Surface bound states in $n$-band systems with the quasiclassical approach

We discuss the tunneling spectroscopy at a surface in multiband systems such as Fe-based superconductors with the use of the quasiclassical approach. We extend the single-band method by M. Matsumoto and H. Shiba [J. Phys. Soc. Jpn. 64, 1703 (1995)] into $n$-band systems $\left(n\ge 2\right)$. We show that the appearance condition of the zero-bias conductance peak does not depend on details of the pair-potential anisotropy, but it depends on details of the normal-state properties in the case of fully gapped superconductors. The surface density of states in a two-band superconductor is presented as a simplest application. The quasiclassical approach enables us to calculate readily the surface-angular dependence of the tunneling spectroscopy.

Figure 1

Figure of a specular surface.

Figure 2

Figures of band dispersions along a $k_x$ line with a fixed $k_y$.

Figure 3

(Color online) Fermi surfaces in the two-band model. (a) The half filling $\left(\mu =0\right)$ and $t^{\prime }=0.1t$. (b) $\mu =0.2t$ and $t^{\prime }=0.2t$.

Figure 4

(Color online) Fermi surfaces ($\mu =0$ and $t^{\prime }=0.1t$) and $k_x$ line with fixed $k_y$.

Figure 5

(Color online) The density of states at the surface for various surface angles. The pair potentials are ${\Delta }_A=\Delta =0.001t$ and ${\Delta }_B=-{\Delta }_A$. (a) The half filling $\left(\mu =0\right)$ and (b) $\mu =0.2t$. The interorbital hopping amplitude is $t^{\prime }=0.1t$. The smearing factor is $\eta =0.1\Delta$.

Figure 6

(Color online) The density of states at the surface for various surface angles. The pair potentials are ${\Delta }_A=\Delta =0.001t$ and ${\Delta }_B=-0.5{\Delta }_A$. (a) The half filling $\left(\mu =0\right)$ and (b) $\mu =0.2t$. The interorbital hopping amplitude is $t^{\prime }=0.1t$. The smearing factor is $\eta =0.1\Delta$.

Figure 7

(Color online) The density of states at [110] surface for various interorbital hopping amplitude $t^{\prime }$. The pair potentials are ${\Delta }_A=\Delta =0.001t$ and ${\Delta }_B=-{\Delta }_A$. (a) The half filling $\left(\mu =0\right)$ and (b) $\mu =0.2t$. The smearing factor is $\eta =0.1\Delta$.