Rashba-induced Kondo screening of a magnetic impurity in a two-dimensional superconductor

We study the Kondo screening of a magnetic impurity in a two-dimensional superconductor with Rashba spin-orbit coupling (SOC). It is found that the Rashba interaction generates a Kondo screening channel, in which the local moment is screened by the exchange coupling with conduction electrons in different spin and orbital states. The Kondo temperature associated with this process is determined by the interplay between the Rashba SOC and superconducting energy gap. As a result, the quantum phase transition between the magnetic doublet and Kondo singlet ground states is significantly affected by increasing Rashba SOC in such a system. This result uncovers that the Rashba SOC plays an instructive role and provides a screening channel for the Kondo effect, which is expected to be observed in future experiments.

Figure 1

(a) Schematic diagram of an Anderson impurity on 2DEG with Rashba spin-orbit coupling (SOC) proximity to the Bardeen-Cooper-Schrieffer (BCS) superconductor. (b) The magnetic moment induces the Yu-Shiba-Rusinov (YSR) bound states at $E_{\mathrm{YSR}}$, which possesses an effective moment, denoted by the red arrow [39]. The Rashba SOC leads to a total angular momentum conserved QST process, such as ($\left|0,\uparrow \right.〉\to \left|1,\downarrow \right.〉$). (c) The spin-up electron on the impurity level is replaced by the excited electron ($\left|1,\downarrow \right.〉$) through the virtual states. And the spin-up electron tunnels into the conduction band to neutralize the hole ($\left|0,\uparrow \right.〉$) in the superconductor. (d) The local moment of impurity as well as the effective moment of YSR bound states are effectively flipped. The magnetic impurity is screened by the coherent superposition of those processes.

Figure 2

(a)–(c) The YSR bound states ($E_{\mathrm{YSR}}$) are tuned from below to above the Fermi level by increasing the tunneling amplitude ${\mathrm{\Gamma }}_0$ with different Rashba SOC energy ${\varepsilon }_R=0.0,0.25\mathrm{\Delta },2.25\mathrm{\Delta }$, respectively. The quantum phase transition (QPT) between the magnetic doublet (MD) and Kondo singlet (KS) ground states occurs when the YSR states get across the Fermi level. (d) The Rashba SOC suppressed superconducting energy gap as a function of ${\varepsilon }_R$. (e) The phase boundary between the MD and KS phases is scaled by $T_K^0\left({\varepsilon }_R\right)/\mathrm{\Delta }\left({\varepsilon }_R\right)$; see the square solid line. The suppression is attributed to the Rashba SOC-induced Kondo screening process, which is confirmed by a quantum states transition (QST) model, as shown the red dash-dotted line. (f) The Kondo temperature $T_K^{SC}\left({\varepsilon }_R\right)$ characterizing the Rashba-induced Kondo screening process in the superconductor. Other parameters used are the impurity level ${\varepsilon }_j=-10\mathrm{\Delta }$, the Coulomb interaction $U=100\mathrm{\Delta }$, the half bandwidth $D=25\mathrm{\Delta }$, and the temperature $T=0$.

Figure 3

(a),(b) The temperature-dependent susceptibility of the YSR state varying with the tunneling amplitude ${\mathrm{\Gamma }}_0$ with different spin-orbit coupling strengths ${\varepsilon }_R=0.0,\mathrm{\Delta }$, respectively. (c) Temperature-dependent susceptibility of the YSR state suppressed by the increasing ${\varepsilon }_R$, and ${\mathrm{\Gamma }}_0=40\mathrm{\Delta }$. (d) Enhancement and suppression of the susceptibility by increasing the Rashba interaction at $T=0$ and ${\mathrm{\Gamma }}_0=40\mathrm{\Delta }$. The other parameters used are the same with those in Fig. 2.