Long-range interaction induced phases in Weyl semimetals

Wei, Huazhou; Chao, Sung-Po; Aji, Vivek

doi:10.1103/physrevb.89.235109

Cited by 29 publications

(20 citation statements)

References 35 publications

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“…These would be point zeros around which the phase of det Q(k) advances by 2π. These lead to topologically protected bulk modes that form the analog of a "Dirac semimetal" in electronic systems like graphene [53,[71][72][73][74][75][76][77][78]. These singularities could be of interest, but they do not occur in lattices derived from the kagome lattice we study below.…”

Section: Topological and Total Mode Countmentioning

confidence: 98%

“…In the latter case, they can occur at specific values of q, in which case they are isolated. These points, which have a topologically protected winding number are called Weyl points, and they have received considerable attention recently in relation to Dirac semimetals and topological insulators [53,[71][72][73][74][75][76][77][78] and in photonic materials [79][80][81]. The distorted square lattices of figure 3(b) has isolated Weyl points [70].…”

Section: Stiffness Matrix Of 2d Periodic Lattices With Guest Modesmentioning

confidence: 99%

“…The total zero-mode count on the surface then follows from equations ( 74), (75), and (78). The polarization of the standard cell is zero so that R L = R L − R stan can be calculated from the displacements ra − r a of the surface cell sites and bonds relative to those of the standard cell.…”

Section: Topological and Total Mode Countmentioning

confidence: 99%

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Phonons and elasticity in critically coordinated lattices

et al. 2015

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Much of our understanding of vibrational excitations and elasticity is based upon analysis of frames consisting of sites connected by bonds occupied by central-force springs, the stability of which depends on the average number of neighbors per site z. When z < zc ≈ 2d, where d is the spatial dimension, frames are unstable with respect to internal deformations. This pedagogical review focuses on properties of frames with z at or near zc, which model systems like randomly packed spheres near jamming and network glasses. Using an index theorem, N0 − NS = dN − NB relating the number of sites, N , and number of bonds, NB, to the number, N0, of modes of zero energy and the number, NS, of states of self stress, in which springs can be under positive or negative tension while forces on sites remain zero, it explores the properties of periodic square, kagome, and related lattices for which z = zc and the relation between states of self stress and zero modes in periodic lattices to the surface zero modes of finite free lattices (with free boundary conditions). It shows how modifications to the periodic kagome lattice can eliminate all but trivial translational zero modes and create topologically distinct classes, analogous to those of topological insulators, with protected zero modes at free boundaries and at interfaces between different topological classes.

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Section: Topological and Total Mode Countmentioning

confidence: 98%

Section: Stiffness Matrix Of 2d Periodic Lattices With Guest Modesmentioning

confidence: 99%

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Phonons and elasticity in critically coordinated lattices

et al. 2015

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“…Moreover, the existence of Weyl nodes also enhances the effect of long-range Coulomb interactions. While the density fluctuations of the

electrons are strongly suppressed in the local-moment regime, it still will be instructive to explore additional nearby phases such as charge-density-wave order ( 36 ); other types of long-range interactions could produce topologically nontrivial Mott insulators ( 37 ). As such, the study of WKSM and related semimetals promises to shed new light on the global phase diagram of quantum critical heavy-fermion systems ( 4 ) and other strongly correlated materials ( 38 ).…”

mentioning

confidence: 99%

Weyl–Kondo semimetal in heavy-fermion systems

Lai

Grefe

Paschen

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

150

116

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SignificanceWhile electronic states with nontrivial topology have traditionally been known in insulators, they have been evidenced in metals during the past 2 years. Such Weyl semimetals show topological protection while conducting electricity both in the bulk and on the surface. An outstanding question is whether topological protection can happen in metals with strong correlations. Here, we report theoretical work on a strongly correlated lattice model to demonstrate the emergence of a Weyl–Kondo semimetal. We identify Weyl fermions in the bulk and Fermi arcs on the surface, both of which are associated with the many-body phenomenon called the Kondo effect. We determine a key signature of this Weyl–Kondo semimetal, which is realized in a recently discovered heavy-fermion compound.

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“…The other indispensable aspect is the interaction effect. There are some theoretical studies with different focuses and approximations to facilitate analytic analyses, including mean-field or renormalization group calculations within or beyond local interactions [22][23][24][25][26] and the formation of spin or charge density waves [27][28][29][30] or Luttinger liquids 31,32 under an external magnetic field. On the other hand, it is well known that an excitonic semimetal-insulator phase transition could occur under the influence of strong enough long-range Coulomb interaction [33][34][35][36][37] .…”

Section: Introductionmentioning

confidence: 99%

Instability and topological robustness of Weyl semimetals against Coulomb interaction

Xue¹,

Zhang²

2017

Phys. Rev. B

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There is a close connection between various new phenomena in Weyl semimetals and the existence of linear band crossings in the single particle description. We show, by a full self-consistent meanfield calculation, how this picture is modified in the presence of long-range Coulomb interactions. The chiral symmetry breaking occurs at strong enough interactions and the internode interband excitonic pairing channel is found to be significant, which determines the gap-opened band profile varying with interaction strength. Remarkably, in the resultant interacting phase, finite band Chern number jumps in the three-dimensional momentum space are retained, indicating the robustness of the topologically nontrivial features.

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Long-range interaction induced phases in Weyl semimetals

Cited by 29 publications

References 35 publications

Phonons and elasticity in critically coordinated lattices

Phonons and elasticity in critically coordinated lattices

Weyl–Kondo semimetal in heavy-fermion systems

Instability and topological robustness of Weyl semimetals against Coulomb interaction

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