Device fabrication of TDBG transistor The samples were fabricated using the ‘cut-and-stack’ method, similar to the previously reported ‘tear-and-stack’ technique31. Typically, a thin (approximately 10–15 nm) hBN flake is picked by a hot pick-up technique32,33 using a poly (bisphenol A carbonate) film on a polydimethylsiloxane stamp at 90 °C. This hBN flake is then later used to pick up a part of pre-cut Bernal BLG flake, mechanically exfoliated on Si++/SiO2 (285 nm) from highly oriented pyrolytic graphite, and pre-characterized using optical microscopy, and Raman spectroscopy34. Subsequently, the remaining BLG flake is rotated to a target angle (~15°) and then picked up by the hBN-BLG stack on the polypropylene carbonate film. Finally, the stack is used to pick up a last layer of hBN and later dropped on a pre-patterned marker chip of Si++/SiO2 (285 nm) at 180 °C, squeezing out the bubbles, and impurities as previously reported. The stack is then shaped into a Hall bar geometry using SF6 plasma, and O2 plasma to etch top hBN, and BLG respectively32, and further metallized using 3 nm/15 nm/30 nm of Cr/Pd/Au. For the devices with a top gate, a top stack of hBN–graphite–hBN was prepared, patterned and contacted, similar to the bottom stack.

Low-temperature infrared photocurrent measurements Mid-infrared measurements were performed at a temperature of 4 K, unless otherwise noted. The samples were placed in a Montana Instruments optical cryostat with anti-reflection coated ZnSe windows. The infrared beam was emitted by a Daylight MIRcat tunable QCL laser. The wavelength used was 11.07 μm, unless otherwise noted. The beam was expanded to a diameter of approximately 13 mm by a set of parabolic mirrors. The power was controlled by rotating a ZnSe holographic polarizer, and the polarization was kept unaltered by a third, fixed ZnSe holographic polarizer. The light was then focused onto the sample with a 15× reflective objective (numerical aperture 0.5). The focus spot is typically 20 μm diameter for 11.07 μm excitation.

The position of the focal point was scanned by moving the objective with stepper motors, with sub-micron resolution. The resulting displacement of the objective’s optical axis from the beam’s optical axis is negligible on the scale of the beam diameter.

The photoconductivity was measured by taking the difference of the sample conductivity with and without illumination. For measuring the two-point probe and four-point probe resistivity, we used two SR860 lock-ins simultaneously. The sample was biased with 500 μV a.c. at 13.1 Hz by lock-in, and the gate voltage was applied with a Keithley 2400 source meter. The d.c. measurements in Fig. 4c were performed by biasing the sample and reading the current with another Keithley 2400 source meter. The two-point probe voltage was measured by a data acquisition card after amplification and filtering by an ITHACO 1201 low-noise voltage pre-amplifier.

Low-temperature broadband photocurrent measurements The broadband photocurrent measurements presented in Fig. 2a were performed in a modified FTIR setup. A liquid 4He-cooled optical cryostat was coupled with a commercial Bruker FTIR, where the laser was redirected onto the TDBG detector instead of the FTIR’s internal deuterated triglycine sulfate (DTGS) detector. For the infrared (2–20 μm) measurement, the FTIR’s internal thermal light source Globar was used instead of the QCL. In the case of THz detection, a cold low-pass THz filter was used to ensure the low temperature of the TDBG detector.