Emergent exotic superconductivity in artificially engineered tricolor Kondo superlattices

In the quest for exotic superconducting pairing states, the Rashba effect, which lifts the electron-spin degeneracy as a consequence of strong spin-orbit interaction (SOI) under broken inversion symmetry, has attracted considerable interest. Here, to introduce the Rashba effect into two-dimensional (2D) strongly correlated electron systems, we fabricate noncentrosymmetric (tricolor) superlattices composed of three kinds of $f$-electron compounds with atomic thickness; $d$-wave heavy fermion superconductor ${\mathrm{CeCoIn}}_5$ sandwiched by two different nonmagnetic metals, ${\mathrm{YbCoIn}}_5$ and ${\mathrm{YbRhIn}}_5$. We find that the Rashba SOI-induced global inversion symmetry breaking in these tricolor Kondo superlattices leads to profound changes in the superconducting properties of ${\mathrm{CeCoIn}}_5$, which are revealed by unusual temperature and angular dependencies of upper critical fields that are in marked contrast with the bulk ${\mathrm{CeCoIn}}_5$ single crystals. We demonstrate that the Rashba effect incorporated into 2D ${\mathrm{CeCoIn}}_5$ block layers is largely tunable by changing the layer thickness. Moreover, the temperature dependence of in-plane upper critical field exhibits an anomalous upturn at low temperatures, which is attributed to a possible emergence of a helical or stripe superconducting phase. Our results demonstrate that the tricolor Kondo superlattices provide a new playground for exploring exotic superconducting states in the strongly correlated 2D electron systems with the Rashba effect.

Figure 1

Schematic representations of Kondo superlattices. (a) Centrosymmetric bicolor superlattices ${\mathrm{CeCoIn}}_5\left(m\right)$/${\mathrm{YbCoIn}}_5$(5). The center of a ${\mathrm{CeCoIn}}_5$ BL (ash plane) is a mirror plane. (b) $ABA{B}^{\prime }$-type superlattices ${\mathrm{CeCoIn}}_5\left(i\right)$/${\mathrm{YbCoIn}}_5\left(j\right)$/${\mathrm{CeCoIn}}_5\left(i\right)$/${\mathrm{YbCoIn}}_5\left(j^{\prime }\right)$ $\left(j\ne j^{\prime }\right)$. The center of a ${\mathrm{CeCoIn}}_5$ BL is not a mirror plane, but the centers of ${\mathrm{YbCoIn}}_5$ BLs (ash planes) are mirror planes. (c) Noncentrosymmetric tricolor superlattices ${\mathrm{YbCoIn}}_5$(3)/${\mathrm{CeCoIn}}_5\left(n\right)$/${\mathrm{YbRhIn}}_5$(3). Crystal structure of $TM{\mathrm{In}}_5$ $(T$: Ce or Yb, $M$: Co or Rh) with tetragonal symmetry is also shown. In the tricolor superlattices, all layers are not the mirror planes. The orange arrows represent the asymmetric potential gradient $-\mathbf{\nabla }V$ due to the broken inversion symmetry. The Rashba SOI splits the Fermi surface into two sheets; spin direction rotates clockwise on one sheet (blue arrows) and anticlockwise on the other (red arrows).

Figure 2

(a) Typical RHEED streak patterns for $n=8$ tricolor superlattice taken during the crystal growth. (b) Typical AFM image for $n=8$ tricolor superlattice grown by MBE. (c) Cu $\mathrm{K}{\alpha }_1$ x-ray diffraction patterns for $n=5$ and 8 superlattices around the main (004) peaks. Red lines represent the step-model simulations ignoring the interface and layer-thickness fluctuations. (d) High-resolution cross-sectional TEM image of the $n=8$ tricolor superlattice with the electron beam aligned along the (110) direction. The right panel is the intensity integrated over the horizontal width of the image. The positions of Ce, Yb, Co, and Rh atoms can be identified from the dips and peaks as shown by arrows, which are consistent with the designed superlattice structure shown in the left panel.

Figure 3

Temperature dependence of the resistivity $\rho \left(T\right)$ in the $n=5$ and 8 tricolor ${\mathrm{YbCoIn}}_5$(3)/${\mathrm{CeCoIn}}_5\left(n\right)$/${\mathrm{YbRhIn}}_5$(3) superlattices and in the $m=5$ and 8 bicolor ${\mathrm{CeCoIn}}_5\left(m\right)$/${\mathrm{YbCoIn}}_5$(5) superlattices. Inset: $\rho \left(T\right)$ for the tricolor ${\mathrm{YbCoIn}}_5$(3)/${\mathrm{CeCoIn}}_5\left(n=5\right)$/${\mathrm{YbRhIn}}_5$(3), bicolor ${\mathrm{CeCoIn}}_5\left(m=5\right)$/${\mathrm{YbCoIn}}_5$(5), and bicolor ${\mathrm{CeCoIn}}_5$(5)/${\mathrm{YbRhIn}}_5$(5) superlattices.

Figure 4

Temperature dependence of resistivity for (a) $n=8$ and (b) $n=5$ tricolor superlattices, respectively, in applied field parallel to the plane. Red and blue curves are taken in every 0.1 and 0.5 T, respectively. Thin solid black curve represents the normal state resistivity ${\rho }_N$, and thin solid lines represent $0.3{\rho }_N,0.5{\rho }_N,0.7{\rho }_N$, and $0.9{\rho }_N$. (c), (d) Expanded views of (a) and (b) around $0.5{\rho }_N$, respectively. The arrows correspond to the shift of $T_c$ by changing the magnetic field of 0.5 T. (e), (f) In-plane upper critical field defined by using four different criteria, $\rho (T,H)=0.3{\rho }_N\left(T\right),0.5{\rho }_N\left(T\right),0.7{\rho }_N\left(T\right)$, and $0.9{\rho }_N\left(T\right)$, as a function of temperature for $n=8$ and 5 tricolor superlattices, respectively.

Figure 5

(a) The anisotropy of upper critical field $H_{c2},H_{c2\parallel }/H_{c2\perp }$, plotted as a function of normalized temperature $T/T_c$ for the tricolor superlattices and ${\mathrm{CeCoIn}}_5$ single crystal. (b) Angular dependence of $H_{c2},H_{c2}\left(\theta \right)$, plotted in an appropriate dimensionless form for the tricolor and bicolor ${\mathrm{CeCoIn}}_5\left(m\right)$/${\mathrm{YbCoIn}}_5$(5) superlattices. The solid and dashed lines represent the Tinkham's formula for a two-dimensional superconductor and the three-dimensional anisotropic mass model, which are described as ${[H_{c2}\left(\theta \right)cos\theta /H_{c2\parallel }]}^2=-|H_{c2}\left(\theta \right)sin\theta /H_{c2\perp }|+1$ [42] and ${[H_{c2}\left(\theta \right)cos\theta /H_{c2\parallel }]}^2=-{[H_{c2}\left(\theta \right)sin\theta /H_{c2\perp }]}^2+1$ [44], respectively. (c) Normalized upper critical field in perpendicular fields, $H_{c2\perp }/H_{c2\perp }^{\mathrm{orb}}\left(0\right)$, as a function of $T/T_c$ for the tricolor superlattices, compared with that for the bicolor ${\mathrm{CeCoIn}}_5\left(m\right)$/${\mathrm{YbCoIn}}_5$(5) superlattices with the same ${\mathrm{CeCoIn}}_5$ block layer thickness. We also plot $H_{c2\perp }/H_{c2\perp }^{\mathrm{orb}}$ for ${\mathrm{CeCoIn}}_5$ single crystal [41] with a strong Pauli pair-breaking effect and the WHH curve [45] without the Pauli pair-breaking effect. In (a)–(c), $H_{c2}$ is defined by using $\rho (T,H)=0.5{\rho }_N\left(T\right)$.

Figure 6

(a) Reduced upper critical field in parallel fields, $H_{c2\parallel }/T_c$, as a function of $T/T_c$ for the tricolor superlattices, compared with that for the bicolor ${\mathrm{CeCoIn}}_5\left(m\right)$/${\mathrm{YbCoIn}}_5$(5) superlattices with the same ${\mathrm{CeCoIn}}_5$ block layer thickness. $H_{c2\parallel }$ is determined by using $\rho (T,H)=0.5{\rho }_N\left(T\right)$. We also plot $H_{c2\parallel }/T_c$ for ${\mathrm{CeCoIn}}_5$ single crystal. Inset illustrates schematic figure of the Fermi surfaces under parallel magnetic fields. Arrows on the Fermi surfaces indicate spins. Fields parallel to $x$ axis shifts the center of the Rashba-split small and large Fermi surfaces by ${\mathit{q}}_{\mathit{M}}$ along $+y$ and $-y$ directions, respectively. Pairing occurs between the states of $\mathit{k}+{\mathit{q}}_{\mathit{M}}$ and $-\mathit{k}+{\mathit{q}}_{\mathit{M}}$, leading to a gap function with spatial modulation, e.g., in a form of $\mathrm{\Delta }\left(\mathit{r}\right)={\mathrm{\Delta }}_0{e}^{i{\mathit{q}}_{\mathit{M}}·\mathit{r}}$ [54]. (b) Temperature derivative of $H_{c2\parallel }$, represented as $r=-d(H_{c2\parallel }/T_c)/d(T/T_c)$, is plotted as a function of $t=T/T_c$. $r\left(t\right)$ shows a minimum for the $n=5$ tricolor superlattice (red arrow). For $n=8,r\left(t\right)$ shows a deviation from $T$-linear temperature dependence (dashed line) below $t\sim 0.25$ (blue arrow). (c) and (d) shows $r\left(t\right)$, replotted as $-d[H_{c2\parallel }/H_{c2\parallel }\left(0\right)]/d(T/T_c)$, for (c) $n=5$ and $n=8$ tricolor superlattices, respectively. Here we use $H_{c2\parallel }$ determined by using different criteria, $\rho (T,H)=0.3{\rho }_N\left(T\right),0.5{\rho }_N\left(T\right),0.7{\rho }_N\left(T\right)$ and $0.9{\rho }_N\left(T\right)$. Solid lines are $r\left(t\right)$ calculated from the WHH formula.