arXiv subjects

Mikhail I. Katsnelson

Publications and source records attributed to Mikhail I. Katsnelson.

At least 181 records · Page 10Linked to original sources

arXiv2014

Quasiparticle band structure and tight-binding model for single- and bilayer black phosphorus

By performing \emph{ab initio} calculations for one- to four-layer black phosphorus within the $GW$ approximation, we obtain a significant difference in the band gap ($\sim$1.5 eV), which is in line with recent experimental data. The results are analyzed in terms of the constructed four-band tight-binding model, which gives accurate descriptions of the mono- and bilayer band structure near the band gap, and reveal an important role of the interlayer hoppings, which are largely responsible for the obtained gap difference.

cond-mat.mtrl-sci↗

arXiv2014

Fermi Condensation Near van Hove Singularities Within the Hubbard Model on the Triangular Lattice

The proximity of the Fermi surface to van Hove singularities drastically enhances interaction effects and leads to essentially new physics. In this work we address the formation of flat bands ("Fermi condensation") within the Hubbard model on the triangular lattice and provide a detailed analysis from an analytical and numerical perspective. To describe the effect we consider both weak-coupling and strong-coupling approaches, namely the renormalization group and dual fermion methods. It is shown that the band flattening is driven by correlations and is well pronounced even at sufficiently high temperatures, of the order of 0.1-0.2 of the hopping parameter. The effect can therefore be probed in experiments with ultracold fermions in optical lattices.

cond-mat.str-el↗

arXiv2013

Origin of Anomalous Water Permeation through Graphene Oxide Membrane

Water inside the low dimensional carbon structures has been considered seriously owing to fundamental interest in its flow and structures as well as its practical impact. Recently, the anomalous perfect penetration of water through graphene oxide membrane was demonstrated although the membrane was impenetrable for other liquids and even gases. The unusual auxetic behavior of graphene oxide in the presence of water was also reported. Here, based on first-principles calculations, we establish atomistic models for hybrid systems composed of water and graphene oxides revealing the anomalous water behavior inside the stacked graphene oxides. We show that formation of hexagonal ice bilayer in between the flakes as well as melting transition of ice at the edges of flakes are crucial to realize the perfect water permeation across the whole stacked structures. The distance between adjacent layers that can be controlled either by oxygen reduction process or pressure is shown to determine the water flow thus highlighting a unique water dynamics in randomly connected two-dimensional spaces.

cond-mat.mes-hall↗

arXiv2013

Interaction phenomena in graphene seen through quantum capacitance

Capacitance measurements provide a powerful means of probing the density of states. The technique has proved particularly successful in studying 2D electron systems, revealing a number of interesting many-body effects. Here, we use large-area high-quality graphene capacitors to study behavior of the density of states in this material in zero and high magnetic fields. Clear renormalization of the linear spectrum due to electron-electron interactions is observed in zero field. Quantizing fields lead to splitting of the spin- and valley-degenerate Landau levels into quartets separated by interaction-enhanced energy gaps. These many-body states exhibit negative compressibility but the compressibility returns to positive in ultrahigh B. The reentrant behavior is attributed to a competition between field-enhanced interactions and nascent fractional states.

cond-mat.mes-hall↗

arXiv2013

Graphene as a Prototype Crystalline Membrane

The understanding of the structural and thermal properties of membranes, low-dimensional flexible systems in a space of higher dimension, is pursued in many fields from string theory to chemistry and biology. The case of a two-dimensional (2D) membrane in three dimensions is the relevant one for dealing with real materials. Traditionally, membranes are primarily discussed in the context of biological membranes and soft matter in general. The complexity of these systems hindered a realistic description of their interatomic structures based on a truly microscopic approach. Therefore, theories of membranes were developed mostly within phenomenological models. From the point of view of statistical mechanics, membranes at finite temperature are systems governed by interacting long-range fluctuations. Graphene, the first truly two-dimensional system consisting of just one layer of carbon atoms, provides a model system for the development of a microscopic description of membranes. In this Account, we review key results in the microscopic theory of structural and thermal properties of graphene and compare them with the predictions of phenomenological theories. The two approaches are in good agreement for the various scaling properties of correlation functions of atomic displacements. However, some other properties, such as the temperature dependence of the bending rigidity, cannot be understood based on phenomenological approaches. We also consider graphene at very high temperature and compare the results with existing models for two-dimensional melting. The melting of graphene presents a different scenario, and we describe that process as the decomposition of the graphene layer into entangled carbon chains.

cond-mat.mes-hall↗

arXiv2012

Non-equilibrium magnetic interactions in strongly correlated systems

We formulate a low-energy theory for the magnetic interactions between electrons in the multi-band Hubbard model under non-equilibrium conditions determined by an external time-dependent electric field which simulates laser-induced spin dynamics. We derive expressions for dynamical exchange parameters in terms of non-equilibrium electronic Green functions and self-energies, which can be computed, e.g., with the methods of time-dependent dynamical mean-field theory. Moreover, we find that a correct description of the system requires, in addition to exchange, a new kind of magnetic interaction, that we name "twist exchange", which formally resembles Dzyaloshinskii-Moriya coupling, but is not due to spin-orbit, and is actually due to an effective three-spin interaction. Our theory allows the evaluation of the related time-dependent parameters as well.

cond-mat.str-el↗

arXiv2012

Spectral flow for Aharonov--Bohm rings generated by zero-mass lines

We found that the spectrum of the linear dispersion mode localized along the zero-mass line for variable mass Dirac fermions shows the nonzero spectral flow as a function of the external magnetic field B. This happens due to the Aharonov--Bohm effect, leading to the linear dependence of every eigenvalue on B. The nonzero spectral flow allows to use the magnetic field slowly varying in time to control the energy of the linear dispersion mode.

cond-mat.mes-hall↗

arXiv2012

Equilibration and Thermalization of Classical Systems

It is demonstrated that the canonical distribution for a subsystem of a closed system follows directly from the solution of the time-reversible Newtonian equation of motion in which the total energy is strictly conserved. It is shown that this conclusion holds for both integrable or nonintegrable systems even though the whole system may contain as little as a few thousand particles. In other words, we demonstrate that the canonical distribution holds for subsystems of experimentally relevant sizes and observation times.

cond-mat.stat-mech↗

arXiv2012

Lattice Expansion in Seamless Bi layer Graphene Constrictions at High Bias

Our understanding of sp2 carbon nanostructures is still emerging and is important for the development of high performance all carbon devices. For example, in terms of the structural behavior of graphene or bi-layer graphene at high bias, little to nothing is known. To this end we investigated bi-layer graphene constrictions with closed edges (seamless) at high bias using in situ atomic resolution transmission electron microscopy. We directly observe a highly localized anomalously large lattice expansion inside the constriction. Both the current density and lattice expansion increase as the bi-layer graphene constriction narrows. As the constriction width decreases below 10 nm, shortly before failure, the current density rises to 4 \cdot 109 A cm-2 and the constriction exhibits a lattice expansion with a uniaxial component showing an expansion approaching 5 % and an isotropic component showing an expansion exceeding 1 %. The origin of the lattice expansion is hard to fully ascribe to thermal expansion. Impact ionization is a process in which charge carriers transfer from bonding states to antibonding states thus weakening bonds. The altered character of C-C bonds by impact ionization could explain the anomalously large lattice expansion we observe in seamless bi-layer graphene constrictions. Moreover, impact ionization might also contribute to the observed anisotropy in the lattice expansion, although strain is probably the predominant factor.

cond-mat.mes-hall↗

arXiv2012

Peculiarities of dynamics of Dirac fermions associated with zero-mass lines

Zero-mass lines result in appearance of linear dispersion modes for Dirac fermions. These modes play an important role in various physical systems. However, a Dirac fermion may not precisely follow a single zero-mass line, due to either tunneling between different lines or centrifugal forces. Being shifted from a zero-mass line the Dirac fermion acquires mass which can substantially influence its expected "massless" behavior. In the paper we calculate the energy gap caused by the tunneling between two zero-mass lines and show that its opening leads to the delocalization of linear dispersion modes. The adiabatic bending of a zero-mass line gives rise to geometric phases. These are the Berry phase, locally associated with a curvature, and a new phase resulting from the mass square asymmetry in the vicinity of a zero-mass line.

cond-mat.mes-hall↗

arXiv2012

Electron-hole puddles in the absence of charged impurities

It is widely believed that carrier-density inhomogeneities ("electron-hole puddles") in single-layer graphene on a substrate like quartz are due to charged impurities located close to the graphene sheet. Here we demonstrate by using a Kohn-Sham-Dirac density-functional scheme that corrugations in a real sample are sufficient to determine electron-hole puddles on length scales that are larger than the spatial resolution of state-of-the-art scanning tunneling microscopy.

cond-mat.mes-hall↗

arXiv2012

Atomically thin boron nitride: a tunnelling barrier for graphene devices

We investigate the electronic properties of heterostructures based on ultrathin hexagonal boron nitride (h-BN) crystalline layers sandwiched between two layers of graphene as well as other conducting materials (graphite, gold). The tunnel conductance depends exponentially on the number of h-BN atomic layers, down to a monolayer thickness. Exponential behaviour of I-V characteristics for graphene/BN/graphene and graphite/BN/graphite devices is determined mainly by the changes in the density of states with bias voltage in the electrodes. Conductive atomic force microscopy scans across h-BN terraces of different thickness reveal a high level of uniformity in the tunnel current. Our results demonstrate that atomically thin h-BN acts as a defect-free dielectric with a high breakdown field; it offers great potential for applications in tunnel devices and in field-effect transistors with a high carrier density in the conducting channel.

cond-mat.mes-hall↗

arXiv2012

Polarization of graphene in a strong magnetic field beyond the Dirac cone approximation

In this paper we study the excitation spectrum of graphene in a strong magnetic field, beyond the Dirac cone approximation. The dynamical polarizability is obtained using a full $π$-band tight-binding model where the effect of the magnetic field is accounted for by means of the Peierls substitution. The effect of electron-electron interaction is considered within the random phase approximation, from which we obtain the dressed polarization function and the dielectric function. The range of validity of the Landau level quantization within the continuum approximation is studied, as well as the non-trivial quantization of the spectrum around the Van Hove singularity. We further discuss the effect of disorder, which leads to a smearing of the absorption peaks, and temperature, which activates additional inter-Landau level transitions induced by the Fermi distribution function.

cond-mat.mes-hall↗

arXiv2011

Optical conductivity of disordered graphene beyond the Dirac cone approximation

In this paper we systemically study the optical conductivity and density of states of disorded graphene beyond the Dirac cone approximation. The optical conductivity of graphene is computed by using the Kubo formula, within the framework of a full π-band tight-binding model. Different types of non-correlated and correlated disorders are considered, such as random or Gaussian potentials, random or Gaussian nearest-neighbor hopping parameters, randomly distributed vacancies or their clusters, and random adsorbed hydrogen atoms or their clusters. For a large enough concentration of resonant impurities, a new peak in the optical conductivity is found, associated to transitions between the midgap states and the Van Hove singularities of the main π-band. We further discuss the effect of doping on the spectrum, and find that small amounts of resonant impurities are enough to obtain a background contribution to the conductivity in the infra-red part of the spectrum, in agreement with recent experiments.

cond-mat.mes-hall↗

arXiv2011

Excitation spectrum and high energy plasmons in single- and multi-layer graphene

In this paper we study the excitation spectrum of single- and multi-layer graphene beyond the Dirac cone approximation. The dynamical polarizability of graphene is computed using a full $π$-band tight-binding model, considering the possibility of inter-layer hopping in the calculation. The effect of electron-electron interaction is considered within the random phase approximation. We further discuss the effect of disorder in the spectrum, which leads to a smearing of the absorption peaks. Our results show a redshift of the $π$-plasmon dispersion of single-layer graphene with respect to graphite, in agreement with experimental results. The inclusion of inter-layer hopping in the kinetic Hamiltonian of multi-layer graphene is found to be very important to properly capture the low energy region of the excitation spectrum.

cond-mat.mes-hall↗

arXiv2011

Landau Level Spectrum of ABA- and ABC-stacked Trilayer Graphene

We study the Landau level spectrum of ABA- and ABC-stacked trilayer graphene. We derive analytic low energy expressions for the spectrum, the validity of which is confirmed by comparison to a π-band tight-binding calculation of the density of states on the honeycomb lattice. We further study the effect of a perpendicular electric field on the spectrum, where a zero-energy plateau appears for ABC stacking order, due to the opening of a gap at the Dirac point, while the ABA-stacked trilayer graphene remains metallic. We discuss our results in the context of recent electronic transport experiments. Furthermore, we argue that the expressions obtained can be useful in the analysis of future measurements of cyclotron resonance of electrons and holes in trilayer graphene.

cond-mat.mes-hall↗

arXiv2011

Suppression of anharmonicities in crystalline membranes by external strain

In practice, physical membranes are exposed to a certain amount of external strain (tension or compression), due to the environment where they are placed. As a result, the behavior of the phonon modes of the membrane is modified. We show that anharmonic effects in stiff two-dimensional membranes are highly suppressed under the application of tension. For this, we consider the anharmonic coupling between bending and stretching modes in the self-consistent screening approximation (SCSA), and compare the obtained height-height correlation function in the SCSA to the corresponding harmonic propagator. The elasticity theory results are compared to atomistic Monte Carlo simulations for a graphene membrane under tension. We find that, while rather high values of strain are needed to avoid anharmonicity in soft membranes, strain fields less than 1% are enough to suppress all the anharmonic effects in stiff membranes, as graphene.

cond-mat.mtrl-sci↗

arXiv2010

Electronic Transport in Disordered Bilayer and Trilayer Graphene

We present a detailed numerical study of the electronic transport properties of bilayer and trilayer graphene within a framework of single-electron tight-binding model. Various types of disorder are considered, such as resonant (hydrogen) impurities, vacancies, short- or long-range Gaussian random potentials, and Gaussian random nearest neighbor hopping. The algorithms are based on the numerical solution of the time-dependent Schr ödinger equation and applied to calculate the density of states and conductivities (via the Kubo formula) of large samples containing millions of atoms. In the cases under consideration, far enough from the neutrality point, depending on the strength of disorders and the stacking sequence, a linear or sublinear electron-density dependent conductivity is found. The minimum conductivity $σ_{\min}\approx 2e^{2}/h$ (per layer) at the charge neutrality point is the same for bilayer and trilayer graphene, independent of the type of the impurities, but the plateau of minimum conductivity around the neutrality point is only observed in the presence of resonant impurities or vacancies, originating from the formation of the impurity band.

cond-mat.mes-hall↗