Topological Lifshitz transitions and Fermi arc manipulation in Weyl semimetal NbAs

Surface Fermi arcs (SFAs), the unique open Fermi-surfaces (FSs) discovered recently in topological Weyl semimetals (TWSs), are unlike closed FSs in conventional materials and can give rise to many exotic phenomena, such as anomalous SFA-mediated quantum oscillations, chiral magnetic effects, three-dimensional quantum Hall effect, non-local voltage generation and anomalous electromagnetic wave transmission. Here, by using in-situ surface decoration, we demonstrate successful manipulation of the shape, size and even the connections of SFAs in a model TWS, NbAs, and observe their evolution that leads to an unusual topological Lifshitz transition not caused by the change of the carrier concentration. The phase transition teleports the SFAs between different parts of the surface Brillouin zone. Despite the dramatic surface evolution, the existence of SFAs is robust and each SFA remains tied to a pair of Weyl points of opposite chirality, as dictated by the bulk topology.

projected on Nb dz2, dx2-y2, dxy, dyz, dxz, and As px, py, pz orbitals of the pristine and K-dosed NbAs. Black curves are bulk states, dispersions marked by red circles are projected surface states with different orbital contributions (bigger red circles represent stronger contribution). While the TSS of the pristine surface harbours a complicated multi-orbital contributions from both As and Nb, the TSS of K-decorated is dominated by Nb d z 2 orbital. Note that although surface states are highly suppressed to enhance the bulk states in the photoemission intensity, some surface states remain to be weak features (not captured by calculations of bulk states), as the probe depth in our measurements is around 1.0 nm. With 158 eV and 144 eV photons, we can reach W2 and W1 Weyl points, respectively. b, Schematic illustration of the measurement plane in 3D bulk BZ when using 158 eV photons. c-d, bulk band dispersion across W2 Weyl points: broadband dispersion and a zoomed-in plot across the Weyl points along ky direction. Calculations of bulk states (red curves) well reproduce measured bulk states. e-g, same as b-d, but across W1 Weyl points using 144eV photons. Figure 12 | Details of K dosing. a, Schematic of K dosing by a commercial Saes K dispenser. b, Detailed dosing parameters and calculated amount of accumulated K atoms on the sample surface. c, Performance curves of K dispenser. Black curves (7.5A and 6.5A) are directly reproduced from the technical book of the commercial SAES K-dispenser (Alkali Metals Dispensers -SAES Getters) 5 , and curves with colors are extrapolated performances curves with different currents. In (ii), the K yield of each dose is marked.

Determine the surface states of pristine and surface decorated NbAs
ARPES is an experimental method that can directly visualize the electronic structures of solids based on the photoelectric effect, where an electron inside the sample under investigation can absorb an incident photon (whose energy is larger than the work function) and then escape the sample as a photoelectron. The kinetic energy and momentum of the photoelectron are then measured to give the information of the initial electronic band structures of the sample 1,2 .
In ARPES measurements, the in-plane electron momentum (k || , parallel to sample surface) can be naturally determined by the momentum conservation of photoelectrons; while determining the out-of-plane momentum component (k z ) and band dispersion along k z requires a series of ARPES measurements performed at different photon energies 1,2 .
Based on the free-electron final state approximation with a potential parameter V 0 (the inner potential) describing the energy difference of photoelectrons before and after leaving the crystal surface, we can derive the k z as: where θ is the emission angle and E k is the kinetic energy of the emitted electron, which satisfies: where hυ is the photon energy, w is the work function of the sample and E B is the electron binding energy.
Therefore, photon-energy dependent ARPES measurements can probe the electronic structure with different k z values, thus can be used to discriminate the surface electronic states (which do not disperse along k z direction) from the bulk ones (which usually show dispersion along k z direction) 1,2 .
In this work, the ARPES measurements were performed at beamline I05 of the Diamond Light Source (DLS) by Scienta R4000 analyzers. The angle resolution was ≤ 0.2° and the overall energy resolutions was ≤ 15 meV. The measurement geometry and the light polarization In the main text, we have presented the general band structure of pristine NbAs. The comparison with our ab initio calculations (Fig. 3) gives a nice agreement which reveals that the bowtie-and spoon-like features are of surface origin and confirms the existence of surface Fermi arcs. To further verify this experimentally, we carried out systematic photon-energy dependent measurements to study the k z variation of the band structure. In the main text, we have presented the general band structure of K-decorated NbAs. The comparison with our ab initio calculations (Fig. 3) gives a nice agreement which reveals that

NbAs surfaces
In the main text, we have shown the calculation results of pristine and K-decorated NbAs surface, both of which exhibit excellent agreements with ARPES data. Here, we present more contributions, which could highly facilitate the investigations on the band structure evolution across the K-dose induced transition. For the pristine, the TSSs is mainly contributed by As p x , p y , and Nb d x 2 -y 2 (and some few contributions from other orbitals like d yz ). By contrast, the TSSs of K-decorated is simply dominated by Nb d z 2 orbital. Moreover, bands stemming from each of these orbitals, e.g. Nb d z 2 , changes dramatically which cannot be explained simply with rigid-band shift.
In our ab initio calculation, K-decorated NbAs surface is treated as the cleaved NbAs surface covered with a monolayer K atoms (see Supplementary Figure 9a Therefore, by controlling the dispenser current and the evaporation time, we were able to control the dosage of K atoms, and the detailed evaporation parameters used in our experiments are presented in Supplementary Figure 12b. The amount of K atoms docked on the sample surface at each dose can be estimated as the following: the K flux (F, per unit area) near the sample is approximately given by F = X*Y M * N A ÷ (2πR 2 ), where X, Y, M, N A , and R are the active length of the dispenser (the length of the K filament), K (mass) yield of unit length from the dispenser (see Supplementary Figure   12), molar mass of K atoms, Avogadro's constant, and the distance between the dispenser and the sample, respectively. Finally, we can get the dosage (D) in the unit of ML as: D = F d *k, where d is the number density for 1-ML of K coverage according to the calculation model (see Supplementary Figure 9), and k is the sticking coefficient of K atoms.