Mechanisms of Pyroelectricity in Three- and Two-Dimensional Materials

Pyroelectricity is a very promising phenomenon in three- and two-dimensional materials, but first-principles calculations have not so far been used to elucidate the underlying mechanisms. Here we report density-functional theory (DFT) calculations based on the Born-Szigeti theory of pyroelectricity, by combining fundamental thermodynamics and the modern theory of polarization. We find satisfactory agreement with experimental data in the case of bulk benchmark materials, showing that the so-called electron-phonon renormalization, whose contribution has been traditionally viewed as negligible, is important. We predict out-of-plane pyroelectricity in the recently synthesized Janus MoSSe monolayer and in-plane pyroelectricity in the group-IV monochalcogenide GeS monolayer. It is notable that the so-called secondary pyroelectricity is found to be dominant in GeS monolayer. The present work opens a theoretical route to study the pyroelectric effect using DFT and provides a valuable tool in the search for new candidates for pyroelectric applications.

Figure 1

Calculated pyroelectric coefficients of ZnO and GaN. Experimental data for ZnO and GaN are from Ref. [68] and Ref. [69], respectively.

Figure 2

Primary pyroelectric effect in ZnO. Polarizations are evaluated with atoms statically displaced along the normal mode $Q$ over a range of “frozen-in” amplitudes. Arrows attached on each atom indicate the eigenvectors of the phonon mode. Left panel: first-order $p_1^{(1)}$. Color indicates the temperature corresponding to the mean atomic thermal displacement. The inset shows the calculated internal thermal expansion $u(T)$, compared with results obtained by one-particle potential (OPP). Right panel: second-order $p_1^{(2)}$. Color indicates the temperature corresponding to the amplitude of thermal vibrations. The inset shows the mean squared displacement of the $E_2^{(\mathrm{low})}$ phonon mode.

Figure 3

Calculated thermal expansion of ZnO with the application of ZSISA. Experimental data for $a$ and $c$ are from Ref. [74] (4.2–300 K) and Ref. [70] (300–900 K) respectively. To stress the agreement in the temperature dependence, the calculated lattice constants at 0 K (including zero-point motion) are aligned to those measured at low temperatures.

Figure 4

Calculated pyroelectric coefficients of MoSSe and GeS monolayers. Piezoelectric coefficients for MoSSe and GeS monolayers are from Ref. [48] and Ref. [41], respectively.

Figure 5

GeS monolayer: (a) Top view. The arrow shows the polarization along the armchair direction. (b) Thermal expansion calculated using the Grüneisen theory at the quasi-harmonic level. (c) Double-well potentials under thermal strains. The curved arrow indicates with increasing temperatures the reduction of both ground-state spontaneous polarization and potential barrier. (d) Pyroelectricity under thermal strains. The total pyroelectricity is denoted by the black short-dot line.