Disorder Driven Non-Anderson Transition in a Weyl Semimetal

Abstract

For several decades, it was widely believed that a non-interacting disordered electronic system could only undergo an Anderson metal-insulator transition due to Anderson localization. However, numerous recent theoretical works have predicted the existence of a disorder-driven non-Anderson phase transition that differ from Anderson localization. The frustration lies in the fact that this non-Anderson disorder-driven transition has not yet been experimentally demonstrated in any system. Here, using angle-resolved photoemission spectroscopy, we present a case study of observing the non-Anderson disorder-driven transition by visualizing the electronic structure of the Weyl semimetal NdAlSi on surfaces with varying amounts of disorder. Our observations reveal that strong disorder can effectively suppress all surface states in the Weyl semimetal NdAlSi, including the topological surface Fermi arcs. This disappearance of surface Fermi arcs is associated with the vanishing of the bulk topological invariant, indicating a quantum phase transition from a Weyl semimetal to a diffusive metal. By analyzing the changes in the electronic structure of NdAlSi, as the surface degrades, we provide a physical picture of this non-Anderson transition from a Weyl semimetal to a diffuse metal. These observations provide the first direct experimental evidence of the non-Anderson disorder-driven transition, a discovery long anticipated by theoretical physicists. The finding dispels longstanding suspicions among researchers that non-Anderson transitions exist in real quantum systems.

Figures (4)

• Figure 1: Crystal structure and calculated electronic structure of NdAlSi. (a) The crystal structure of NdAlSi with the space group $I4_{1}md$ (no. 109). (b) The 3D BZ of the original unit cell of NdAlSi, and the corresponding two-dimensional BZ projected on the (001) plane (red lines) in the pristine phase in (a). (c) Surface projected DFT calculated Fermi surface on the terminal surface of Nd atoms cleavage at the Al-Nd layer. (d) The DFT calculated 3D bulk Fermi surface of NdAlSi. (e) The DFT calculated bulk Fermi surface of NdAlSi which integrate all of the BZ along k$_z$ direction. (f) The surface projected DFT calculated band dispersion along $\overline{M}-\overline{\Gamma}-\overline{Y}-\overline{M}-\overline{X}-\overline{\Gamma}$ directions on the terminal surface of Nd atoms cleavage at the Al-Nd layer. (g) Calculated band structures of NdAlSi along high-symmetry directions across the BZ. (h) The DFT calculated bulk band structure of NdAlSi which integrate all of the BZ along k$_z$ direction.
• Figure 2: Surface and bulk electronic structures of NdAlSi. (a) Fermi surface of NdAlSi measured with photon energy of 41 eV under LH polarization in the area 1 (red circle) of sample. (b) Surface projected DFT calculated Fermi surface on the terminal surface of Nd atoms cleavage at the Al-Nd layer with considering two domain structures. (c), (e), (g) and (i) Measured band dispersions along $\overline{Y}-\overline{\Gamma}-\overline{Y}$ [Cut1, (c)], $\overline{M}-\overline{\Gamma}-\overline{M}$ [Cut2, (e)], Cut3 and Cut4 directions in the area 1 of sample under LH polarization. Cut3 and Cut4 go right through the Weyl points. (d), (f), (h) and (j) The corresponding surface projected DFT calculations of the bands along $\overline{Y}-\overline{\Gamma}-\overline{Y}$ (d), $\overline{M}-\overline{\Gamma}-\overline{M}$ (f), Cut3 (h) and Cut4 (j) directions, considering the two domain structures. (k) Fermi surface of NdAlSi measured with photon energy of 41 eV under LH polarization in the area 2 (orange circle) of sample. According to the previous report, bulk state measurements with photon energy of 41 eV corresponds to the k$_z$$\sim$ 0 $\pi$/c planeCLi_NC2023_OTjernberg. (l) The DFT calculated bulk Fermi surface at the k$_z$= 0 $\pi/c$ plane which integrate 0$\pm$0.1 $\pi/c$ of BZ along k$_z$ direction. (m), (o), (q) and (s) The similar measurements as (c), (e), (g) and (i) but measured in the area 2 of sample. (n), (p), (r) and (t) The DFT calculated bulk band structures along $Y-\Gamma-Y$ (n), $M-\Gamma-M$ (p), Cut3 (r) and Cut4 (t) directions. The trivial surface states (SSs) are marked by black arrows, and the SFAs are marked by red arrows which was well studied in Ref.CLi_NC2023_OTjernberg. The green and red dots in (r) and (t) mark the Weyl points (WPs), while the red dots representing nodes with chiralities +1 and green dots representing -1.
• Figure 3: The STM measurements and evolution of the electronic structure with time. (a) STM images of NdAlSi measured at 4.7 K on Nd atom terminated surface cleavage at the Al-Nd layer. (a) is the overview image. (b) and (c) are the magnified topography images measured at different positions. Scan conditions: (a) 1 V, 0.1 nA, (b) 0.5 V, 0.5 nA, (c) 0.01V, 0.1 nA. (d-g) Fermi surface of NdAlSi measured with photon energy of 41 eV under LH (d,f,g) and NC (e) polarizations on flat area of the fresh sample (d), the sample 3 hours after cleavage (e), the sample 10 hours after cleavage (f). (g-i) The corresponding band dispersions along $\overline{Y}-\overline{\Gamma}-\overline{Y}$ [Cut1, green line in (d)] directions. (j-l) The corresponding bands along Cut2 [red line in (d)] directions. The corresponding DFT bulk calculations are overlaid on (i) and (l). The red arrows mark the SFA. (m) Band dispersions extracted from (j-l) by fitting the energy dependent MDCs. The corresponding fitting band dispersions are also appended to (j-l). (n) The time dependent Fermi velocity of SFAs which obtained by linear fitting the band dispersions in (m). (o) The normalized integrated EDC of bands in (j-l) at energy range of -0.9 eV to -0.7 eV.
• Figure 4: Weyl semimetal-diffusive metal quantum phase transition. (a-d) Photon energy dependent Fermi surface measured on fresh surface of flat sample with photon energies of 30 eV (a), 41 eV (b), 49 eV (c) and 53 eV (d). (e-h) Photon energy dependent band structures measured on fresh surface of flat sample with photon energies of 30 eV (e), 41 eV (f), 49 eV (g) and 53 eV (h) along Cut1 in (a). The red arrows mark the SFAs. (i-p) The similar measurements as (a-k) but measured on the surface 10 hours after the sample cleaved. (q) Schematic diagram of SFA suppressed by disorder. (r) Schematic phase diagram of the Weyl semimetal as the increase of disorder. The red dashed lines mark the quantum critical point (QCP).