Merging of momentum-space monopoles by controlling Zeeman field: From cubic-Dirac to triple-Weyl fermion systems

Abstract

We analyze a generalized Dirac system, where the dispersion along the kx and ky axes is N -th power and linear along the kz axis. When we apply magnetic field, there emerge N monopole-antimonopole pairs beyond a certain critical field in general. As the direction of the magnetic field is rotated toward the z axis, monopoles move to the north pole while antimonopoles move to the south pole. When the magnetic field becomes parallel to the z axis, they merge into one monopole or one antimonopole whose monopole charge is ±N . The resultant system is a multiple-Weyl semimetal. Characteristic properties of such a system are that the anomalous Hall effect and the chiral anomaly are enhanced by N times and that N Fermi arcs appear. These phenomena will be observed experimentally in the cubic-Dirac and triple-Weyl fermion systems (N = 3).Introduction: Topological objects in the momentum space play intriguing roles in the field of condensed matter physics [1][2][3][4] . Examples are monopoles, skyrmions and merons. They have fascinating properties that are not shared by the corresponding ones in the real space, since they are purely static because of the absence of the kinetic energy. For instance, a monopole carrying a large magnetic charge cannot exist in the real space due to a large Coulomb repulsion but can in the momentum space. It is an interesting problem if we may generate N monopole-antimonopole pairs and successively make them merged into one monopole-antimonopole pair each of which carries monopole charge ±N just by controlling an external parameter.

Exact solutions of Kondo problems in higher-order fermions

“…These are in similar forms as the Hamiltonians mapped from single band normal metals. In particular, we see from (18) that the Kondo exchange coupling remains short-ranged in the new fermionic degrees of freedom; the impurity spin S only couples to the new fermionic field Ψ ←αi (τ, r) at r = 0. This means that H I is only confined to the boundary r = 0, with H = H 0 in the bulk r = 0, and the problem is suitable for further analysis by techniques in 2D boundary CFT.…”

“…In particular, most recently, even more exotic Weyl and Dirac semimetals which exhibit effective fermions with higher-order dispersion relations have been proposed. These higher-order dispersion relations take a form that is linear in one direction, but quadratic or cubic in the orthogonal plane [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] . Such materials are named quadratic and cubic Weyl/Dirac semimetals respectively 12,17,22 , with their corresponding emergent fermions referred to as quadratic and cubic Weyl/Dirac fermions respectively 11,12,15 , and they are classified as Weyl/Dirac according to their 2-fold/4fold band degeneracies at their band crossings 12,13,15 .…”

“…Examples of quadratic Weyl/Dirac semimetals include HgCr 2 Se 4 , SiSr 2 , bandinverted α−Sn and PdSb 2 11,14,16 , and examples of cubic Weyl/Dirac semimetals include LiO S O 3 and quasi-onedimensional molybdenum monochalcogenide compounds A I (MoX VI ) 3 , where A I = Na, K, Rb, In or Tl, X VI = S, Se or Te 17,19,22,23 . Moreover, various novel quantum phenomena are predicted to take place in these semimetals, such as charge density wave, non-Fermi liquid, and topological superconductivity 12,18,19,[22][23][24][26][27][28][29][30][31][32][33][34][35] . It is therefore timely and of theoretical importance to study Kondo problems in these higher-order fermion (KHOF) systems, in particular, using analytically exact methods.…”

Topological quantum critical point in a triple-Weyl semimetal: Non-Fermi-liquid behavior and instabilities

“…In this article, we consider the transition between topological triple-Weyl SM (WSM) and BI. In a triple-WSM, the fermion energy spectrum disperses cubically along two directions and linearly along the third one, and the monopole charges of one pair of Weyl points are ±3 [42][43][44][45][46][47][48][49][50][51][52][53][54]. In the process of turning triple-WSM into BI, two Weyl points carrying opposite monopole charges merge to form one single band-touching point that carries zero monopole charge.…”

Kondo effect in multi-dirac and weyl fermions

“…The 2-Weyl semimetals were found in HgCr 2 Se 4 (XU et al, 2011;FANG et al, 2012) and SrSi 2 (HUANG et al, 2016) crystals and 3-Weyl semimetals were predicted in A(M oX) 3 (with A = Rb, T I and X = T e) (LIU; ZUNGER, 2017). Theoretical studies are also being conducted in the direction of multi-Weyl (EZAWA, 2017;LIU;ZHANG, 2019;LÜ et al, 2019). In order to contribute to Kondo physics in multi-Dirac and multi-Weyl systems and different regimes.…”