We report a quantum magnetotransport signature of a change in Fermi surface topology in the Rashba semiconductor BiTeI with systematic tuning of the Fermi level $E_F$. Beyond the quantum limit, we observe a marked increase/decrease in electrical resi
stivity when $E_F$ is above/below the Dirac node that we show originates from the Fermi surface topology. This effect represents a measurement of the electron distribution on the low-index ($n=0,-1$) Landau levels and is uniquely enabled by the finite bulk $k_z$ dispersion along the $c$-axis and strong Rashba spin-orbit coupling strength of the system. The Dirac node is independently identified by Shubnikov-de Haas oscillations as a vanishing Fermi surface cross section at $k_z=0$. Additionally we find that the violation of Kohlers rule allows a distinct insight into the temperature evolution of the observed quantum magnetoresistance effects.
Optical excitations of BiTeI with large Rashba spin splitting have been studied in an external magnetic field ($B$) applied parallel to the polar axis. A sequence of transitions between the Landau levels (LLs), whose energies are in proportion to $sq
rt{B}$ were observed, being characteristic of massless Dirac electrons. The large separation energy between the LLs makes it possible to detect the strongest cyclotron resonance even at room temperature in moderate fields. Unlike in 2D Dirac systems, the magnetic field induced rearrangement of the conductivity spectrum is directly observed.
We have investigated the behavior of the resistance of graphene at the $n=0$ Landau Level in an intense magnetic field $H$. Employing a low-dissipation technique (with power $P<$3 fW), we find that, at low temperature $T$, the resistance at the Dirac
point $R_0(H)$ undergoes a 1000-fold increase from $sim$10 k$Omega$ to 40 M$Omega$ within a narrow interval of field. The abruptness of the increase suggests that a transition to an insulating, ordered state occurs at the critical field $H_c$. Results from 5 samples show that $H_c$ depends systematically on the disorder, as measured by the offset gate voltage $V_0$. Samples with small $V_0$ display a smaller critical field $H_c$. Empirically, the steep increase in $R_0$ fits acccurately a Kosterlitz-Thouless-type correlation length over 3 decades. The curves of $R_0$ vs. $T$ at fixed $H$ approach the thermal-activation form with a gap $Deltasim$15 K as $Hto H_c^{-}$, consistent with a field-induced insulating state.
