Zero-bias mid-infrared graphene photodetectors with bulk photoresponse and calibration-free polarization detection

Bulk photovoltaic effect (BPVE), featuring polarization-dependent uniform photoresponse at zero external bias, holds potential for exceeding the Shockley-Queisser limit in the efficiency of existing opto-electronic devices. However, the implementation of BPVE has been limited to the naturally existing materials with broken inversion symmetry, such as ferroelectrics, which suffer low efficiencies. Here, we propose metasurface-mediated graphene photodetectors with cascaded polarization-sensitive photoresponse under uniform illumination, mimicking an artificial BPVE. With the assistance of non-centrosymmetric metallic nanoantennas, the hot photocarriers in graphene gain a momentum upon their excitation and form a shift current which is nonlocal and directional. Thereafter, we demonstrate zero-bias uncooled mid-infrared photodetectors with three orders higher responsivity than conventional BPVE and a noise equivalent power of 0.12 nW Hz−1/2. Besides, we observe a vectorial photoresponse which allows us to detect the polarization angle of incident light with a single device. Our strategy opens up alternative possibilities for scalable, low-cost, multifunctional infrared photodetectors.


Supplementary Note 1. Seebeck coefficient of graphene
As a bipolar semiconductor with zero-bandgap, the Seebeck coefficient of graphene (1) where Φ, σ, kB, T and e are chemical potential, electrical conductance, Boltzmann constant, temperature and elementary charge, respectively. Note that the conductance σ of graphene is a function of its chemical potential (Φ). 2 where W and L are the width and length of the graphene device. 0 is the residual carrier concentration. h, v and µ are Planck constant, Fermi velocity and mobility, respectively.
The Fermi velocity of graphene is about 10 6 m/s. 1 By substituting Supplementary Equation (2) into Supplementary Equation (1), we can obtain the expression of S, which is directly dependent on Φ: Therefore, we can plot the Seebeck coefficient of graphene as a function of its chemical potential as Supplementary Figure 1. Here we have assumed a typical value of 0 as 2×10 12 cm -2 and room temperature operation (T=300K). As we can see from the graph, the Seebeck coefficient of graphene is non-monotonous and changes its sign for p-and ntype doping. Besides, due to the Fermi level pinning, the graphene covered by metals shows fixed Seebeck coefficients (Smg). In contrast, since the chemical potential of uncovered graphene can be tuned electrically via gate voltage, its Seebeck coefficient (Sg) can be moved along the curves. The resultant difference of Seebeck coefficients, ∆S = Smg − Sg, controls the sign and amplitude of photocurrents generated at metal-graphene interfaces.
Supplementary Figure 1 | Seebeck coefficient of graphene (S) as a function of the chemical potential (∆Φ). The yellow dot represents the graphene covered with metal contact, while the grey dot denotes the uncovered graphene. Unlike the covered graphene whose chemical potential is pinned, that of the uncovered graphene can be tuned electrically, so that the ∆S = Smg − Sg is also tunable. The estimated thickness of graphene is matched with that of Raman spectra 5 .

Supplementary Note 5. Photocurrent generation from nanoantennas with different degrees of asymmetry
To investigate the dependence of photocurrents on the degree of asymmetry, we simulated By moving the device, we obtain the photocurrent map and hence the beam profile.
The measured beam profile can be fitted with Gaussian beam as where I is the intensity, and I0 is the intensity at the center of the beam. r1 and r2 are the radii along the two axes, which are extracted as 271 and 171 µm. The peak intensity I0 is related to the total power of Gaussian beam 6 In our experiment, we have always optimized the photocurrent by moving the device to the center of beam. Since the area of our device (S) is small, we can consider that the power density on our device is I0, and hence the incident power onto our device is P= I0*S.

Supplementary
where Q1, Q2 and Q3 are the oscillating charges at the top, bottom left and bottom right ends of the triangle nanoantennas. According to Gaussian law, the near-field amplitude at the three tips are where α is the parameter that relates the photocurrents with the field intensity. E0 is a fitting factor. ����⃗, ������⃗ and �������⃗ are the unit vectors in the normal direction of metal-graphene interfaces at the top, bottom left, and bottom right tips of triangle nanoantennas. The angle of the vectorial photocurrents at θ polarization angle is -π/2-2θ.

Supplementary Note 11. Photocurrents at circular polarization states
In the BPVE, the shift currents only emerge from linearly polarized light. When the incident light is circularly polarized, however, another mechanism may also lead to shortcircuit current, namely, the injection current 7,8 . This is also usually referred to as circular photogalvanic effect. In Supplementary Figure 12, we investigate the possible photoresponse of the T-shaped nanoantennas under circular polarized illumination. It is dependent on whether the circularly polarized light will excite asymmetric near field, which is related to the spectral detuning between the two eigenmodes excited by orthogonal linearly polarized light. As a result, we anticipate a negligible photoresponse for nanoantennas with Lh = 600 nm, but non-zero and opposite photoresponse for nanoantennas with Lh = 500 nm and 700 nm. Furthermore, we consider the circular dependence of photoresponse for our threeport device as shown in Figure 4 (main manuscript). Supplementary Figure 13 shows the near-field profile under illumination at circular polarization states. Obviously, the near field also possesses a three-fold rotation symmetry as our theoretical analysis. Therefore, we anticipate that the photocurrents in such devices will vanish.  *The abbreviations of mechanisms represent photo-thermoelectric (PTE), photovoltaic (PV), pyroelectric (PyE), photoconducting (PC) and bulk photovoltaic (BPVE) effects. λ denotes the working range of wavelength. NEP means noise equivalent power. ** The modulation frequency used for NEP measurement is shown in the bracket. "Calc"

Supplementary
indicates that the value is derived without direct measurement of either the frequency dependent responsivity or the frequency dependent noise.