Experimental observation of bulk nodal lines and electronic surface states in ZrB2

Abstract

Topological nodal-line semimetals are characterized by the line-contact bulk band crossings and the topological surface states. Breaking certain protecting symmetry turns this system into a Dirac semimetal or Weyl semimetal that hosts zero-dimensional isolated nodal points. Recent advances in band theory predicted a topological nodal-line semimetal state possessing a new type of nodal line in AlB 2 -type diborides. Here, we report an experimental realization of nodal-line fermions and associated surface states near the Fermi energy in ZrB 2 by angleresolved photoemission spectroscopy combined with first-principles calculations. The Dirac nodal lines in ZrB 2 wind into two groups of nodal rings, which are linked together along the Γ-K direction. We further observe a distinct surface state connecting to each nodal line, indicative of the nontrivial topological nature of the bulk nodal lines. Therefore, our results provide convincing experimental evidence of the nodal-line semimetal states in ZrB 2 both in the bulk and on the surface, suggesting ZrB 2 as a remarkable platform for discovering unique phenomena induced by nodal-line fermions.

Disorder-Driven Multifractality Transition in Weyl Nodal Loops

“…We will argue that this crossing point should correspond to W c . W=1.75, L∈ [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] W=1.75, L∈ [16][17][18][19][20][21][22][23][24][25][26] W=2.25, L∈ [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] W=2.25, L∈ [16][17][18][19][20][21][22][23][24][25][26] W=2.5, L∈…”

“…When m(β) = 0, W max (L) becomes L-independent for a given range of sizes. If we consider for instance L ∈ Fit to W max (β) =m(β)/L +c(β) L∈ [14,20] L∈ [16,22] L∈ [18,24] L∈ [20,26] The method for finding β c (L) is as follows: β c is defined through the condition m(β c ) = 0. The value of β c for the set {L i } of 4 consecutive sizes is attributed to L = {L i } , that is, the average size of the corresponding set.…”

“…The results are shown in Fig. S13(a) for sizes L ∈ [16,26] and show that although our ability to resolve the wave function increases with L 2 , it is still bounded by the value of R L . As shown in the main text, in the MF phase, we have Γ(W, L) = f (W )/L and f (W ) increases with the disorder strength.…”

“…Among these, are the Weyl nodal loop (WNL) semimetals, for which the valence and conduction bands linearly touch along one-dimensional (1D) loops in the three-dimensional (3D) momentum space [5]. Their recent theoretical prediction [6][7][8] and experimental discovery [9, 10] triggered intense experimental [11][12][13][14][15][16][17][18][19][20] and theoretical interest [21][22][23][24][25][26][27][28][29][30][31][32][33].A manifestation of WNL's topological nature is the presence of surface ("drumhead") edge states [7,24,[34][35][36] on surfaces parallel to the loop plane, which are induced by chiral symmetry. Since the Fermi surface is reduced to a 1D nodal line, the density of states (DOS), ρ(E), vanishes linearly for low energies, i.e.…”

Dirac nodal lines and flat-band surface state in the functional oxide RuO2

“…Dirac nodal lines in RuO 2 .-The significance of non-symmorphicity in RuO 2 was recently discussed within the framework of topology and relativistic Dirac physics 13 . Symmetry considerations in conjunction with DFT predicted a network of two types of Dirac nodal lines (DNL) [14][15][16][17][18][19][20][21][22][23] , where the valence-and conduction bands touch close to the Fermi level along continuous lines in momentum space: (A) First, time reversaland inversion symmetry in unison with a mirror symmetry protect a band crossing within the (110) and (110) planes. This produces a network of 4-fold degenerate (2 × spin and 2 × orbital) and topologically nontrivial DNLs (DNL1) 13 , outlined by blue lines in the Brillouin zone (BZ) of Fig.…”