Magnetic injection photocurrents in valley polarized states of twisted bilayer graphene

TL;DR

The study introduces a magnetically switchable injection photocurrent as a diagnostic for valley polarization in magic-angle twisted bilayer graphene. By combining the Topological Heavy Fermion Model with Hartree–Fock theory, it computes shift and injection photogalvanic responses across continuous flat-band filling, showing that magnetic injection currents emerge in time-reversal-broken, valley-polarized states and can distinguish QAH from VH/SVH phases. The results indicate that injection currents are enhanced in clean samples (large $\tau$) and predominantly reveal the underlying spin-valley order, offering a concrete optical probe to identify symmetry-breaking ground states in TBG. These insights provide experimentally testable signatures for valley ordering, substrate effects, and Hund-coupling mechanisms in the correlated moiré system.

Abstract

Magic-angle twisted bilayer graphene displays a complex phase diagram as a function of flat band filling, featuring compressibility cascade transitions and a variety of competing ground states with broken spin, valley and point group symmetries. Recent THz photocurrent spectroscopy experiments have shown a dependence on the filling which is not consistent with the simplest cascade picture of sequential filling of equivalent flat bands. In this work, we show that when time-reversal symmetry is broken due to valley polarization, a magnetic injection photocurrent develops which can be used to distinguish different spin-valley polarization scenarios. Using the topological heavy fermion model we compute both shift and injection currents as a function of filling and argue that current experiments can be used to determine the spontaneous valley polarization.

Figures (6)

• Figure 1: (a) Sketch of a TBG flake in the presence of an incident in-plane electric field $\boldsymbol{E}(t)$ and the resulting induced non-linear current $\boldsymbol{J}(t)$. The two local $f$ orbitals (per valley and spin) in the heavy fermion description of TBG are depicted in red and blue at the AA positions of the moiré pattern, whereas the $c$ electrons of the delocalized conduction bands are shown in black. The high symmetry points of the moiré Brillouin zone (MBZ) are shown in the figure inset. (b) Bands of the non-interacting THFM close to magic angle in the absence (gray) and presence (black) of a layer-even sublattice mass. (c) Schematic of the allowed optical transitions between occupied and unoccupied bands at integer $\nu$. Flat to flat (FF) transitions are depicted in pink and flat to dispersive (FD) in black. Solid and dashed, and red and blue encode different valley and spin flavors, respectively.
• Figure 2: Bandstructure comparison between the non-interacting THFM and the continuum model in the absence (a) and presence of the three sublattice potentials in Eq \ref{['subs']}: $\Delta_1 = \Delta$ (b), $\Delta_2 = \Delta$ (c), and $\Delta_3 = \Delta$ (d), with $\Delta = 0.25$ meV. The continuum model parameters are: the twist angle $\theta = 1.05 \deg$, the intralayer hopping $t = -2.46575$ eV, and the interlayer hopping between AA and AB regions $t_{AA} = 0.078975 \text{eV}$, $t_{AB} = 0.0975 \text{eV}$, respectively. The THFM parameters $v_\star$, $v_\star'$, $M$, and $\gamma$ values are taken from Ref. Song22.
• Figure 3: Sequence of mean-field ground states as a function of filling in the THFM: (a) Normalized density of states referred to the Fermi surface as a function of filling. (b) Valley polarization of $f$-electrons as a function of the filling. (c-e) Occupation of the spin (s) and valley ($\eta$) $f$ degrees of freedom vs filling for three distinct ground states corresponding to VH (c), SVH (d), and QAH (e) phases
• Figure 4: (a) Shift and (b,c) magnetic injection components as a function of frequency and filling in the presence of a layer-even sublattice mass $\Delta_1 = 2.5 \text{ meV}$ for the different interacting ground states described in Fig. 2. Whereas the QAH, VH, and SVH phases give rise to the same $\sigma_{yyy}^\text{shift}$, those with different Chern number: $0$ (VH/SVH) and $2$ (QAH), lead to a different $\sigma_{xxx}^\text{inj}$ response in (b) and (c) between fillings 2 and 3, respectively. Filling regions where $\sigma_{xxx}^\text{inj}$ vanishes at all frequencies are highlighted by arrows corresponding to the VH/SVH states. Same parameters as in Fig. 2.
• Figure 5: In-plane photocurrents in the presence of a layer-odd sublattice mass for the QAH (a-d) and VH/SVH (e-h) phases as a function of frequency and filling. (a,e) $\sigma_{xxx}^{\rm sh}$ (b,f) $\sigma_{yyy}^{\rm sh}$ (c,g) $\sigma_{xxx}^{\rm inj}$ and (d,h) $\sigma_{yyy}^{\rm inj}$. Parameters: $\Delta_{1} = 2.5 \text{ meV, } \Delta_{2} = 2.4 \text{ meV}$, the rest as in Fig. \ref{['fig:layerevenmass']}.