Strained-graphene-based highly efficient quantum heat engine operating at maximum power

A strained graphene monolayer is shown to operate as a highly efficient quantum heat engine delivering maximum power. The efficiency and power of the proposed device exceeds that of recent proposals. The reason for these excellent characteristics is that strain enables complete valley separation in transmittance through the device, implying that increasing strain leads to very high Seebeck coefficient as well as lower conductance. In addition, since time-reversal symmetry is unbroken in our system, the proposed strained graphene quantum heat engine can also act as a high-performance refrigerator.

Figure 1

Top: The graphene layer with a strained region between $x=0$ and $x=L$. Electric and heat currents are generated due to the applied potential bias and finite-temperature difference between probes 1 and 2. Bottom: A incident electron at the interface between regions 1 and 2 is transmitted or reflected by the strained region with a finite probability. Here $\varphi$ is the incident angle and $\theta$ is the refracted angle in the strained region.

Figure 2

Conductance (in units of “$2e^2/h$”) at $30\text{K}$ for various values of strain with $L=40\text{nm}$ and width $W=20\text{nm}$.

Figure 3

Seebeck coefficient S in units of ($k_b/e$) at $30\text{K}$ for different values of strain with $L=40\text{nm}$ and width $W=20\text{nm}$.

Figure 4

Maximum Power ($P_{\text{max}}$) in units of $[{\left(k_B\mathrm{\Delta }T\right)}^2/\text{h}]$ at $30\text{K}$ for different lengths (L) of strained region with strain $=50\text{meV}$ and width (W) of strained region $=20\text{nm}$.

Figure 5

Maximum Power ($P_{\text{max}}$) in units of $[{\left(k_B\mathrm{\Delta }T\right)}^2/\text{h}]$ at $T=30\mathrm{K}$, where strain is along the $y$ direction and Fermi energy $E_f$ is along the $x$ direction with $L=40\text{nm}$ and width $W=20\text{nm}$.

Figure 6

Efficiency at maximum power in units of (${\eta }_c$) at $30\text{K}$ with strain $=50\text{meV}$ and width $W=20\text{nm}$.

Figure 7

Efficiency at maximum power $\left[\eta \left(P_{\text{max}}\right)\right]$ in units of (${\eta }_c$) at $T=30\text{K}$, with width $W=20\text{nm}$ and $L=40\text{nm}$.

Figure 8

(a) Maximum power $P_{\text{max}}$ in units of (${\left(k_B\mathrm{\Delta }T\right)}^2/\text{h}$) and $\eta \left(P_{\text{max}}\right)$ in units of (${\eta }_c$) at $30\text{K}$, for $v_f={10}^6\text{m}/\text{s}$, and (b) maximum power $P_{\text{max}}$ in units of (${\left(k_B\mathrm{\Delta }T\right)}^2/\text{h}$) and $\eta \left(P_{\text{max}}\right)$ in units of (${\eta }_c$) at $30\text{K}$, $v_f=6*{10}^5\text{m}/\text{s}$, with width $W=20\text{nm}$.