arXiv subjects

Emil Prodan

Publications and source records attributed to Emil Prodan.

97 records · Page 6Linked to original sources

arXiv2009

An edge index for the Quantum Spin-Hall effect

Quantum Spin-Hall systems are topological insulators displaying dissipationless spin currents flowing at the edges of the samples. In contradistinction to the Quantum Hall systems where the charge conductance of the edge modes is quantized, the spin conductance is not and it remained an open problem to find the observable whose edge current is quantized. In this paper, we define a particular observable and the edge current corresponding to this observable. We show that this current is quantized and that the quantization is given by the index of a certain Fredholm operator. This provides a new topological invariant that is shown to take same values as the Spin-Chern number previously introduced in the literature. The result gives an effective tool for the investigation of the edge channels' structure in Quantum Spin-Hall systems. Based on a reasonable assumption, we also show that the edge conducting channels are not destroyed by a random edge.

cond-mat.mes-hall↗

arXiv2009

The edge spectrum of Chern insulators with rough boundaries

Chern insulators are periodic band insulators with the property that their projector onto the occupied bands have non-zero Chern number. Chern insulator with a homogeneous boundary display continuum spectrum that fills the entire insulating gap. The local density of states corresponding to this part of the spectrum is localized near the boundary, hence the terminology edge spectrum. An interesting question arises, namely, if a rough boundary, which can be seen as a strong random potential acting on these quasi 1-dimensional states, would destroy the continuum edge spectrum. This paper shows how such question can be answered via a newly formulated abstract framework in which the expectation value of the current of a general observable is connected to the index of a specific Fredholm operator. For the present application, we will connect the expectation value of the charge edge current with the index of a Fredholm operator that remains invariant under arbitrary deformations of the boundary.

cond-mat.mes-hall↗

arXiv2008

Topological quantization of ensemble averages

We define the current of a quantum observable and, under well defined conditions, we connect its ensemble average to the index of a Fredholm operator. The present work builds on a formalism developed by Kellendonk and Schulz-Baldes \cite{Kellendonk:2004p597} to study the quantization of edge currents for continuous magnetic Schroedinger operators. The generalization given here may be a useful tool to scientists looking for novel manifestations of the topological quantization. As a new application, we show that the differential conductance of atomic wires is given by the index of a certain operator. We also comment on how the formalism can be used to probe the existence of edge states.

cond-mat.mes-hall↗

arXiv2008

The dielectric response of spherical live cells in suspension: An analytic solution

We develop a theoretical framework to describe the dielectric response of live cells in suspensions when placed in low external electric fields. The treatment takes into account the presence of the cell's membrane and of the charge movement at the membrane's surfaces. For spherical cells suspended in aqueous solutions, we give an analytic solution for the dielectric function, which is shown to account for the alpha and beta plateaus seen in many experimental data. The effect of different physical parameters on the dielectric curves is methodically analyzed.

cond-mat.soft↗

arXiv2008

Band Alignment in Molecular Devices: Influence of Anchoring Group and Metal Work Function

We present periodic Density Functional Theory calculations of the electronic properties of molecular junctions formed by amine-, and thiol-terminated alkane chains attached to two metal (Au, Ag) electrodes. Based on extensive analysis that includes molecular monolayers of varying densities, we establish a relationship between the alignment of the molecular energy levels and the interface dipoles, which shows that the band alignment (BA) in the limit of long, isolated chains is independent of the link group and can be computed from a reference system of non interacting molecule + metal electrodes. The main difference between the amine and thiol linkers is the effective dipole moment at the contact. This is very large, about 4.5 D, for amine linkers, leading to a strong dependence of the BA on the monolayer density and a slow convergence to the isolated molecule limit. Instead, this convergence is fast for S anchors due to the very small, ~ 0.2 D, effective dipoles at the contacts.

cond-mat.mes-hall↗

arXiv2008

Tunneling conductance of amine linked alkyl chains

The tunneling transport theory developed in Phys. Rev. B {\bf 76}, 115102 (2007) is applied to molecular devices made of alkyl chains linked to gold electrodes via amine groups. Using the analytic expression of the tunneling conductance derived in our previous work, we identify the key physical quantities that characterize the conductance of these devices. By investigating the transport characteristics of three devices, containing 4, 6, and 8 methyl groups, we extract the dependence of the tunneling conductance on the chain's length, which is an exponential decay law in close agreement with recent experimental data.

cond-mat.mes-hall↗

arXiv2005

Norm estimates of complex symmetric operators applied to quantum systems

This paper communicates recent results in theory of complex symmetric operators and shows, through two non-trivial examples, their potential usefulness in the study of Schrödinger operators. In particular, we propose a formula for computing the norm of a compact complex symmetric operator. This observation is applied to two concrete problems related to quantum mechanical systems. First, we give sharp estimates on the exponential decay of the resolvent and the single-particle density matrix for Schrödinger operators with spectral gaps. Second, we provide new ways of evaluating the resolvent norm for Schrödinger operators appearing in the complex scaling theory of resonances.

math-ph↗