We study the electronic properties of actual-size graphene nanoribbons subjected to substitutional disorder particularly with regard to the experimentally observed metal-insulator transition. Calculating the local, mean and typical density of states, as well as the time-evolution of the particle density we comment on a possible disorder-induced localisation of charge carriers at and close to the Dirac point within a percolation transition scenario.
The experimentally observed metal-to-insulator transition in hydrogenated graphene is numerically confirmed for actual sized graphene samples and realistic impurity concentrations. The eigenstates of our tight-binding model with substitutional disorder corroborate the formation of electron-hole-puddles with characteristic length scales comparable to the ones found in experiments. The puddles cause charge inhomogeneities and tend to suppress Anderson localization. Even though, monitoring the charge carrier quantum dynamics and performing a finite-size scaling of the local density of states dist…
Based on distributions of local Green's functions we present a stochastic approach to disordered systems. Specifically we address Anderson localisation and cluster effects in binary alloys. Taking Anderson localisation of Holstein polarons as an example we discuss how this stochastic approach can be used for the investigation of interacting disordered systems.
We investigate the properties of the gap-edge states of half-filled interacting disordered zigzag graphene nanoribbons. We find that the midgap states can display the quantized fractional charge of 1/2. These gap-edge states can be represented by topological kinks with their site probability distribution divided between the opposite zigzag edges with different chiralities. In addition, there are numerous spin-split gap-edge states, similar to those in a Mott-Anderson insulator.
We investigate interacting disordered zigzag nanoribbons at low doping, using the Hubbard model to treat electron interactions within the density matrix renormalization group and Hartree-Fock method. Extra electrons that are inserted into an interacting disordered zigzag nanoribbon divide into anyons. Furthermore, the fractional charges form a new disordered anyon phase with a highly distorted edge spin density wave, containing numerous localized magnetic moments residing on the zigzag edges, thereby displaying spin-charge separation and a strong non-local correlation between the opposite zigz…
Localisation phenomena in highly disordered metals close to the extreme conditions determined by the Mott-Ioffe-Regel (MIR) limit when the electron mean free path is approximately equal to the interatomic distance is a challenging problem. Here, to shed light on these localisation phenomena, we studied the dc transport and optical conductivity properties of nanoscaled multilayered films composed of disordered metallic Ta and magnetic FeNi nanoisland layers, where ferromagnetic FeNi nanoislands have giant magnetic moments of 10^3-10^5 Bohr magnetons (μ_B). In these multilayered structures, FeNi…
We numerically compute the density of states (DOS) of interacting disordered zigzag graphene nanoribbon (ZGNR) having midgap states showing $e/2$ fractional edge charges. The computed Hartree-Fock DOS is linear at the critical disorder strength where the gap vanishes. This implies an $I\mbox{-}V$ curve of $I\propto V^2$. Thus, $I\mbox{-}V$ curve measurement may yield evidence of fractional charges in interacting disordered ZGNR. We show that even a weak disorder potential acts as a singular perturbation on zigzag edge electronic states, producing drastic changes in the energy spectrum. Spin-ch…
We examine the magnetic correlations in quantum spin models that were derived recently as effective low-energy theories for electronic correlation effects on the edge states of graphene nanoribbons. For this purpose, we employ quantum Monte Carlo simulations to access the large-distance properties, accounting for quantum fluctuations beyond mean-field-theory approaches to edge magnetism. For certain chiral nanoribbons, antiferromagnetic inter-edge couplings were previously found to induce a gapped quantum disordered ground state of the effective spin model. We find that the extended nature of …
We report direct experimental evidence that the insulating phase of a disordered, yet strongly interacting two-dimensional electron system (2DES) becomes unstable at low temperatures. As the temperature decreases, a transition from insulating to metal-like transport behaviour is observed, which persists even when the resistivity of the system greatly exceeds the quantum of resistivity h/e^2. The results have been achieved by measuring transport on a mesoscopic length-scale while systematically varying the strength of disorder.
Using a combination of ground state quantum Monte-Carlo and finite size scaling techniques, we perform a systematic study of the effect of Coulomb interaction on the localisation length of a disordered two-dimensional electron gas. We find that correlations delocalise the 2D system. In the absence of valley degeneracy (as in GaAs heterostructures), this delocalization effect corresponds to a finite increase of the localization length. The delocalisation is much more dramatic in the presence of valley degeneracy (as in Si MOSFETSs) where the localization length increases drastically. Our result…
The electronic and magnetic properties of ferromagnetic doped manganites are investigated by means of model tight-binding and \textit{ab initio} self-interaction corrected local spin density approximation calculations. It is found that the surface alone by breaking the cubic symmetry induces a difference in the occupation of the two $e_{g}$ orbitals at the surface. With \textit{ab initio} calculations we found surface localisation of one orbital and hence a change in the Mn valency from four in the bulk to three at the sub-surface. Different surface or disordered interface induced localisation…
Interacting disordered zigzag graphene nanoribbons have fractional charges, are quasi-one-dimensional, and display an exponentially small gap. Our numerical computations showed that the topological entanglement entropy of these systems has a small finite but universal value, independent of the strength of the interaction and the disorder. The result that was obtained for the topological entanglement entropy shows that the disorder-free phase is critical and becomes unstable in the presence of disorder.
The Kondo temperature of a magnetic impurity in a weakly disordered metal is distributed due to the randomness in the local exchange coupling, and the local electronic density of states (LDOS). We show that in a closed, phase coherent metal particle the resulting distribution of $T_K$ is strongly asymmetric and scales with the mean level spacing $Δ$. Its width is $2 \sqrt{Δ/βT_K}$, where $Δ$ is the mean level spacing, and $β=1,2$, with, without time reversal symmetry, respectively. Increasing the density of magnetic impurities, the distribution of Kondo temperatures (DKT) is found to become mo…
A recent experiment by P. Bordia et al. (Periodically Driving a Many Body Localized Quantum System, Nat Phys, Jan 2017) has demonstrated that periodically modulating the potential of a localised many-body quantum system described by the Aubry-André Hamiltonian with on-site interactions can lead to a many-body localisation-delocalisation transition, provided the modulation amplitude is big enough. Here, we consider the noninteracting counterpart of that model in order to explore its phase diagram as a function of the strength of the disordered potential, the driving frequency and its amplitude.…
The quantum phase diagram of disordered electron systems as function of the concentration of magnetic impurities nm and the local exchange coupling J is studied in the dilute limit. We take into account the Anderson localisation of the electrons by a nonperturbative numerical treatment of the disorder potential. The competition between RKKY interaction JRKKY and the Kondo effect, as governed by the temperature scale TK, is known to gives rise to a rich magnetic quantum phase diagram, the Doniach diagram. Our numerical calculations show that in a disordered system both the Kondo temperature TK …
Motivated by Weyl semimetals and weakly doped semiconductors, we study transport in a weakly disordered semiconductor with a power-law quasiparticle dispersion $ξ_{\bf k}\propto k^α$. We show, that in $2α$ dimensions short-correlated disorder experiences logarithmic renormalisation from all energies in the band. We study the case of a general dimension $d$ using a renormalisation group, controlled by an $\varepsilon=2α-d$-expansion. Above the critical dimensions, conduction exhibits a localisation-delocalisation phase transition or a sharp crossover (depending on the symmetries of the Hamilton…
We explore the Fock-space structure of eigenstates across the many-body localisation (MBL) transition in a disordered, interacting quantum spin-1/2 chain. Eigenstate expectation values of spatially local observables, which distinguish an MBL phase from an ergodic one, can be represented in terms of eigenstate amplitudes on the Fock space. Motivated by this, we introduce and study spatial correlations on the Fock space. From these, a correlation length emerges, which is found to vary discontinuously across the MBL transition; and is intimately connected to the discontinuous jump in the multifra…
Nodal semimetals (e.g. Dirac, Weyl and nodal-line semimetals, graphene, etc.) and systems of pinned particles with power-law interactions (trapped ultracold ions, nitrogen defects in diamonds, spins in solids, etc.) are presently at the centre of attention of large communities of researchers working in condensed-matter and atomic, molecular and optical physics. Although seemingly unrelated, both classes of systems are abundant with novel fundamental thermodynamic and transport phenomena. In this paper, we demonstrate that low-energy field theories of quasiparticles in semimetals may be mapped …
It has become increasingly clear that a full understanding of the physics of electrons in disordered systems requires an approach in which both disorder and interactions are taken into account. Work on small numbers of electrons has suggested that interactions can substantially increase the localisation length in 1 dimensional systems and possibly lead to delocalisation in 2D. It has not been clear, however, to what extent these results are applicable to systems with a finite density of electrons. Among numerical approaches the transfer matrix method combined with finite size scaling has been …
The so-called stripe phase of the manganites is an important example of the complex behaviour of metal oxides, and has long been interpreted as the localisation of charge at atomic sites. Here, we demonstrate via resistance measurements on La_{0.50}Ca_{0.50}MnO_3 that this state is in fact a prototypical charge density wave (CDW) which undergoes collective transport. Dramatic resistance hysteresis effects and broadband noise properties are observed, both of which are typical of sliding CDW systems. Moreover, the high levels of disorder typical of manganites result in behaviour similar to that …
It is commonly believed that a non-interacting disordered electronic system can undergo only the Anderson metal-insulator transition. It has been suggested, however, that a broad class of systems can display disorder-driven transitions distinct from Anderson localisation that have manifestations in the disorder-averaged density of states, conductivity and other observables. Such transitions have received particular attention in the context of recently discovered 3D Weyl and Dirac materials but have also been predicted in cold-atom systems with long-range interactions, quantum kicked rotors and…
