arXiv subjects

Johan Nilsson

Publications and source records attributed to Johan Nilsson.

At least 37 records · Page 2Linked to original sources

arXiv2014

Discrete tomography: Magic numbers for $N$-fold symmetry

We consider the problem of distinguishing convex subsets of $n$-cyclotomic model sets $\varLambda$ by (discrete parallel) X-rays in prescribed $\varLambda$-directions. In this context, a `magic number' $m_{\varLambda}$ has the property that any two convex subsets of $\varLambda$ can be distinguished by their X-rays in any set of $m_{\varLambda}$ prescribed $\varLambda$-directions. Recent calculations suggest that (with one exception in the case $n=4$) the least possible magic number for $n$-cyclotomic model sets might just be $N+1$, where $N=\operatorname{lcm}(n,2)$.

math.MG↗

arXiv2013

Ferromagnetism in the one-dimensional Kondo lattice: mean-field approach via Majorana fermion canonical transformation

Using a canonical transformation it is possible to faithfully represent the Kondo lattice model in terms of Majorana fermions. Studying this representation we discovered an exact mapping between the Kondo lattice Hamiltonian and a Hamiltonian describing three spinless fermions interacting on a lattice. We investigate the effectiveness of this three fermion representation by performing a zero temperature mean-field study of the phase diagram at different couplings and fillings for the one-dimensional case, focusing on the appearance of ferromagnetism. The solutions agree in many respects with the known numerical and analytical results. In particular, in the ferromagnetic region connected to the solution at zero electron density, we have a quantitative agreement on the value of the commensurability parameter discovered in recent DMRG (in one dimension) and DMFT (in infinite dimensions) simulations; furthermore we provide a theoretical justification for it, identifying a symmetry of the Hamiltonian. This ferromagnetic phase is stabilized by the emergence of a spin-selective Kondo insulator that is described quite conveniently by the three spinless fermions. We discovered also a different ferromagnetic phase at high filling and low couplings. This phase resembles the RKKY ferromagnetic phase existing at vanishing filling, but it incorporates much more of the Kondo effect, making it energetically more favorable than the typical spiral (spin ordered) mean field ground states. We believe that this second phase represents a prototype for the strange ferromagnetic tongue identified by numerical simulations inside the paramagnetic dome. At the end of the work we also provide a discussion of possible orders different from the ferromagnetic one. In particular at half-filling, where we obtain as ground state at high coupling the correct Kondo insulating state.

cond-mat.str-el↗

arXiv2013

Majorana fermion description of the Kondo lattice: Variational and Path integral approach

All models of interacting electrons and spins can be reformulated as theories of interacting Majorana fermions. We consider the Kondo lattice model that admits a symmetric representation in terms of Majorana fermions. In the first part of this work we study two variational states, which are natural in the Majorana formulation. At weak coupling a state in which three Majorana fermions tend to propagate together as bound objects is favored, while for strong coupling a better description is obtained by having deconfined Majorana fermions. This way of looking at the Kondo lattice offers an alternative phenomenological description of this model. In the second part of the paper we provide a detailed derivation of the discretized path integral formulation of any Majorana fermion theory. This general formulation will be useful as a starting point for further studies, such as Quantum Monte Carlo, perturbative expansions, and Renormalization Group analysis. As an example we use this path integral formalism to formulate a finite temperature variational calculation, which generalizes the ground state variational calculation of the first part. This calculation shows how the formation of three-body bound states of Majorana fermions can be handled in the path integral formalism.

cond-mat.str-el↗

arXiv2013

Trapping massless Dirac particles in a rotating saddle

We study particle motion in rotating saddle-shaped potentials. It is known that such rotating potentials can generate bounded motion for particles with a parabolic dispersion law through the combination of potential, centrifugal and Coriolis forces in the rotating frame. When applied to massless Dirac particles, for example electrons in graphene, such a potential is shown to lead to eigenstates that are spatially localized near the center of the saddle at certain energies. Although other states also exist at these energies, they have non-overlapping support in the oscillator basis, which tend to give the localized states a substantial life-time also when imperfections are present.

cond-mat.mes-hall↗

arXiv2013

On the Entropy of a Two Step Random Fibonacci Substitution

We consider a random generalisation of the classical Fibonacci substitution. The substitution we consider is defined as the rule mapping $\mathtt{a}\mapsto \mathtt{baa}$ and $\mathtt{b} \mapsto \mathtt{ab}$ with probability $p$ and $\mathtt{b} \mapsto \mathtt{ba}$ with probability $1-p$ for $0<p<1$ and where the random rule is applied each time it acts on a $\mathtt{b}$. We show that the topological entropy of this object is given by the growth rate of the set of inflated random Fibonacci words, and we exactly calculate its value.

math.CO↗

arXiv2012

A Space Efficient Algorithm for the Calculation of the Digit Distribution in the Kolakoski Sequence

With standard algorithms for generating the classical Kolakoski sequence, the numerical calculation of the digit distribution requires a linear amount of space. Here, we present an algorithm for calculating the distribution of the digits in the classical Kolakoski sequence, that only requires a logarithmic amount of space and still runs in linear time. The algorithm is easily adaptable to generalised Kolakoski sequences.

math.CO↗

arXiv2012

On the Entropy of a Family of Random Substitutions

The generalised random Fibonacci chain is a stochastic extension of the classical Fibonacci substitution and is defined as the rule mapping $0\mapsto 1$ and $1 \mapsto 1^i01^{m-i}$ with probability $p_i$, where $p_i\geq 0$ with $\sum_{i=0}^m p_i=1$, and where the random rule is applied each time it acts on a 1. We show that the topological entropy of this object is given by the growth rate of the set of inflated generalised random Fibonacci words.

math.CO↗

arXiv2011

Probing Majorana edge states with a flux qubit

A pair of counter-propagating Majorana edge modes appears in chiral p-wave superconductors and in other superconducting systems belonging to the same universality class. These modes can be described by an Ising conformal field theory. We show how a superconducting flux qubit attached to such a system couples to the two chiral edge modes via the disorder field of the Ising model. Due to this coupling, measuring the back-action of the edge states on the qubit allows to probe the properties of Majorana edge modes.

cond-mat.mes-hall↗

arXiv2011

Faithful fermionic representations of the Kondo lattice model

We study the Kondo lattice model using a class of canonical transformations that allow us to faithfully represent the model entirely in terms of fermions without constraints. The transformations generate interacting theories that we study using mean field theory. Of particular interest is a new manifestly O(3)-symmetric representation in terms of Majorana fermions at half-filling on bipartite lattices. This representation suggests a natural O(3)-symmetric trial state that is investigated and characterized as a gapped spin liquid.

cond-mat.str-el↗

arXiv2011

Unified description of the dc conductivity of monolayer and bilayer graphene at finite densities based on resonant scatterers

We show that a coherent picture of the dc conductivity of monolayer and bilayer graphene at finite electronic densities emerges upon considering that strong short-range potentials are the main source of scattering in these two systems. The origin of the strong short-range potentials may lie in adsorbed hydrocarbons at the surface of graphene. The equivalence among results based on the partial-wave description of scattering, the Lippmann-Schwinger equation, and the T-matrix approach is established. Scattering due to resonant impurities close to the neutrality point is investigated via a numerical computation of the Kubo formula using a kernel polynomial method. We find that relevant adsorbate species originate impurity bands in monolayer and bilayer graphene close to the Dirac point. In the midgap region, a plateau of minimum conductivity of about $e^2/h$ (per layer) is induced by the resonant disorder. In bilayer graphene, a large adsorbate concentration can develop an energy gap between midgap and high-energy states. As a consequence, the conductivity plateau is supressed near the edges and a "conductivity gap" takes place. Finally, a scattering formalism for electrons in biased bilayer graphene, taking into account the degeneracy of the spectrum, is developed and the dc conductivity of that system is studied.

cond-mat.mes-hall↗

arXiv2010

Electronic properties of a biased graphene bilayer

We study, within the tight-binding approximation, the electronic properties of a graphene bilayer in the presence of an external electric field applied perpendicular to the system -- \emph{biased bilayer}. The effect of the perpendicular electric field is included through a parallel plate capacitor model, with screening correction at the Hartree level. The full tight-binding description is compared with its 4-band and 2-band continuum approximations, and the 4-band model is shown to be always a suitable approximation for the conditions realized in experiments. The model is applied to real biased bilayer devices, either made out of SiC or exfoliated graphene, and good agreement with experimental results is found, indicating that the model is capturing the key ingredients, and that a finite gap is effectively being controlled externally. Analysis of experimental results regarding the electrical noise and cyclotron resonance further suggests that the model can be seen as a good starting point to understand the electronic properties of graphene bilayer. Also, we study the effect of electron-hole asymmetry terms, as the second-nearest-neighbor hopping energies $t'$ (in-plane) and $γ_{4}$ (inter-layer), and the on-site energy $Δ$.

cond-mat.mes-hall↗

arXiv2010

The Fine Structure of Dyadically Badly Approximable Numbers

We consider badly approximable numbers in the case of dyadic diophantine approximation. For the unit circle $\mathbb{S}$ and the smallest distance to an integer $\|\cdot\|$ we give elementary proofs that the set $F(c) = \{x \in \mathbb{S}: \|2^nx\| \geq c, n\geq 0\}$ is a fractal set whose Hausdorff dimension depends continuously on $c$, is constant on intervals which form a set of Lebesgue measure 1 and is self-similar. Hence it has a fractal graph. Moreover, the dimension of $F(c)$ is zero if and only if $c\geq 1-2τ$, where $τ$ is the Thue-Morse constant. We completely characterise the intervals where the dimension remains unchanged. As a consequence we can completely describe the graph of $ c\mapsto \dim_H \{x\in[0,1]: \|x-\frac{m}{2^n}\|< \frac{c}{2^n} \textnormal{finitely often}\}$.

math.DS↗

arXiv2010

On the Entropy of Random Fibonacci Words

The random Fibonacci chain is a generalisation of the classical Fibonacci substitution and is defined as the rule mapping $0\mapsto 1$ and $1 \mapsto 01$ with probability $p$ and $1 \mapsto 10$ with probability $1-p$ for $0<p<1$ and where the random rule is applied each time it acts on a 1. We show that the topological entropy of this object is given by the growth rate of the set of inflated random Fibonacci words.

math.CO↗

arXiv2009

Theory of non-Abelian Fabry-Perot interferometry in topological insulators

Interferometry of non-Abelian edge excitations is a useful tool in topological quantum computing. In this paper we present a theory of a non-Abelian edge state interferometer in a 3D topological insulator brought in proximity to an s-wave superconductor. The non-Abelian edge excitations in this system have the same statistics as in the previously studied 5/2 fractional quantum Hall (FQH) effect and chiral p-wave superconductors. There are however crucial differences between the setup we consider and these systems, like the need for a converter between charged and neutral excitations and the neutrality of the non-Abelian excitations. These differences manifest themselves in a temperature scaling exponent of -7/4 for the conductance instead of -3/2 as in the 5/2 FQH effect.

cond-mat.mes-hall↗

arXiv2009

On the Order Dimension of Outerplanar Maps

Schnyder characterized planar graphs in terms of order dimension. Brightwell and Trotter proved that the dimension of the vertex-edge-face poset $\Pvef{M}$ of a planar map $M$ is at most four. In this paper we investigate cases where $\dim(\Pvef{M}) \leq 3$ and also where $\dim(\Qvf{M}) \leq 3$; here $\Qvf{M}$ denotes the vertex-face poset of $M$. We show: - If $M$ contains a $K_4$-subdivision, then $\dim(\Pvef{M}) = \dim(\Qvf{M}) = 4$. - If $M$ or the dual $M^*$ contains a $K_{2,3}$-subdivision, then $\dim(\Pvef{M}) = 4$. Hence, a map $M$ with $\dim(\Pvef{M}) \leq 3$ must be outerplanar and have an outerplanar dual. We concentrate on the simplest class of such maps and prove that within this class $\dim(\Pvef{M}) \leq 3$ is equivalent to the existence of a certain oriented coloring of edges. This condition is easily checked and can be turned into a linear time algorithm returning a 3-realizer. Additionally, we prove that if $M$ is 2-connected and $M$ and $M^*$ are outerplanar, then $\dim(\Qvf{M}) \leq 3$. There are, however, outerplanar maps with $\dim(\Qvf{M}) = 4$. We construct the first such example.

math.CO↗

arXiv2009

Electrically detected interferometry of Majorana fermions in a topological insulator

We show how a chiral Dirac fermion (a massless electron or hole) can be converted into a pair of neutral chiral Majorana fermions (a particle equal to its own antiparticle). These two types of fermions exist on the metallic surface of a topological insulator, respectively, at a magnetic domain wall and at a magnet-superconductor interface. Interferometry of Majorana fermions is a key operation in topological quantum computation, but the detection is problematic since these particles have no charge. The Dirac-Majorana converter enables electrical detection of the interferometric signal.

cond-mat.mes-hall↗

arXiv2008

Adatoms in Graphene

We review the problem of adatoms in graphene under two complementary points of view, scattering theory and strong correlations. We show that in both cases impurity atoms on the graphene surface present effects that are absent in the physics of impurities in ordinary metals. We discuss how to observe these unusual effects with standard experimental probes such as scanning tunneling microscopes, and spin susceptibility.

cond-mat.mtrl-sci↗

arXiv2008

Bound states and magnetic field-induced valley splitting in gate-tunable graphene quantum dots

The magnetic field dependence of energy levels in gapped single- and bilayer graphene quantum dots (QDs) defined by electrostatic gates is studied analytically in terms of the Dirac equation. Due to the absence of sharp edges in these types of QDs, the valley degree of freedom is a good quantum number. We show that its degeneracy is efficiently and controllably broken by a magnetic field applied perpendicular to the graphene plane. This opens up a feasible route to create well-defined and well controlled spin- and valley-qubits in graphene QDs. We also point out the similarities and differences in the spectrum between single- and bilayer graphene quantum dots. Striking in the case of bilayer graphene is the anomalous bulk Landau level (LL) that crosses the gap which results in crossings of QD states with this bulk LL at large magnetic fields in stark contrast to the single-layer case where this LL is absent. The tunability of the gap in the bilayer case allows us to observe different regimes of level spacings directly related to the formation of a pronounced ``Mexican hat'' in the bulk bandstructure. We discuss the applicability of such QDs to control and measure the valley isospin and their potential use for hosting and controlling spin qubits.

cond-mat.mes-hall↗