arXiv subjects

D. O. Oriekhov

Publications and source records attributed to D. O. Oriekhov.

At least 19 recordsLinked to original sources

arXiv2026

Size and Impurity Effects on Scattering of Valley Hall Modes in Gate-Defined Bilayer Graphene Superlattices

In the present paper we perform a tight-binding simulation of gate-defined islands in Bernal bilayer graphene (BLG). The inversion of the gap sign on the boundaries of the islands creates topologically-protected valley Hall modes. We focus on the specific questions of whether the valley Hall modes around such islands could serve as a host for quantum walks or simulate weakly coupled systems, and how their tunneling is affected by in-gap impurities. In addition, we discuss the effect of misalignment of top and bottom gate patterns on the tunneling properties between islands. Our main results show that resonant tunneling via an impurity enhances overlap between superlattice islands, while misalignment does not break topological protection over a wide parameter regime. In addition, we study the two-island geometry and show that it is possible to leverage suppressed scattering to place islands more densely on a single sample.

cond-mat.mes-hall↗

arXiv2025

Why is topology hard to learn?

Much attention has been devoted to the use of machine learning to approximate physical concepts. Yet, due to challenges in interpretability of machine learning techniques, the question of what physics machine learning models are able to learn remains open. Here we bridge the concept a physical quantity and its machine learning approximation in the context of the original application of neural networks in physics: topological phase classification. We construct a hybrid tensor-neural network object that exactly expresses real space topological invariant and rigorously assess its trainability and generalization. Specifically, we benchmark the accuracy and trainability of a tensor-neural network to multiple types of neural networks, thus exemplifying the differences in trainability and representational power. Our work highlights the challenges in learning topological invariants and constitutes a stepping stone towards more accurate and better generalizable machine learning representations in condensed matter physics.

cond-mat.mes-hall↗

arXiv2025

Twist-modulated magnetic interactions in bilayer van der Waals materials

The ability to control magnetic interactions at the nanoscale is crucial for the development of next-generation spintronic devices and functional magnetic materials. In this work, we investigate theoretically, by means of many-body perturbation theory, how interlayer twisting modulates magnetic interactions in bilayer van der Waals systems composed of two ferromagnetic layers. We demonstrate that the relative strengths of the interlayer Heisenberg exchange interaction, the Dzyaloshinskii-Moriya interaction, and the anisotropic exchange interaction can be significantly altered by varying the twist angle between the layers, thus leading to tunable magnetic textures. We further show that these interactions are strongly dependent on the chemical potential, enabling additional control via electrostatic gating or doping. Importantly, our approach is applicable to arbitrary twist angles and does not rely on the construction of a Moiré supercell, making it particularly efficient even at small twist angles.

cond-mat.mes-hall↗

arXiv2025

RKKY quadratic and biquadratic spin-spin interactions in twisted bilayer graphene

We study the competition between the RKKY quadratic and biquadratic spin-spin interactions of two magnetic impurities in twisted bilayer graphene away from the magic angle. We apply the Bistritzer-MacDonald model of two graphene layers twisted with respect to each other by a small angle. By reducing the model to the Dirac-type one with modified Fermi velocity, we derive expressions for the RKKY quadratic and biquadratic spin interactions using perturbation theory for the free energy. The biquadratic interaction is suppressed by a larger power of the interaction constant and decreases faster with a the distance between impurities comparing to the quadratic one. Nevertheless, due to the different period of oscillations with impurity separation distance, chemical potential, twist angle and temperature, it is possible to fine-tune the system to the regime of dominating biquadratic interaction. The existence of such fine-tuned regime might provide a promising opportunity to observe non-conventional spin ordering.

cond-mat.mes-hall↗

arXiv2025

Density of states and differential entropy in Dirac materials in crossed magnetic and in-plane electric fields

The density of states and differential entropy per particle are analyzed for Dirac-like electrons in graphene subjected to a perpendicular magnetic field and an in-plane electric field. For comparison, the derived density of states is contrasted with the well-known case of nonrelativistic electrons in crossed magnetic and electric fields. The study considers ballistic electrons and also includes the effect of small impurity scattering. In the latter case, the limit of zero magnetic field and the so-called collapse of Landau levels in graphene are examined analytically. By comparing the results with numerical calculations on graphene ribbons, we demonstrate that the Landau state counting procedure must be modified for Dirac-like electrons, leading to a fields-dependent Landau level degeneracy factor. Additionally, it is shown that peaks in the differential entropy arise from the dispersionless surface mode localized at the zigzag edges of the ribbon.

cond-mat.mes-hall↗

arXiv2025

Dynamical localization in 2D topological quantum random walks

We study the dynamical localization of discrete time evolution of topological split-step quantum random walk (QRW) on a single-site defect starting from a uniform distribution. Using analytical and numerical calculations, we determine the high localization probability regions in the parameter space of the quantum walker. These regions contain two or more pairs of trapped states, forming near a lattice defect. By investigating the spectral properties of the discrete-time evolution operators, we show that these trapped states have large overlap with the initial uniformly distributed state, thus offering a simple interpretation of the localization effect. As this localization scheme could be interpreted as a variation of spatial quantum search algorithm, we compare the localization probability and time with other types of two-dimensional quantum walks that do not have topological phases and realize localization time scaling similar to Grover's algorithm. Finally we show that mechanism of localization we identified is robust against the influence of disorder.

quant-ph↗

arXiv2024

Topological finite size effect in one-dimensional chiral symmetric systems

Topological phases of matter have been widely studied for their robustness against impurities and disorder. The broad applicability of topological materials relies on the reliable transition from idealized, mathematically perfect models to finite, real-world implementations. In this paper, we explore the effects of finite size and disorders on topological properties. We propose a new criterion for characterizing finite topological systems based on the bulk conductivity of topological edge modes. We analyze the behavior of bulk conductivity and real space topological invariants both analytically and numerically for the family of SSH models. We show that our approach offers practical insights for topology determination in contemporary intermediate scale experimental applications.

cond-mat.mes-hall↗

arXiv2024

Electron binding energy of a donor in bilayer graphene with gate-tunable gap

In gapped bilayer graphene, similarly to conventional semiconductors, Coulomb impurities (such as nitrogen donors) may determine the activation energy of its conductivity and provide low temperature hopping conductivity. However, in spite of the importance of Coulomb impurities, nothing is known about their electron binding energy $E_b$ in the presence of gates. To close this gap, we study numerically the electron binding energy $E_b$ of a singly charged donor in BN-enveloped bilayer graphene with the top and bottom gates at distance $d$ and gate-tunable gap $2Δ$. We show that for $10 < d < 200$ nm and $1 < Δ< 100$ meV the ratio $E_b/Δ$ changes from 0.4 to 1.5. The ratio $E_b/Δ$ stays close to unity because of the dominating role of the bilayer polarization screening which reduces the Coulomb potential well depth to values $\sim Δ$. Still the ratio $E_b/Δ$ somewhat decreases with growing $Δ$, faster at small $Δ$ and slower at large $Δ$. On the other hand, $E_b/Δ$ weakly grows with $d$, again faster at small $Δ$ and slower at large $Δ$. We also studied the effect of trigonal warping and found only a small reduction of $E_b/Δ$.

cond-mat.mes-hall↗

arXiv2024

Landau quantization near generalized Van Hove singularities: Magnetic breakdown and orbit networks

We develop a theory of magnetic breakdown (MB) near high-order saddle points in the dispersions of two-dimensional materials, where two or more semiclassical cyclotron orbits approach each other. MB occurs due to quantum tunneling between several trajectories, which leads to non-trivial scattering amplitudes and phases. We show that for any saddle point this problem can be solved by mapping it to a scattering problem in a 1D tight-binding chain. Moreover, the occurrence of magnetic breakdown on the edges of the Brillouin zone facilitates the delocalization of the bulk Landau level states and the formation of 2D orbit networks. These extended network states compose dispersive mini-bands with finite energy broadening. This effect can be observed in transport experiments as a strong enhancement of the longitudinal bulk conductance in a quantum Hall bar. In addition, it may be probed in STM experiments by visualizing bulk current patterns.

cond-mat.mes-hall↗

arXiv2023

Size effects on atomic collapse in the dice lattice

We study the role of size effects on atomic collapse of charged impurity in the flat band system. The tight-binding simulations are made for the dice lattice with circular quantum dot shapes. It is shown that the mixing of in-gap edge states with bound states in impurity potential leads to increasing the critical charge value. This effect, together with enhancement of gap due to spatial quantization, makes it more difficult to observe the dive-into-continuum phenomenon in small quantum dots. At the same time, we show that if in-gap states are filled, the resonant tunneling to bound state in the impurity potential might occur at much smaller charge, which demonstrates non-monotonous dependence with the size of sample lattice. In addition, we study the possibility of creating supercritical localized potential well on different sublattices, and show that it is possible only on rim sites, but not on hub site. The predicted effects are expected to naturally occur in artificial flat band lattices.

cond-mat.str-el↗

arXiv2023

Stackings and effective models of bilayer dice lattices

We introduce and classify nonequivalent commensurate stackings for bilayer dice or $\mathcal{T}_3$ lattice. For each of the four stackings with vertical alignment of sites in two layers, a tight-binding model and an effective model describing the properties in the vicinity of the threefold band-crossing points are derived. Focusing on these band-crossing points, we found that although the energy spectrum remains always gapless, depending on the stacking, different types of quasiparticle spectra arise. They include those with flat, tilted, anisotropic semi-Dirac, and $C_3$-corrugated energy bands. We use the derived tight-binding models to calculate the density of states and the spectral function. The corresponding results reveal drastic redistribution of the spectral weight due to the inter-layer coupling that is unique for each of the stackings.

cond-mat.mes-hall↗

arXiv2023

Optical conductivity of bilayer dice lattices

We calculate optical conductivity for bilayer dice lattices in commensurate vertically aligned stackings. The interband optical conductivity reveals a rich activation behavior unique for each of the four stackings. We found that the intermediate energy band, which corresponds to the flat band of a single-layer dice lattice, plays a different role for different stackings. The interband selection rules, which are crucial for the single-layer lattice, may become lifted in bilayer lattices. The results for effective and tight-binding models are found to be in qualitative agreement for some of the stackings and the reasons for the discrepancies for others are identified. Our findings propose optical conductivity as an effective tool to distinguish between different stackings in bilayer dice lattices.

cond-mat.mes-hall↗

arXiv2023

Kondo effect in twisted bilayer graphene

The emergence of flat bands in twisted bilayer graphene at the magic angle can be understood in terms of a vanishing Fermi velocity of the Dirac cone. This is associated with van Hove singularities approaching the Fermi energy and becoming higher-order. In the density of states this is reflected by flanking logarithmic van Hove divergences pinching off the central Dirac cone in energy space. The low-energy pseudogap of the Dirac cone away from the magic angle is replaced by a power-law divergence due to the higher-order van Hove singularity at the magic angle. This plays an important role in the exotic phenomena observed in this material, such as superconductivity and magnetism, by amplifying electronic correlation effects. Here we investigate one such correlation effect -- the Kondo effect due to a magnetic impurity embedded in twisted bilayer graphene. We use the Bistritzer-MacDonald model to extract the low-energy density of states of the material as a function of twist angle, and study the resulting quantum impurity physics using perturbative and numerical renormalization group methods. Although at zero temperature the impurity is only Kondo screened precisely at the magic angle, we find highly nontrivial behavior at finite temperatures relevant to experiment, due to the complex interplay between Dirac, van Hove, and Kondo physics.

cond-mat.str-el↗

arXiv2022

Bloch oscillations in the magnetoconductance of twisted bilayer graphene

We identify a mapping between two-dimensional (2D) electron transport in a minimally twisted graphene bilayer and a 1D quantum walk, where one spatial dimension plays the role of time. In this mapping a magnetic field B perpendicular to the bilayer maps onto an electric field. Bloch oscillations due to the periodic motion in a 1D Bloch band can then be observed in purely DC transport as magnetoconductance oscillations with periodicity set by the Bloch frequency.

cond-mat.mes-hall↗

arXiv2022

Breathing mode in open-orbit magnetotransport: a magnetic lens with a quantum mechanical focal length

We consider the propagation of electrons in a lattice with an anisotropic dispersion in the $x$--$y$ plane (lattice constant $a$), such that it supports open orbits along the $x$-axis in an out-of-plane magnetic field $B$. We show that a point source excites a "breathing mode", a state that periodically spreads out and refocuses after having propagated over a distance $\ell =(eaB/h)^{-1}$ in the $x$-direction. Unlike known magnetic focusing effects, governed by the classical cyclotron radius, this is an intrinsically quantum mechanical effect with a focal length $\propto\hbar$.

cond-mat.mes-hall↗

arXiv2022

Differential entropy per particle as a probe of van Hove singularities and flat bands

In the present paper we derive the general expressions for the differential entropy per particle near van Hove singularities (vHs) in the density of states. The dependence of entropy per particle on chemical potential and temperature demonstrates different behavior depending on the type of vHs, and distinguishes high-order vHs with different divergence exponents and flat bands. In addition, it allows one to test the ``flatness" of the band in experiment. We compare the analytic predictions with the numerical calculation of the differential entropy for tight-binding models of graphene, Lieb lattice and square-octagon lattice. Our results show that the obtained analytic expressions capture the main features of the differential entropy, thus serving as a good probe for details of the density of states structure.

cond-mat.str-el↗

arXiv2022

Optical conductivity of semi-Dirac and pseudospin-1 models: Zitterbewegung approach

We present a method to calculate the optical conductivity of semi-Dirac and pseudospin models based on the evaluation of quasiparticle velocity correlators which also describe the phenomenon of zitterbewegung. Applying this method to the semi-Dirac model with merging Dirac cones and gapped dice and Lieb lattice models we find exact analytical expressions for optical longitudinal and Hall conductivities. For the semi-Dirac model the obtained expressions allow us to analyze the role of spectrum anisotropy, van Hove singularities and Dirac cones in longitudinal conductivity. In addition, we predict signatures of topological phase transition with changing gap parameter in such a system that are manifested in dc transport at low temperatures. For the dice and Lieb lattices we emphasize the role of spectral gap, which defines frequency thresholds related to transitions to and from flat band.

cond-mat.str-el↗

arXiv2021

Orbital susceptibility of T-graphene: Interplay of high-order van Hove singularities and Dirac cones

Square-octagon lattice underlies the description of a family of two-dimensional materials such as tetragraphene. In the present paper we show that the tight-binding model of square-octagon lattice contains both conventional and high-order van Hove points. In particular, the spectrum of the model contains flat lines along some directions composed of high-order saddle points. Their role is analyzed by calculating orbital susceptibility of electrons. We find that the presence of van Hove singularities of different kinds in the density of states leads to strong responses: paramagnetic for ordinary singularities and more complicated for high-order singularities. It is shown that the orbital susceptibility as a function of hoppings ratio $α$ reveals the dia- to paramagnetic phase transition at $α\approx 0.94$. This is due to the competition of paramagnetic contribution of high-order VHS and diamagnetic contribution of Dirac cones. The results for the tight-binding model are compared with low-energy effective pseudospin-1 model near the three band touching point.

cond-mat.str-el↗