Observation and control of maximal Chern numbers in a chiral topological semimetal

Abstract

<jats:p>Topological semimetals feature protected nodal band degeneracies characterized by a topological invariant known as the Chern number (<jats:italic>C</jats:italic>). Nodal band crossings with linear dispersion are expected to have at most <jats:inline-formula><m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"><m:mrow><m:mrow><m:mo>|</m:mo><m:mi>C</m:mi><m:mo>|</m:mo></m:mrow><m:mo>=</m:mo><m:mn>4</m:mn></m:mrow></m:math></jats:inline-formula>, which sets an upper limit to the magnitude of many topological phenomena in these materials. Here, we show that the chiral crystal palladium gallium (PdGa) displays multifold band crossings, which are connected by exactly four surface Fermi arcs, thus proving that they carry the maximal Chern number magnitude of 4. By comparing two enantiomers, we observe a reversal of their Fermi-arc velocities, which demonstrates that the handedness of chiral crystals can be used to control the sign of their Chern numbers.</jats:p>

Electronic structure studies of FeSi: A chiral topological system

“…However, qualitatively, our ARPES data are consistent with some of the earlier ARPES reports [54,55]. Next, coming to the main point of this paper, recent ARPES and theoretical reports on CoSi and RhSi showed topological surface Fermi arcs spanned over a large area of two-dimensional (2D) Brillouin zone [36,37,39,[40][41][42][43][44]90]. Moreover, they could record manyfold bulk Weyl fermions at and R high symmetry points.…”

Handedness-dependent quasiparticle interference in the two enantiomers of the topological chiral semimetal PdGa

“…These crossings act as a source (red dot) or a sink (blue dot) of Berry curvature. They correspond to a Chern number of magnitude 4, i.e., the maximum Chern number achievable at a multifold node crossing 22 , and reverse sign under a mirror operation 23 . Note that, contrary to non-chiral topological semimetals, these crossings are well-separated in energy.…”

“…This is particularly important in the present case. Photoemission studies have shown that Fermi arcs are overlapping with topologically trivial bulk bands for occupied states, complicating their identification 23 . On the other hand, theoretical calculations predict them to become strongly decoupled from bulk states at positive energies, a scenario favoring their experimental detection (see Supplementary Fig.…”

Optical method to detect the relationship between chirality of reciprocal space chiral multifold fermions and real space chiral crystals

“…In addition to the wide separation between opposite topological charges in the momentum space, the absence of mirror symmetry also leads to their large separation in energy space, providing an ideal platform for the study of quantized circular photogalvanic effects (CPGE) [3,5,7,8]. Following their theoretical predictions, long Fermi arcs, high-order degenerated band crossings, and topological CPGE were soon observed in the expected chiral crystals via angle-resolved photoemission spectroscopty (ARPES) [9][10][11][12][13], scanning tunneling microscopy (STM) [14], and optical measurements [15][16][17].…”

“…Recently, based on ARPES and STM measurements, a sign change was detected in the Fermi velocity of surface Fermi arcs in semimetals possessing chiral multifold fermions and crystals of opposite chiralities. This implied a deep relationship between chiral lattices in the real space and chiral fermions in the momentum space [13,14,18]. This relationship offers a degree of freedom to modulate chiral fermions and their corresponding physical properties.…”