This work theoretically analyzes electronic instabilities in AA-stacked bilayer graphene and the role of the Coulomb interaction in stabilization of electronic ordered states in this system. The Coulomb interaction screening is accounted with the help of the random phase approximation. We observe that the repulsion between charge carriers located in the same graphene layers is much larger than that between the electrons moving in different layers (moreover, under certain circumstances the inter-layer effective interaction becomes attractive). At zero doping, the intra-layer Coulomb repulsion is responsible for arising of the spin-density wave (SDW) state. The Neel temperature for this phase is estimated to be about several tens K. The SDW is the dominating order in undoped system, but it is destroyed completely by sufficiently strong doping, allowing a superconducting phase to emerge. As for the superconducting mechanism, we demonstrate that the effective inter-layer attraction can give rise to superconductivity. However, the corresponding critical temperature is negligibly small, and phonon-mediated attraction must be introduced into the model to make the superconductivity observable. Strong intra-layer Coulomb repulsion favors the order parameters that couple electrons in different layers. In this case two different types of the superconducting phase can exist in the system. The first type is a usual superconductivity with Copper pairs having zero total momentum in the ground state. Such superconductivity exists if the coupling between electrons with momenta near different Dirac cones dominates. When the interaction between electrons near the same Dirac cones is larger, the Cooper pairs have a non-zero momenta in the ground state. Superconducting gap can increase or decrease with doping depending on the relationship between intra-band and inter-band BCS interaction.

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.

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.

We study the influence of the antiferromagnetic order on the surface states of topological insulators. We derive an effective Hamiltonian for these states, taking into account the spatial structure of the antiferromagnetic order. We obtain a typical (gapless) Dirac Hamiltonian for the surface states when the surface of the sample is not perturbed. Gapless spectrum is protected by the combination of time-reversal and half-translation symmetries. However, a shift in the chemical potential of the surface layer opens a gap in the spectrum away from the Fermi energy. Such a gap occurs only in systems with finite antiferromagnetic order. We observe that the system topology remains unchanged even for large values of the disorder. We calculate the spectrum using the tight-binding model with different boundary conditions. In this case we get a gap in the spectrum of the surface states. This discrepancy arises due to the violation of the combined time-reversal symmetry. We compare our results with experiments and density functional theory calculations.

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.

Уважаемые коллеги!Благодарим Вас за проявленный интерес к Четвертой российской конференции «Графен: молекула и 2D кристалл» и желание принять участие в её работе.Конференция проходит в научно-образовательном центре города Новосибирска -Академгородке.Мероприятие посвящено актуальным направлениям исследований и разработок в области углеродных и низкоразмерных материалов.Проведение конференции поможет координации усилий ученых в решении современных проблем материаловедения и привлечению молодых исследователей для решения актуальных научных задач.Оргкомитет выражает особую благодарность НГУ, Центру компетенций НТИ «Моделирование и разработка новых функциональных материалов с заданными свойствами», компаниям «Диаэм», «НТ-МДТ Спектрум Инструментс» и корпорации "Графеновая Долина" за финансовую поддержку и журналам Аналитика, Наноиндустрия и РЭНСИТ за информационную поддержку.Искренне надеемся, что пребывание в Новосибирском Академгородке и в стенах Новосибирского государственного университета оставит множество положительных эмоций и

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.

In the topological superconductor with the nematic superconductivity in $E_u$ representation, it is possible to have different types of vortices. One is associated with the vorticity in the particle-hole space and corresponds to the Abrikosov vortex. Another type corresponds to the vorticity in the spin space and is called spin vortex. We study the interaction of the Abrikosov vortex with the spin vortices. We derive the free energy of the sample with the Abrikosov and the strain-induced spin vortices using the Ginzburg-Landau approach for the two-component superconducting order parameter. We calculate the critical strain at which the spin vortex is formed. We show that the spin vortex and the Abrikosov vortex attract to each other and, as a result, they have a common core. We show that there are no zero-energy states (Majorana fermions) localized near the common vortex core of the Abrikosov vortex and the spin vortex of any type. Possible experimental realization is discussed.

We study analytically and numerically electronic properties of a circular quantum dot made from AA-stacked 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.

The spin density wave existing on the background of the inhomogeneous charge distribution is examined as a possible ground state of the magic-angle twisted bilayer graphene. When interactions are not included, the spectrum of the material has four (eight 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, a possible charge density wave contribution to the order parameter; i.e., an inhomogeneous distribution of the charge density within a twisted graphene supercell is taken into account. The spin structure of the order parameter is calculated self-consistently. It is found 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. It is demonstrated that the local spin magnetization in energy units is much stronger than the charge density variation, unless doping exceeds three extra electrons or holes per supercell.

Theoretical studies of the theory of nematic superconductivity in doped insulators of the Bi 2 Se 3 family have been reviewed. It is experimentally shown that their transition to the superconducting state is accompanied by spontaneous rotational symmetry breaking. This superconductivity is called nematic superconductivity and is described well by a triplet vector order parameter. The main concepts of the microscopic theory and the Ginzburg–Landau theory for nematic superconductivity have been presented. The competition between possible superconducting order parameters in topological insulators has been discussed. It has been shown that hexagonal distortions of the Fermi surface are necessary for implementing the nematic phase. This phase is very sensitive to disorder because charged impurities reduce the critical temperature. The doping-induced transition from the closed to open Fermi surface affects the competition of superconducting phases. Surface Andreev states in nematic superconductors have been discussed. The phenomenological Ginzburg–Landau theory for the two-component order parameter is derived from the microscopic theory. Using the Ginzburg–Landau theory, it has been shown that the ground state is either the real nematic order parameter with the spontaneous deformation of the lattice or a complex chiral order parameter with spontaneous magnetization. The vector structure of the order parameter is responsible for an unconventional relation between superconductivity and the lattice deformation and magnetization. This leads to strong anisotropy of the second critical field, to the appearance of spin vortices (which can be carried by Kramers pairs of Majorana fermions), and to unconventional Pauli paramagnetism for triplet Cooper pairs.

We study the physics of the Josephson effect in nematic superconductors with $E_u$ odd parity in the Ginzburg-Landau approach. Two-component vector superconducting order parameter makes this effect rather unusual. We get that the Meissner kernel has off-diagonal components. We derive current-phase relations for different configurations of the junction, crystallographic axes of the sample, and nematicity direction. We show that an anomalous Josephson Hall effect can be observed in such a system without any magnetization. That is, for definite orientations of the junction and crystal axes, a component of the Josephson current along the junction is induced by the order parameter phase difference across the contact. We also calculate the magnetic field dependence of the maximum current through the junction. We find that the period of the Fraunhofer oscillations of the maximum Josephson current depends on the geometry of the junction, direction of the magnetic field, and nematicity vector.

A review of the basic concepts and mechanisms related to the electronic phase separation and the formation of nanoscale inhomogeneities in magnetic materials is given. We put the main emphasis onto strongly correlated electron systems such as manganites, where phase separation occurs due to the competition of ferro- and antiferromagnetic states, as well as cobaltites, where the spin-state transitions play an important role. Special attention is paid to the mechanism of phase separation related to the imperfect nesting of sheets of the Fermi surface, which is especially important for systems with spin density waves, a striking example of which are iron-containing pnictides.

Twisted bilayer graphene at the so-called magic twist angle θ ∼ 1° is theoretically studied. In the absence of interaction between electrons, the system under study is characterized by four almost degenerate flat bands near the Fermi level. The electron-electron interaction lifts this degeneracy and stabilizes a certain order parameter in the system. We assume that the arising order parameter corresponds to a spin density wave. The evolution of such spin density wave state upon doping is analyzed. It is shown that, in the doping range where this order parameter exists, the homogeneous state of the system can be unstable to phase separation. Namely, the doping dependence of the chemical potential is nonmonotonic, which is consistent with recent experiments. Phases in the inhomogeneous state are characterized by an even number (ν = 0, ±2, ±4) of electrons per supercell. This allows explaining some features in the behavior of the conductivity of the doped system.

M.I. Bannikov, 2 R.S. Akzyanov, 4 N.K. Zhurbina, 2 S.I. Khaldeev, 2 Yu.G. Selivanov, V.V. Zavyalov, 2 A. L. Rakhmanov, 4 and A.Yu. Kuntsevich P.N. Lebedev Physical Institute, Russian Academy of Sciences, Moscow 119991, Russia National Research University Higher School of Economics, Moscow 101000, Russia Dukhov Research Institute of Automatics, Moscow, 127055 Russia Institute for Theoretical and Applied Electrodynamics, Russian Academy of Sciences, Moscow, 125412 Russia P.L. Kapitza Institute of Physical Problems, Moscow, Russia

Nematic superconductors are characterized by an apparent crystal symmetry breaking that results in the anisotropy of the in-plain upper critical magnetic field $H_{c2}$. The symmetry breaking is usually attributed to the strain of the crystal lattice. The nature and the value of the strain are debatable. We perform systematic measurements of the $H_{c2}$ anisotropy in the high-quality Sr$_x$Bi$_2$Se$_3$ single crystals in the temperature range 1.8~K$<T<T_c\approx 2.7$~K using temperature stabilization with an accuracy of 0.0001 K. We observe that in all tested samples the anisotropy is practically constant when $T<0.8 T_c$ and smoothly decreases at higher temperatures without any sign of singularity when $T\rightarrow T_c$. Such a behavior can be understood in the framework of the Ginzburg-Landau (GL) theory for the nematic superconductors assuming that the samples are appreciably deformed. The nature of the strain, the values of the GL parameters, and the effects of disorder near $T_c$ are discussed. Similar measurements can be used to study a nature of the symmetry breaking in the other nematic superconductors.

Nematic superconductors are characterized by an apparent crystal symmetry breaking that results in the anisotropy of the in-plane upper critical magnetic field $H_{c2}$. The symmetry breaking is usually attributed to the strain of the crystal lattice. The nature and the value of the strain are debatable. We perform systematic measurements of the $H_{c2}$ anisotropy in the high-quality Sr$_x$Bi$_2$Se$_3$ single crystals in the temperature range 1.8~K$

We consider the nanoscale electronic phase separation in a wide class of different materials, mostly in strongly correlated electron systems. The phase separation turns out to be quite ubiquitous manifesting itself in different situations, where the itineracy of charge carriers competes with their tendency toward localization. The latter is often related to some specific type of magnetic ordering, e.g. antiferromagnetic in manganites and low-spin states in cobaltites. The interplay between the localization-induced lowering of potential energy and metallicity (which provides the gain in the kinetic energy) favors an inhomogeneous ground state such as nanoscale ferromagnetic droplets in an antiferromagnetic insulating background. The present review article deals with the advances in the subject of electronic phase separation and formation of different types of nanoscale ferromagnetic (FM) metallic droplets (FM polarons or ferrons) in antiferromagnetically ordered (AFM), charge-ordered (CO), or orbitally-ordered (OO) insulating matrices, as well as the colossal magnetoresistance (CMR) effect and tunneling electron transport in the nonmetallic phase-separated state of complex magnetic oxides. It also touches upon the compounds with spin-state transitions, inhomogeneous phase-separated state in strongly correlated multiband systems, and electron polaron effect. A special, attention is paid to the systems with the imperfect Fermi surface nesting such as chromium alloys, iron-based pnictides, and AA stacked graphene bilayers.

Using the Ginzburg-Landau approach, we show that the strain of the nematic superconductor can generate a specific (nematic) vorticity. In the case of doped topological insulators that vorticity forms a spin vortex. We find two types of topologically different spin vortices that either enhance (type I) or suppress (type II) superconductivity far from the vortex core. We apply Bogoliubov-de Gennes equations to study electronic states in the nematic superconductor with spin vortices. We find that in the case of the type I vortex, zero-energy states are localized near the vortex core. These states can be identified as Majorana Kramers pairs. In the case of the type II vortex, there are no localized zero-energy states. Thus, we establish a nontrivial connection between the strain and Majorana fermions in the doped topological insulators with nematic superconductivity.

Studies of a recently suggested mechanism for the stabilization of half-metallic states in doped systems with the nesting of Fermi surface sheets are briefly reviewed. The characteristic features of such states are described. In addition, a theoretically formulated method to identify such states using inelastic neutron scattering is analyzed.