Kondo Breakdown in a Spin-$1/2$ Chain of Adatoms on a Dirac Semimetal

We consider a spin-$1/2$ Heisenberg chain coupled via a Kondo interaction to two-dimensional Dirac fermions. The Kondo interaction is irrelevant at the decoupled fixed point, leading to the existence of a Kondo-breakdown phase and a Kondo-breakdown critical point separating such a phase from a heavy Fermi liquid. We reach this conclusion on the basis of a renormalization group analysis, large-$N$ calculations as well as extensive auxiliary-field quantum Monte Carlo simulations. We extract quantities such as the zero-bias tunneling conductance which will be relevant to future experiments involving adatoms on semimetals such as graphene.

Figure 1

Renormalization group flow of the Kondo coupling $J_k$ for a spin-$1/2$ chain on a semimetallic substrate.

Figure 2

The zero-temperature mean-field phase diagram in a parameter space of $J_k/t$ and $J_h/t$.

Figure 3

$C(r)$ as a function of distance $r$ along the spin chain on a log-log scale for (a) $J_k/t=0$, (b) $J_k/t=1.5$, (c) $J_k/t=2$ and (d) $J_k/t=3$ at $J_h/t=1$ and $L_x=L_y=L=\beta t$. The gray dashed line corresponds to $1/r$ decay and the insets plot the corresponding $S(k)$.

Figure 4

(a) $\chi (k=\pi )$ as a function of $J_k/t$ for $J_h/t=1$ and $\beta t=L$. (b) Plots $\partial F/\partial J_k$ as a function of $J_k/t$.

Figure 5

$S(k,\omega )$ along spin chain as a function of energy ($\omega /t$) and momentum ($k$) for $L=\beta t=44$ at $J_h/t=1$ and  (a) $J_k/t=0$, (b) $J_k/t=1.5$, (c) $J_k/t=2$, and (d) $J_k/t=3$.

Figure 6

$A_0(k,\omega )$ as a function of energy ($\omega /t$) and momentum ($k$) for $L=\beta t=44$ at $J_h/t=1$ and  (a) $J_k/t=1.5$, (b) $J_k/t=2$, (c) $J_k/t=2.5$, and (d) $J_k/t=3$.

Figure 7

Zero-bias tunneling through the magnetic adatom.