Magnetic Bulk Photovoltaic Effect in Bernal Bilayer Graphene

TL;DR

This paper analyzes how magnetic fields modify the bulk photovoltaic effect in AB-stacked Bernal bilayer graphene, focusing on shift current (SC) and magnetic ballistic current (MBC). Using a tight-binding AB-BG model with Peierls substitutions and ribbon geometries, the authors compute the SC, injection current (ignored for linear polarization), and MBC tensors, highlighting symmetry constraints and the regime where TRS breaking enables MBC. They find that in-plane fields leave SC nearly unchanged (even in field) while enabling a linearly field-dependent MBC, and that vertical fields reveal a striking dichotomy: weak fields suppress edge-state contributions to SC, whereas strong fields via Landau levels amplify edge-state–driven SC peaks whose intensity scales as $1/L_y$. The results emphasize that a high density of states (or JDOS) does not guarantee a large SC, since localized edge or Landau-state contributions can be dark due to vanishing interband matrix elements. These insights have implications for graphene-based heterostructures and magnetic-field–tuned nonlinear optoelectronics.

Abstract

Magnetic fields break time-reversal symmetry (TRS) and reshape a material's spatial symmetry. Because the bulk photovoltaic effect (BPVE) is exquisitely sensitive to symmetry, it offers a natural arena for magnetic-field control. Here, we explore how shift current (SC) and magnetic ballistic current (MBC) evolve and emerge in AB-stacked Bernal bilayer graphene subjected to in-plane and out-of-plane magnetic fields. We find that the SC responds only mildly to weak fields, behaving as an almost even function of field strength. In contrast, the MBC is activated directly by TRS breaking and grows linearly with weak fields at selected photon energies. Focusing on AB-bilayer graphene ribbon we investigate the behavior of SC and MBC under both weak and strong vertical fields. We uncover the strikingly opposite roles played by edge states in the SC: under weak fields these highly localized, sublattice- and layer-polarized edge modes are essentially dark, yet under strong fields - when Landau levels dominate - the same edge states swell in spatial extent and become intensely bright contributors to the SC response.

Figures (17)

• Figure 1: Lattice structure of AB-stacked bilayer graphene. Solid lines show the connection between sublattices of the top layer, while gray dashed lines the bottom layer. The zigzag edges of graphene flakes are aligned along the $x$-direction, while the armchair edges are along the $y$ direction. Orange dots mark the position of both $A$-sublattice of top layer and $B$-sublattice of bottom layer on the $xy$-plane. Red dots represent the $B$-sublattice of top layer. Light blue dots signifies the $A$-sublattice of the bottom layer.
• Figure 2: Band structure of AB-BG under different magnetic field along $y$ direction with intensity ranging from $0$ to 1000 Tesla. The band structures are not shown for the whole route $\mathrm{\Gamma-K-M}$. Only the part inside in the orange circle is presented to concentrate on the band structures near the Fermi level (as we have set the chemical potential $\mu = 0$). No substantial change can be found on the band structures unless the magnetic field is unrealistically strong.
• Figure 3: (a) The variation of $\sigma^{yxx}$ with respect to zero magnetic field. In the inset plot of (a) we also show the complete curve of $\sigma^{yxx}$ under different magnetic field. The vertical dashed lines indicate the photon energies at which we track the variation of $\sigma^{yxx}$ in (b) and (c), respectively. (b) The variation of $\sigma^{yxx}$ with photon energy fixed at $\omega = 0.32~\mathrm{eV}$. (c) The variation of $\sigma^{yxx}$ with photon energy fixed at $\omega = 0.42~\mathrm{eV}$.
• Figure 4: (a) JDOS of AB-BG in the absence of external magnetic field. (b) The variation of JDOS under different intensity of the magnetic field with respect to the zero-field JDOS.
• Figure 5: (a) Shift vector $R^{yx}_{23}$ distribution near $K$ point of AB-BG in the absence of magnetic field. (b) The variation of the shift vector. Data are exaggerated by a factor of $10$ for better visibility. Here $|b| = 4\pi/3d$ is the length of the reciprocal lattice base vector of AB-BG, with $d = 1.43~\text{\AA}$ being the C-C bond length in the graphene sheet.