Temperonic Crystal: A Superlattice for Temperature Waves in Graphene

The temperonic crystal, a periodic structure with a unit cell made of two slabs sustaining temperature wavelike oscillations on short timescales, is introduced. The complex-valued dispersion relation for the temperature scalar field is investigated for the case of a localized temperature pulse. The dispersion discloses frequency gaps, tunable upon varying the slabs’ thermal properties. Results are shown for the paradigmatic case of a graphene-based temperonic crystal. The temperonic crystal extends the concept of superlattices to the realm of temperature waves, allowing for coherent control of ultrafast temperature pulses in the hydrodynamic regime at above liquid nitrogen temperatures.

Figure 1

Sketch of the temperonic crystal. Spatially periodic heating of a graphene layer leads to periodic stripes of length $d_a$, $d_b$, and temperature $T_a$, $T_b$, respectively, the u.c. dimension being $L=d_a+d_b$. $S_j=\{C,{\kappa }_T,{\tau }_T,{\tau }_q{\}}_j$ is the set of thermal properties of stripe $j$, with $j=\{\mathrm{a},\mathrm{b}\}$. On a general basis, any periodic structure based on a unit cell composed of two slabs sustaining temperature wavelike oscillations on short timescales can serve as a TC.

Figure 2

Temperature band structure: dispersion relation ${\omega }_1$ (a) and quality factor Q (b). Black full line: graphene TC with $T_a=100$ and $T_b=80\mathrm{K}$. Black dashed line: ${\omega }_1^{\mathrm{eff}}$ (a) and $Q^{\mathrm{eff}}$ (b) for the corresponding homogeneous effective material. The unit cell size is $5\mu \mathrm{m}$.

Figure 3

Normalized dispersion relations for a graphene TC with $T_a=100\mathrm{K}$ kept fixed and $T_b=110$ (red full line), 120 (blue full line), and 80 K (black full line). Black dashed line: normalized dispersion relation for the corresponding homogeneous effective materials (same curve for all three cases). Inset: 1st gap location and extent (vertical bars) for each TC in actual, i.e., non-normalized, units.