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Dirac electrons in solids show characteristic physical properties due totheir linear dispersion relation and two-band nature. Although the transportphenomena of Dirac electrons in a normal state have intensively been studied,the transport phenomena in a superconducting state have not been fullyunderstood. In particular, it is not clear whether Dirac electrons in asuperconducting state show Meissner effect (ME), since a diamagnetic term of acurrent operator is absent as a result of the linear dispersion. We investigatethe ME of three dimensional massive Dirac electrons in a superconducting stateon the basis of Kubo formula, and clarify that Meissner kernel becomes finiteby use of the inter-band contribution. This mechanism of the ME for Diracelectrons is completely different from that for the electrons in usual metals.Our result shows that the Meissner kernel remains finite even when thesuperconducting gap vanishes. This is an unavoidable problem in the Diracelectron system as reported in the previous works. Thus, we use a prescriptionin which we subtract the normal state contribution. In order to justify thisprescription, we develop a specific model where the Meissner kernel is obtainedby the prescription. We also derive the result for the electron gas by takingthe non-relativistic limit of Dirac Hamiltonian, and clarify that thediamagnetic term of the Meissner kernel can be regarded as the inter-bandcontribution between electrons and positrons in terms of the Dirac model.

Meissner Effect of Dirac Electrons in Superconducting State due to Inter-band Effect