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

Abstract

We theoretically study the Kondo screening of a spin-1/2 magnetic impurity in the bulk of a type-II Weyl semimetal (WSM) by use of the variational wave function method. We consider a type-II WSM model with two Weyl nodes located on the kz-axis, and the tilting of the Weyl cones are along the kx direction. Due to co-existing electron and hole pockets, the density of states at the Fermi energy becomes finite, leading to a significant enhancement of Kondo effect. Consequently, the magnetic impurity and the conduction electrons always form a bound state, this behavior is distinct from that in the type-I WSMs, where the bound state is only formed when the hybridization exceeds a critical value. Meanwhile, the spin-orbit coupling and unique geometry of the Fermi surface lead to strongly anisotropic Kondo screening cloud in coordinate space. The tilting terms break the rotational symmetry of the type-II WSM about the kz-axis, but the system remains invariant under a combined transformation T R y (π), where T is the time-reversal operation and R y (π) is the rotation about the y-axis by π. Largely modified diagonal and off-diagonal components of the spin-spin correlation function on three principal planes reflect this change in band symmetry. Most saliently, the tilting terms trigger the emergence of non-zero off-diagonal components of spin-spin correlation function on the x-z principal plane. -1 0 1 J y z ( r ) J y z ( r ) J y z ( r ) J y y ( r ) J y y ( r ) J y y ( r ) J z z ( r ) J z z ( r ) J x x ( r ) J z z ( r ) J z z ( r ) z

Quantum phases driven by strong correlations

“…Weyl physics is being explored also in other Ce-and Yb-based intermetallic compounds [139][140][141] , creating the exciting opportunity to discover signatures of strong correlation-driven electronic topology also there. Together with theoretical efforts 136,[142][143][144][145][146][147][148][149][150] this may help to establish the new field of strongly correlated electronic topology.…”

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

“…We utilize the well-known trial wavefunction approach which has been used to study the ground state of the Anderson impurity problem in the conventional metal, [35,36] 2D helical metals, [38] antiferromagnets, [37] and various novel topological insulators [46] and topological semimetals. [33,34,39,42] We assume that the Coulomb repulsion U is large enough, and the impurity energy level ε d is below the Fermi energy, so that the impurity site is always singly occupied by a local moment. For the simplest case, we first discuss the case of H V = 0, in which the magnetic impurity and the NLSM are completely decoupled from each other.…”

“…In Lorentzviolating host systems like tilted Dirac surface states and type-II WSMs, the formation of the impurity-conduction electron bound states is also determined by the DOS of the Fermi surface, and the spatial screening shows very rich features due to the unique dispersion relations. [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.…”

“…[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.…”

Tunable correlation effects of magnetic impurities by the cubic Rashba spin-orbit couplings

“…[43][44][45] In this paper, we combine the variational method and the Hirsch-Fye quantum Monte Carlo (HFQMC) 46 simulations to study the correlation effects of the impurities induced by the cubic Rashba SOC. The variational method has been widely used in the ground states of Anderson impurity problems in normal metals, 47,48 systems with SOCs, 37,[49][50][51][52][53] and superconductors. [54][55][56][57] The HFQMC technique is a numerically exact method which has been used to study magnetic impurities in metals, 46,[58][59][60][61][62] dilute magnetic semiconductors, 63 graphene based systems [64][65][66][67] and in the presence of SOCs.…”