Link between T-Linear Resistivity and Quantum Criticality in Ambipolar Black Phosphorus.

The interplay between strong Coulomb interactions and kinetic energy leads to intricate many-body competing ground states owing to quantum fluctuations in 2D electron and hole gases. However, the simultaneous observation of quantum critical phenomena in both electron and hole regimes remains elusive. Here, we utilize anisotropic black phosphorus (BP) to show density-driven metal-insulator transition with a critical conductance ∼e2/h which highlights the significant role of quantum fluctuations in both hole and electron regimes. We observe a T-linear resistivity from the deep metallic phase to the metal-insulator boundary at moderate temperatures, while it turns to Fermi liquid behavior in the deep metallic phase at low temperatures in both regimes. An analysis of the resistivity suggests that disorder-dominated transport leads to T-linear behavior in the hole regime, while in the electron regime, the T-linear resistivity results from strong Coulomb interactions, suggestive of strange-metal behavior. Successful scaling collapse of the resistivity in the T-linear region demonstrates the link between quantum criticality and the T-linear resistivity in both regimes. Our study provides compelling evidence that ambipolar BP could serve as an exciting testbed for investigating exotic states and quantum critical phenomena in hole and electron regimes of 2D semiconductors.

Percolation-Based Metal-Insulator Transition in Black Phosphorus Field Effect Transistors.

The existence of a novel phenomenon, such as the metal-insulator transition (MIT) in two-dimensional (2D) systems, affords emerging functional properties that provide new aspects for future electronics and optoelectronics. Here, we report the observation of the MIT in black phosphorus field effect transistors by tuning the carrier density (n) controlled by back-gate bias. We find that the conductivity follows an n dependence as σ(n) ∝ nα with α ∼ 1, which indicates the presence of screened Coulomb impurity scattering at high carrier densities in the temperature range of 10-300 K. As n decreases, the screened Coulomb impurity scattering breaks down, developing strong charge density inhomogeneity leading to a percolation-based transition at the critical carrier density (nC). At low carrier densities (n < nC), the system is in the insulating regime, which is expressed by Mott variable range hopping that demonstrates the role of disorder in the system. In addition, the extracted average values of critical exponent δ are ∼1.29 ± 0.01 and ∼1.14 ± 0.01 for devices A and B, respectively, consistent with the 2D percolation exponent of 4/3, confirming the 2D percolation-based MIT in BP devices. Our findings strongly suggest that the 2D MIT observed in BP is a classical percolation-based transition caused by charge inhomogeneity induced by screened Coulomb charge impurity scattering around a transition point controlled by n through back-gate bias.