Comparison on thermal transport properties of graphene and phosphorene nanoribbons

Abstract

We investigate ballistic thermal transport at low temperatures in graphene and phosphorene nanoribbons (PNRS) modulated with a double-cavity quantum structure. A comparative analysis for thermal transport in these two kinds of nanomaterials is made. The results show that the thermal conductance in PNRS is greater than that in graphene nanoribbons (GNRS). The ratio kG/kP (kG is the thermal conductivity in GNRS and kP is the thermal conductivity in PNRS) decreases with lower temperature or for narrower nanoribbons, and increases with higher temperature or for wider nanoribbons. The greater thermal conductance and thermal conductivity in PNRS originate from the lower cutoff frequencies of the acoustic modes.

Figure 1

Lattice structures of (a) PNRS and (b) GNRS.

Figure 2

(a,b) correspond to the dependence of the total transmission probability on the reduced frequency ω/∆₁ with ∆₁ = πv_ZP/w₁ along the zigzag direction and ω/∆₂ with ∆₂ = πv_AP/w₂ along the armchair direction.The solid and dashed curves describe the transmission spectra of the PNRS with ideal structure and with double-cavity structure. The dotted and dash-dotted curves describe the transmission spectra of the GNRS with ideal structure and with double-cavity structure. The parameters are taken as the defect with the width t = 4.6 Å for ZPNRS, 3.3 Å for APNRS, 2.9 Å for ZGNRS, and 2.5 Å for AGNRS, and the length d = 3.3 Å for ZPNRS, 4.6 Å for APNRS, 2.5 Å for ZGNRS, and 2.9 Å for AGNRS. Here, w = Wa + Wb + t, and the lengths between the defect region and the two lateral sides of main quantum wire are Wa = Wb = 9.2 Å for ZPNRS, 8.3 Å for APNRS, 8.7 Å for ZGNRS, and 6.3 Å for AGNRS.

Figure 3

(a,b) correspond to the total reduced thermal conductance divided by temperature K/T reduced by the zero-temperature universal value π²k_B²/3h as a function of temperature along the zigzag and along the armchair directions, respectively.The solid and dashed curves describe the total reduced thermal conductance of the PNRS with ideal structure and with double-cavity structure, respectively. The dotted and dash-dotted curves describe the total reduced thermal conductance of the GNRS with ideal structure and with double-cavity structure. The parameters are taken as the defect with the width t = 4.6 Å for ZPNRS, 3.3 Å for APNRS, 2.9 Å for ZGNRS, and 2.5 Å for AGNRS, and the length d = 3.3 Å for ZPNRS, 4.6 Å for APNRS, 2.5 Å for ZGNRS, and 2.9 Å for AGNRS. Here, the lengths between the defect region and the two lateral sides of main quantum wire Wa = Wb = 9.2 Å for ZPNRS, 8.3 Å for APNRS, 8.7 Å for ZGNRS, and 6.3 Å for AGNRS. The top-left inset describes the ratio k_G/k_P as a function of temperature relative to the same chains across the ribbon.

Figure 4

(a,b) correspond to the total thermal conductance divided by temperature K/T reduced by the zero-temperature universal value π²k_B²/3h as a function of temperature along the zigzag direction and along the armchair direction. Figure 4(c,d) correspond to the total thermal conductance as a function of temperature along the zigzag direction and along the armchair direction, respectively. Solid and dotted curves of (a) correspond to the width W = 2.30 nm and 4.14 nm for ZPNRS, and dashed and dash-dotted curves of (a) correspond to the width W = 1.16 nm and 2.03 nm for ZGNRS, respectively. Solid and dotted curves of (b) correspond to the width W = 1.98 nm and 2.64 nm for APNRS, and dashed and dash-dotted curves of (b) correspond to the width W = 1.51 nm and 2.01 nm for AGNRS, respectively. Solid and dotted curves of (c,d) correspond to the width W = 1.60 nm for PNRS and GNRS, and the dashed and dash-dotted curves of (c,d) correspond to the width W = 5.00 nm for PNRS and GNRS. The top-left insets describe the ratio k_G/k_P as a function of temperature relative to the same chains across the ribbon for (a,b) and the same width for (c,d).

Figure 5

(a,b) correspond to the ratio k_G/k_P as a function of width W along the zigzag and armchair directions. Solid, dashed, dotted, and dash-dotted curves correspond to the temperatures T = 2 K, 10 K, 20 K, and 30 K.