Magnetic impurity in topological nodal loop semimetals

Abstract

We investigate the Kondo effect of a spin-1/2 magnetic impurity in a topological nodal loop semimetal, in which band touchings form a nodal loop. The Fermi surface of a nodal loop semimetal is a torus or a drum-like structure, which is determined by chemical potential. When the chemical potential μ lies at the nodal loop ([Formula: see text]), the magnetic impurity and the conduction electrons form bound states only if their coupling exceeds a critical value. As the chemical potential is tuned away from the nodal loop, the Fermi surface becomes a torus or drum-like structure and the impurity and the host material always favor a bound state due to the finite density of state. Due to the anisotropic dispersion relationship in the energy band, the spatial spin-spin correlations [Formula: see text]([Formula: see text]) are of power-law decay with the decay rates proportional to [Formula: see text] and [Formula: see text] in different directions, respectively. The product [Formula: see text] and [Formula: see text] oscillates in coordinate space and the period is enhanced gradually as the Fermi surface evolves from a torus surface into a drum-like structure.

Magnetic impurity in hybrid and type-II nodal line semimetals*

“…This behavior is independent of the chemical potential and DOS, and is also independent of real space axis directions. The r −3 decay behavior in our type-II NLSM Hamiltonian is qualitatively consistent with the results obtained in the type-I case, [40] considering that the dispersion relation contains quadratic terms along the k z -axis. However, the r −2 decay rate observed in the hybrid NLSM is much distinct from the type-I and type-II cases.…”

“…The Kondo effect of a single magnetic impurity in a type-I NLSM has been studied, and it has been reported that when the chemical potential lies at the nodal loop, the magnetic impurity and the conduction electrons form bound states only if their coupling exceeds a critical value and the spatial decay ratio is either proportional to 1/r 2 or 1/r 3 , depending on the real space directions. [40] Distinct from the type-I case already studied, in the hybrid and type-II NLSMs discussed in this paper, the DOS is always significant, so the magnetic impurity and the conduction electrons always form bound states. The DOS of the hybrid case is much larger than that of the type-II case, so in general the binding energy takes larger values in the hybrid case.…”

“…[33,34] In this paper, we systematically study the binding energy and real space spin-spin correlations of a magnetic impurity in both the hybrid and type-II NLSMs. The variational method we apply has been used to study the ground state of the Kondo problem in normal metals, [35,36] antiferromagnet, [37] 2D helical metals, [38] 3D Weyl semimetals, [34,39] tilted Dirac surface states, [33] type-I NLSMs [40] and multi-WSMs, [41] and the Fermi arc surface states of WSMs. [42] Due to the intriguing nodal loop structure of the hybrid and type-II NLSMs, the Kondo screening in these systems is expected to show very interesting features.…”

Electron scattering by magnetic impurity in Weyl semimetals

“…To this regard, the analysis of how these materials behave in presence of impurities becomes essential. In this context, several studies have been conducted in Weyl, Dirac, nodal loop and triple-component semimetals [12][13][14][15][16][17][18][19][20][21][22][23] and topological insulators [24][25][26][27][28][29][30][31][32][33][34], where signatures of the Kondo effect are observed, the appearance of resonances is displayed and the stability of these materials against impurities is discussed. In this work, we will work along the lines of Ref.…”

Spatial anisotropy of the Kondo screening cloud in a type-II Weyl semimetal

“…The variational method we apply has been used to study the ground state of the Kondo problem in normal metals, 44,57 antiferromagnet, 58 2D helical metals, 53 and various novel topological materials. 56,[59][60][61][62] The paper is organized as follows. We present the model Hamiltonian, dispersion as well as the electron and hole pockets at the Fermi level in Sec.…”