Mobility of spin polarons with vertex corrections

Abstract

The mobility of holes in the spin polaron theory is discussed in this paper using a representation where holes are described as spinless fermions and spins as normal bosons. The hard-core bosonic operator is introduced through the Holstein–Primakoff transformation. Mathematically, the theory is implemented in the finite temperature (Matsubara) Green’s function method. The expressions for the zeroth-order term of the hole mobility is determined explicitly for hole occupation factor taking the form of Fermi–Dirac distribution and the classical Maxwell–Boltzmann distribution function. These are proportional to the relaxation time and the square of the renormalization factor. In the Ising limit, we showed that the mobility is zero and the holes are localized. The calculation of the hole mobility is generalized by considering the vertex corrections, which included the ladder diagrams. One of the vertex functions in the hole mobility can be evaluated using the Ward identity for hole-spin wave weak interaction. We also derived an expression for the hole mobility with vertex corrections in the low-temperature limit and vanishing self-energy effects. Our calculation is made up to second-order correction in the case where the hole occupation factor follows the Fermi–Dirac distribution.