Selectively enhanced photocurrent generation in twisted bilayer graphene with van Hove singularity

Graphene with ultra-high carrier mobility and ultra-short photoresponse time has shown remarkable potential in ultrafast photodetection. However, the broad and weak optical absorption (∼2.3%) of monolayer graphene hinders its practical application in photodetectors with high responsivity and selectivity. Here we demonstrate that twisted bilayer graphene, a stack of two graphene monolayers with an interlayer twist angle, exhibits a strong light–matter interaction and selectively enhanced photocurrent generation. Such enhancement is attributed to the emergence of unique twist-angle-dependent van Hove singularities, which are directly revealed by spatially resolved angle-resolved photoemission spectroscopy. When the energy interval between the van Hove singularities of the conduction and valance bands matches the energy of incident photons, the photocurrent generated can be significantly enhanced (up to ∼80 times with the integration of plasmonic structures in our devices). These results provide valuable insight for designing graphene photodetectors with enhanced sensitivity for variable wavelength.


Supplementary Note 1. The measurement of interlayer twist angle by TEM
The hexagonal shapes of the over-and underlayers of tBLG supply us an opportunity to measure the twist angle () from the linear edges directly. To verify accuracy of this method, we observed the selected area electron diffraction (SAED) of tBLG by transmission electron microscopy (TEM). The tBLG samples with different twist angles were firstly transferred to TEM grids with marks and then identified by scanning electron microscopy (SEM). Finally the SAED of the marked tBLG samples were performed to read the twisted angles from the two sets of diffraction spots which are derived from the over-and underlayers of tBLG. As shown in Supplementary Fig. 1, the twist angles measured from linear edges of tBLG and SAED agree well with each other, but the former method is more convenient. The former method was used to measure the twist angles of tBLG in this work.

Supplementary Note 2. Dependence of VHS positions with twited angles.
Since the over-and underlayer of tBLG are twisted with a rotation angle in real space, their Brillouin zones rotates accordingly (hexagons in Supplementary Fig 2a). The Dirac cones of the over-and underlayer graphene located at k and k  points are shown in Supplementary Fig 2a. We define a vector ∆ = − , which is the separation between k and k  points, then where | | = | | = 1.7Å −1 . The value of ∆ can be measured by micro-ARPES, while the value of twist angle  can be calculated.
The Dirac cones of over-and underlayer graphene of tBLG keep independent near the Fermi level. The energy band of one monolayer graphene has the form of 1 where t and t' is the nearest-neighbor hopping energy and next nearest-neighbor hopping energy respectively. The value of t is about 2.8 eV and the value of t' is between 0.02t and 0.2, for example ~0.1 eV 2,3 . On the other hand, the energy band of another monolayer graphene with a twist angle , has the form where T() is the rotation matrix.
If we consider the energy band below the Dirac point, the intersection points are confined by both of the two equations, as The VHS located around the intersection point with maximum energy value 4,5 , while it is the lowest point along the direction perpendicular to Cut 2. As indicated by the red arrow in inset of Supplementary Fig. 2b, it's a saddle points. The relation of this point with twist angle ( is derived from the numerical solutions, as shown in Supplementary Fig. 2b.

Supplementary Note 3. Raman G-band enhancement at 10.5 o tBLG domain
The difference between Supplementary Fig. 3a Supplementary Fig. 3b. The Raman G-band intensity mapping of the 10.5 o tBLG domain exhibits a quite uniform feature, which implies a highly crystalline quality ( Supplementary Fig. 3c). Although the mechanism of the Raman G-band enhancement is still under controversy, its correlation with the new band topology and VHSs is widely accepted [5][6][7][8][9][10][11] . The Raman G band enhancement could be understood by the  -dependent value of 2E VHS , which is defined as the energy interval of the two VHSs (above and under the Dirac point, as shown in Fig. 1a). If this value matches the energy of incident photon, the intensity of Raman G band increases by ~20 folds [5][6][7][8][9][10][11] . According to the micro-ARPES data in

Supplementary Note 4. Selectively enhanced photocurrent generation in 10.5 o tBLG domain
The tBLG device comprises of tBLG domains with different twist angles ( Supplementary Fig. 4a).
The enhancement of Raman G-band intensities (Supplementary Fig. 4b) indicates that the tBLG domain has a twist angle of ~10. So far, the reported mechanism of photocurrent generation at the metal-graphene interface is quite controversial. In this article, photothermoelectric (PTE) effect [12][13][14][15] was considered to explain the photocurrent generation, but the photovoltaic (PV) effect [16][17][18][19] cannot be excluded. In graphene devices, the metal would dope graphene underneath (The doped area was reported to extend into the graphene channel by ~100 nm 16,17 ) and then introduce pn junction between graphene underneath and graphene in channel (For some occasions pn junction can also be introduced by the same doping type