Thermoelectric response across the semiconductor-semimetal transition in black phosphorus

TL;DR

This study investigates how the Seebeck coefficient in black phosphorus evolves across the transition from semiconductor to semimetal under pressure, revealing distinct behaviors in different conduction regimes and the role of scattering mechanisms.

Contribution

It provides a systematic analysis of thermoelectric response during the semiconductor-semimetal transition in black phosphorus, highlighting the intrinsic response and scattering effects.

Findings

Seebeck coefficient behavior aligns with theory in intrinsic and saturation regimes.

In VRH regime, theories do not fully explain the Seebeck response.

Carrier scattering mechanisms influence the sign and magnitude of the Seebeck coefficient.

Abstract

In spite of intensive studies on thermoelectricity in metals, little is known about thermoelectric response in semiconductors at low temperature. An even more fascinating and unanswered question is what happens to the Seebeck coefficient when the semiconductor turns to a metal. By precisely tuning the ground state of black phosphorus with pressure from the semiconducting to semimetallic state, we track a systematic evolution of the Seebeck coefficient. Thanks to a manifest correlation between the Seebeck coefficient and resistivity, the Seebeck response in each conduction regime, i.e., intrinsic, saturation, extrinsic, and variable range hopping (VRH) regimes, is identified. In the former two regimes, the Seebeck coefficient behaves in accordance with the present theories, whereas in the later two regimes available theories do not give a satisfactory account for its response. However, by eliminating the extrinsic sample dependence in the resistivity $\rho$ and Seebeck coefficient $S$, the Peltier conductivity $\alpha=S/\rho$ allows to unveil the intrinsic thermoelectric response, revealing vanishing fate for $\alpha$ in the VRH regime. The emerged ionized impurity scattering on entry to the semimetallic state is easily surpassed by electron-electron scattering due to squeezing of screening length accompanied by an increase of carrier density with pressure. In the low temperature limit, a small number of carriers enhances a prefactor of $T$-linear Seebeck coefficient as large as what is observed in prototypical semimetals. A crucial but largely ignored role of carrier scattering in determining the magnitude and sign of the Seebeck coefficient is indicated by the observation that a sign reversal of the $T$-linear prefactor is concomitant with a change in dominant scattering mechanism for carriers.