Two-carrier analyses of the transport properties of black phosphorus under pressure

Abstract

We report on the electronic transport properties of black phosphorus and analyze them using a two-carrier model in a wide range of pressure up to 2.5 GPa. In semiconducting state at 0.29 GPa, the remarkable non-linear behavior in the Hall resistance is reasonably reproduced by assuming the coexistence of two kinds of hole with different densities and mobilities. On the other hand, twocarrier analyses of the magnetotransport properties above 1.01 GPa suggest the coexistence of high mobility electron and hole carriers that have almost the same densities, i.e., nearly compensated semimetallic nature of black phosphorus. In the semimetallic state, analyses of both the twocarrier model and quantum oscillations indicate a systematic increase in the carrier densities as pressure increases. An observed sign inversion of Hall resistivity at low magnetic fields suggests the existence of high mobility electrons (∼10 5 cm 2 V −1 s −1 ) that is roughly ten times larger than that of holes, in the semimetallic black phosphorus. We conclude that the extremely large positive magnetoresistance that has been observed in semimetallic state cannot be reproduced by a conventional two-carrier model.

Pressure-induced phase transitions and superconductivity in a black phosphorus single crystal

“…In zero field, the application of 1 GPa pressure closes up the direct band gap and results in a metallic behavior, as has also been reported previously (24). The anomalous hump around 220 K has been attributed to reduced thermal excitation of carriers during cooling at T > 220 K (21). This argument is not fully supported by the result of thermoelectric power measurement under the same pressure, in which no anomaly can be detected near 220 K (see the results in SI Appendix, Fig.…”

“…A negative magnetoresistance (MR) for B // I, consistent with the chiral anomaly characteristic of a Weyl semimetal, has indeed been reported in a high-pressure transport study (7). The Weyl semimetal phase of BP shows no sign of superconductivity down to 45 mK (21). Most previous studies were performed in the A17 phase Significance A high-pressure study of a black phosphorus crystal establishes a rich phase diagram, including Weyl semimetal and superconducting states, Lifshitz-type semiconductor-semimetal transitions, and two structural phase transitions.…”

“…and report an extremely large MR effect and quantum Shubnikovde Haas (SdH) oscillations under high pressure (7,10,16,(19)(20)(21)(22)(23)(24)(25)(26). Superconductivity in BP occurring right after the A7 phase is induced at P ≥ 5 GPa (27)(28)(29).…”

Temperature-dependent carrier transport: Low-complexity model for the infrared optical and radiative properties of nickel

“…7 Since that time, the concept of a multi-carrier model has been leveraged in a number of contexts to accurately capture the complex optical and radiative responses for a wide range of media. 4,[26][27][28] One notable realization of the two-carrier model that bears relevance to the present study is that described by Nagel and Schnatterly for modeling the effects of highly disordered regimes of electron dynamics. 8 In that study, the authors describe a single effective carrier type having a time constant that becomes modified in regions of high disorder.…”

“…These include data obtained at helium temperatures (T = 4 K), data that exhaust the full range of mid-infrared wavelengths, and modern nonlinear programming techniques that make it possible to ensure the optimality of our fits (inclusive of any desired physical constraints). Enforcing the constraint implied by (28) and then once more optimizing the independent fits yields the temperature-conductivity pairings at each experimental temperature. The determination of these pairings represents the completion of step (i) in the model application procedure.…”