Effect of an External Magnetic Field on the Coherent Kondo State — Upper Critical Field in UBe13

Abstract

Intensive experimental and theoretical investigations have been done concerning the normal and superconducting state in the heavy fermion compounds [1] such as CeCu2Si2 [2] and UBe13 [3]. It has been shown in the previous paper [4] that the temperature dependence of the upper critical field in CeCu2Si2 [5] is well explained, if the singlet superconducting state is assumed and the saturation effect due to the Pauli paramagnetism is taken into account. However, in UBe13 the upper critical field at low temperatures could not be explained by any choice of the values of parameters. When we calculated the upper critical field of UBe13, we did not take account of the following fact. The upper critical field Hc2 of UBe13 is extremely high, although the superconducting transition temperature is rather low [6]. The upper critical field of UBe13 is about 9 Tesla at low temperatures. This intensity of the field is comparable to the Kondo temperature or the condensation energy of the coherent state in the compound. Therefore, the coherent state itself is affected by the external magnetic field. In this paper we take account of this effect in the following way. We assume the Anderson lattice model for the heavy fermion compounds. Then, we derive the Ward-Takahashi relations among the self-energy and vertex functions which originate from spin rotations. The field and frequency dependence of the self-energy and vertex functions are determined so as to fulfill the relations.