Superconductivity in a system of fractional spectral dimension

Fracton Excitations in the Magnetic "Net Fractal" Systems

“…The ratio of α and β in Eq. (2) determines the fractional spectral (fracton) dimension, which in turn governs the thermodynamical behavior of the spin system [1,4]. Since there are many definitions of fractional derivatives in any approach, which involves the fractional calculus techniques, one should define, which definition of fractional pseudo--differential is used.…”

“…It is natural to assume that the self-similarity of the fractal is reflected also in the symmetry of exchange interactions. We assume therefore that also the exchange integrals exhibit the power law scaling with the separation, we take it in the form I(λr ij ) = λ −σ I(r ij ) (for the Ruderman-Kittel-Kasuya-Yosida (RKKY)-like interactions the σ can be approximated by the spectral dimension of the system [3,4]). Let us now recall the (log-scale) isomorphism of "net fractals" and some crystal lattices.…”

Electron Mediated Mn-Mn Interaction in Quantum Dots

“…The interdot RKKY interaction is mediated by the free electrons of the lead that joins the adjacent QD of a qubit. As it was shown earlier [10], the electron density is also given by the formula (9). This means that the RKKY interaction is given by the formula (10), however, one should note that due to the dierent geometry of the lead the parameter D s in this case takes another value [11].…”

“…which in many cases, is a fraction [9]. The RKKY exchange integral in the case is given by [10] J(r) In practical realization the simplest case of the qubit spin coded device contains two magnetically coupled quantum dots with electron spins trapped in them.…”

Magnetic and Magnetoelectric Effects within a Sandwich Structure with the Parabolic Quantum Well

“…It is worthwhile to mention here that in general in the case of quasi-2D electron gas systems the effective spectral dimension can take any value from the 1 ≤ d ≤ 4 range [8].…”