Controllable Rashba Spin-Orbit Interaction in Artificially Engineered Superlattices Involving the Heavy-Fermion Superconductor ${\mathrm{CeCoIn}}_5$

By using a molecular beam epitaxy technique, we fabricate a new type of superconducting superlattices with controlled atomic layer thicknesses of alternating blocks between the heavy-fermion superconductor ${\mathrm{CeCoIn}}_5$, which exhibits a strong Pauli pair-breaking effect, and nonmagnetic metal ${\mathrm{YbCoIn}}_5$. The introduction of the thickness modulation of ${\mathrm{YbCoIn}}_5$ block layers breaks the inversion symmetry centered at the superconducting block of ${\mathrm{CeCoIn}}_5$. This configuration leads to dramatic changes in the temperature and angular dependence of the upper critical field, which can be understood by considering the effect of the Rashba spin-orbit interaction arising from the inversion symmetry breaking and the associated weakening of the Pauli pair-breaking effect. Since the degree of thickness modulation is a design feature of this type of superlattices, the Rashba interaction and the nature of pair breaking are largely tunable in these modulated superlattices with strong spin-orbit coupling.

Figure 1

Schematic representations of the ${\mathrm{CeCoIn}}_5(n)/{\mathrm{YbCoIn}}_5(m)/{\mathrm{CeCoIn}}_5(n)/{\mathrm{YbCoIn}}_5(m^{\prime })$ artificial superlattices. (a) $S$-type ($m=m^{\prime }$): Superlattice with alternating layers of 5-UCT ${\mathrm{CeCoIn}}_5$ and 5-UCT ${\mathrm{YbCoIn}}_5$, $(n:m:n:m^{\prime })=(5:5:5:5)$. The middle ${\mathrm{CeCoIn}}_5$ layer in a given ${\mathrm{CeCoIn}}_5$ block layer indicated by the gray plane is a mirror plane. The green (small) arrows represent the asymmetric potential gradient associated with the local ISB, $-\nabla V_{\text{local}}$. The Rashba splitting occurs at the interface between the ${\mathrm{CeCoIn}}_5$ and ${\mathrm{YbCoIn}}_5$ due to the local ISB. The spin direction is rotated in the $ab$ plane and is opposite between the top and bottom ${\mathrm{CeCoIn}}_5$ layers. (b) $S^{*}$-type ($m\ne m^{\prime }$): 5-UCT ${\mathrm{CeCoIn}}_5$ block layers are sandwiched by 8- and 2-UCT ${\mathrm{YbCoIn}}_5$ layers, $(n:m:n:m^{\prime })=(5:8:5:2)$. The middle ${\mathrm{CeCoIn}}_5$ layer (gray plane) is not a mirror plane. The orange (large) arrows represent the asymmetric potential gradient associated with the ${\mathrm{YbCoIn}}_5$ layer thickness modulation $-\nabla V_{\text{block}}$.

Figure 2

(a) Temperature dependence of the resistivity in each superlattice, along with that of 120 nm–thick ${\mathrm{CeCoIn}}_5$ and ${\mathrm{YbCoIn}}_5$ epitaxial thin films. $T_c$, defined as the temperature where the resistance is 50% of the normal state resistance, is 1.16, 1.18, and 1.13 K for $(n:m:n:m^{\prime })=(5:5:5:5)$, ($5:7:5:3$), and ($5:8:5:2$), respectively. (b) Temperature dependence of the anisotropy of upper critical field $H_{c2}$, $H_{c2\parallel }/H_{c2\perp }$ for the superlattices and ${\mathrm{CeCoIn}}_5$ thin film.

Figure 3

Normalized upper critical field $H_{c2\perp }/H_{c2\perp }^{\text{orb}}(0)$ as a function of $T/T_c$ for $S^{*}$-type superlattices with $(n:m:n:m^{\prime })=(5:7:5:3)$ and ($5:8:5:2$), compared with that for $S$-type ($5:5:5:5$). We also plot $H_{c2\perp }/H_{c2\perp }^{\text{orb}}(0)$ for ${\mathrm{CeCoIn}}_5$ single crystal with a strong Pauli pair-breaking effect and the WHH curve without the Pauli pair-breaking effect. Inset: The same plot for $S$-type ${\mathrm{CeCoIn}}_5(n)/{\mathrm{YbCoIn}}_5(5)$ superlattices.

Figure 4

Angular dependence of $H_{c2}$ in ${\mathrm{CeCoIn}}_5/{\mathrm{YbCoIn}}_5$ superlattices. (a) $H_{c2}(\theta )$ for the $S^{*}$-type ($5:8:5:2$) superlattice. (b) Comparison of $H_{c2}(\theta )$ in ($5:8:5:2$) (red triangles, left axis), ($5:7:5:3$) (green circles, right axis), and ($5:5:5:5$) (blue squares, right axis) superlattices near $T_c$. (c) $H_{c2}$ of these superlattices near $T_c$, replotted in an appropriate dimensionless form. The solid lines are the fits to the data using the model described in Eq. (1). (d) ${\beta }_T/{\beta }_P$, which quantifies the relative importance of orbital and Pauli pair-breaking effects, is plotted as a function of the thickness modulation of ${\mathrm{YbCoIn}}_5$ layers $|m-m^{\prime }|$ (right panel). For comparison, ${\beta }_T/{\beta }_P$ in $S$-type superlattice ${\mathrm{CeCoIn}}_5(n)/{\mathrm{YbCoIn}}_5(5)$ is plotted as a function of $n$ (left panel).