Maxim Kharitonov

Electron screening and excitonic condensation in double-layer graphene systems

We theoretically investigate the possibility of excitonic condensation in a system of two graphene monolayers separated by an insulator, in which electrons and holes in the layers are induced by external gates. In contrast to the recent studies of this system, we take into account the screening of the interlayer Coulomb interaction by the carriers in the layers, and this drastically changes the result. Due to a large number of electron species in the system (two projections of spin, two valleys, and two layers) and to the suppression of backscattering in graphene, the maximum possible strength of the screened Coulomb interaction appears to be quite small making the weak-coupling treatment applicable. We calculate the mean-field transition temperature for a clean system and demonstrate that its highest possible value

Canted Antiferromagnetic Phase of the ν = 0 Quantum Hall State in Bilayer Graphene

T_c^\text{max}\sim 10^{-7}\epsilon_F\lesssim 1 \text{mK}

Universal conductance fluctuations in graphene

is extremely small (

Antiferromagnetic state in bilayer graphene

\epsilon_F

Anomalous Hall effect in granular ferromagnetic metals and effects of weak localization.

is the Fermi energy). In addition, any sufficiently short-range disorder with the scattering time

Edge excitations of the canted antiferromagnetic phase of the ν = 0 quantum Hall state in graphene: A simplified analysis

\tau \lesssim \hbar /T_c^\text{max}

Universality and Stability of the Edge States of Chiral-Symmetric Topological Semimetals and Surface States of the Luttinger Semimetal

would suppress the condensate completely. Our findings renders experimental observation of excitonic condensation in the above setup improbable even at very low temperatures.

Hall resistivity of granular metals.

Motivated to understand the nature of the strongly insulating ν=0 quantum Hall state in bilayer graphene, we develop the theory of the state in the framework of quantum Hall ferromagnetism. The generic phase diagram, obtained in the presence of the isospin anisotropy, perpendicular electric field, and Zeeman effect, consists of the spin-polarized ferromagnetic (F), canted antiferromagnetic (CAF), and partially (PLP) and fully (FLP) layer-polarized phases. We address the edge transport properties of the phases. Comparing our findings with the recent data on suspended dual-gated devices, we conclude that the insulating ν=0 state realized in bilayer graphene at lower electric field is the CAF phase. We also predict a continuous and a sharp insulator-metal phase transition upon tilting the magnetic field from the insulating CAF and FLP phases, respectively, to the F phase with metallic edge conductance 2e(2)/h, which could be within the reach of available fields and could allow one to identify and distinguish the phases experimentally.

Interaction-enhanced magnetically ordered insulating state at the edge of a two-dimensional topological insulator

Mesoscopic conductance fluctuations in graphene samples at energies not very close to the Dirac point are studied analytically. We demonstrate that the conductance variance 〈[δG]〉 is very sensitive to the elastic scattering breaking the valley symmetry. In the absence of such scattering (disorder potential smooth at atomic scales, trigonal warping negligible), the variance 〈[δG]〉 = 4〈[δG]〉metal is four times greater than that in conventional metals, which is due to the two-fold valley degeneracy. In the absence of intervalley scattering, but for strong intravalley scattering and/or strong warping 〈[δG]〉 = 2〈[δG]〉metal. Only in the limit of strong intervalley scattering 〈[δG] 〉 = 〈[δG]〉metal. Our theory explains recent numerical results and can be used for comparison with existing experiments.

Interplay of topology and interactions in quantum Hall topological insulators: U(1) symmetry, tunable Luttinger liquid, and interaction-induced phase transitions

Motivated by the recent experiment of Velasco Jr. {\em et al.} [J. Velasco Jr. {\em et al.}, Nat. Nanotechnology 7, {\bf 156} (2012)], we develop a mean-field theory of the interaction-induced antiferromagnetic (AF) state in bilayer graphene at charge neutrality point at arbitrary perpendicular magnetic field B. We demonstrate that the AF state can persist at all