Electronic transport properties of a tilted graphene $p\text{−}n$ junction

Spatial manipulation of current flow in graphene could be achieved through the use of a tilted $p\text{−}n$ junction. We show through numerical simulation that a pseudo-Hall effect (i.e., nonequilibrium charge and current density accumulating along one of the sides of a graphene ribbon) can be observed under these conditions. The tilt angle and the $p\text{−}n$ transition length are two key parameters in tuning the strength of this effect. This phenomenon can be explained using classical trajectory via ray analysis, and is therefore relatively robust against disorder. Lastly, we propose and simulate a three terminal device that allows direct experimental access to the proposed effect.

Figure 1

(Color online) (a) Schematic of a tilted $p\text{−}n$ junction device built on a graphene ribbon. The top and bottom gate allows the tunability of the electron/hole carrier density on each side of the junction. Tilt angle defined as $\delta$. [(b)–(e)] Polar plots of the carrier transmission probability across a symmetric graphene $p\text{−}n$ junction for different values of magnetic field using the WKB model outlined in Ref. 8 (solid lines). The calculation is done for an experimentally typical $p\text{−}n$ junction with transition width of 100 nm and a built-in potential of 0.4 eV, i.e., ${ϵ}_f=\pm 0.2\text{eV}$ for the $n/p$ regions (Ref. 9). Similar plots for different $\delta$ at $B=0T$ using WKB are also shown (dashed lines).

Figure 2

(Color online) NEGF derived mode-to-mode transmission probability function ${\text{log}}_2\left[T_{negf}\left({\theta }_m,{\theta }_n\right)\right]$ for a symmetric $p\text{−}n$ junction device biased at ${ϵ}_f=0.4\text{eV}$, for tilt angles of $\delta =0°$, $15°$, $30°$, $45°$, respectively. The device width is 100 nm and the $p\text{−}n$ transition length $D=10\text{nm}$.

Figure 3

(Color online) [(a)–(c)] Polar plots of the transmission probability $T_{negf}\left({\theta }_m\right)={\Sigma }_n{T}_{negf}^{mn}$ for different $\delta$, where $T_{negf}^{mn}$ is computed using the same device parameters as for Fig. 2. The WKB plots are obtained using the usual WKB formula (Ref. 13) (see text)

Figure 4

(Color online) (a) Normalized conductance, $\sigma /{\sigma }_0$, of a $p\text{−}n$ junction as a function of the tilt angle $\delta$, computed for various values of transition length $D$ and biased symmetrically at ${ϵ}_f=0.4\text{eV}$. ${\sigma }_0$ is defined as the conductance when $\delta =0$, which by construction means $\sigma /{\sigma }_0=1$ when $\delta =0$. (b) Absolute conductance for the $D=10\text{nm}$ device with (i) perfectly smooth armchair edges (round symbol), roughened armchair edges, i.e., rms roughness of 1 atomic layer (square symbol) and perfectly smooth zigzag edges (triangle symbol). Dashed line is the result from simple WKB model.

Figure 5

(Color online) (a)–(c) shows the nonequilibrium real-space longitudinal current density for $p\text{−}n$ devices with $D=0$, 5, and 10 nm, respectively. All devices considered here have $\delta =30°$ and ${ϵ}_f=0.4\text{eV}$. (d)–(e) are the same device as (c) excepts with sidewall roughness and $p\text{−}n$ interface roughness, respectively. The rms roughness are 1 atomic layer and 1.7 nm, respectively. (f) is the device with $D=10\text{nm}$ and $\delta =45°$ with no disorder.

Figure 6

(Color online) (a) Schematic of a multiplexer device where the drain contact is partitioned into two via graphene stubs. (b) Ratio of the current through the two drain terminals as a function of $\delta$. Parameters assumed are $D=10\text{nm}$, ${ϵ}_f=0.4\text{eV}$ and under small source drain bias.

Figure 7

Schematic on a graphene ribbon with armchair edges. Each slice of supercell consist of an intracell interaction denoted by $\alpha$ and a right/left neighboring-cell interaction represented by $\tau /{\tau }^{†}$, respectively.