Metallicity-driven polar transitions in topological epilayers

Abstract

Polar metals, materials that exhibit both electric polarization and high conductivity, can also host topological phases. Because free carriers strongly suppress distortive polar order and change the Fermi level, controlling charge dynamics is crucial for simultaneously tuning ferroelectric and topological phases in the same material. Here, we explore the experimental conditions that enable access to these phases in bismuth-doped Pb$_{1-x}$Sn$_x$Te epilayers. For samples in the topological phase at $x = 0.5$, we use terahertz time-domain spectroscopy to evaluate their complex permittivity as a function of temperature. We observe a non-monotonic variation in carrier concentration with bismuth doping, indicating a change in carrier type. By tracking the transverse optical phonon mode, we identify a ferroelectric phase transition when distortive polar order emerges below a critical temperature that depends on carrier concentration. We show that bismuth doping controls the metallicity-dependent order parameters in the softening and hardening phases. Our work demonstrates a tunable platform for engineering exotic states of matter that integrate metallicity, ferroelectricity and topology.

Figures (7)

• Figure 1: THz transmittance of Pb$_{0.5}$Sn$_{0.5}$Te epilayers. (a) Schematic diagram of the THz-TDS measurements, depicting the transmission of a THz beam through a sample (film-coated substrate). (b) Distorted cubic unit cell structure of the Bi-doped Pb$_{0.5}$Sn$_{0.5}$Te in the polar phase. (c) THz transmittance at 300 for the films with 0 (dark blue curve), 0.06 (light blue curve), and 0.15 (red curve) Bi-doping levels.
• Figure 2: Complex permittivity spectra. (a, c, e) Real and (b, d, f) imaginary parts of the frequency-dependent permittivity spectra of the Pb$_{0.5}$Sn$_{0.5}$Te epilayers, extracted from the THz-TDS measurements at various temperatures, ranging from 300 (dark red lines) to 10 (dark blue lines) in approximately 10 steps. The rows in the grid of the figure panels corresponds to the (a, b) undoped, (c, d) 0.06 Bi-doped, and (e, f) 0.15 Bi-doped samples.
• Figure 3: Permittivity fits. (a) Real and (b) imaginary parts of the complex permittivity data for the 0.06 Bi-doped film at 10 (blue circles), 137 (green circles), and 287 (red circles). The black lines represent the optimal fits using equation \ref{['eq:drude-lorentz']}.
• Figure 4: Carrier dynamics. Temperature dependence of the (a) squared plasma frequency and (b) inverse of the carrier collision rate for the undoped (dark blue circles), 0.06 Bi-doped (light blue circles), and 0.15 Bi-doped (red circles) films, calculated from the optimal fit parameters of equation \ref{['eq:drude-lorentz']} to the experimental permittivity data. (c) Ratio of the carrier concentration to its effective mass at a fixed temperature of 15, plotted as a function of the Bi-doping level. Error bars are smaller than the data point symbols. Blue and red circles represent the $p$- and $n$-type conductivity regimes, respectively. The shaded curve indicates the observed trend.
• Figure 5: Lattice dynamics. (a--g) Temperature dependence of the TO phonon frequency (white circles, left axes) and static dielectric constant (red squares, right axes) for each investigated Bi-doping level, obtained from the optimal fit parameters of equation \ref{['eq:drude-lorentz']} to the experimental permittivity data. Background maps show the imaginary part of the permittivity as a function of temperature and frequency. (h) Carrier concentration dependence of the critical temperature (squares, left axis), and minimum value attained for the TO phonon frequency (green circles, right axis). Blue and red squares represent the $p$- and $n$-type conductivity regimes, respectively. The shaded curves indicate the observed trends.