Quantum transport evidence of isolated topological nodal-line fermions

Abstract

Anomalous transport responses, dictated by the nontrivial band topology, are the key for application of topological materials to advanced electronics and spintronics. One promising platform is topological nodal-line semimetals due to their rich topology and exotic physical properties. However, their transport signatures have often been masked by the complexity in band crossings or the coexisting topologically trivial states. Here we show that, in slightly hole-doped SrAs₃, the single-loop nodal-line states are well-isolated from the trivial states and entirely determine the transport responses. The characteristic torus-shaped Fermi surface and the associated encircling Berry flux of nodal-line fermions are clearly manifested by quantum oscillations of the magnetotransport properties and the quantum interference effect resulting in the two-dimensional behaviors of weak antilocalization. These unique quantum transport signatures make the isolated nodal-line fermions in SrAs₃ desirable for novel devices based on their topological charge and spin transport.

Fig. 1. Crystal and electronic structures of a nodal-line semimetal SrAs₃.

a The crystal structure of SrAs_3. b The schematic band crossing for asymmetric nodal-line states with a tilted energy dispersion (E_tilt), a finite spin–orbit-coupling gap (Δ_SOC) and a band overlap energy (Δ). The corresponding Fermi surfaces at different Fermi levels (E_F) are shown in the right, a crescent-type for E_F,1 and a torus-type for E_F,2. c The smoke-ring-type pseudospin texture imprinted on the Fermi surface. d The Brillouin zone of SrAs₃ with a single nodal ring (red circle) centered at the Y point. e The ARPES spectra of SrAs₃ taken at the Y point along k_x with the photon energy of 99 eV. The overlaid red and blue lines indicate the conduction and valence bands, respectively. f The temperature dependence of the in-plane resistivity (ρ). The inset shows the carrier densities (n) for electron (e) and hole (h). g The magnetic field-dependent Hall resistivity (ρ_xy) of SrAs₃ at different temperatures. h A series of ARPES spectra taken along k_x at different photon energies (85-104 eV) corresponding to k_y marked on top of each panel. i The nodal-ring of the crossing points between the conduction and valence bands in ARPES data, with dashed red circle as a guide to the eye.

Fig. 2. Shubnikov-de Hass oscillations of SrAs₃.

a, b Magnetoresistance (MR) Δρ(H)/ρ(0) of SrAs₃ with different magnetic field orientations in the (k_y,k_z) plane (a, S1) and in the (k_x,k_y) plane (b, S2). The second derivative of ρ(H) with respect to 1/H at H∥k_z is also shown in a. The overlaid dashed gray curve corresponds to the coexisting SdH oscillations with a lower frequency. The black arrows indicate peaks and deeps of the higher-frequency oscillations. The polar (θ) and azimuthal (ϕ) angles are defined with respect to the torus-shaped Fermi surface as shown in the insets. c SdH oscillations (Δρ_osc./ρ(0)) at various magnetic field orientations in the planes of (k_x,k_y), (k_y,k_z) and (k_x,k_z) for S1. The inset shows torus-shaped Fermi surface of SrAs₃ with the poloidal orbit (α) and the inner (β) and outer (δ) toroidal orbits. d, e, f Fast Fourier transform (FFT) amplitudes for α orbit (d), and β orbit (d) and δ orbit (f), taken at various temperatures for H∥k_y (d) and H∥k_z (e, f). The insets show the temperature-dependent FFT amplitudes, together with the fits (red lines) to the Lifshitz–Kosevich equation. In e, the FFT amplitude of the δ orbit, F > 100 T, is magnified for comparison.

Fig. 3. Toroidal Fermi surface and Berry phase evolution of SrAs₃.

a Angle-dependent SdH frequency (F) and the phase offset of SdH oscillation (ϕ_SdH) for two samples S1 (black) and S2 (red). The spin-splitting phase (ϕ_s) and the characteristic phase (ϕ₀) are also shown in the lower panels. The calculated F using the model Hamiltonian is overlaid with red lines. The corresponding extremal orbits on the torus-shaped Fermi surface are also presented for selected field orientations in the inset. b Torus-shaped Fermi surface of SrAs₃ with the poloidal orbit (α) and the inner (β) and outer (δ) toroidal orbits. c Poloidal cross-section of the Fermi surface (α) with pseudospin textures indicated by the arrows. d–g Landau fan diagram for various field orientations with different polar (θ) angles (d, f) and azimuthal (ϕ) angles (e, g) for S1. The maxima (solid circles) and minima (open circles) of Δρ(H)/ρ(0) are assigned with integer and half-integer of the Landau index. h, i The second derivative of ρ(H), − d²ρ/dH², as a function of the nomalized F/H for various magnetic field orientations with different polar (θ) (h) and azimuthal (ϕ) angles (i) for S2. The spin-splitting peaks of SdH oscillations are indicated by triangle symbols. The shaded dashed lines correspond to the spin-split Landau levels, indicated by the color-coded integer index and the + and – symbols.

Fig. 4. Weak antilocalization of nodal-line fermions in SrAs₃.

a Back-scattering processes of nodal-line fermions on the poloidal plane of the torus-shaped Fermi surface in the momentum space (upper panel). The π Berry flux (yellow line) along the nodal-loop leads to weak antilocalization (WAL). The corresponding diffusion of nodal-fermions in the real space is two-dimensional (lower panel), which significantly enhances the quantum interference effect. b The low-field transverse magnetoconductivity Δσ(H)/σ(0), taken at T = 2 K and H⊥J, from eleven SrAs₃ crystals with different hole carrier densities (n_h) and the ratio (K₀/κ) between the radii of the nodal-loop (K₀) and the poloidal orbit (κ). c The transverse magnetoconductivity Δσ(H) for S1 together with the fits to the 2D WAL (red line) and 3D WAL (blue line) models. d Temperature-dependent phase coherence length l_ϕ for S1, following T⁻¹ dependence (blue dashed line) at high temperatures. The fit to the 2D WAL model is also shown (green solid line). e The excess conductivity Δσ_WAL as a function of σ₀ for various topological semimetals. The inset shows the Δσ_WAL of SrAs₃ crystals taken at 2 K with variation of the ratio K₀/κ.