Idempotent geometry in generic algebras

Using the syzygy method, established in our earlier paper, we characterize the combinatorial stratification of the variety of two-dimensional real generic algebras. We show that there exist exactly three different homotopic types of such algebras and relate this result to potential applications and known facts from qualitative theory of quadratic ODEs. The genericity condition is crucial. For example, the idempotent geometry in Clifford algebras or Jordan algebras of Clifford type is very different: such algebras always contain nontrivial submanifolds of idempotents.Comment: 17 pages, 3 figures, submitted (some typos corrected

Size-dependent transformation from triangular to rectangular fluxon lattice in Bi-2212 mesa structures

We present a systematic study of the field and size dependencies of the static fluxon lattice configuration in Bi-2212 intrinsic Josephson junctions and investigate conditions needed for the formation of a rectangular fluxon lattice required for a high power flux-flow oscillator. We fabricate junctions of different sizes from Bi2Sr2CaCu2O8+x and Bi1.75Pb0.25Sr2CaCu2O8+x single crystals using the mesa technique and study the Fraunhofer-like modulation of the critical current with magnetic field. The modulation can be divided into three regions depending on the formed fluxon lattice. At low field, no periodic modulation and no ordered fluxon lattice is found. At intermediate fields, modulation with half-flux quantum periodicity due to a triangular lattice is seen. At high fields, the rectangular lattice gives integer flux quantum periodicity. We present these fields in dependence on the sample size and conclude that the transitions between the regions depend only on lambdaJ(Jc) and occur at about 0.4 and 1.3 fluxons per lambdaJ, respectively. These numbers are universal for the measured samples and are consistent with performed numerical simulations.Comment: Conference paper LT2

Persistent electrical doping of Bi2Sr2CaCu2O8+x mesa structures

Application of a significantly large bias voltage to small Bi2Sr2CaCu2O8+x mesa structures leads to persistent doping of the mesas. Here we employ this effect for analysis of the doping dependence of the electronic spectra of Bi-2212 single crystals by means of intrinsic tunneling spectroscopy. We are able to controllably and reversibly change the doping state of the same single crystal from underdoped to overdoped state, without changing its chemical composition. It is observed that such physical doping is affecting superconductivity in Bi-2212 similar to chemical doping by oxygen impurities: with overdoping the critical temperature and the superconducting gap decrease, with underdoping the c-axis critical current rapidly decreases due to progressively more incoherent interlayer tunneling and the pseudogap rapidly increases, indicative for the presence of the critical doping point. We distinguish two main mechanisms of persistent electric doping: (i) even in voltage contribution, attributed to a charge transfer effect, and (ii) odd in voltage contribution, attributed to reordering of oxygen impurities

Word and bit line operation of a 1x1 {\mu}m2 superconducting vortex-based memory

The lack of dense random access memory is one of the main bottlenecks for the creation of a digital superconducting computer. In this work we study experimentally vortex-based superconducting memory cells. Three main results are obtained. First, we test scalability and demonstrate that the cells can be straightforwardly miniaturized to submicron sizes. Second, we emphasize the importance of conscious geometrical engineering. In the studied devices we introduce an asymmetric easy track for vortex motion and show that it enables a controllable manipulation of vortex states. Finally, we perform a detailed analysis of word and bit line operation of a 1x1 {\mu}m2 cell. High-endurance, nonvolatile operation at zero magnetic field is reported. Remarkably, we observe that the combined word and bit line threshold current is significantly reduced compared to the bare word-line operation. This could greatly improve the selectivity of individual cell addressing in a multibit RAM. The achieved one square micron area is an important milestone and a significant step forward towards creation of a dense cryogenic memory.Comment: 9 pages, 6 figure