Physica Scripta (00318949)99(9)
The concept of topological Fano resonance, characterized by an ultrasharp asymmetric line shape, is a promising candidate for robust sensing applications due to its sensitivity to external parameters and immunity to structural disorder. In this study, the vacancy-induced topological Fano resonance in a nanoribbon made up of a hexagonal lattice with armchair sides is examined by introducing several on-site vacancies, which are deliberately created at regular distances, along a zigzag chain that stretches across the width of the ribbon. The presence of the on-site vacancies can create localized energy states within the electronic band structure, leading to the formation of an impurity band, which can result in Fano resonance phenomena by forming a conductivity channel between the edge modes on both armchair sides of the ribbon. Consequently, an ultracompact tunable on-chip integrated topological Fano resonance derived from the graphene-based nanomechanical phononic crystals is proposed. The Fano resonance arises from the interference between topologically protected even and odd edge modes at the interface between trivial and nontrivial insulators in a nanoribbon structure governed by the Kane-Mele model describing the quantum spin Hall effect in hexagonal lattices. The simulation of the topological Fano resonance is performed analytically using the Lippmann-Schwinger scattering formulation. One of the advantages of the present study is that the related calculations are carried out analytically, and in addition to the simplicity and directness, it reproduces the results obtained from the Landauer-Büttiker formulation very well both quantitatively and qualitatively. The findings open up possibilities for the design of highly sensitive and accurate robust sensors for detecting extremely tiny forces, masses, and spatial positions. © 2024 IOP Publishing Ltd. All rights, including for text and data mining, AI training, and similar technologies, are reserved.
Quantum Information Processing (15700755)23(5)
A novel method has been devised to compute the local integrals of motion (LIOMs) for a one-dimensional many-body localized system. In this approach, a class of optimal unitary transformations is deduced in a tensor network formalism to diagonalize the Hamiltonian of the specified system. To construct the tensor network, we utilize the eigenstates of the subsystems’ Hamiltonian to attain the desired unitary transformations. Subsequently, we optimize the eigenstates and acquire appropriate unitary localized operators that will represent the LIOMs tensor network. The efficiency of the method was assessed and found to be both fast and almost accurate. In framework of the introduced tensor network representation, we examine how the entanglement spreads along the considered many-body localized system and evaluate the outcomes of the approximations employed in this approach. The important and interesting result is that in the proposed tensor network approximation, if the length of the blocks is greater than the length of localization, then the entropy growth will be linear in terms of the logarithmic time. Also, it has been demonstrated that the entanglement can be calculated by only considering two blocks next to each other, if the Hamiltonian has been diagonalized using the unitary transformation made by the provided tensor network representation. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.
Al-marzoog, R.,
Rezaei, A.,
Noorinejad z., Z.,
Amini, M.,
Ghanbari, E.,
Jafari, S.A. Physical Review B (24699950)110(16)
This study is devoted to the profound implications of tilted Dirac cones on the quantum transport properties of two-dimensional (2D) Dirac materials. These materials, characterized by their linear conic energy dispersions in the vicinity of Dirac points, exhibit unique electronic behaviors, including the emulation of massless Dirac fermions and the manifestation of relativistic phenomena such as Klein tunneling. Expanding beyond the well-studied case of graphene, the manuscript focuses on materials with tilted Dirac cones, where the anisotropic and tilted nature of the cones introduces additional richness to their electronic properties that arises from an emergent underlying spacetime geometry. The investigation begins by considering a heterojunction of 2D Dirac materials, where electrons undergo quantum tunneling between regions with upright and tilted Dirac cones. The role of tilt in characterizing the transmission of electrons across these interfaces is thoroughly examined, shedding light on the influence of the tilt parameter on the transmission probability and the fate of the pseudospin of the Dirac electrons, particularly upon a sudden change in the tilting. We also investigate the probability of reflection and transmission from an intermediate slab with arbitrary subcritical tilt, focusing on the behavior of electron transmission across regions with varying Dirac cone tilts. The study demonstrates that for certain thicknesses of the middle slab, the transmission probability is equal to unity, and both reflection and transmission exhibit periodic behavior with respect to the slab thickness. This is reminiscent of Klein tunneling across scalar potential barriers in PNP junctions, no gate voltage is applied. Such a tilt-induced potential can be considered as the quantum transport manifestation of the "gravitomagnetic"effect of underlying spacetime structure. © 2024 American Physical Society.
Physical Review B (24699950)107(20)
Although one of the most important and intriguing features of the topological insulators is the presence of edge states, the closed-form expressions for the edge states of some famous topological models are still lacking. Here, we focus on the Kane-Mele model with and without Rashba spin-orbit coupling as a well-known model to describe a two-dimensional version of the Z2 topological insulator to study the properties of its edge states analytically. By considering the tight-binding model on a honeycomb lattice with zigzag boundaries and introducing a perturbative approach, we derive explicit expressions for the wave functions, energy dispersion relations, and the spin rotations of the (generic) helical edge states. To this end, we first map the edge states of the ribbon geometry into an effective two-leg ladder model with momentum-dependent energy parameters. Then, we split the Hamiltonian of the system into an unperturbed part and a perturbation. The unperturbed part has a flat-band energy spectrum and can be solved exactly, which allows us to consider the remaining part of the Hamiltonian perturbatively. The resulting energy dispersion relation within the first-order perturbation, surprisingly, is in excellent agreement with the numerical spectra over a very wide range of wave numbers. Our perturbative framework also allows deriving an explicit form for the rotation of the spins of the momentum edge states in the absence of axial spin symmetry due to the Rashba spin-orbit interaction. © 2023 American Physical Society.
Journal of Physics A: Mathematical and Theoretical (17518113)56(15)
The emergent integrability in a many-body localized (MBL) system can be well characterized by the existence of the complete set of local integrals of motion (LIOMs). Such exactly conserved and exponentially localized operators are often understood as quasiparticle operators which can be expanded in terms of single-particle operators dressed with different numbers of particle-hole pairs. Here, we consider a one-dimensional XXZ spin- 1 2 Heisenberg chain in the presence of a random field and try to quantify the corrections needed to be considered in the picture of quasiparticles associated with LIOMs due to the presence of particle-hole excitations. To this end, we explicitly present the multibody expansion of LIOM creation operators of the system in the MBL regime. We analytically obtain the coefficients of this expansion and discuss the effect of higher-order corrections associated with different numbers of particle-hole excitations. Our analysis shows that depending on the localization length of the system, there exist a regime in which the contributions that come from higher-order terms can break down the effective one-particle description of the LIOMs and such quasiparticles become essentially many-body-like. © 2023 IOP Publishing Ltd.
Physica Scripta (00318949)98(1)
We have theoretically investigated strain-induced thermoelectric power generation properties of zigzag bilayer phosphorene nanoribbon. Since energy bandgap size and edge state dispersion play a significant role in the thermoelectric properties of such a structure, we have investigated the effect of strain in different directions on these two quantities. We have shown that by applying both tensile and compressive strains in different directions, it is possible to properly tune the energy bandgap size and adjust the edge state dispersion. We have also selected strain combinations in different directions that simultaneously increase the size of the energy bandgap and decrease the dispersion of the edge state. It has shown that with such combinations of strains, the maximal figure of merit has been improved by about two times compared to the pristine case. © 2022 IOP Publishing Ltd.
Scientific Reports (20452322)13(1)
Studying the edge states of a topological system and extracting their topological properties is of great importance in understanding and characterizing these systems. In this paper, we present a novel analytical approach for obtaining explicit expressions for the edge states in the Kane-Mele model within a ribbon geometry featuring armchair boundaries. Our approach involves a mapping procedure that transforms the system into an extended Su–Schrieffer–Heeger model, specifically a two-leg ladder, in momentum space. Through rigorous derivation, we determine various analytical properties of the edge states, including their wave functions and energy dispersion. Additionally, we investigate the condition for topological transition by solely analyzing the edge states, and we elucidate the underlying reasons for the violation of the bulk-edge correspondence in relatively narrow ribbons. Our findings shed light on the unique characteristics of the edge states in the quantum spin Hall phase of the Kane–Mele model and provide valuable insights into the topological properties of such systems. © 2023, Springer Nature Limited.
European Physical Journal Plus (21905444)137(6)
Zigzag Phosphorene nanoribbon supports topological edge states in the gap region near the Ferm level. We consider a bilayer system consisting of two coupled Phosphorene layers with zigzag edges and investigate the thermoelectric properties of the system by engineering its corresponding edge modes. To this end, we first map the edge states of zigzag bilayer phosphorene nanoribbon (ZBPNR) into an effective Su-Schrieffer-Heeger (SSH) ladder model with momentum dependent hopping probabilities which allow us to obtain their corresponding band dispersion and wave functions analytically. Then, by applying the energy filtering method and employing non-equilibrium Green’s function approach, we show that the electric power and thermoelectric efficiency of the ZBPNRs can be improved remarkably in the presence of mid-gap edge states. We also argue how to engineer the edge modes to further optimize thermoelectric power and efficiency of the system by applying periodic point potentials at the boundaries © 2022, The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature.
Skvortsov m.a., ,
Amini, M.,
Kravtsov v.e., V.E. Physical Review B (24699950)106(5)
We study the response of an isolated quantum system governed by the Hamiltonian drawn from the Gaussian Rosenzweig-Porter random matrix ensemble to a perturbation controlled by a small parameter. We focus on the density of states, local density of states, and the eigenfunction amplitude overlap correlation functions which are calculated exactly using the mapping to the supersymmetric nonlinear sigma model. We show that the susceptibility of eigenfunction fidelity to the parameter of perturbation can be expressed in terms of these correlation functions and is strongly peaked at the localization transition: It is independent of the effective disorder strength in the ergodic phase, grows exponentially with increasing disorder in the fractal phase, and decreases exponentially in the localized phase. As a function of the matrix size, the fidelity susceptibility remains constant in the ergodic phase and increases in the fractal and in the localized phases at modestly strong disorder. We show that there is a critical disorder strength inside the insulating phase such that for disorder stronger than the critical, the fidelity susceptibility decreases with increasing the system size. The overall behavior is very similar to the one observed numerically in a recent work by Sels and Polkovnikov [Phys. Rev. E 104, 054105 (2021)2470-004510.1103/PhysRevE.104.054105] for the normalized fidelity susceptibility in a disordered XXZ spin chain. © 2022 American Physical Society.
Physical Review B (24699950)106(5)
Many-body localization (MBL) is a novel prototype of ergodicity breaking due to the emergence of local integrals of motion (LIOMs) in a disordered interacting quantum system. To better understand the role played by the existence of such LIOMs, we explore and study some of their structural properties across the MBL transition. We first consider a one-dimensional XXZ spin chain in a disordered magnetic field and introduce and implement a nonperturbative, fast, and accurate method of constructing LIOMs. In contrast to already existing methods, our scheme allows obtaining LIOMs not only in the deep MBL phase but, rather, near the transition point too. Then, we take the matrix representation of LIOM operators as an adjacency matrix of a directed graph whose elements describe the connectivity of ordered eigenbasis in the Hilbert space. Our cluster-size analysis for this graph shows that the MBL transition coincides with a percolation transition in the Hilbert space. By performing finite-size scaling, we compare the critical disorder and correlation exponent ν both in the presence and absence of interactions. Finally, we also discuss how the distribution of diagonal elements of LIOM operators in a typical cluster signals the transition. © 2022 American Physical Society.
Physics Letters, Section A: General, Atomic and Solid State Physics (03759601)387
Double-level quantum systems are good candidates for revealing coherent quantum transport properties. Here, we consider quantum interference effects due to the formation of a two-level system (TLS) coupled to the edge channel of a zigzag Phosphorene nanoribbon (ZPNR). Using the tight-binding approach, we first demonstrate the formation of a TLS in bulk Phosphorene sheet due to the existence of two nearby vacancy impurities. Then, we show that such a TLS can couple to the quasi-one-dimensional continuum of the edge states in a ZPNR which results in the appearance of two-dip Fano-type line shapes. To this end, we generalize the Lippmann–Schwinger approach to study the scattering of edge electrons in a ZPNR by two coupled impurity defects. We obtain an analytical expression of the transmission coefficient which shows that the positions and widths of the antiresonances can be controlled by changing the intervacancy distance as well as their distance from the edge of the ribbon. This work constitutes a clear example of the multiple Fano resonances in mesoscopic transport. © 2020 Elsevier B.V.
Nanotechnology (09574484)32(37)
Armchair phosphorene nanoribbons (APNRs) are known to be semiconductors with an indirect bandgap. Here, we propose to introduce new states in the gap of APNRs by creating a periodic structure of vacancies (antidots). Based on the tight-binding model, we show that a periodic array of vacancies or nanopores leads to the formation of an impurity band inside the gap region. We first present an analytical expression for the dispersion relation of an impurity band induced by hybridization of bound states associated with each single vacancy defect. Then, we increase the size of vacancy defects to include a bunch of atoms and theoretically investigate the effect of nanopores size and their spacing on electronic band structure, carrier transmission function, and thermoelectric properties. Our analysis of the power generation rate and thermoelectric efficiency of these structures reveals that an ANPR can be used as a superb thermoelectric power generation module. © 2021 IOP Publishing Ltd.
Physical Review B (24699950)101(11)
The existence of robust chiral edge states in a finite topologically nontrivial Chern insulator is a consequence of the bulk-boundary correspondence. In this paper, we present a theoretical framework based on lattice Green's function to study the scattering of such chiral edge electrons by a single localized impurity. To this end, in the first step, we consider the standard topological Haldane model on a honeycomb lattice with strip geometry. We obtain analytical expressions for the wave functions and their corresponding energy dispersion of the low-energy chiral states localized at the edge of the ribbon. Then, we employ the T-matrix Lippmann-Schwinger approach to explicitly show the robustness of chiral edge states against the impurity scattering. This backscattering-free process has an interesting property that the transmitted wave function acquires an additional phase factor. Although this additional phase factor does not affect quantum transport through the chiral channel, it can carry quantum information. As an example of such quantum information transport, we investigate the entanglement of two magnetic impurities in a Chern insulator through the dissipationless scattering of chiral electrons. © 2020 American Physical Society.
Indian Journal of Physics (09731458)93(6)pp. 733-738
Functionalized graphene sheets have attracted increasing attention due to their novel micro-/nano-electromechanical applications. In this paper, the aggregation of the gold nano-clusters on the defected graphene sheet is studied by using the molecular dynamics simulation method. It is shown that a model defected graphene with randomly distributed vacancies can affect the formation and aggregation of the Au nano-clusters on the graphene sheet. It is found that the Au nano-clusters agglomerate on the pristine parts of the surface rather than on the defected parts. In addition, the results show that increasing the temperature amplifies the above result and varies the Au nano-cluster sizes. Moreover, it is observed that the aggregation of Au clusters changes the surface roughness. The results presented here would help to design more efficient functionalized graphene-based electronic devices. © 2018, Indian Association for the Cultivation of Science.
Journal of Physics Condensed Matter (09538984)31(21)
Zigzag phosphorene nanoribbons have quasi-flat band edge modes entirely detached from bulk states. We analytically study the electronic transport through such edge states in the presence of a localized defect for semi-infinite and finite ribbon widths. Using the tight-binding model, we derive analytical expressions for the Green's function and transmission amplitude of both pristine and defective nanoribbons. We find that the transmission of ribbons with both semi-infinite and finite width is sensitive to the location of a single impurity defect with respect to the edge. By the presence of an impurity on the outermost edge site of the ribbon, the transmission through the edge channel, similar to a one-dimensional chain, strongly suppresses for the entire energy spectrum of the quasi-flat band. In contrast, the transmission of low-energy (E ≈ 0) states, is robust as the impurity is moved one position far away from the edge on the same sub-lattice. The analytical calculations are also complemented by exact numerical transport computations using the Landauer approach. © 2019 IOP Publishing Ltd Printed in the UK.
De tomasi, G.,
Amini, M.,
Bera, S.,
Khaymovich, I.M.,
Kravtsov v.e., V.E. SciPost Physics (25424653)6(1)
We study analytically and numerically the dynamics of the generalized Rosenzweig-Porter model, which is known to possess three distinct phases: ergodic, multifractal and localized phases. Our focus is on the survival probability R(t), the probability of finding the initial state after time t. In particular, if the system is initially prepared in a highly-excited non-stationary state (wave packet) confined in space and containing a fixed fraction of all eigenstates, we show that R(t) can be used as a dynamical indicator to distinguish these three phases. Three main aspects are identified in different phases. The ergodic phase is characterized by the standard power-law decay of R(t) with periodic oscillations in time, surviving in the thermodynamic limit, with frequency equals to the energy bandwidth of the wave packet. In multifractal extended phase the survival probability shows an exponential decay but the decay rate vanishes in the thermodynamic limit in a non-trivial manner determined by the fractal dimension of wave functions. Localized phase is characterized by the saturation value of R(t → ∞) = k, finite in the thermodynamic limit N → ∞, which approaches k = R(t → 0) in this limit. Copyright G. De Tomasi et al.
Europhysics Letters (02955075)125(6)
Transport of the edge-state electrons along zigzag phosphorene nanoribbons in the presence of two impurities/vacancies is analytically investigated. Considering the places of the defects, a number of different situations are examined. When both defects are placed on the edge zigzag chain, as is expected, by changing the energy of the traveling electrons the electrical conductance exhibits a resonance behavior. In this case, for two vacancies the observed resonant peaks become extremely sharp. An amazing behavior is seen when the second vacancy is located along an armchair chain while the first is placed at the intersection of the edge zigzag and this armchair chain. In this case, in a considerable range of energy, the conductance is strongly strengthened. In fact the presence of the second vacancy creates a shielded region around the first vacancy, consequently, the traveling wave bypasses this region and enhances the conductance. The analytical results are compared with numerical simulations showing very good agreement. © 2019 EPLA.
Quantum Information Processing (15700755)18(3)
In this paper, we investigate how two on-site doped impurities with net magnetic moments in an edge chain of a zigzag phosphorene nanoribbon (zPNR) can be entangled by scattering of the traveling edge-state electrons. To this end, in the first step, we employ the Lippmann–Schwinger equation as well as the Green’s function approach to study the scattering of the free traveling electrons from two magnetic impurities in a one-dimensional tight-binding chain. Then, following the same formalism, that is shown that the behavior of two on-site spin impurities in the edge chain of a zPNR in responding to the scattering of the edge-state traveling electrons is very similar to what happens for the one-dimensional chain. In both cases, considering a known incoming wave state, the reflected and transmitted parts of the final wave state are evaluated analytically. Using the obtained results, the related partial density matrices and the reflection and transmission probabilities are computable. Negativity as a measure of the produced entanglement in the final state is calculated, and the results are discussed. Our theoretical model actually proposes a method, which is perhaps experimentally performable to create the entanglement in the state of the impurities. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.
Physical Review B (24699950)99(8)
Motivated by recent scanning tunneling microscopy and spectroscopy experiments on probing single vacancies in black phosphorus, we present a theory for Fano antiresonances induced by coupling between vacancy states and edge states of zigzag phosphorene nanoribbons (zPNRs). To this end, in the first step, using the tight-binding Hamiltonian, we obtain an analytic solution on the lattice for the state associated with a single vacancy located in the bulk phosphorene which shows a highly anisotropic localization in real space. For a finite zigzag ribbon, in the absence of particle-hole symmetry, the localized state induced by vacancies can couple with the wave functions of the edge states, which results in the formation of a new bound state. The energy of the vacancy bound state lies inside the quasiflat band composed of edge states when the vacancy locates sufficiently far away from the edge. Then, we employ the T-matrix Lippmann-Schwinger approach to obtain an explicit analytical expression for the scattering amplitude of the edge electrons of a zPNR through the presence of a single vacancy which shows a Fano resonance profile with a tunable dip. We demonstrate that varying the position of the vacancy produces substantially different effects on the resonance width, the resonance energy position, and the asymmetry parameter of the Fano line shape. Furthermore, the validity of the theoretical descriptions is verified numerically by using the Landauer approach. © 2019 American Physical Society.
European Physical Journal D (14346060)71(1)
Abstract: Motivated by the problem of Casimir energy, we investigate the idea of usinginhomogeneity of surfaces instead of their corrugation, which leads to Casimir interactionbetween two inhomogeneous semi-transparent concentric cylinders. Using the multiplescattering method, we study the Casimir energy and torque between the cylinders withdifferent potentials subjected to Dirichlet boundary conditions, both in weak and strongcoupling regimes. We also extend our formalism to the case of two inhomogeneousdielectrics in a weak coupling regime. Graphical abstract: [Figure not available: see fulltext.] © 2017, EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.
Europhysics Letters (02955075)117(3)
We consider the spreading of a wave packet in the generalized Rosenzweig-Porter random matrix ensemble in the region of the non-ergodic extended states 1 > γ > 2. We show that although non-trivial fractal dimensions 0 > Dq = 2-γ > 1 characterize wave function statistics in this region, the wave packet spreading 〈r2〉 ∞ t2 is governed by the diffusion exponent β = 1 outside the ballistic regime t < τ ∼ 1 and 〈r2〉 ∞ t2 in the ballistic regime for t > τ ∼ 1. This emonstrates that the multifractality appears only in local quantities like the wave packet survival probability but not in the large-distance spreading of the wave packet. © EPLA, 2017.
Kravtsov v.e., V.E.,
Khaymovich, I.M.,
Cuevas e., ,
Amini, M. New Journal Of Physics (13672630)17(12)
Motivated by the problem of many-body localization and the recent numerical results for the level and eigenfunction statistics on the random regular graphs, a generalization of the Rosenzweig-Porter random matrix model is suggested that possesses two transitions. One of them is the Anderson localization transition from the localized to the extended states. The other one is the ergodic transition from the extended non-ergodic (multifractal) states to the extended ergodic states.Weconfirm the existence of both transitions by computing the two-level spectral correlation function, the spectrum of multifractality f (α) and thewave function overlapwhich consistently demonstrate these two transitions.
New Journal Of Physics (13672630)16
We study the interaction-driven localization transition, which a recent experiment (Richardella et al 2010 Science 327 665) in Ga1-xMnxAs has shown to come along with the multifractal behavior of the local density of states (LDoS) and the intriguing persistence of critical correlations close to the Fermi level. We show that the bulk of these phenomena can be understood within a Hartree-Fock (HF) treatment of disordered, Coulomb-interacting spinless fermions. A scaling analysis of the LDoS correlation demonstrates multifractality with the correlation dimension d2 ≈ 1.57, which is significantly larger than at a non-interacting Anderson transition and is compatible with the experimental value dexp2 = 1.8 ± 0.3. At the interaction-driven transition, the states at the Fermi level become critical, while the bulk of the spectrum remains delocalized up to substantially stronger interactions. The mobility edge stays close to the Fermi energy in a wide range of disorder strength, as the interaction strength is further increased. The localization transition is concomitant with the quantum-to-classical crossover in the shape of the pseudo-gap in the tunneling density of states, and with the proliferation of metastable HF solutions that suggest the onset of a glassy regime with poor screening properties. © 2014 IOP Publishing and Deutsche Physikalische Gesellschaft.
AIP Advances (21583226)4(5)
Crack propagation in a defected graphene sheet is investigated at finite temperature using molecular dynamics simulation. The effects of several initial cracks, temperature and different percentage of vacancies are considered. It is found that i) the critical load, which is a criteria for crack propagation, is larger when the load is applied on the zigzag direction, ii) the critical load decreases with increasing temperature, iii) a hole in the center of the sheet and the presence of randomly distributed vacancies reduce the critical load giving different crack propagation trajectory. Our new results would help to understand the crack propagation phenomena in defected graphene at finite temperature. © 2014 Author(s).
Zare m.h., ,
Amini, M.,
Shahbazi, F.,
Jafari, S.A. Journal of Physics Condensed Matter (09538984)22(25)
Employing the kernel polynomial method (KPM), we study the electronic properties of the graphene bilayers with Bernal stacking in the presence of diagonal disorder, within the tight-binding approximation and nearest neighbor interactions. The KPM method enables us to calculate local density of states (LDOS) without the need to exactly diagonalize the Hamiltonian. We use the geometrical averaging of the LDOS at different lattice sites as a criterion to distinguish the localized states from extended ones. We find that this model undergoes an Anderson metal-insulator transition at a critical value of disorder strength. © 2010 IOP Publishing Ltd.
Europhysics Letters (02955075)87(3)
We use the regularized kernel polynomial method (RKPM) to numerically study the effect disorder on a single layer of graphene. This accurate numerical method enables us to study very large lattices with millions of sites, and hence is almost free of finite-size errors. Within this approach, both weak- and strong-disorder regimes are handled on the same footing. We study the tight-binding model with on-site disorder, on the honeycomb lattice. We find that in the weak-disorder regime, the Dirac fermions remain extended and their velocities decrease as the disorder strength is increased. However, if the disorder is strong enough, there will be a mobility edge separating localized states around the Fermi point, from the remaining extended states. © 2009 Europhysics Letters Association.
