arXiv subjects

A. O. Sboychakov

Publications and source records attributed to A. O. Sboychakov.

At least 19 recordsLinked to original sources

arXiv2026

Weak-coupling theory of half-metals and other fractional metallic phases in biased doped Bernal bilayer graphene

The paper presents a theoretical study of many-body electronic phases in doped and electrically biased Bernal-stacked (AB) bilayer graphene. We develop a variational mean-field theory with no fitted parameters. For the electron-electron interaction, we employ a parameter-free random-phase approximation to model the short-range screened Coulomb repulsion. The remaining long-range Coulomb potential energy is dictated by the geometry of the sample, behaving as a parallel-plate capacitor. We formulate the theory directly in terms of the experimentally controlled displacement field $\frak D$ rather than the interaction-renormalized interlayer potential difference. It makes our theory better suited for direct comparison with experiment. The resulting phase diagram is quite rich. It hosts several fractional-metal states connected by first- and second-order transitions. At higher bias and doping, three distinct fractional metallic states emerge. We classify these phases by the number of doped sectors and the symmetry of the order parameters. Our results - obtained without any parameter fitting - reproduce key qualitative and quantitative features of recent experiments. This includes the energy scale associated with the loss of fractional metallic order. At lower bias and doping, the model stabilizes a broad spectrum of fractional-metal phases with more exotic symmetry-breaking patterns. This suggests that further experimental exploration of the latter regime is warranted.

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arXiv2026

Kohn-Luttinger like superconductivity in twisted bilayer graphene at large twist angles

We predict that twisted bilayer graphene with large twist angle and small superlattice cell can be superconducting. Such a bilayer graphene can have a gap in the spectrum. This gap appears due to the hybridization of electrons moving in different layers with Fermi momenta close to the Dirac points which are equivalent to each other in the superlattice Brillouin zone. Small doping of the bilayer introduces charge carries having large density of states. We show that the screened Coulomb interaction is enough to stabilize superconducting state in the material. The symmetry of the order parameter is of the $d$-wave type. Application of the bias voltage increases the superconducting transition temperature. For realistic values of the model parameters the transition temperature can be as large as several hundreds of milikelvin.

cond-mat.supr-con↗

arXiv2026

Ordered states of undoped AB bilayer graphene: bias induced cascade of transitions

Using mean-field theory, we determine the electronic phase diagram of undoped AB-stacked bilayer graphene in the presence of a transverse electric field. In addition to multiple competing electronic instabilities characterized by excitonic order parameters, our framework incorporates the long-range Coulomb energy associated with interlayer polarization. This long-range interaction plays a crucial role, as it significantly influences both the structure and the relative energies of the competing ordered states. We derive a set of self-consistency equations and solve them both numerically and analytically. Our findings reveal that, as the bias field is varied, the bilayer undergoes a cascade of first-order transitions between several ordered insulating phases for which order-parameter structures are explicitly identified. Some of these phases are characterized by two inequivalent single-particle gaps, whose magnitudes depend on the valley and spin quantum numbers. Field-driven transitions are accompanied by discontinuous and non-monotonic variations of the single-electron gap. We relate our results to Hartree-Fock numerical calculations and to experimental research, including observations of fractional metallic phases that emerge upon doping the bilayer system.

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arXiv2025

Nesting-driven ferromagnetism of itinerant electrons

We theoretically investigate a model with electrons and holes whose Fermi surfaces are perfectly nested. The fermions are assumed to be interacting, both with each other and with the lattice. To suppress inhomogeneous states, a sufficiently strong long-range Coulomb repulsion is included into the model. Using the mean field approximation, one can demonstrate that in the absence of doping, the ground state of such a model is insulating and possesses a density-wave order, either SDW, or CDW. Upon doping, a finite ferromagnetic polarization emerges. It is argued that the mechanism driving the ferromagnetism is not of the Stoner type. A phase diagram of the model is constructed, and various properties of the ordered phases, such as half-metallicity and cone magnetic structure, are studied.

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arXiv2025

High frequency permeability of the composite with ferromagnetic spherical shells

The paper studies high-frequency permeability of the composite materials consisting of hollow ferromagnetic particles embedded into the non-magnetic media. We model the ferromagnetic particles in composite by spherical shells: the thickness of the ferromagnetic region $d$ compared to the particles' diameter $D$ can vary in a wide range, from $d\ll D$ to $d\sim D$. We assume that the magnetization distribution in such a particle is non-uniform, but forms a vortex-like structure: the magnetization is twisted in some plane outside two vortex cores placed at the poles of the particle. We consider two types of magnetic anisotropy, which help to stabilize such a magnetic configuration: the easy-plane magnetic anisotropy and the ``circular'' uniaxial magnetic anisotropy with easy axis rotated together with the magnetization direction outside the vortex core. The high-frequency permeability of such a composite material has been studied in the limit of non-interacting particles. We study the dependence of the permeability on the ratio $d/D$. We showed that for $d\sim D$ the composite's permeability behaves in similar manner for both types of magnetic anisotropy. It was shown also that for the second type of magnetic anisotropy and in the limit $d/D\ll1$ the frequency dependence of the particle's susceptibility is quite similar to that for the thin film. At the same time, the magnetization oscillations in the ac field are non-homogeneous for both types of anisotropy.

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arXiv2025

Anomalous superconductivity and unusual normal state properties of bilayer and twisted graphene (Brief review)

It has been shown that the Kohn--Luttinger superconductivity mechanism interplaying with other types of ordering can be implemented in systems with a hexagonal lattice. A number of unusual properties of such systems in the normal phase have also been considered. Our previous results on Kohn--Luttinger superconductivity with $p$-, $d$-, and $f$-wave pairing in monolayer and AB bilayer graphene, obtained disregarding the effect of substrate potential and impurities, have been presented in the first part. Then, the interplay of the superconducting Kohn--Luttinger state with the spin density wave state in actual AB, AA, and twisted bilayer graphene has been discussed in detail. In the last parts, a number of anomalous properties in the normal phase and the appearance of nematic superconductivity alongside with the spin density wave in the twisted bilayer graphene have been presented.

cond-mat.supr-con↗

arXiv2025

Ordered states in AB bilayer graphene in SU(4)-symmetric model

We apply SU(4)-symmetric model to examine possible ordered states in AB stacked bilayer graphene (AB-BLG). The Hamiltonian of the system possesses this symmetry under certain assumptions. In such a model the multicomponent order parameter can be presented as a $4\times4$ matrix $\hat{Q}$. Using a mean field approximation, we derive a self-consistency equation for $\hat{Q}$. Among possible solutions of the obtained equation there are anomalous quantum Hall states, spin, charge, spin-valley density waves, inter-layer excitonic phases and their combinations. We argue that the proposed approach is a useful tool for classification of the ordered states in AB-BLG. The ordered states of the SU(4)-symmetric model demonstrate extensive degeneracies. The degeneracies can be removed by taking into account the neglected non-SU(4)-symmetric terms, disorder, substrate, as well as other perturbations. The ordered states have varying sensitivity to these factors. This suggests that, for AB-BLG, a ground state ordering type is a non-universal property, susceptible to particulars of extrinsic conditions.

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arXiv2024

Superconductivity and spin density wave in AA stacked bilayer graphene

This work theoretically analyzes electronic ordering in AA-stacked bilayer graphene and the role of the Coulomb interaction in these many-body phenomena. Using the random phase approximation to account for screening, we find intra-layer effective interactions to be much stronger than inter-layer interactions; under certain circumstances, the latter may also become attractive. At zero doping, the Coulomb repulsion stabilizes the spin-density wave state, with a N{é}el temperature in the tens of Kelvin. While dominant in the undoped system, the spin-density wave is destroyed by sufficiently strong doping and a superconducting phase emerges. We find that the effective Coulomb inter-layer interaction can give rise to superconductivity. However, the corresponding critical temperature is negligibly small, and phonon-mediated attraction must be introduced to observe it. Strong intra-layer repulsion suppresses order parameters that couple two intra-layer electrons. We point out a possible superconducting state with finite Cooper pair momentum.

cond-mat.supr-con↗

arXiv2024

Coexistence of nematic superconductivity and spin density wave in magic-angle twisted bilayer graphene

We argue that doped twisted bilayer graphene with magical twist angle can become superconducting. In our theoretical scenario, the superconductivity coexists with the spin-density-wave-like ordering. Numerical mean-field analysis demonstrates that the spin-density-wave order, which is much stronger than the superconductivity, leaves parts of the Fermi surface ungapped. This Fermi surface serves as a host for the superconductivity. Since the magnetic texture at finite doping breaks the point group of the twisted bilayer graphene, the stabilized superconducting order parameter is nematic. We also explore the possibility of a purely Coulomb-based mechanism of superconductivity in the studied system. The screened Coulomb interaction is calculated within the random phase approximation. It is shown that near the half-filling the renormalized Coulomb repulsion indeed induces the superconducting state, with the order parameter possessing two nodes on the Fermi surface. We estimate the superconducting transition temperature, which turns out to be very low. The implications of our proposal are discussed.

cond-mat.supr-con↗

arXiv2023

Triplet superconductivity and spin density wave in biased AB bilayer graphene

We examine spin density wave and triplet superconductivity as possible ground states of the Bernal bilayer graphene. The spin density wave is stable for the unbiased and undoped bilayer. Both the doping and the applied bias voltage destroy this phase. We show that, when biased and slightly doped, bilayer can host a triplet superconducting phase. The mechanisms for both ordered phases rely on the renormalized Coulomb interaction. Consistency of our theoretical conclusions with recent experimental results are discussed.

cond-mat.supr-con↗

arXiv2023

Ordering in SU(4)-symmetric model of AA bilayer graphene

We examine possible ordered states of AA stacked bilayer graphene arising due to electron-electron coupling. We show that under certain assumptions the Hamiltonian of the system possesses an SU(4) symmetry. The multicomponent order parameter is described by a $4\times4$ matrix $\hat{Q}$, for which a mean-field self-consistency equation is derived. This equation allows Hermitian and non-Hermitian solutions. Hermitian solutions can be grouped into three topologically-distinct classes. First class corresponds to the charge density wave. Second class includes spin density wave, valley density wave, and spin-valley density wave. An ordered state in the third class is a combination of all the aforementioned density-wave types. For anti-Hermitian $\hat{Q}$ the ordered states are characterized by spontaneous inter-layer loop currents flowing in the bilayer. Depending on the topological class of the solution these currents can carry charge, spin, valley, and spin-valley quanta. We also discuss the special case when matrix $\hat{Q}$ is not Hermitian and not anti-Hermitian. Utility and weak points of the proposed SU(4)-based classification scheme of the ordered states are analyzed.

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arXiv2023

Magic radius of AA bilayer graphene quantum dot

We study analytically and numerically electronic properties of a circular quantum dot made from AA bilayer graphene. We observe a discrete set of dot radii for which the low-energy electron states are degenerate with respect to the layer parity. By analogy with the ``magic angles" in the twisted bilayer graphene we refer to these radii as ``magic". Such a feature is unique for the AA structures and is related to a specific layer-symmetry of the AA graphene bilayer: the parity of the highest occupied level changes from layer-symmetric to layer-antisymmetric when the radius of the AA dot is equal to its magic value. We explore an analogy in the electronic structure between twisted bilayer graphene at the magic twist angle and the AA quantum dot with magic radius. We argue that this analogy can be helpful for theoretical description of the electronic properties of the twisted bilayer graphene.

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arXiv2023

Half-metal and other fractional metal phases in doped AB bilayer graphene

We theoretically argue that, in doped AB bilayer graphene, the electron-electron coupling can give rise to the spontaneous formation of fractional metal phases. These states, being generalizations of a more common half-metal, have a Fermi surface that is perfectly polarized not only in terms of a spin-related quantum number, but also in terms of the valley index. The proposed mechanism assumes that the ground state of undoped bilayer graphene is a spin density wave insulator, with a finite gap in the single-electron spectrum. Upon doping, the insulator is destroyed, and replaced by a fractional metal phase. As doping increases, transitions between various types of fractional metal (half-metal, quarter-metal, etc.) are triggered. Our findings are consistent with recent experiments on doped AB bilayer graphene, in which a cascade of phase transitions between different isospin states was observed.

cond-mat.mes-hall↗

arXiv2022

Charge distribution and spin textures in magic-angle twisted bilayer graphene

We examine the coexisting spin and charge density waves as a possible ground state of the magic-angle twisted bilayer graphene. When interactions are not included, the spectrum of the material has 4 (8 if spin is taken into account) almost flat almost degenerate bands. Interactions break down the degeneracy forming an order parameter which is usually assumed to be a spin density wave with a preset spin structure. Here we take into account a possible charge density wave contribution to the order parameter, that is, inhomogeneous distribution of the charge density within a twisted graphene supercell. We also calculate self-consistently the spin structure of the order parameter. We find that the density wave order is stable in the whole doping range from $-4$ to $+4$ extra electrons per supercell. The spin texture changes from collinear at zero doping to almost coplanar at finite doping. The density wave order shows nematic distortion when we dope the system. We demonstrate that the local spin magnetization is much stronger than the charge density variation, unless the doping exceeds $3$ extra electrons or holes per supercell.

cond-mat.str-el↗

arXiv2022

Moir{é}-like superlattice generated van Hove singularities in strained CuO$_2$ double layer

While it is known that the double-layer Bi$_2$Sr$_2$CaCu$_2$O$_{8+y}$ (BSCCO) cuprate superconductor exhibits a one-dimensional (1D) incommensurate superlattice (IS), the effect of IS on the electronic structure remains elusive. Following the recent shift of the interest from underdoped to optimum and overdoped phase in BSCCO by increasing the hole doping $x$, controlled by the oxygen interstitials concentration $y$, here we focus on the multiple splitting of the density of states (DOS) peaks and emergence of higher order van Hove singularities (VHS) due to the 1D incommensurate superlattice. It is known that 1D incommensurate wave vector $\textbf{q} = ε\textbf{b}$ (where $\textbf{b}$ is the reciprocal lattice vector of the orthorhombic lattice) is controlled by the misfit strain between different atomic layers in the range $0.209$ - $0.215$ in BSCCO and in the range $0.209$ - $0.25$ in Bi$_2$Sr$_2$Ca$_{1-x}$Y$_x$Cu$_2$O$_{8+y}$ (BSCYCO). This work reports the theoretical calculation of a complex pattern of VHS due to the 1D incommensurate superlattice with large 1D quasi-commensurate supercells with the wave vector $ε=9/η$ in the range $36 > η> 43$. The similarity of the complex VHS splitting and appearing of higher order VHS in a mismatched CuO$_2$ bilayer with VHS due to the moir{é} lattice in strained twisted bilayer graphene is discussed. This makes mismatched CuO$_2$ bilayer quite promising for constructing quantum devices with tuned physical characteristics.

cond-mat.str-el↗

arXiv2022

Graphene on a ferromagnetic substrate: instability of the electronic liquid

We previously show [JETP Letters, {\bf 114}, 763 (2021)] that a graphene sample placed on a ferromagnetic substrate demonstrates a cooperative magnetoelectronic instability. The instability induces a gap in the electronic spectrum and a canting deformation of the magnetization near the graphene-substrate interface. In this paper we prove that the interaction between the electrons in graphene strongly enhances the instability. Our estimates suggest that in the presence of even a moderate interaction the instability can be sufficiently pronounced to be detected experimentally in a realistic setting.

cond-mat.mes-hall↗

arXiv2020

Spin density wave and electron nematicity in magic-angle twisted bilayer graphene

We study theoretically many-body properties of magic-angle twisted bilayer graphene for different doping levels. Our investigation is focused on the emergence, stability, and manifestations of nematicity of the ordered low-temperature electronic state. It is known that, at vanishing interactions, the low-energy spectrum of the system studied consists of four almost-flat almost-degenerate bands. Electron-electron repulsion lifts this degeneracy. To account for such an interaction effect, a numerical mean-field theory is used. Assuming that the ground state has spin-density-wave-like order, we introduce a multicomponent order parameter describing spin magnetization. Our simulations show that the order parameter structure depends on the doping level. In particular, doping away from the charge neutrality point reduces the rotational symmetry of the ordered state, indicating the appearance of an electron nematic state. Manifestations of the nematicity can be observed in the spatial distribution of the spin magnetization within a moir{é} cell, as well as in the single-electron band structure. The nematicity is strongest at half-filling (two extra electron or holes per supercell). We argue that nematic symmetry breaking is a robust feature of the system ground state, stable against model parameters variations. Specifically, it is shown that, away from the charge neutrality point, it persists for all three parametrizations of the interlayer hopping amplitudes discussed in the paper. Obtained theoretical results are consistent with the available experimental data.

cond-mat.str-el↗

arXiv2020

Can bilayer graphene become a fractional metal?

It is known that electron interactions can cause a perfect spin polarization of the Fermi surface of a metal. In such a situation only half of the non-interacting Fermi surface is available, and thus this phase is commonly referred to as a 'half-metal'. Here we argue that, in multi-band electronic systems with nesting, further 'fractionalization' of the Fermi surface is possible. Taking the AA bilayer graphene as a convenient test case, we demonstrate that, under suitable conditions imposed on the electron interactions, doped AA bilayer graphene can host a 'quarter-metal' state. In such a state, only one quarter of the non-interacting Fermi surface (Fermi contour) reaches the Fermi energy. At higher doping level, other 'fractional' metals can emerge. We briefly analyze the transport properties of these proposed phases.

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