Charge qubit in van der Waals heterostructures

In this Rapid Communication, we develop the concept of charge qubits in van der Waals heterostructures. A theoretical proof of concept is provided for the ${\mathrm{ZrSe}}_2/{\mathrm{SnSe}}_2$ system, in which a framework connecting the electronic structure with quantum information is described. The quantum state is prepared by applying a vertical electric field, manipulated by short field pulses, and measured via electric currents. The proposed qubit is robust, operational at high temperature, and compatible with two-dimensional material technology, opening different avenues for the field.

Figure 1

Band structures of ${\mathrm{ZrSe}}_2/{\mathrm{SnSe}}_2$ heterostructure with applied vertical electric field of (a) $-0.3$ V/Å, (b) 0.0 V/Å, and (c) $+0.3$ V/Å. The inset in (c) shows the positive field orientation is considered from the ${\mathrm{SnSe}}_2$ layer to the ${\mathrm{ZrSe}}_2$ layer. The color of the marker represents the relative contribution of each monolayer to the eigenvalue. The VBM is chosen as energy zero.

Figure 2

Conduction-band energy-level diagram vs gate-field strength $F$ formed by the localized electron states for an uncoupled system $\left|A\right.〉$ and $\left|B\right.〉$ (dashed lines) with eigenenergies $E_A$ and $E_B$, respectively. The hybridization of the states for the coupled system results in new eigenstates $\left|0\right.〉$ and $\left|1\right.〉$, with eigenenergies $E_0$ and $E_1$, respectively, and anticrossing energy ${\mathrm{\Delta }}_{\text{ac}}$ (solid lines). For strong fields the qubit eigenstates are well approximated by $\left|A\right.〉$ and $\left|B\right.〉$, but for field values around $F_{\text{ac}}$ the eigenstates are strongly delocalized. For the zero field, the energy difference $E_B-E_A=\mathrm{\Delta }{E}_C$ characterizes the conduction-band discontinuity.

Figure 3

Weights $|{\alpha }_{\psi }{|}^2$ (red) and $|{\beta }_{\psi }{|}^2$ (blue), for $\left|\psi \right.〉$ equals $\left|0\right.〉$ (solid lines) and $\left|1\right.〉$ (dashed lines), as a function of the applied vertical electric field. The inset represents the area of the Bloch sphere in the $A/B$ basis in which $\left|0\right.〉$ and $\left|1\right.〉$ are comprised for the considered electric fields $(\left|F\right|<0.3\mathrm{V}$/Å) (light gray), and for small fields $(\left|F\right|<0.1\mathrm{V}$/Å) (dark gray) considering a generic azimuthal angle $\varphi$. The horizontal axis indicates the direction of the vector $\widehat{v}=cos\varphi \widehat{x}+sin\varphi \widehat{y}$ in the $xy$ plane.

Figure 4

Schematic representation of a possible physical implementation of the qubit. The electrode $V_G$ applies the field on the stacking direction, changing the state $\left|\psi \left(V_G\right)\right.〉$ of the electron in the conduction band, represented by the green Bloch sphere. By inducing a drift in the horizontal direction, the electron wave function will collapse in one of the two electrodes of the isolated portion of the sheets $(\left|A\right.〉\left.〈A\right|$ or $\left|B\right.〉\left.〈B\right|)$, with the probability depending on its localization in each sheet. The Zr, Sn, and Se atoms are represented in red, blue, and gray, respectively.