Exact magnetic properties of two-dimensional spin-1 Cooper pairs

Abstract

Abstract Exact magnetic properties of two-dimensional (2D) spin-1 Cooper pairs are investigated within the framework of quantum statistical mechanics. We derive an exact analytical expression of the magnetization of 2D spin-1 Cooper pairs, which involves a q-digamma function and a q-Pochhammer symbol in mathematics. The magnetization density m(T) is a function of temperature T, Landé factor g, number density σ, and magnetic field B. Firstly, we examine the evolution of the magnetization density m(T) with the Landé factor g. m(T) is negative when g < 1, and changes gradually to positive after g c . Here, g c = 1 is the critical value of the Landé factor g, at which m ( T ) = 0 . Secondly, we examine the evolution of the magnetization density m(T) with the temperature T. When g < 1, there are the two asymptotic lines for the magnetization density m(T). The low-temperature asymptotic line is m ( T ) = − 387.5  nC s−1 and the high-temperature asymptotic line is m ( T ) = 0 . Finally, we examine the evolution of the magnetization density m(T) with the number density σ. No matter how large the Landé factor g is, there is a lower cutoff σ c of the number density σ. The lower cutoff number density is about σ c = 10 12  cm−2. If σ < σ c , the Cooper pair system does not support a solution of the reduced chemical potential x. As the number density σ is increased, the Bose–Einstein condensation of 2D Cooper pairs is strengthened.