Superconductivity of the magnetized electron gas of a quantum cylinder

Semiconductor nanotube plasma

“…In this case, the dependences of the critical temperature and free energy on nanotube parameters, including the parameter 2Φ/Φ 0 , were obtained in study [34] and confirmed in study [43]. With regard to the periodic dependence of the gap on the magnetic flux, it is sufficient to extend the results of study [34] to the entire range of the values of param eter 2Φ/Φ 0 with a period of unity. In the mentioned studies, the equation was obtained and investigated that determines the dependence of the critical temper ature on the geometric sizes of a quantum cylinder, surface density of electrons, and the Aharonov-Bohm parameter.…”

“…Folding the graphene sheet in a nanotube makes it possible to observe the macroscopic Aharonov-Bohm effect [32][33][34]. In study [35], the measured magneti zations of the ropes of single layer carbon nanotubes in the superconducting state were reported.…”

“…Under the condition , it is energetically favorable to pair electrons with quantum numbers of the oppo site signs [44,45]. In this case, the dependences of the critical temperature and free energy on nanotube parameters, including the parameter 2Φ/Φ 0 , were obtained in study [34] and confirmed in study [43]. With regard to the periodic dependence of the gap on the magnetic flux, it is sufficient to extend the results of study [34] to the entire range of the values of param eter 2Φ/Φ 0 with a period of unity.…”

“…The nanotube curvature leads to crit ical temperature oscillations, similar to the van Haasvan Alphen oscillations related to quantization of the energy of the transverse motion of electrons and the root features of the electron density of energy states at the cylindrical surface. In study [43], it was demon strated how the equation for the gap derived in [34] for the superconducting electron gas at the cylindrical surface by the Bogolyubov method is obtained by thẽ 11 30…”

“…The microscopic theory of superconductivity of a magnetized electron gas was built in studies [34,[41][42][43]. According to the results of the analysis made first in [44], in a longitudinal magnetic field, it is energeti cally favorable to pair states with azimuth numbers n 1 and n 2 , which ensure the minim quantity |n 1 + n 2 -2Φ/Φ 0 |, where is the single electron mag netic flux quantum, and the highest binding energy is observed at where M is an integer.…”