Phonon thermal transport in ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ from first principles

We present first-principles calculations of the thermal and thermal transport properties of ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ that combine an ab initio molecular dynamics (AIMD) approach to calculate interatomic force constants (IFCs) along with a full iterative solution of the Peierls-Boltzmann transport equation for phonons. The newly developed AIMD approach allows determination of harmonic and anharmonic interatomic forces at each temperature, which is particularly appropriate for highly anharmonic materials such as ${\mathrm{Bi}}_2{\mathrm{Te}}_3$. The calculated phonon dispersions, heat capacity, and thermal expansion coefficient are found to be in good agreement with measured data. The lattice thermal conductivity, ${\kappa }_l$, calculated using the AIMD approach nicely matches measured values, showing better agreement than the ${\kappa }_l$ obtained using temperature-independent IFCs. A significant contribution to ${\kappa }_l$ from optic phonon modes is found. Already at room temperature, the phonon line shapes show a notable broadening and onset of satellite peaks reflecting the underlying strong anharmonicity.

Figure 1

Phonon dispersion relations along high symmetry directions for ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ calculated using AIMD determined IFCs at 77 K (red curves) compared to measured data [17] also at 77 K (green points).

Figure 2

Heat capacity, $c_P$, at constant pressure of ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ as a function of temperature. The red curve gives the $c_P$ obtained using IFCs obtained with the TDEP formalism; the blue curve gives the $c_P$ using IFCs determined within the QHA; points with error bars are measured data taken from Bessas et al. [18].

Figure 3

The volume coefficient of thermal expansion for ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ calculated using the AIMD approach (red curve) and with IFCs determined within the QHA (blue curve). The experimental point at 300 K is from Bessas et al. [18].

Figure 4

The thermal conductivity calculated at zero pressure using $T$-dependent IFCs. The top line is the in-plane (${\kappa }_{xx}$) and the bottom line the out-of-plane (${\kappa }_{zz}$) thermal conductivity. In-plane experimental values from two samples (black circles) are from Goldsmid [28].

Figure 5

Comparison of ${\kappa }_{xx}$ (upper curves) and ${\kappa }_{zz}$ (lower curves) using the temperature-dependent approach (red curves), the quasiharmonic approximation (blue curves), and temperature independent results (gold curves).

Figure 6

The in-plane and out-of-plane acoustic phonon dispersions vs temperature.

Figure 7

${\kappa }_{xx}$ calculated using the temperature-dependent approach (red curve), and temperature-independent IFCs (gold curve) shown over an expanded temperature range to illustrate the increasing error introduced using the $T$-independent IFCs above about 100 K.

Figure 8

Cumulative in-plane thermal conductivity ${\kappa }_{xx}$ as a function of phonon mean free path at $T=300$ K decomposed per phonon branch. The gold shaded region gives the contribution from the acoustic branches while the green shaded region gives the contribution from the optic branches. The purple shaded region gives mixed acoustic/optic phonon contributions, as described in the text.

Figure 9

${\mathrm{Bi}}_2{\mathrm{Te}}_3$ phonon line shapes at temperature 77, 300, and 450 K in panels (a), (b), and (c) respectively. Brighter color reflects higher intensity.