Quasiparticle interference in the heavy-fermion superconductor ${\mathrm{CeCoIn}}_5$

We investigate the quasiparticle interference in the heavy fermion superconductor ${\mathrm{CeCoIn}}_5$ as a direct method to confirm the $d$-wave gap symmetry. The ambiguity between $d_{xy}$ and $d_{x^2-y^2}$ symmetry remaining from earlier specific heat and thermal transport investigations has been resolved in favor of the latter by the observation of a spin resonance that can occur only in $d_{x^2-y^2}$ symmetry. However, these methods are all indirect and depend considerably on theoretical interpretation. Here we propose that quasiparticle interference (QPI) spectroscopy by scanning tunneling microscopy (STM) can give a direct fingerprint of the superconducting gap in real space that may lead to a definite conclusion on its symmetry for ${\mathrm{CeCoIn}}_5$ and related 115 compounds. The QPI pattern for both magnetic and nonmagnetic impurities is calculated for the possible $d$-wave symmetries and characteristic differences are found that may be identified by use of the STM method.

Figure 1

(a) Calculated Fermi surface for ${\mathrm{CeCoIn}}_5$ using the band structure parameters defined in Ref. 31. (b) The first column indicates a cut through the Fermi surface for the normal state, and the second and third columns indicate a cut through the Fermi surface for $d_{xy}$ and $d_{x^2-y^2}$ gap symmetries, respectively (solid red lines) for bias voltage $\omega =0.1{\Delta }_0$. (At $k_z=0$ first row, at $k_z=0.5\pi$ second row, and at $k_z=\pi$ last row.) The dashed (green) lines indicate the node lines, $\pm$ denotes the sign of the superconducting gap, and ${\mathbf{q}}_i$ are the typical scattering vectors defining the QPI pattern.

Figure 2

The quasiparticle interference due to nonmagnetic impurity scattering for individual layers at $k_{z}c=0.0,0.2\pi ,0.4\pi ,0.6\pi ,0.8\pi ,\pi$, for the normal state (first columns), the superconducting state with $d_{xy}$ gap symmetry (second column), and $d_{x^2-y^2}$ gap symmetry (third column). (For small bias voltage $\omega =0.01{\Delta }_0$ and using ${\Delta }_0/W=0.086$ where $W$ is the total quasiparticle band width.)

Figure 3

Total quasiparticle interference (quasiparticle interference in Fig. 2 averaged over $k_z$) for the normal state (first column), the superconducting state with $d_{xy}$ gap symmetry (second column), and the superconducting state with $d_{x^2-y^2}$ gap symmetry (third column). (For bias voltage, $\omega =0.01{\Delta }_0$ and ${\Delta }_0/W=0.086$.) The first row corresponds to the nonmagnetic impurity, the second row refers to magnetic impurity, and last one shows the difference, $\delta \mathrm{QPI}$, between quasiparticle interference for magnetic and nonmagnetic impurity scattering.

Figure 4

Same as described in the caption to Fig. 3 but for bias voltage $\omega =0.1{\Delta }_0$.