arXiv subjects

Mikhail I. Katsnelson

Publications and source records attributed to Mikhail I. Katsnelson.

At least 109 records · Page 6Linked to original sources

arXiv2019

Hall conductivity of Sierpinski carpet

We calculate the Hall conductivity of a Sierpinski carpet using Kubo-Bastin formula. The quantization of Hall conductivity disappears when we increase the depth of the fractal. The Hall conductivity is no more proportional to the Chern number. Nevertheless, these quantities behave in a similar way showing some reminiscence of a topological nature of the Hall conductivity. We also study numerically the bulk-edge correspondence and find that the edge states become less manifested when the depth of Sierpinski carpet is increased.

cond-mat.dis-nn↗

arXiv2019

Atom-by-atom construction of attractors in a tunable finite size spin array

We demonstrate that a two-dimensional finite and periodic array of Ising spins coupled via RKKY-like exchange can exhibit tunable magnetic states ranging from three distinct magnetic regimes: (1) a conventional ferromagnetic regime, (2) a glass-like regime, and (3) a new multi-well regime. These magnetic regimes can be tuned by one gate-like parameter, namely the ratio between the lattice constant and the oscillating interaction wavelength. We characterize the various magnetic regimes, quantifying the distribution of low energy states, aging relaxation dynamics, and scaling behavior. The glassy and multi-well behavior results from the competing character of the oscillating long-range exchange interactions. The multi-well structure features multiple attractors, each with a sizable basin of attraction. This may open the possible application of such atomic arrays as associative memories.

cond-mat.stat-mech↗

arXiv2019

Large-area, periodic, and tunable intrinsic pseudo-magnetic fields in low-angle twisted bilayer graphene

A properly strained graphene monolayer or bilayer is expected to harbour periodic pseudo-magnetic fields with high symmetry, yet to date, a convincing demonstration of such pseudo-magnetic fields has been lacking, especially for bilayer graphene. Here, we report the first definitive experimental proof for the existence of large-area, periodic pseudo-magnetic fields, as manifested by vortex lattices in commensurability with the moiré patterns of low-angle twisted bilayer graphene. The pseudo-magnetic fields are strong enough to confine the massive Dirac electrons into circularly localized pseudo-Landau levels, as observed by scanning tunneling microscopy/spectroscopy, and also corroborated by tight-binding calculations. We further demonstrate that the geometry, amplitude, and periodicity of the pseudo-magnetic field can be fine-tuned by both the rotation angle and heterostrain applied to the system. Collectively, the present study substantially enriches twisted bilayer graphene as a powerful enabling platform for exploration of new and exotic physical phenomena, including quantum valley Hall effects and quantum anomalous Hall effects.

cond-mat.str-el↗

arXiv2019

Anisotropic destruction of the Fermi surface in inhomogeneous holographic lattices

We analyze fermionic response of strongly correlated holographic matter in presence of inhomogeneous periodically modulated potential mimicking the crystal lattice. The modulation is sourced by a scalar operator that explicitly breaks the translational symmetry in one direction. We compute the fermion spectral function and show that it either exhibits a well defined Fermi surface with umklapp gaps opening on the Brillouin zone boundary at small lattice wave vector, or, when the wave vector is large, the Fermi surface is anisotropically deformed and the quasiparticles get significantly broadened in the direction of translation symmetry breaking. Making use of the ability of our model to smoothly extrapolate to the homogeneous Q-lattice like setup, we show that this novel effect is not due to the periodic modulation of the potential and Umklapp physics, but rather due to the anisotropic features of the holographic horizon. That means it encodes novel physics of strongly correlated critical systems which may be relevant for phenomenology of exotic states of electron matter.

hep-th↗

arXiv2019

Dodecagonal bilayer graphene quasicrystal and its approximants

Dodecagonal bilayer graphene quasicrystal has 12-fold rotational order but lacks translational symmetry which prevents the application of band theory. In this paper, we study the electronic and optical properties of graphene quasicrystal with large-scale tight-binding calculations involving more than ten million atoms. We propose a series of periodic approximants which reproduce accurately the properties of quasicrystal within a finite unit cell. By utilizing the band-unfolding method on the smallest approximant with only 2702 atoms, the effective band structure of graphene quasicrystal is derived. Novel features, such as the emergence of new Dirac points (especially the mirrored ones), the band gap at M point and the Fermi velocity are all in agreement with recent experiments. The properties of quasicrystal states are identified in the Landau level spectrum and optical excitations. Importantly, our results show that the lattice mismatch is the dominant factor determining the accuracy of layered approximants. The proposed approximants can be used directly for other layered materials in honeycomb lattice, and the design principles can be applied for any quasi-periodic incommensurate structures.

cond-mat.mes-hall↗

arXiv2019

Anisotropic two-dimensional screening at the surface of black phosphorus

Screening in reduced dimensions has strong consequences on the electronic properties in van der Waals semiconductors, impacting the quasiparticle band gap and exciton binding energy. Screening in these materials is typically treated isotropically, yet black phosphorus exhibits in-plane electronic anisotropy seen in its effective mass, carrier mobility, excitonic wavefunctions, and plasmonic dispersion. Here, we use the adsorption of individual potassium atoms on the surface of black phosphorus to vary the near-surface doping over a wide range, while simultaneously probing the dielectric screening via the ordering of the adsorbed atoms. Using scanning tunneling microscopy, we visualize the role of strongly anisotropic screening which leads to the formation of potassium chains with a well-defined orientation and spacing. We quantify the mean interaction potential utilizing statistical methods and find that the dimensionality and anisotropy of the screening is consistent with the presence of a band-bending induced confinement potential near the surface. We corroborate the observed behavior with coverage-dependent studies of the electronic structure with angle-resolved photoemission.

cond-mat.mes-hall↗

arXiv2019

Josephson lattice model for phase fluctuations of local pairs in copper-oxide superconductors

We derive an expression for the effective Josephson coupling from the microscopic Hubbard model. It serves as a starting point for the description of phase fluctuations of local Cooper pairs in $d_{x^2-y^2}$-wave superconductors in the framework of an effective $XY$ model of plaquettes, the Josephson lattice. The expression for the effective interaction is derived by means of the local-force theorem, and it depends on local symmetry-broken correlation functions that we obtain using the cluster dynamical mean-field theory. Moreover, we apply the continuum limit to the Josephson lattice to obtain an expression for the gradient term in the Ginzburg-Landau theory and compare predicted London penetration depths and Kosterlitz-Thouless transition temperatures with experimental data for YBa$_2$Cu$_3$O$_{7-x}$.

cond-mat.str-el↗

arXiv2019

Two-particle Fermi liquid parameters at the Mott transition: Vertex divergences, Landau parameters, and incoherent response in dynamical mean-field theory

We consider the interaction-driven Mott transition at zero temperature from the viewpoint of microscopic Fermi liquid theory. To this end, we derive an exact expression for the Landau parameters within the dynamical mean-field theory (DMFT) approximation to the single-band Hubbard model. At the Mott transition the symmetric and the anti-symmetric Landau parameter diverge. The vanishing compressibility at the Mott transition directly implies the divergence of the forward scattering amplitude in the charge sector, which connects the proximity of the Mott phase to a tendency towards phase separation. We verify the expected behavior of the Landau parameters in a DMFT application to the Hubbard model on the triangular lattice at finite temperature. Exact conservation laws and the Ward identity are crucial to capture vertex divergences related to the Mott transition. We furthermore generalize Leggett's formula for the static susceptibility of the Fermi liquid to the static fermion-boson response function. In the charge sector the limits of small transferred momentum and frequency of this response function commute at the Mott transition.

cond-mat.str-el↗

arXiv2019

Exactly solvable model of strongly correlated $d$-wave superconductivity

We present an infinite-dimensional lattice of two-by-two plaquettes, the quadruple Bethe lattice, with Hubbard interaction and solve it exactly by means of the cluster dynamical mean-field theory. It exhibits a $d$-wave superconducting phase that is related to a highly degenerate point in the phase diagram of the isolated plaquette at that the groundstates of the particle number sectors $N=2,3,4$ cross. The superconducting gap is formed by the renormalized lower Slater peak of the correlated, hole-doped Mott insulator. We engineer parts of the interaction and find that pair hoppings between $X/Y$-momenta are the main two-particle correlations of the superconducting phase. The suppression of the superconductivity in the overdoped regime is caused by the diminishing of pair hopping correlations and in the underdoped regime by charge blocking. The optimal doping is $\sim 0.15$ at which the underlying normal state shows a Lifshitz transition. The model allows for different intra- and inter-plaquette hoppings that we use to disentangle superconductivity from antiferromagnetism as the latter requires larger inter-plaquette hoppings.

cond-mat.str-el↗

arXiv2019

On the feasibility of saltational evolution

Is evolution always gradual or can it make leaps? We examine a mathematical model of an evolutionary process on a fitness landscape and obtain analytic solutions for the probability of multi-mutation leaps, that is, several mutations occurring simultaneously, within a single generation in one genome, and being fixed all together in the evolving population. The results indicate that, for typical, empirically observed combinations of the parameters of the evolutionary process, namely, effective population size, mutation rate, and distribution of selection coefficients of mutations, the probability of a multi-mutation leap is low, and accordingly, the contribution of such leaps is minor at best. However, we show that, taking sign epistasis into account, leaps could become an important factor of evolution in cases of substantially elevated mutation rates, such as stress-induced mutagenesis in microbes. We hypothesize that stress-induced mutagenesis is an evolvable adaptive strategy.

q-bio.PE↗

arXiv2019

Bandwidth renormalization due to the intersite Coulomb interaction

The theory of correlated electrons is currently moving beyond the paradigmatic Hubbard $U$, towards the investigation of intersite Coulomb interactions. Recent investigations have revealed that these interactions are relevant for the quantitative description of realistic materials. Physically, intersite interactions are responsible for two rather different effects: screening and bandwidth renormalization. We use a variational principle to disentangle the roles of these two processes and study how appropriate the recently proposed Fock treatment of intersite interactions is in correlated systems. The magnitude of this effect in graphene is calculated based on cRPA values of the intersite interaction. We also observe that the most interesting charge fluctuation phenomena actually occur at elevated temperatures, substantially higher than studied in previous investigations.

cond-mat.str-el↗

arXiv2019

Separation of conditions as a prerequisite for quantum theory

We introduce the notion of "separation of conditions" meaning that a description of statistical data obtained from experiments, performed under a set of different conditions, allows for a decomposition such that each partial description depends on mutually exclusive subsets of these conditions. Descriptions that allow a separation of conditions are shown to entail the basic mathematical framework of quantum theory. The Stern-Gerlach and the Einstein-Podolsky-Rosen-Bohm experiment with three, respectively nine possible outcomes are used to illustrate how the separation of conditions can be used to construct their quantum theoretical descriptions. It is shown that the mathematical structure of separated descriptions implies that, under certain restrictions, the time evolution of the data can be described by the von Neumann/Schrödinger equation.

quant-ph↗

arXiv2019

Thermal fluctuations in crystalline membranes with long-range dipole interactions

We study the effects of long-range electrostatic interactions on the thermal fluctuations of free-standing crystalline membranes exhibiting spontaneous electric polarization directed at each point along the local normal to the surface. We show that the leading effect of dipole-dipole interactions in the long-wavelength limit consists in renormalizations of the bending rigidity and the elastic coefficients. A completely different result was obtained in the case of scalar two-point interactions decaying as $R^{-3}$, where $R$ is the distance. In the latter case, which was addressed in previous theoretical research, the energy of long-wavelength bending fluctuations is controlled by power-law interactions and it scales with the wavevector $q$ as $q^{3}$, leading to a modified large-distance behaviour of correlation functions. By contrast, in the case of dipole interactions, the $q^{3}$ dependence of the bending energy vanishes. Non-local terms generated by the expansion of the electrostatic energy are suppressed in the limit of small wavevectors. This suggests that the universal scaling behaviour of elastic membranes holds even in presence of dipole interactions. At the same time, the shift of the Lamé coefficients and the bending rigidity induced by electrostatic interactions can be quantitatively important for two-dimensional materials with a permanent out-of-plane polarization.

cond-mat.stat-mech↗

arXiv2018

Tuning 2D hyperbolic plasmons in black phosphorus

Black phosphorus presents a very anisotropic crystal structure, making it a potential candidate for hyperbolic plasmonics, characterized by a permittivity tensor where one of the principal components is metallic and the other dielectric. Here we demonstrate that atomically thin black phosphorus can be engineered to be a hyperbolic material operating in a broad range of the electromagnetic spectrum from the entire visible spectrum to ultraviolet. With the introduction of an optical gain, a new hyperbolic region emerges in the infrared. The character of this hyperbolic plasmon depends on the interplay between gain and loss along the two crystalline directions.

cond-mat.mtrl-sci↗

arXiv2018

Power-law energy level-spacing distributions in fractals

In this article we investigate the energy spectrum statistics of fractals at the quantum level. We show that the energy-level distribution of a fractal follows a power-law behaviour, if its energy spectrum is a limit set of piece-wise linear functions. We propose that such a behaviour is a general feature of fractals, which can not be described properly by random matrix theory. Several other arguments for the power-law behaviour of the energy level-spacing distributions are proposed.

cond-mat.dis-nn↗

arXiv2018

Fermion-boson vertex within Dynamical Mean-Field Theory

In the study of strongly interacting systems, correlations on the two-particle level are receiving more and more attention. In this work, we study a particular two-particle correlation function: the fermion-boson vertex. It describes the response of the Green's function when an external field is applied and is an important ingredient of diagrammatic extensions of Dynamical Mean-Field Theory. We provide several perspectives on this object, using Ward identities, sum rules, perturbative analysis and asymptotic relations. We then use these tools to study the vertex across the doping-driven metal-insulator transition and find a divergence in the imaginary part.

cond-mat.str-el↗

arXiv2018

Electronic structure of monolayer antimonene nanoribbons under out-of-plane and transverse bias

A systematic study of the electronic properties of single layer Sb (antimonene) nanoribbons is presented. By using a 6-orbital tight-binding Hamiltonian, we study the electronic band structure of finite ribbons with zigzag or armchair termination. We show that there is good agreement between ab initio calculations and the tight-binding model. We study how the size of the gap can be controlled by applying an external bias potential. An electric field applied perpendicular to the antimonene layer is found to increase the band gap, while a transverse bias potential leads to a position dependent reduction of the band gap. Both kinds of bias potential break inversion symmetry of the crystal. This, together with the strong intrinsic spin-orbit coupling of antimonene, leads to spin-splitting of the valence band states.

cond-mat.mes-hall↗

arXiv2018

Second-order dual fermion approach to the Mott transition in the two-dimensional Hubbard model

We apply the dual fermion approach with a second-order approximation to the self-energy to the Mott transition in the two-dimensional Hubbard model. The approximation captures nonlocal dynamical short-range correlations as well as several features observed in studies using cluster dynamical mean-field theory. This includes a strong reduction of the critical interaction and inversion of the slope of the transition lines with respect to single-site dynamical mean-field theory. We show that these effects coincide with a much smaller momentum differentiation compared to cluster methods. We further discuss the role of the self-consistency condition and show that the approximation behaves as an asymptotic series at low temperature.

cond-mat.str-el↗