Strong correlations at topological insulator surfaces and the breakdown of the bulk-boundary correspondence

The criteria for strong correlations on surfaces of three-dimensional topological insulators are discussed. Usually, the Coulomb repulsion at such surfaces is too weak for driving a phase transition to a strongly correlated regime. I discuss a mechanism and possibilities of its experimental implementation by which the strength of the Coulomb interaction can be tuned over a wide range. In the strongly interacting regime, the surface states are gapped, even though the topological classification of the bulk band structure predicts gapless surface states

Bosonic field theory of tunable edge magnetism in graphene

A bosonic field theory is derived for the tunable edge magnetism at graphene zigzag edges. The derivation starts from an effective fermionic theory for the interacting graphene edge states, derived previously from a two-dimensional interacting tight-binding model for graphene. The essential feature of this effective model, which gives rise to the weak edge magnetism, is the momentum-dependent non-local electron-electron interaction. It is shown that this momentum-dependence may be treated by an extension of the bosonization technique, and leads to interactions of the bosonic fields. These interactions are reminiscent of a \phi^4 field theory. Focussing onto the regime close to the quantum phase transition between the ferromagnetic and the paramagnetic Luttinger liquid, a semiclassical interpretation of the interacting bosonic theory is given. Furthermore, it is argued that the universal critical behavior at the quantum phase transition between the paramagnetic and the ferromagnetic Luttinger liquid is governed by a small number of terms in this theory, which are accessible by quantum Monte-Carlo methods

On a discrete-to-continuum convergence result for a two dimensional brittle material in the small displacement regime

We consider a two-dimensional atomic mass spring system and show that in the small displacement regime the corresponding discrete energies can be related to a continuum Griffith energy functional in the sense of Gamma-convergence. We also analyze the continuum problem for a rectangular bar under tensile boundary conditions and find that depending on the boundary loading the minimizers are either homogeneous elastic deformations or configurations that are completely cracked generically along a crystallographic line. As applications we discuss cleavage properties of strained crystals and an effective continuum fracture energy for magnets

An analysis of crystal cleavage in the passage from atomistic models to continuum theory

We study the behavior of atomistic models in general dimensions under uniaxial tension and investigate the system for critical fracture loads. We rigorously prove that in the discrete-to-continuum limit the minimal energy satisfies a particular cleavage law with quadratic response to small boundary displacements followed by a sharp constant cut-off beyond some critical value. Moreover, we show that the minimal energy is attained by homogeneous elastic configurations in the subcritical case and that beyond critical loading cleavage along specific crystallographic hyperplanes is energetically favorable. In particular, our results apply to mass spring models with full nearest and next-to-nearest pair interactions and provide the limiting minimal energy and minimal configurations.Comment: The final publication is available at springerlink.co

Rejecting capital-skill complementarity at all costs

Any serious empirical study of factor substitutability has to allow the data to display complementarity as well as substitutability. The standard approach reflecting this idea is a translog specification – this is also the approach used by numerous studies analyzing the relative capital-skill complementarity hypothesis formulated by GRILICHES (1969). According to this hypothesis, the degree of substitutability between skilled labor and capital is lower than that for unskilled labor and capital. Yet, the results of empirical studies investigating this hypothesis are controversial. This paper offers a straightforward explanation: Using a translog approach reduces the issue of factor substitutability or complementarity to a question of cost shares. Our review of translog studies mentioned in HAMERMESH?s (1993) summary on the demand for heterogeneous labor demonstrates that this argument is empirically relevant – all these studies can be reconciled with each other on the basis of the cost-share argument. --Substitutability,Translog Cost Function

On the Restrictiveness of Separability: The Significance of Energy in German Manufacturing

Any researcher would certainly agree with Hamermesh’s (1993:34) intuition about separability that the ease of substitution between any two production factors should be unaffected by a third factor that is separable from the others. This paper emphasizes that such a notion of separability needs to be more restrictive than the classical separability concept is.We thus coin the notion of strict separability that implies the classical concept. By applying both separability concepts in a translog approach to German manufacturing data (1978–1990), we focus on the empirical question of whether the omission of energy affects the conclusions about the ease of substitution among nonenergy factors. We find ample empirical evidence to doubt the assumption that energy is separable from all other production factors even in the relatively mild form of classical separability. At least under separability aspects, therefore, energy appears to be an indispensable production factorSubstitution, Translog Cost Functions

Measuring Energy Security – A Conceptual Note

Along with the oil price, concerns about the security of energy supply have soared once again in recent years.Yet, more than 30 years after the OPEC oil embargo in 1973, energy security still remains a diffuse concept. This paper conceives a statistical indicator that aims at characterizing the energy supply risk of nations that are heavily dependent on energy imports. Our indicator condenses the bulk of empirical information on the imports of fossil fuels originating from a multitude of export countries as well as data on the indigenous contribution to the domestic energy supply into a single parameter. Applying the proposed concept to empirical energy data on Germany and the U.S. (1980–2004), we find that there is a large gap in the energy supply risks between both countries, with Germany suffering much more from a tensed energy supply situation today than the U.S.Herfindahl index, energy supply risk indicator

Decoherence of Majorana qubits by noisy gates

We propose and study a realistic model for the decoherence of topological qubits, based on Majorana fermions in one-dimensional topological superconductors. The source of decoherence is the fluctuating charge on a capacitively coupled gate, modeled by non-interacting electrons. In this context, we clarify the role of quantum fluctuations and thermal fluctuations and find that quantum fluctuations do not lead to decoherence, while thermal fluctuations do. We explicitly calculate decay times due to thermal noise and give conditions for the gap size in the topological superconductor and the gate temperature. Based on this result, we provide simple rules for gate geometries and materials optimized for reducing the negative effect of thermal charge fluctuations on the gate

Quantum Nature of Edge Magnetism in Graphene

It is argued that the subtle crossover from decoherence-dominated classical magnetism to fluctuation-dominated quantum magnetism is experimentally accessible in graphene nanoribbons. We show that the width of a nanoribbon determines whether the edge magnetism is on the classical side, on the quantum side, or in between. In the classical regime, decoherence is dominant and leads to static spin polarizations at the ribbon edges, which are well described by mean-field theories. The quantum Zeno effect is identified as the basic mechanism which is responsible for the spin polarization and thereby enables the application of graphene in spintronics. On the quantum side, however, the spin polarization is destroyed by dynamical processes. The great tunability of graphene magnetism thus offers a viable route for the study of the quantum-classical crossover.Comment: 5 pages, 3 figure