Resonant Zener Interferometry in van der Waals Heterostructures

Abstract

We demonstrate the presence of quantum interference effects in van der Waals heterostructures subject to in-plane electric fields. The in-plane field $F$ accelerates carriers through a hybridized band edge, and interlayer Zener tunneling occurs by distinct pathways, resulting in a solid-state quantum interferometer with imprints in transport observables. For parabolic-band bilayers, we identify two characteristic signatures which are observable in lateral conductance: Landau-Zener-Stuckelberg oscillations in the band-overlap regime periodic in $1/F$ at small fields, resembling electric-field induced quantum oscillations, and a pronounced resonance at $F\propto T_0^{3/2}$ set by the interlayer tunneling $T_0$. These features provide a directly accessible probe of coherent interferometric dynamics in van der Waals heterostructures, and could be harnessed for more precise engineering and characterization.

Figures (3)

• Figure 1: (a) Schematic of a semiconductor van der Waals heterobilayer in an in-plane electric field $F$. Interlayer bias $\Delta$ and tunneling $T_0$ control field-driven interlayer charge transfer, measured by two-terminal conductance $G$. (b) For $\Delta <0$, $G$ exhibits interference-induced oscillations with period $\sim F^{2}/m^{\ast 1/2}|\Delta|^{3/2}$ at small fields (i.e. periodic in $1/F$), with $m^*$ the effective mass. For all $\Delta$, $G$ shows a resonant peak at a characteristic field $F_0\sim m^{\ast 1/2}T_0^{3/2}$. These features realize a tunable solid-state interferometer whose signatures can probe $T_0$ and other device characteristics.
• Figure 2: Lateral conductance $G$ (in units $ge^2 L_y k_Z/h$) for an electron-hole bilayer in an in-plane electric field $F$. (a) For $s$-wave tunneling $T_0/E_Z = \lambda$ and interlayer bias $\Delta/E_Z = \delta$, where $E_Z = (\hbar^2e^2 F^2/2m^* )^{1/3}$ is the energy scale set by $F$. (b) For $p$-wave tunneling $T_1\hbar k_Z/E_Z = \lambda_1$, where $k_Z = eF/E_Z$. (c) Line cuts for $s$-wave at $\lambda = 0.7$ and $\delta = 0.3$, showing Landau--Zener--Stückelberg oscillations and a resonant peak in conductance, respectively. (d) Line cuts for $p$-wave at $\lambda_1 = 0.5$ and $\delta = 0.3$, respectively, showing similar behavior.
• Figure 3: (a,b) Tunneling probabilities for the two-level system Eq. \ref{['eq:Hoftau']} (and the $p$-wave analog), computed exactly. (c,d) Probabilities computed using the Landau-Zener-Stückelberg approximation, showing good agreement for $\Delta <0$. $P$ and $P_{\mathrm{LZS}}$ exhibit clear oscillations for $\Delta < 0$, a ridge of maximum probability, and isolated points of maximal transmission. The analytical predictions are superposed on (a,b): curves indicate $P_{\text{LZ}} = 1/2$ (Eqs. \ref{['eq:ridgeswave']},\ref{['eq:ridgepwave']}) and dots indicate perfect-transmission $P_{\text{LZS}} = 1$. For $p$-wave cases, $p_y=0$.