Low energy theory of disordered graphene

At low values of external doping graphene displays a wealth of unconventional transport properties. Perhaps most strikingly, it supports a robust 'metallic' regime, with universal conductance of the order of the conductance quantum. We here apply a combination of mean field and bosonization methods to explore the large scale transport properties of the system. We find that, irrespective of the doping level, disordered graphene is subject to common mechanisms of Anderson localization. However, at low doping a number of renormalization mechanisms conspire to protect the conductivity of the system, to an extend that strong localization may not be seen even at temperatures much smaller than those underlying present experimental work.Comment: 4 page

Crossover of magnetoconductance autocorrelation for a ballistic chaotic quantum dot

The autocorrelation function C_{\varphi,\eps}(\Delta\varphi,\,\Delta \eps)= \langle \delta g(\varphi,\,\eps)\, \delta g(\varphi+\Delta\varphi,\,\eps+\Delta \eps)\rangle ($\varphi$ and \eps are rescaled magnetic flux and energy) for the magnetoconductance of a ballistic chaotic quantum dot is calculated in the framework of the supersymmetric non-linear $\sigma$-model. The Hamiltonian of the quantum dot is modelled by a Gaussian random matrix. The particular form of the symmetry breaking matrix is found to be relevant for the autocorrelation function but not for the average conductance. Our results are valid for the complete crossover from orthogonal to unitary symmetry and their relation with semiclassical theory and an $S$-matrix Brownian motion ensemble is discussed.Comment: 7 pages, no figures, accepted for publication in Europhysics Letter

Quantum phase transitions in the quasi-periodic kicked rotor

We present a microscopic theory of transport in quasi-periodically driven environments (`kicked rotors'), as realized in recent atom optic experiments. We find that the behavior of these systems depends sensitively on the value of Planck's constant $\tilde h$: for irrational values of $\tilde h/(4\pi)$ they fall into the universality class of disordered electronic systems and we derive the microscopic theory of the ensuing localization phenomena. In contrast, for rational values the rotor-Anderson insulator acquires an infinite (static) conductivity and turns into a `super-metal'. Signatures of the corresponding metal/super-metal transition are discussed.Comment: 4 pages, 1 figure, 1 tabl

Universal spectral statistics in quantum graphs

We prove that the spectrum of an individual chaotic quantum graph shows universal spectral correlations, as predicted by random--matrix theory. The stability of these correlations with regard to non--universal corrections is analyzed in terms of the linear operator governing the classical dynamics on the graph.Comment: 4 pages, reftex, 1 figure, revised version to be published in PR

Majorana Fermions in Strongly Interacting Helical Liquids

Majorana fermions were proposed to occur at edges and interfaces of gapped one-dimensional systems where phases with different topological character meet due to an interplay of spin-orbit coupling, proximity-induced superconductivity and external magnetic fields. Here we investigate the effect of strong particle interactions, and show that the helical liquid offers a mechanism that protects the very existence of Majorana edge states: whereas moderate interactions close the proximity gap which supports the edge states, in helical liquids the gap re-opens due to two-particle processes. However, gapless fermionic excitations occur at spatial proximity to the Majorana states at interfaces and may jeopardize their long term Majorana coherence.Comment: 7 pages, 4 figure

Parametric Level Correlations in Random-Matrix Models

We show that parametric level correlations in random-matrix theories are closely related to a breaking of the symmetry between the advanced and the retarded Green's functions. The form of the parametric level correlation function is the same as for the disordered case considered earlier by Simons and Altshuler and is given by the graded trace of the commutator of the saddle--point solution with the particular matrix that describes the symmetry breaking in the actual case of interest. The strength factor differs from the case of disorder. It is determined solely by the Goldstone mode. It is essentially given by the number of levels that are strongly mixed as the external parameter changes. The factor can easily be estimated in applications.Comment: 8 page

Phonons in Random Elastic Media and the Boson Peak

We show that the density of states of random wave equations, normalized by the square of the frequency, has a peak - sometimes narrow and sometimes broad - in the range of wave vectors between the disorder correlation length and the interatomic spacing. The results of this letter may be relevant for understanding vibrational spectra and light propagation in disordered solids

Enhancement of Persistent Current in Metal Rings by Correlated Disorder

We study analytically the effect of a correlated random potential on the persistent current in a one-dimensional ring threaded by a magnetic flux $\phi$, using an Anderson tight-binding model. In our model, the system of $N=2M$ atomic sites of the ring is assumed to be partitioned into $M$ pairs of identical nearest-neighbour sites (dimers). The site energies for different dimers are taken to be uncorrelated gaussian variables. For this system we obtain the exact flux-dependent energy levels to second order in the random site energies, using an earlier exact transfer matrix perturbation theory. These results are used to study the mean persistent current generated by $N_e\leq N$ spinless electrons occupying the $N_e$ lowest levels of the flux-dependent energy band at zero temperature. Detailed analyses are carried out in the limit $1\ll N_e\ll N$ and for a half-filled band ($N_e=N/2$), for magnetic fluxes $-1/2 <\phi/\phi_0<1/2$. While the uncorrelated disorder leads to a reduction of the persistent current, the disorder correlation acts to enhance it. In particular, in the half-filled band case the correlated disorder leads to a global flux-dependent enhancement of persistent current which has the same form for even and odd $N_e$. At low filling of the energy band the effect of the disorder on the persistent current is found to depend on the parity of $N_e$: the correlated disorder yields a reduction of the current for odd $N_e$ and an enhancement of the current for even $N_e$.Comment: 1

Roadmap to Majorana surface codes

Surface codes offer a very promising avenue towards fault-tolerant quantum computation. We argue that two-dimensional interacting networks of Majorana bound states in topological superconductor/semiconductor heterostructures hold several distinct advantages in that direction, both concerning the hardware realization and the actual operation of the code. We here discuss how topologically protected logical qubits in this Majorana surface code architecture can be defined, initialized, manipulated, and read out. All physical ingredients needed to implement these operations are routinely used in topologically trivial quantum devices. In particular, we show that by means of quantum interference terms in linear conductance measurements, composite single-electron pumping protocols, and gate-tunable tunnel barriers, the full set of quantum gates required for universal quantum computation can be implemented.Comment: 23 pages, 8 figure

Reply to the Comment of den Hartog and van Wees on "Conductance Fluctuations in Mesoscopic Normal-Metal/Superconductor Samples"

In their comment cond-mat/9710285 [Phys. Rev. Lett. 80, 5024 (1998)] den Hartog and van Wees (HW) raise objections against our analysis of the experimental data presented in cond-mat/9708162 [Phys. Rev. Lett. 79, 1547 (1997)]. According to HW, we did not account for the quantum phase incoherence introduced by the Niobium compounds of the investigated Nb/Au hybrid samples. Here we show that and why this criticism is not justified. Some difficulties associated with a precise determination of the coherence lengths are discussed. It is discussed why these uncertainties do not have a qualitative impact on the results reported in our paper.Comment: Reply to the comment cond-mat/9710285 by den Hartog and van Wees; 1 page REVTE