Related papers: Anderson Transition in Disordered Graphene
We establish spectral and dynamical localization for several Anderson models on metric and discrete radial trees. The localization results are obtained on compact intervals contained in the complement of discrete sets of exceptional…
Disorder in moire superlattices simultaneously degrades flat-band localization and induces Anderson localization, yet how these two regimes interact has remained unclear. Here, we introduce a combined framework linking localization-length…
We investigate disorder-induced localization in metals that break time-reversal and inversion symmetries through their energy dispersion, $\epsilon_{k}\neq\epsilon_{-k}$, but lack Berry phases. In the perturbative regime of disorder, we…
We present a full analytical solution for the localisation length in the one-dimensional Anderson model with weak diagonal disorder in the vicinity of the band centre. The results are obtained with the Hamiltonian map approach that turns…
We consider a tight-binding model on the regular honeycomb lattice with uncorrelated on-site disorder. We use two independent methods (recursive Green's function and self-consistent Born approximation) to extract the scattering mean free…
Recently, it was predicted that an RKKY-type interaction between adatoms in graphene can drive an ordering transition to a state with broken sublattice symmetry (arXiv:1004.3678). In this state, due to Bragg scattering of electron waves on…
Within the framework of tight binding models, aperiodic systems are mapped to a renormalized lattice with a dimer defect. In models exhibiting metal-insulator transition, the dimer acts like a resonant cavity and explains the existence of…
We study two lattice models, the honeycomb lattice (HCL) and a special square lattice (SQL), both reducing to the Dirac equation in the continuum limit. In the presence of disorder (gaussian potential disorder and random vector potential),…
This work extends the applications of Anderson-type Hamiltonians to include transport characterized by anomalous diffusion. Herein, we investigate the transport properties of a one-dimensional disordered system that employs the discrete…
We perform a detailed analysis of electronic polarizability of graphene with different theoretical approaches. From Kubo's linear response formalism, we give a general expression of frequency and wave-vector dependent polarizability within…
We study the Anderson localization of atomic gases exposed to simple-cubic optical lattices with a superimposed disordered speckle pattern. The two mobility edges in the first band and the corresponding critical filling factors are…
The formation of charge-density-wave order in Dirac fermion systems via electron-phonon coupling represents a significant topic in condensed matter physics. In this work, we investigate this phenomenon within the Holstein model on the…
This paper is devoted to the study of the random displacement model on $\R^d$. We prove that, in the weak displacement regime, Anderson and dynamical localization holds near the bottom of the spectrum under a generic assumption on the…
Our recently established criterion for the formation of extended states on tree graphs in the presence of disorder is shown to have the surprising implication that for bounded random potentials, as in the Anderson model, there is no…
We show that electron states in disordered graphene, with an onsite potential that induces inter-valley scattering, are localised for all energies at disorder as small as 1/6 of the band width of clean graphene. We clarify that, in order…
Disorder plays a crucial role in many systems particularly in solid state physics. However, the disorder in a particular system can usually not be chosen or controlled. We show that the unique control available for ultracold atomic gases…
We introduce an extension of the non-equilibrium dynamical mean field theory to incorporate the effects of static random disorder in the dynamics of a many-particle system by integrating out different disorder configurations resulting in an…
When electrons are confined in a two dimensional (2D) system, typical quantum mechanical phenomena such as Landau quantization can be detected. Graphene systems, including the single atomic layer and few-layer stacked crystals, are ideal 2D…
We propose a simplified version of the Multi-Scale Analysis of tight-binding Anderson models with strongly mixing random potentials which leads directly to uniform exponential bounds on decay of eigenfunctions in arbitrarily large finite…
We propose a new viewpoint on the study of localization transitions in disordered quantum systems, showing how critical properties can be seen also as a geometric transition in the data space generated by the classically encoded…