Polar Kerr Effect and Time Reversal Symmetry Breaking in Bilayer Graphene

The unique sensitivity of optical response to different types of symmetry breaking can be used to detect and identify spontaneously ordered many-body states in bilayer graphene. We predict a strong response at optical frequencies, sensitive to electronic phenomena at low energies, which arises because of nonzero interband matrix elements of the electric current operator. In particular, the polar Kerr rotation and reflection anisotropy provide fingerprints of the quantum anomalous Hall state and the nematic state, characterized by spontaneously broken time-reversal symmetry and lattice rotation symmetry, respectively. These optical signatures, which undergo a resonant enhancement in the near-infrared regime, lie well within reach of existing experimental techniques.

Figure 1

Kerr angle (in units of fine structure constant $\alpha =e^2/\hslash c$) as a function of photon energy for BLG in the QAH phase. Note the resonant enhancement near $E_0=0.4\mathrm{eV}$, arising from direct transitions to the higher BLG bands, Eq. (12). Inset: Schematic band structure of BLG near the $K$ point, for the QAH phase. The Kerr response arises from transitions $1^{\prime }\to 2$ and $1\to 2^{\prime }$, involving states in the bands 1 and 2 which are affected by broken TRS.