Tunneling spectra of inhomogeneous d-wave superconductor

The tunneling spectrum of an inhomogeneous d-wave superconductor is discussed in the framework of self-consistent slave-boson mean-field theory. Distinct from the usual BCS-type mean-field theory, an electron is now described using both fermionic and bosonic degree of freedom. We show that one can define two types of tunneling spectra in this theory, which also corresponds to two ways of calibrating the STM spectra. In good agreement with the experimental observation, we show that one type of tunneling spectrum remains inhomogeneous while the other type shows a remarkable degree of homogeneity at low energy, despite the underlying disorder. Physical implications of this result, in particular in relation to thermodynamic measurement such as heat capacity, are discussed.