against disorder and smooth deformations of the Hamiltonian have important physical consequences. The properties of the Spin-Chern number remain valid even when the time reversal invariance is broken.

cond-mat.mes-hall↗

arXiv2009

Theory of tunneling transport in periodic chains

We present an extended discussion of a recently proposed theoretical approach for off-resonance tunneling transport. The proofs and the arguments are explained at length and simple analogies and illustrations are used where possible. The result is an analytic formula for the asymptotic tunneling conductance which involves the overlap of three well defined physical quantities. We argue that the formula can be used to gain fresh insight into the tunneling transport characteristics of various systems. The formalism is applied here to molecular devices consisting of planar phenyl chains connected to gold electrodes via amine linkers.

cond-mat.mes-hall↗