Laser-irradiated Kondo insulators: Controlling the Kondo effect and topological phases

We investigate theoretically the nature of laser-irradiated Kondo insulators. Using Floquet theory and the slave-boson approach, we study a periodic Anderson model and derive an effective model that describes laser-irradiated Kondo insulators. In this model, we find two generic effects induced by laser light. One is dynamical localization, which suppresses hopping and hybridization. The other is laser-induced hopping and hybridization, which can be interpreted as synthetic spin-orbit coupling or a magnetic field. The first effect drastically changes the behavior of the Kondo effect. In particular, the Kondo effect under laser light qualitatively changes its character depending on whether the hybridization is on-site or off-site. The second effect triggers topological phase transitions. In topological Kondo insulators, linearly polarized laser light realizes phase transitions between trivial, weak topological, and strong topological Kondo insulators. Moreover, circularly polarized laser light breaks time-reversal symmetry and induces Weyl semimetallic phases. Our results make it possible to dynamically control the Kondo effect and topological phases in heavy-fermion systems. We also discuss experimental setups to detect the signatures.

Figure 1

Schematic picture of our setup. A three-dimensional bulk Kondo insulator is irradiated by laser light in the $z$ direction. We assume a pulse laser wide enough to apply Floquet theory, which is a theoretical prescription for time-periodic systems.

Figure 2

Schematic picture of $c\text{−}f$ hybridization. (a) On-site model: the $c$- and $f$-electrons hybridize only at the same site. (b) Off-site model: the $c$- and $f$-electrons hybridize only at the nearest-neighbor sites. There is no on-site hybridization. Note that, although this figure treats one-dimensional systems for simplicity, we consider three-dimensional systems in our study.

Figure 3

Numerical solutions of the self-consistent equations for (a) the on-site model and (b) the off-site model with linearly polarized laser light. We show the temperature dependence of (a.1) the renormalization factor $b$ and (a.2) the energy shift $\lambda$ for the on-site model. The same things for the off-site model are shown in (b.1) and (b.2), respectively. Here $A_x=A_y=A$, and we use the parameters $t_c=1,t_f=-0.2,V=3,{\epsilon }_f=-4$, and $\omega =12.5$.

Figure 4

Numerical solutions of the self-consistent equations for the off-site model with the circularly polarized laser light. In (a), we show the temperature dependence of the renormalization factor $b$. Here $A_x=A_y=A$, and we use the parameters $t_c=1,t_f=-0.2,V=3,{\epsilon }_f=-4$, and $\omega =12.5$. In (b), to clarify the effect of laser-induced hybridization, we compare the results of $\omega =3.0$ and 12.5 at the same intensity $\left(A=2.0\right)$. All the parameters except for the frequency are set the same as in (a).

Figure 5

(a) The schematic picture of the enhancement of the density of states near the Fermi energy ${\rho }_0$. It is the origin of the enhancement of the Kondo effect in the on-site model. (b) Schematic Doniach phase diagram. Changing the Kondo coupling $J_{cf}$ or the density of states ${\rho }_0$ by some perturbations, e.g., pressure, we can induce the quantum phase transition. AFM represents an antiferromagnetic phase.

Figure 6

Numerical solutions of the self-consistent equations for the model of a topological Kondo insulator with linearly polarized laser light. In (a) and (b), we show the temperature dependence of the renormalization factor $b$ and the energy shift $\lambda$, respectively. Here $A_x=A_y=A$, and we use the parameters $t_c=1,t_f=-0.2,V=3,{\epsilon }_f=-6$, and $\omega =12.5$.

Figure 7

Topological invariants (a) ${\nu }_{\mathrm{STI}}$, (b) ${\nu }_{\mathrm{WTI}}^{x,y}$, and (c) ${\nu }_{\mathrm{WTI}}^z$. Above the Kondo temperature, the topological invariants are not defined since the system is a paramagnetic metal. Here we use the parameters $t_c=1,t_f=-0.2,V=3,{\epsilon }_f=-4$, and $\omega =12.5$.

Figure 8

The phase diagram of the topological Kondo insulators irradiated by linearly polarized laser light. There are two topologically trivial phases and three topologically nontrivial phases: the trivial Kondo insulator phase (tKI, $b\ne 0$, all the topological invariants are zero), the trivial metal phase (tMetal, $b=0)$, the strong topological insulator phase (STI, $b\ne 0,{\nu }_{\mathrm{STI}}=1)$, and two kinds of weak topological insulator phases (WTI), ${\mathrm{WTI}}_1[\mathbf{\nu }=({\nu }_{\mathrm{WTI}}^x,{\nu }_{\mathrm{WTI}}^y,{\nu }_{\mathrm{WTI}}^z)=(1,1,1)]$ and ${\mathrm{WTI}}_2[\mathbf{\nu }=(1,1,0)]$. Here we use the parameters $t_c=1,t_f=-0.2,V=3,{\epsilon }_f=-4$, and $\omega =12.5$.

Figure 9

Laser-induced topological phase transition of the topological Kondo insulators with linearly polarized laser light. We show the calculated band structure for $k_x$ (both $k_y$ and $k_z$ are fixed to $\pi )$. (a) Without laser light $\left(A=0.0\right)$, the system is in the STI phase. (b) Applying the laser light $\left(A=0.54\right)$, the band gap closes at the topological phase transition point. (c) Applying the strong laser light $\left(A=0.8\right)$, the system is changed to the ${\mathrm{WTI}}_2$ phase. Here we use the parameters $T=6.2,t_c=1,t_f=-0.2,V=3,{\epsilon }_f=-4$, and $\omega =12.5$.

Figure 10

Numerical solutions of the self-consistent equations for the model of the topological Kondo insulator with circularly polarized laser light. In (a) and (b), we show the temperature dependence of the renormalization factor $b$ and the energy shift $\lambda$, respectively. Here $A_x=A_y=A$, and we use the parameters $t_c=1,t_f=-0.2,V=1.5,{\epsilon }_f=-4$, and $\omega =12.5$. In (c), to clarify the effect that appears only in the case of circularly polarized laser, we compare the results of $\omega =3.0$ and 12.5 at the same intensity $\left(A=2.0\right)$. LH and LM represents the case that only includes the effect of laser-induced hybridization and laser-induced magnetic field, respectively. The parameters other than the frequency are the same as in (a) and (b).

Figure 11

Laser-induced topological phase transition of the topological Kondo insulators with circularly polarized laser light. We show the calculated band structure for $k_z[(k_x,k_y)=(0,\pi )]$ near $k_z=\pm \pi$. (a) Without laser light $\left(A=0.0\right)$, the system is in the STI phase. (b) Applying the laser light $\left(A=0.1\right)$, the Kramers degeneracy is lifted and the bands are split by the LM. (c) Making the laser light stronger $\left(A=0.2\right)$, the crossing points (Weyl nodes) appear near $k_z=\pm \pi$ and the system is changed to the Weyl semimetallic phase. Here we use the parameters $T=0.1,t_c=1,t_f=-0.2,V=1.5,{\epsilon }_f=-4$, and $\omega =12.5$.

Figure 12

(a) The phase diagram of the topological Kondo insulators irradiated by circularly polarized laser light. There are two topologically trivial phases and four topologically nontrivial phases: the trivial Kondo insulator phase (tKI, $b\ne 0$, all the topological invariants are zero), the trivial metal phase (tMetal, $b=0)$, and four kinds of Weyl semimetallic phases $({\mathrm{WSM}}_1,{\mathrm{WSM}}_2,{\mathrm{WSM}}_3$, and ${\mathrm{WSM}}_4)$ shown below. Here we use the parameters $t_c=1,t_f=-0.2,V=1.5,{\epsilon }_f=-4$, and $\omega =12.5$. (b) The four kinds of Weyl semimetallic phases. We show the position of the Weyl nodes (red points) in the three-dimensional Brillouin zone. The white (orange) regions represent the Chern number $C\left(k_z\right)$ as zero (finite).