Theory of Tunneling Spectroscopy in the Larkin-Ovchinnikov State

We present a theory of tunneling spectroscopy for normal metal/Larkin-Ovchinnikov state junctions in which the spatial periodic modulation in the pair potential amplitude is taken into account. The tunneling spectra show the characteristic line shapes reflecting the minigap structures under the periodic pair potentials depending on the boundary condition of the pair potentials at the junction interface. These features are qualitatively different from the tunneling spectra of the Fulde-Ferrell state. We propose an experimental setup which identifies the superconducting state of ${\mathrm{CeCoIn}}_5$.

Figure 1

A normal metal/insulator/superconductor in the LO state junction. In a node contact junction and a maximum contact junction, $Q_1$ is set to be $-\pi /2$ and 0, respectively. We also show pairing symmetries in this coordinate.

Figure 2

Calculated results for $s$-wave N/I/LO junctions. Normalized tunneling conductance ${\sigma }_T$ is plotted as a function of bias voltages for the node contact junction in (a) and for the maximum contact junction in (c). Local density of states ${\rho }_T$ at a nodal point and that at a maximum point of the bulk LO state are shown in (b) and (d), respectively. In all panels, $a$: $L=L_0$ and $b$: $L=10L_0$. By the Zeeman shift, the zero bias peak is shifted to $\epsilon =\pm {\mu }_{B}H$ in (b), and peaks of the gap edge are split to $\epsilon ={\Delta }_0\pm {\mu }_{B}H$ in (d).

Figure 3

Calculated results for $d_{xy}$-wave N/I/LO junctions. ${\sigma }_T$ is plotted as a function of bias voltages for the node contact junction in (a) and for the maximum contact junction in (c). ${\rho }_T$ at a nodal point and that at a maximum point of the bulk LO state are shown in (b) and (d), respectively. In all panels, $a$: $L=L_0$ and $b$: $L=10L_0$.

Figure 4

Calculated results for N/I/FF junctions. ${\sigma }_T$ is plotted as a function of bias voltages for the $s$ wave in (a) and for the $d_{xy}$ wave in (b). $a$: $L=a_0$ and $b$: $L=10a_0$.