Rectifying the Optical-Field-Induced Current in Dielectrics: Petahertz Diode

Investigating a theoretical model of the optical-field-induced current in dielectrics driven by strong few-cycle laser pulses, we propose an asymmetric conducting of the current by forming a heterojunction made of two distinct dielectrics with a low hole mass ($m_h^{*}\ll m_e^{*}$) and low electron mass ($m_e^{*}\ll m_h^{*}$), respectively. This proposition introduces the novel concept of a petahertz (${10}^{15}\mathrm{Hz}$) diode to rectify the current in the petahertz domain, which should be a key ingredient for the electric signal manipulation of future light-wave electronics. Further, we suggest the candidate dielectrics for the heterojunction.

Figure 1

(a),(b) Optical-field-induced current at $\varphi =0$ and $\pi /2$. Necessary parameters are taken as follows: ${ϵ}_c=5\mathrm{eV}$, ${\mathrm{\Delta }}_c=-3\mathrm{eV}$, ${ϵ}_v=5\mathrm{eV}$, ${\mathrm{\Delta }}_v=-1\mathrm{eV}$, $t_c/\omega =1.76\AA$, $t_v/\omega =0.59\AA$, $\overline{d}/\omega =1.6\AA$, and $E_0=A_0\omega =0.43\mathrm{V}/\AA$. (c) Displacements of the effective conduction and valence bands $E_k^c(\tau )$ and $-E_{-k}^v(\tau )$ at an instant of $A(\tau )>0$ (gray dashed bands). Black solid bands are at $A(\tau )=0$. Feynman diagrams describe the physical processes of creation of the optical-field-induced current, where the wavy line denotes the optical field. $e^{-}$ (shaded ball) and $h^{+}$ (empty ball) represent the photoexcited electron and hole, respectively. (d) Total charge transfer $Q$ with respect to $\varphi$.

Figure 2

(a) Heterojunction made of two different dielectrics in the left ($L$) and right ($R$) sides. (b) A dielectric with the low hole mass ($m_h^{*}\ll m_e^{*}$) is assumed to be in the left side and the other with the low electron mass ($m_e^{*}\ll m_h^{*}$) in the right side. Effective conduction and valence bands shift according to an oscillation of the optical field.

Figure 3

(a) Schematic drawings of the tunneling conduction across the junction under the strong optical pumping. Gray-colored areas mean the bandwidths and $E_F$ is the Fermi level of the junction. Left panel depicts the worst situation and right panel the best situation for the tunneling conduction. Thickness of red arrows may be understood as the current density. (b)–(e) Tunneling current $J_T(\tau )$ and transferred charge $P(\tau )$ with respect to $\tau$ at $\varphi =0$, $\pi /2$, $\pi$, and $3\pi /2$ and $E_0=1.32\mathrm{V}/\AA$. Rectified optical-field-induced currents are obtained. (f) Total transferred (tunneling) charge $Q_T$ with respect to $\varphi$ at $E_0=1.32\mathrm{V}/\AA$.

Figure 4

Tunneling currents $J_T(\tau )$ at the electric field strengths $E_0=1.32$, 0.88, and $0.44\mathrm{V}/\AA$ and $\varphi =0$. Inset shows the behavior of $|Q|$ [for an homogeneous dielectric, i.e., Fig. 1; blue empty squares] and $Q_T$ (red empty squares) with respect to the electric field strength $E_0$ at $\varphi =0$. Blue and red filled squares indicate $|Q|\times 500$ and $Q_T\times 5000$, respectively.

Figure 5

(a) Electronic structure of a good low-electron-mass dielectric, $\alpha \text{−}{\mathrm{SiO}}_2$ (quartz). (b)-(d) Electronic structures of candidates for the low-hole-mass dielectric: (b) ${\mathrm{K}}_2{\mathrm{Pb}}_2{\mathrm{O}}_3$, (c) ZrSO, and (d) ${\mathrm{CaCl}}_2$. Insets show the Brillouin zone and the symmetry directions (red lines).