Crossed Andreev reflection in a d-wave superconductor with two quantum point contacts

We theoretically study the crossed Andreev reflection in a hybrid nanostructure which comprises a d-wave superconductor and two normal-metal quantum wires. When the superconductor of the (110) oriented surface is in contact with the wires parallel and placed close to each other, the Andreev bound state is formed by the crossed Andreev reflection. When the contact barrier potential is sufficiently large, two sharp peaks appear in the conductance well below the gap structure, which originate from the bonding and antibonding Andreev bound states. We propose that these Andreev bound states form a two-level quantum system (qubit).