2011/06/27 by E. G. Batyev, É. G. Batyev · 1 citation
Physics and Astronomy · #Condensed matter physics #Cooper pair #Critical field #Landau quantization #Magnetic field #Magnetic properties of thin films #Operator (biology) #Physics #Physics of Superconductivity and Magnetism #Quantum Hall effect #Quantum and electron transport phenomena #Quantum mechanics #Superconductivity #Type-II superconductor #Vortex #Vortex state #Wave function #cond-mat.supr-con
paper · pdf · doi:10.1134/s1063776112060039
published in Journal of Experimental and Theoretical Physics 115(1), 136-140 (Pleiades Publishing) · 7 pages
arxiv created 2011/06/27 · openalex publication_date 2012/07/01 · arxiv updated 2015/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A model is proposed for describing Cooper pairs near the transition (in temperature and magnetic field) point when their spacing is larger than their size. The essence of the model is as follows: the Ginzburg-Landau functional is written in operator form in terms of field operators of the Bose type so that the average value of the density operator gives the concentration of Cooper pairs, and the same Ginzburg-Landau expression is obtained for the Bose condensate. The model is applied to a superconducting plate with a thickness smaller than the size of a pair in a transverse magnetic field near its upper critical value H c2. A new state is discovered that is energetically more advantageous in a certain interval in the vicinity of the transition point as compared to the Abrikosov vortex state. The wavefunction of the system in this state is of the type of the Laughlin function used in the fractional quantum Hall effect (naturally, as applied to Cooper pairs as Bose particles in our case) and corresponds to a homogeneous incompressible fluid. The energy of this state is proportional to the first power of quantity (1 − H/H c2) in contrast to the energy of the vortex state containing the square of this quantity. The interval of the existence of the new state is the larger, the dirtier the sample.