Anomalous Photogalvanic Effect in Twisted Bilayer Graphene

Theoretical Background

As proposed by Y. Gao et al., it is expected that a chirally twsited bilayer heterostructure can exhibit the layer circular photogalvanic effect (LCPGE), a second-order optoelectronic effect that couples the chirality of the moiré superlattice with the handness of the light. The mathematical expression of the photo-generated out-of-plane layer dipole moment is:

where β=-iχ_xy^as is the corresponding LCPGE coefficient. According to second-order perturbation theory, this coefficient can be reformulated into the contributions of quantum geometry weighted by the joint density of states (jdos) at equilibrium limit:

where (f_n-f_l )δ(ωnl+ξω) is the jdos weight, g_ij is the quantum metric and Ω_z is the Berry curvature, while R(s/as) is the symmetric/asymmetric part of the layer shift vector. In real experiments, we measure the photogalvanic voltage generated by the dipole:

According to the numerical calculations done by Y. Gao et al., for twisted bilayer graphene stimulated by a laser at a power of 1mW/μm2, one should obtain a V_pg value against the twist angle and the corresponding peak laser energy (equivalently, the resonance wavelength) position shown in Fig. 1.

Fig. 1 The peak position (black) and the corresponding potential difference (red) generated by the LCPGE at different twisting angles. We have assumed a laser power 1mW/μm2.

Device Fabrication

Fig. 2(a) shows the current structure of our LCPGE devices. Two monolayer graphene are stacked at a (60-x)° angle at the top region to form a small TBG region with area around 2μm × 2μm, encapsulated by a top and bottom hBN. The heterostructure is transferred through PC polymer in a top-down way as shown in Fig. 2(b), and then etched into the current design with only a small TBG region left as the sharp point through EBL and RIE. 5nm Cr and 60nm Au are deposited subsequently on two graphite contacts to serve as an electrode contacts. For future measurement of the photogalvanic voltage , four Cu wires can be bonded at the four electrode contacts, with 2 contacts as a group connected with one graphite in contact with one graphene monolayer. One can select one wire in each group to connect with the lock-in amplifier to form a voltmeter. Fig. 2(c) shows the optical image (with linear contrast) of all five devices we fabricated.

Fig. 2 Device fabrication. (a) Schematic diagram of the LCPGE device structure. (b) Optical image of the heterostructure being transferred by PC (last step), under the special RGB contrast color mode.  (c) Optical images of five measurable LCPGE devices (D4 to D8), under the special RGB contrast color mode.

Experimental Setup

Our experimental setup is a self-built far-field near-infrared (NIR) optoelectronic detecting and scanning system. It uses a MaiTai fs laser at NIR regime, a delicate far-field optical system that brings the NIR laser to the sample with the laser polarization being fully tunable through a liquid-crystal electronic polarizer, and the sample image obtained simultaneously at NIR band through a InGaAs detector, and a cryogenic electronic transport measurement circuit connected with a SR-830 lock-in amplifier, a chopper set around 1kHz and an attocube piezo-positioner. Fig. 3 shows the schematic diagram of our optoelectronic system.

Fig. 3 Schematic diagram of the far-field NIR optoelectronic detecting and scanning system. (a) Optical path of the optical part. (b) Electronic system and the equivalent electrical circuit of the electronic part.

The current experimental setup can achieve the following functions:

1. Generating NIR laser with tunable wavelength, power and polarization.
2. Simultaneously shining steady fs-level laser onto the sample and receiving high quality μm-level image of the sample at NIR band.
3. Semi-automated scanning the photogalvanic voltage topography of the sample at near-field NIR regime. To achieve semi-automation, we connect the attocube piezo-positioner with our local computer at the LUA terminal thus sending commands through Ethernet to program it. A simple tutorial can be found at the manual of attocube piezo-positioner ANC 350 documentary.

We usually use the following code to control the positioner movement.

function sleep(n) local t0 = os.clock() while (os.clock() - t0 <= n) do end end for i = 1, 10 do m2:step(UP, 10) sleep(4) end

There are also some drawbacks of the current experimental setup which needs further improvements:

1. Stability of the current optical system is not good enough. Usually it takes at least 30min to calibrate the optical path to obtain a NIR laser spot at the sample with a good quality. A slight change of the status of the laser spot will affect the photogalvanic voltage badly. There were occasions that the voltage read jumped abruptly or owned a low S/N. A steadier optical system coupled with the cryogenic electronic system is necessary.
2. Full automation of the scanning measurement system. The current scanning measurement of the  topography is semi-automated. Though the attocube piezo-positioner is connected with the computer remotely and is programmed to be automated, the Keithley measurement software is not connected with the computer, thus one still needs manually implement the voltage measurement part. If one desires a fully automated scanning measurement optoelectronic system, one should write a code (based on Python or LabVIEW. We have tried Python to connect with the Ethernet LUA terminal as well as the Keithley software but failed) to connect the attocube positioner and the Keithley software.
3. Continuous tunability of laser wavelength to facilitate wavelength-dependent probe. Right now, our MaiTai laser is of fixed wavelength laser output, in which the wavelength needs re-set and the whole optical system needs re-calibration every time. 

Optoelectronic Measurements

We measured the photogalvanic behavior of device D4(6^◦), D5(6^◦), D6(7^◦), D7(6^◦) and D8(6.5^◦).

Fig. 4 shows the optoelectronic measurement of D4. Here, we first show the comparison between the photogalvanic voltage of D4 in the TBG region at room temperature and 7K, stimulated by a wavelength 1200nm (tested to be nearly resonant) laser with power around 1mW, as shown in Fig. 4(b). An obvious enhancement of the voltage value beyond the noise level is detected at 7K, which suggests a photogalvanic signal emerging at cryogenic region. Fig. 4(d)-(e) shows the second measurement of D4 (Fig. 4(c)) under the current experimental setup, all data shown at temperature 7.3K. With the help of our semi-automated scanning technique, a V_pg topography is measured under different polarization. In conclusion, D4 exhibits a strong and steady V_pg signal at TBG region, but weak at all other regions. An obvious sign changes relative to the center signal both at above and under the TBG region shows up. No apparent polarization response is detected.

Fig. 4. Optoelectronic measurement of D4 device. (a) Optical image of the old device (scale bar: 1um) and part of the experimental setup. (b) Comparison between the photo-generated voltage-polarization curve measured at the room temperature and 7K of the old device architecture, at the TBG region. A strike enhanced signal above the noise level is detected at 7K, with an obvious polarization dependence.  The bi-periodic arrows drawn at certain polarization angle denote the left handness or right handness of the circular light. (c) Optical image of the current device, under the special color contrast mode. Left: bigger view (scale bar: 10um). Right: zoom-in area used to be scanned. The device components are sketched in different colors: gold contact (golden), graphite contact (purple), graphene (yellow), TBG (red). (d) Absolute value |V_pg| topography scanned at 7.3K and zero gate voltage, with fixed laser power of 1mW and 1200nm wavelength, at circular polarization and linear polarization. The V_pg signal is singular around the TBG region at both polarizations, with absolute value around 40uV. The signal decays rapidly once away from the TBG region. No apparent polarization differences are shown. (e) V_pg topography at the same conditions above. Dramatic sign reverts of V_pg are detected above/under the TBG region (from around -40uV at TBG region to around 20-30uV above/under the TBG region) at both circular and linear polarizations.

The same type of measurements is carried for the rest of the devices, where the experimental setup and the comparison of the signal at room temperature and at around 7K remain the same so we omit the data, only showing the cryogenic data. The temperature is controlled around 7K and the laser power is controlled around 1mW, so there are weak thermal noises, and since we are using SR-830 lock-in, the electrical noises are also extremely low (both less than 0.01uV), only leaving optical noises due to the miscalibration of the optical system (within 0.1-1uV level). In each measurement, we first tune the signal to reach its maximum at TBG region by varying the optoelectronic system, the sample location and the laser wavelength. Due to the incapability of the continuous tunning of the wavelength, we only measured 2-3 points in experiments that are roughly determined around the theoretical value (calculated by the twist angle of the device) and make a simple comparison of the signal strength to choose the nearly resonance wavelength. Then, a V_pg topography and polarization dependence of the signal are measured.

Fig. 5 shows the experimental results of D5. In conclusion, D5 exhibits a strong and steady signal at TBG region that reaches 30uV, and on top of the TBG region (near gold contact) that reaches -50uV, remaining all weak at all other regions, see Fig. 5(b). Again, an obvious nearly  phase reverse is detected respect to the center peak above the TBG region, as shown in Fig. 5(c). Moreover, for D5, we found out an anomalous V_pg phase-polarization dependence, see the long-time measurement in Fig. 5(d), where by varying the laser polarization from circular to linear, the phase of the V_pg changes around 2° accordingly, which is reproducible in our repeated tests. This seems to suggest a small polarization dependence of the photogalvanic signal in D5, which is absent among all other devices.

Fig. 5. Optoelectronic measurement of D5 device. (a) Optical image of the device, under the special color contrast mode. Left: bigger view (scale bar: 10um). Right: zoom-in area used to be scanned. The device components are sketched in different colors: gold contact (golden), graphite contact (purple), graphene (black), TBG (red). (b) V_pg topography scanned at 7.5K and zero gate voltage, with fixed laser power of 1mW and 1350nm wavelength, at linear polarization. The V_pg signal is singular around the TBG region, with absolute value reaching 30uV. The signal decays rapidly once away from the TBG region, but rises up at another singularity with opposite phase above it. (c) V_pg phase topography at the same conditions above. The phase reverse of V_pg are detected above the TBG region (from near  at TBG region to near –  above the TBG region). (d) Phase at the TBG region vs. time measurement of different polarization group. A slight and reproducible polarization dependence of the V_pg phase can be roughly noticed, where at circular light the mean phase is around -29°, whereas at linear light the mean phase is around -31°.

Fig. 6 shows the experimental results of D6. Compared to other devices, D6 owns a much weaker and more unstable V_pg signal at the TBG region, only reaching around 4uV with a strong turbulence.  Instead, the photo-generated signal is super strong at the gold-graphite contact region, reaching nearly 20uV magnitude. No apparent polarization response of the signal is detected.

Fig. 6 Optoelectronic measurement of D6 device. Top: optical image of the device (scale bar: 10um), under the special RGB contrast color mode, and the IR-CCD image of the device (scale bar: 20um). Bottom: |V_pg| topography scanned at 6.7K (log scaled) and zero gate voltage, with fixed laser power of 1mW and 1350nm wavelength, at linear polarization. The device components are sketched in different colors: gold contact (golden), graphite contact (purple), graphene (black), TBG (red). The V_pg signal is the most singular around the two gold-graphite contact regions, with absolute value reaching 40uV. The signal decays rapidly once away from the contact regions. At the TBG region, as shown in the zoom-in topography, a slightly stronger signal can be identified with value around 4uV. No apparent polarization differences are shown.

Fig. 7 shows the experimental results of D7. Similar to D6, D7 owns a weaker and but relatively stable V_pg signal at the TBG region, only reaching around 7uV.  Instead, the photo-generated signal is strong at the gold-graphite contact region, reaching nearly 30uV magnitude. For D7, the phase topography shown in Fig. 7(c) shows the most obvious clues of the phase reverse up/under the TBG region. A clear nearly 2\pi  jump is identified once scanned across the TBG region from above to beneath it. No apparent polarization response of the signal is detected.

Fig. 7 Optoelectronic measurement of D7 device. (a) Optical image of the device, under the special color contrast mode. Left: bigger view (scale bar: 10um). Right: zoom-in area used to be scanned. The device components are sketched in different colors: gold contact (golden), graphite contact (purple), graphene (black), TBG (red). (b) |V_pg| topography scanned at 7.5K (log scaled) and zero gate voltage, with fixed laser power of 1mW and 1200nm wavelength, at linear polarization. The V_pg signal is the most singular around the two gold-graphite contact regions, with absolute value reaching 30uV. The signal decays rapidly once away from the contact regions. At the TBG region, as shown in the zoom-in topography, a slightly stronger signal can be identified with value around 7uV. No apparent polarization differences are shown. (c) V_pg phase topography at the same conditions above. The clear and robust phase reverse of V_pg is detected above the TBG region (from near \pi at TBG region to near -\pi  above the TBG region) as shown in the zoom-in topography.

Fig. 8 shows the experimental results of D8. In conclusion, D8 exhibits a relatively weaker but steady signal at TBG region that is around -7uV, and on top of the TBG region jumps to around 10uV, then reverses back and reaches maximal near gold contact that reaches -20uV, remaining all weak at all other regions, see Fig. 8(b). Again, an obvious nearly 2\pi phase reverse is detected respect to the center peak above the TBG region, as shown in Fig. 8(c). No apparent polarization response.

Fig. 8 Optoelectronic measurement of D8 device. (a) Optical image of the device, under the special color contrast mode. Left: bigger view (scale bar: 10um). Right: zoom-in area used to be scanned. The device components are sketched in different colors: gold contact (golden), graphite contact, graphene (yellow), TBG (red). (b) V_pg topography scanned at 7.5K and zero gate voltage, with fixed laser power of 1mW and 1100nm wavelength, at linear polarization. The V_pg signal is the most singular on the top of the TBG region near gold-graphite contact, with absolute value reaching 20uV. The signal decays rapidly once away from the contact region. At the TBG region, as shown in the zoom-in topography, a slightly stronger signal can be identified with value around 7uV. No apparent polarization differences are shown. (c) V_pg phase topography at the same conditions above. The clear and robust phase reverse of V_pg is detected above the TBG region (from near -\pi at TBG region to near \pi above the TBG region) as shown in the zoom-in topography.

Tentative Conclusions

Based on the current measurement results, we conclude that a bilayer graphene heterostructure with an artificial twist angle can generate a photogalvanic voltage at cryogenic temperature (7K) under the stimulation of a NIR laser with around 1mW power. The voltage can also be detected around the gold-graphite contact regions, and for most devices it is around one magnitude higher than the voltage at the moiré region.  Unlike the theory has proposed, the signal exhibits no polarization dependence for most devices, only for D5 there is a slight phase-polarization dependence. The phase of the photogalvanic voltage, which is ignored in the theories, shows to have a steady and significant effect in all devices, in which the relative phase would always reverse above and under the TBG region with nearly 2\pi magnitude. If we adhere the dipole moment picture, then this might be explained as the reverse of the dipole moment crossover the TBG region. Otherwise we suspect that this photogalvanic effect may be related to some junction effect, which might be trivial. The relationship between this photogalvanic effect we observed and the quantum geometry of TBG remains unclear. If possible, we suggest continue to explore this system with both the device structure and the experimental techniques and methods to be improved.