Giant Shift Current in Electrically-Tunable Superlattice Bilayer Graphene

TL;DR

The paper addresses how to realize a giant shift current in moiré-engineered AB-stacked bilayer graphene by applying an electrostatic moiré potential that yields topologically nontrivial, flat moiré bands near charge neutrality. It develops a valley-projected BLG model with a tunable moiré coupling and computes the nonlinear shift-current response $\sigma_{abb}(0;\omega,-\omega)$ under linearly polarized light using a sum-rule based formalism for the quantum geometric quantities $C^{bab}_{mn}$ and the shift vector $\mathcal{R}^{ab}_{mn}$, at zero temperature. The study reports a peak shift-current conductivity up to $\sim 10^6\ \mu\text{A nm V}^{-2}$ arising from direct transitions between nearly flat bands with Chern numbers $-1$ and $+1$, with the response enhanced near topological phase boundaries controlled by the displacement field $V_0$, moiré strength $V_{\text{ESL}}$, phase $\phi$, and moiré period $L$; sign reversals occur across gap closings that alter band Chern numbers. The results indicate that external superlattice potentials in BLG offer a highly tunable, robust path toward large DC photocurrents in the far infrared, outperforming twisted bilayer graphene in knobs and resilience to disorder.

Abstract

Recent introduction of superlattice potentials has opened new avenues for engineering tunable electronic band structures featuring topologically nontrivial moiré-like bands. Here we consider optoelectronic properties of Bernal-stacked graphene subjected to a superlattice potential either electrostatically or through lattice twisting to show that it exhibits a giant shift current response that is orders of magnitude larger than existing predictions in twisted mulitlayer systems. Effects of gate voltage and the strength and phase of the superlattice potential on the shift current are delineated systematically across various topological regimes. Our study gives insight into the nature of nonlinear responses of materials and how these responses could be optimized by tuning the superlattice potential.

Figures (5)

• Figure 1: (a) Schematic of a device for generating a moiré potential by placing a layer of twisted hexagonal Boron Nitride (hBN) below a sheet of bilayer graphene. (b) Mini-Brillouin Zone (mBZ) showing four high-symmetry points. (c) Band structure and the associated density of states using a representative set of model parameters ($V_{\text{ESL}} = 5 \ \text{meV}$ and $V_0 = -5 \ \text{meV}$). (d) $\sigma_{xxx}$ component of the shift current conductivity as a function of photon frequency for model parameters in (c)
• Figure 2: (a-c): Real space profiles of the moiré potential [the sum in Eq.\ref{['eq:MoireModel']}] for $V_{\text{ESL}} = 5 \ \text{meV}$ at three different values of $\phi$. For $\phi = 0$, the potential minima form a honeycomb lattice and the potential maxima form a triangular lattice. For $\phi = \frac{\pi}{3}$, the potential minima and maxima form a triangular and a honeycomb lattice respectively. For $\phi = \frac{\pi}{6}$, both the maxima and minima form triangular lattices in real space. (d-f): Contour plots for the top valence band for $V_{\text{ESL}} = 5 \ \text{meV}$, $V_{\text{0}} = -5 \ \text{meV}$, and $L = 50 \ \text{nm}$ for the three $\phi$ values in (a-c). (g-i): Energy bands along high-symmetry lines in the Brillouin zone for three values of $\phi$ as in (a-c), with other parameters fixed to the values in (d-f). In (g) and (h) the band structure is invariant under inversion (compare energy levels at $K$ and $K^{\prime}$ points). In contrast, energy bands for $\phi = \frac{\pi}{6}$ in (i) are not invariant under inversion symmetry.
• Figure 3: Shift-current photoconductivity dependence on the displacement field for (a) $V_{\text{ESL}} = 5 \ \text{meV}$ and (b) $V_{\text{ESL}} = 10 \ \text{meV}$. Superlattice period and $\phi$ are $50 \ \text{nm}$ and $\frac{\pi}{6}$, respectively. $\sigma_{xxx}$ component of the conductivity tensor is plotted as a function of the incident photon energy $\hbar\omega$ and the displacement field $V_0$.
• Figure 4: Chern phase diagram, band gap, and the dominant shift current peak as a function of $\phi$ and $V_0$. In all cases, $L = 50 \ \text{nm}$. $V_{\text{ESL}} = 5 \ \text{meV in the top row and} 10 \ \text{meV}$ in the bottom row. (a) and (e): Chern number of the top valence band. (b) and (f): Chern number of the bottom conduction band. (c) and (g): Band gap between the top valence and bottom conduction bands. (d) and (h): Strength of the largest peak in $\sigma_{xxx}$ in units of $\mu \text{A nm V}^{-2}$. Irregularities that are especially noticeable in panels (e) and (f) reflect computational inaccuracies resulting from very small band gaps.
• Figure 5: Dependence of $\sigma_{xxx}$ on the moiré period $L$ for fixed values of $V_0=$$5 \ \text{meV}$ and $\phi$ = ${\pi}/{6}$. Inset: Band structure at two values of the period [$30$ nm (left) and $65 \ \text{nm}$ (right)] showing a topological phase transition, where the Chern numbers of the two bands near the Fermi energy vanish as $L$ increases.