How realistic may be relativistic field models to describe phenomena occurring in a condensed matter system ? Such question should be particularly relevant for the systems with massless Dirac fermions. The first unambiguous experim
ental evidence for Dirac fermions occurrence in solids has been reported by I.Lukyanchuk and Y.Kopelevich for graphite in 2004, one year before discovery of Dirac Fermions in graphite mono-layer (Graphene). The identification of Dirac fermions became possible due to phase-frequency analysis of quantum de Haas van Alphen and Shubnikov de Haas oscillations. Actually, this method allows the efficient phase definition in any quantum oscillation phenomena and can be considered as a new tool in the condensed matter research. The identification of two-dimensional Dirac fermions in graphite undoubtedly makes this system a natural solid state laboratory to test predictions of relativistic theories of (2+1)-dimensional Dirac fermions. Read more: Phase analysis of quantum oscillations in graphite,Dirac and normal fermions in graphite and graphene: Implications of the quantum Hall effectLattice-induced double-valley degeneracy lifting in graphene by a magnetic field,Searching for the Fractional Quantum Hall Effect in Graphite Y. Kopelevich, B. Raquet, M. Goiran,...
I. A. Lukyanchuk,.; et al., Phys. Rev. Lett., 103, 116802 (2009) |

The favorite Landau sentence: "Nobody can cancel the Coulomb's law" is often overlooked in understanding of spontaneous polarization in Ferroelectric materials that, paradoxically, should be completely destabilized by the backward depolarizing electrostatic field produced by the charge 4πρ=divP of the polarization surface breakdown. This puzzle is partially resolved in samples of >500nm where the unfavorable depolarizing field is screened by the free semi-conducting charges. Alternatively, the smaller samples are segregated onto up- and down- polarized domains, as was initially proposed by Landau and Kittel for magnetic materials. This alternates the surface charge and vanishes the bulk depolarizing field. Current tendency of miniaturization of ferroelectric-based computer memories challenges the study of non-uniform polarization distribution in nano-samples. However the first-principle modeling by the ensemble of electrostatic dipoles is possible only for the very small systems < 50nm because of the non-local Coulomb interaction. So, how the surface of nano-device of realistic size of 50-500nm drives the polarization texture inside? To understand this we use the analytical approach of solution of nonlinear equations of condensation to ferroelectric state coupled with electrostatic (Maxwell) equations. Such approach was proposed in early 80s by Chensky and Tarasenko but never explored after... Periodic domains, vortices, skyrmions and other exotic formations can be created inside of finite-size ferroelectric devices by long-range Coulomb forces of surface. For sure they can be useful as the memory-units of future memory devices. And this is not all ! Integration of ferroelectric elements into nano-electronic silicon environment again produces the polarization domains to compensate the interface-junction-created elastic stress. Surprisingly, the experimental group from Belfast and Cambridge reported that such ferro-elastic domains exist even inside of samples with no interface. This discovery, confirmed by our modeling, implies that the several-atom-thickness surface skin can trigger the intrinsic stress and produce the drastic domain-structuring of device. Figures: (a) Modeling of 3D vortices, (b) Modeillng geometry of domain-structured nano-device (c) Experimental discovery of ferroelastic domains in 3D nano-rod of BaTiO3 ( A.Schilling, M. Gregg, G. Catalan,and J. Scott )Read more:Domain-enhanced interlayer coupling in ferroelectric/paraelectric superlattices; Ferroelectric domains in thin fims and superlattices: Results of numerical modeling F. DeGuerville, M. ElMarssi, I. Luk'yanchuk, and L. Lachoche, Ferroelectrics,
359, 14, (2007)Stability of vortex phases in ferroelectric easy-planes nano-cylindersG. Pascoli L. Lahoche,
I. Luk'yanchuk, Integrated Ferroelectrics, vol. 99, 60 (2008)Universal Properties of Ferroelectric DomainsOrigin of ferroelastic domains in free-standing single-crystal ferroelectric films
Effect of wall thickness on the ferroelastic domain size of BaTiO3, G. Catalan,
I. Luk'yanchuk, A. Schilling, J. M. Gregg, and J. F. Scott, Journ. of Mat. Sci. 44, 5307 (2009) |