Fig. 1: Topological-phase-transition-induced forbidden backscattering and band properties of β-Ag₂Se.

a The two last Landau bands (LLBs) of typical strong topological insulator (TI) go across a phase transition driven by external magnetic field. Only two states, denoted as black dots \(\left\vert \pm {k}_{x}\right\rangle\), are involved in this 1D channel. b \(\left\vert \pm {k}_{x}\right\rangle\) are orthogonal to each other when mass term m is zero, which causes the spinor-prohibited backscattering. c As a result, a dip appears on the longitudinal magneto-resistance (MR) at critical magnetic field (B_c). d A photo of single crystalline β-Ag₂Se. e The orthorhombic crystal structure of β-Ag₂Se. f High symmetric k point in a unit cell. g Band calculations of β-Ag₂Se based on PBE and HSE approxiamations. h Angle-dependent Shubnikov-de Haas (SdH) oscillations in ab (θ) and ac (ϕ) planes. i The extracted frequencies of SdH along the two tilted angles, θ and ϕ, respectively. Inset shows the mapped Fermi surface with a Fermi level determined by experimental carrier concentration (n). The slight mismatch of frequency around zero angle was probably caused by sample bending, in the different rounds of measurement.