The chiral edge state and Majorana fermion in hole-doped YBa ₂ Cu ₃ O _{7− δ} mesoscopic strip

Abstract

Edge states of nontrivial topology are investigated by diagonalizing the tight-binding Hubbard model Hamiltonian for the copper-oxide superconductor YBCO strip in the presence of the Rashba spin-orbit interaction and the Zeeman field. It is found that chiral edge states may develop under appropriate spin-orbit coupling and the exchange field strengths. By defining the quasi-particle creation (annihilation) operators in terms of the obtained particle and hole functions, the zero-energy chiral edge states are proved to be the Majorana zero-energy modes on the opposite edges of the superconductor strip. Manipulations on the Majorana modes are promising by applying an external magnetic field normal to the strip plane. It is also showed that the chiral edge state and the Majorana fermions are more feasible in the underdoped samples. Moreover, domains distinguishing the d-wave pairings from the s-wave pairings are found, implying the coexistence of the d-wave and s-wave gaps for the underdoped YBCO samples.