Gate-Dependent THz Photocurrent Spectroscopy

• Gate-dependent THz photocurrent spectroscopy is a measurement strategy that converts THz excitations into dc signals through nonlinear rectification and gate-controlled symmetry breaking.
• It employs various device architectures—including dual-grating HEMTs, graphene superlattices, and plasmonic FETs—to selectively probe polarization channels, plasma resonances, and band-structure features.
• Gate tunability enables both resonant and off-resonant detection regimes, offering innovative paths for THz spectroscopy, imaging, and high-sensitivity quantum sensing.

Gate-dependent terahertz photocurrent spectroscopy comprises a family of measurements in which terahertz-driven dc current or photovoltage is recorded while one or more gate voltages tune carrier density, electrostatic asymmetry, plasmonic boundary conditions, or the nonlinear transfer characteristic of the detector. In the literature represented here, the method spans dual-grating-gate high electron mobility transistors, graphene lateral superlattices, hydrodynamic field-effect transistors, antenna-coupled graphene TeraFETs, terahertz scanning tunneling microscopy, graphene Josephson junctions, and graphene/hBN moiré superlattices. Across these platforms, the gate is not only a conductivity-control electrode: it can also act as a tunable symmetry-breaking element, a cavity-defining boundary, a carrier-type selector, or a nanoscale temporal gate, thereby converting gate sweeps into spectroscopic probes of polarization, plasma resonances, miniband gaps, Berry-curvature-related photocurrents, and thermal switching dynamics (Faltermeier et al., 2015, Olbrich et al., 2015, Riolo et al., 16 Jan 2025, Li et al., 2023, Delgado-Notario et al., 22 Jul 2025, Zhou et al., 1 Apr 2026).

1. Formal structure of the measurement

In dual-grating-gate InAlAs/InGaAs/InAlAs/InP HEMTs, symmetry allows the dc photocurrent to be written as a superposition of the Stokes parameters,

$$J_y = J^{(0)} s_0 + J^{(1)} s_1 + J^{(2)} s_2 + J^{(3)} s_3,$$

with

$$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$

Under rotation of a quarter-wave plate by $\phi$, these become $s_1(\phi)=\tfrac12[1+\cos4\phi]$, $s_2(\phi)=\tfrac12\sin4\phi$, and $s_3(\phi)=-\sin2\phi$ (Faltermeier et al., 2015).

In graphene lateral superlattices, the polarization-resolved ratchet response is separated phenomenologically into

$$j_x = \langle[\chi_0 E^2 + \chi_L(|E_x|^2-|E_y|^2)]\,dV/dx\rangle,$$

and

$$j_y = \langle[\tilde\chi_L(E_xE_y^*+E_x^*E_y) + \gamma\, i(E_xE_y^*-E_x^*E_y)]\,dV/dx\rangle.$$

Here the polarization-independent Seebeck thermoratchet, the linear ratchet, and the circular ratchet are encoded in distinct coefficients, while the gate enters through the spatially periodic potential $V(x)$ and through the carrier density (Olbrich et al., 2015).

In the generalized Dyakonov–Shur formulation for finite-length and multiple-gate transistors, the central observable is the rectified photovoltage

$\Delta U = \langle \phi(0,t) - \phi(L,t)\rangle_t,$

and the dimensionless response

$$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$0

Riolo et al. formulate the problem in the local-capacitance approximation, with alternating single-gate and dual-gate regions, and derive a closed-form second-order response together with thin-gate limits that directly expose gate-position dependence (Riolo et al., 16 Jan 2025).

Taken together, these formulations show that gate-dependent terahertz photocurrent spectroscopy is not defined by a single microscopic mechanism. Rather, it is a measurement logic: a THz field drives a nonlinear rectification process, while the gate sweep parameterizes a family of electronic configurations whose photocurrent signatures can be decomposed into polarization channels, resonant cavity modes, or thermodynamic operating points.

2. Noncentrosymmetric ratchets and polarization-resolved detection

The 2015 demonstration of helicity-sensitive photocurrent in dual-grating-gate HEMTs established one of the clearest gate-controlled realizations of terahertz polarization spectroscopy. The device comprised an InP-based heterostructure grown by MBE, with the active channel formed in a 16 nm undoped InGaAs quantum well, sandwiched between two 23 nm Si-doped InAlAs layers. A two-dimensional electron gas with sheet density $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$1, effective mass $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$2 and room-temperature mobility $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$3 resided at the upper InAlAs/InGaAs interface. Two interdigitated Ti/Au/Ti gates formed a lateral superlattice with $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$4, $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$5, $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$6, and $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$7. At $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$8 and $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$9, the current measured between source and drain contacts changed sign with inversion of the radiation helicity, and by variation of gate voltages applied to individual gratings the photocurrent could be defined either by the Stokes parameter defining the radiation helicity or those for linear polarization. The helicity-sensitive term $\phi$0 was zero at $\phi$1, grew in magnitude as $\phi$2 increased, reached $\phi$3 per $\phi$4 at optimal bias, and reversed sign if the asymmetry was inverted. For three nominally identical samples, $\phi$5 at open-circuit and $\phi$6 in $\phi$7-loaded measurements (Faltermeier et al., 2015).

The underlying ratchet picture is explicit: a spatially periodic dc gate potential $\phi$8 and a phase-shifted near-field distribution $\phi$9 jointly rectify ac drift and diffusion in a laterally noncentrosymmetric two-dimensional electron system. The observed gate-tunable photocurrent is therefore attributed to electronic and plasmonic ratchet effects, with the helicity-driven term emerging from the interplay of the two orthogonal in-plane field components $s_1(\phi)=\tfrac12[1+\cos4\phi]$0 and the lateral potential (Faltermeier et al., 2015).

An analogous gate-controlled ratchet phenomenology was demonstrated in graphene with a lateral superlattice. In the interdigitated dual-grating-gate graphene device, asymmetric top-gate bias reversed the superlattice asymmetry and inverted $s_1(\phi)=\tfrac12[1+\cos4\phi]$1 over the entire back-gate range, while the magnitude of $s_1(\phi)=\tfrac12[1+\cos4\phi]$2 was enhanced by $s_1(\phi)=\tfrac12[1+\cos4\phi]$3 when asymmetry was maximized. If only one top gate was biased, $s_1(\phi)=\tfrac12[1+\cos4\phi]$4 nearly vanished, consistent with a near-symmetric potential profile. The photocurrent included the Seebeck thermoratchet effect as well as the effects of “linear” and “circular” ratchets, sensitive to the corresponding polarization of the driving electromagnetic force (Olbrich et al., 2015).

Bilayer graphene with asymmetric dual grating gates extended this picture into the nonlinear-intensity regime. At low power, the measured current was decomposed as

$s_1(\phi)=\tfrac12[1+\cos4\phi]$5

Sweeping the individual subgate voltages inverted the lateral asymmetry parameter $s_1(\phi)=\tfrac12[1+\cos4\phi]$6 and reversed the ratchet current polarity. At room temperature, the low-power linear photocurrent was replaced at high intensity by a saturation law $s_1(\phi)=\tfrac12[1+\cos4\phi]$7 with saturation intensity ranging from $s_1(\phi)=\tfrac12[1+\cos4\phi]$8 at $s_1(\phi)=\tfrac12[1+\cos4\phi]$9 to several $s_2(\phi)=\tfrac12\sin4\phi$0 at $s_2(\phi)=\tfrac12\sin4\phi$1. At $s_2(\phi)=\tfrac12\sin4\phi$2, the response could first saturate and then reverse sign, a behavior attributed to the competition between the Seebeck ratchet and the dynamic redistribution ratchet together with the nonlinear $s_2(\phi)=\tfrac12\sin4\phi$3 itself (Mönch et al., 2023).

A recurrent misconception is that gate tuning in these ratchet geometries merely rescales responsivity. The experiments instead show selective suppression, enhancement, and sign inversion of distinct polarization channels. In dual-grating architectures, the gate configuration determines whether the device behaves primarily as a linear-polarization detector, a helicity detector, or a mixed Stokes analyzer (Faltermeier et al., 2015).

3. Plasma-wave rectification and Dyakonov–Shur spectroscopy

A second major branch of gate-dependent terahertz photocurrent spectroscopy is rooted in plasma-wave rectification in field-effect transistors. In the graphene hydrodynamic analysis of Tomadin et al., the source and drain are driven by antenna-fed boundary conditions

$s_2(\phi)=\tfrac12\sin4\phi$4

with $s_2(\phi)=\tfrac12\sin4\phi$5 setting the average carrier density $s_2(\phi)=\tfrac12\sin4\phi$6. The rectified dc current density is obtained from the second-order hydrodynamic solution,

$s_2(\phi)=\tfrac12\sin4\phi$7

and the fundamental plasma-wave frequency is

$s_2(\phi)=\tfrac12\sin4\phi$8

Because $s_2(\phi)=\tfrac12\sin4\phi$9 and $s_3(\phi)=-\sin2\phi$0, the resonance scales as $s_3(\phi)=-\sin2\phi$1. The theory predicts a peculiar change of sign when the frequency of the incoming radiation matches an even multiple of the fundamental frequency of plasma waves in the FET channel, and it further states that the noise equivalent power per unit bandwidth is much smaller than that of a Dyakonov-Shur detector in a wide spectral range (Tomadin et al., 2013).

Riolo et al. generalized the Dyakonov–Shur theory to short gates and multiple gates, explicitly addressing the common experimental situation in which the gate is not as long as the channel itself. In each region $s_3(\phi)=-\sin2\phi$2, the linearized plasma mode is characterized by

$s_3(\phi)=-\sin2\phi$3

and in the single-gate thin-gate limit the response admits a compact analytical formula. The optimal gate position is, to leading order,

$s_3(\phi)=-\sin2\phi$4

and deviations reduce the response roughly as

$s_3(\phi)=-\sin2\phi$5

The same framework shows that for $s_3(\phi)=-\sin2\phi$6 gates, plasma-wave interference among the $s_3(\phi)=-\sin2\phi$7 regions produces a rich spectral structure of additional side-bands and minima (Riolo et al., 16 Jan 2025).

The plasmonic FET spectrometer extends the same physics to device engineering. In a symmetrical FET illuminated by two antennas, the rectified THz voltage between source and drain is proportional to the sine of the phase shift between the voltages induced between gate-to-drain and gate-to-source. In the lossless limit, the resonant frequency is

$s_3(\phi)=-\sin2\phi$8

and the crossover frequency

$s_3(\phi)=-\sin2\phi$9

can be tuned continuously. Simulations reported continuous coverage from $$j_x = \langle[\chi_0 E^2 + \chi_L(|E_x|^2-|E_y|^2)]\,dV/dx\rangle,$$0 to $$j_x = \langle[\chi_0 E^2 + \chi_L(|E_x|^2-|E_y|^2)]\,dV/dx\rangle,$$1 across Si MOSFETs, AlGaN/GaN HEMTs, AlGaAs/InGaAs HEMTs, and p-diamond FETs, with extracted crossover frequencies agreeing with the analytic relation to within $$j_x = \langle[\chi_0 E^2 + \chi_L(|E_x|^2-|E_y|^2)]\,dV/dx\rangle,$$2 across all materials (Liu et al., 2020).

These studies place gate-dependent THz photocurrent spectroscopy squarely between spectroscopy and device physics: the measured signal is not only a detector output but also a map of plasma dispersion, damping, geometry, and boundary-condition symmetry.

4. Graphene carrier-type control, Dirac physics, and magnetoplasmons

Graphene devices add two forms of gate tunability that are especially useful spectroscopically: transport through the Dirac point and the density dependence of the effective mass. In graphene lateral superlattices, the back gate drives the system through the Dirac point, and for symmetric top-gate bias the photocurrent displays sign changes through the Dirac point with enhanced $$j_x = \langle[\chi_0 E^2 + \chi_L(|E_x|^2-|E_y|^2)]\,dV/dx\rangle,$$3 close to charge neutrality. Applying equal top-gate voltages shifts both the resistance and $$j_x = \langle[\chi_0 E^2 + \chi_L(|E_x|^2-|E_y|^2)]\,dV/dx\rangle,$$4 curves laterally by the same back-gate offset, confirming $$j_x = \langle[\chi_0 E^2 + \chi_L(|E_x|^2-|E_y|^2)]\,dV/dx\rangle,$$5 (Olbrich et al., 2015).

In graphene TeraFETs, the gated segment of length $$j_x = \langle[\chi_0 E^2 + \chi_L(|E_x|^2-|E_y|^2)]\,dV/dx\rangle,$$6 acts as a plasmonic Fabry–Pérot cavity within a total channel length $$j_x = \langle[\chi_0 E^2 + \chi_L(|E_x|^2-|E_y|^2)]\,dV/dx\rangle,$$7. The discrete modes satisfy

$$j_x = \langle[\chi_0 E^2 + \chi_L(|E_x|^2-|E_y|^2)]\,dV/dx\rangle,$$8

and the gate controls the density through

$$j_x = \langle[\chi_0 E^2 + \chi_L(|E_x|^2-|E_y|^2)]\,dV/dx\rangle,$$9

with $$j_y = \langle[\tilde\chi_L(E_xE_y^*+E_x^*E_y) + \gamma\, i(E_xE_y^*-E_x^*E_y)]\,dV/dx\rangle.$$0. At low frequencies, $$j_y = \langle[\tilde\chi_L(E_xE_y^*+E_x^*E_y) + \gamma\, i(E_xE_y^*-E_x^*E_y)]\,dV/dx\rangle.$$1 with $$j_y = \langle[\tilde\chi_L(E_xE_y^*+E_x^*E_y) + \gamma\, i(E_xE_y^*-E_x^*E_y)]\,dV/dx\rangle.$$2, and $$j_y = \langle[\tilde\chi_L(E_xE_y^*+E_x^*E_y) + \gamma\, i(E_xE_y^*-E_x^*E_y)]\,dV/dx\rangle.$$3 is monotonic and antisymmetric about the charge neutrality point. As $$j_y = \langle[\tilde\chi_L(E_xE_y^*+E_x^*E_y) + \gamma\, i(E_xE_y^*-E_x^*E_y)]\,dV/dx\rangle.$$4 increases above $$j_y = \langle[\tilde\chi_L(E_xE_y^*+E_x^*E_y) + \gamma\, i(E_xE_y^*-E_x^*E_y)]\,dV/dx\rangle.$$5, $$j_y = \langle[\tilde\chi_L(E_xE_y^*+E_x^*E_y) + \gamma\, i(E_xE_y^*-E_x^*E_y)]\,dV/dx\rangle.$$6 and discrete resonant peaks emerge in $$j_y = \langle[\tilde\chi_L(E_xE_y^*+E_x^*E_y) + \gamma\, i(E_xE_y^*-E_x^*E_y)]\,dV/dx\rangle.$$7 (Delgado-Notario et al., 28 Nov 2025).

The monolayer and bilayer cases then diverge spectroscopically. In monolayer graphene, $$j_y = \langle[\tilde\chi_L(E_xE_y^*+E_x^*E_y) + \gamma\, i(E_xE_y^*-E_x^*E_y)]\,dV/dx\rangle.$$8 with $$j_y = \langle[\tilde\chi_L(E_xE_y^*+E_x^*E_y) + \gamma\, i(E_xE_y^*-E_x^*E_y)]\,dV/dx\rangle.$$9, so the plasmon frequency inherits Dirac-type gate scaling. Experimentally, for $V(x)$0–$V(x)$1, multiple peaks are observed, and plotting the extracted plasmon wavelength $V(x)$2 versus $V(x)$3 places all modes on straight lines. Under finite perpendicular magnetic field, each resonant peak shifts toward lower $V(x)$4 as $V(x)$5 grows, and the resonance condition yields a non-monotonic $V(x)$6 dependence with an inflection, identified as a distinctive signature of Dirac carriers. In bilayer graphene, by contrast, $V(x)$7 is gate-independent, $V(x)$8 scales linearly with $V(x)$9, and the magnetoplasmon resonance follows the conventional Schrödinger-type dispersion with no inflection (Delgado-Notario et al., 28 Nov 2025).

The performance metrics reinforce the spectroscopic utility of the gate sweep. Reported responsivity peaks at the gate voltages matching plasmonic resonances, with typical values $\Delta U = \langle \phi(0,t) - \phi(L,t)\rangle_t,$0–$\Delta U = \langle \phi(0,t) - \phi(L,t)\rangle_t,$1 at $\Delta U = \langle \phi(0,t) - \phi(L,t)\rangle_t,$2 and $\Delta U = \langle \phi(0,t) - \phi(L,t)\rangle_t,$3, while $\Delta U = \langle \phi(0,t) - \phi(L,t)\rangle_t,$4 lies in the $\Delta U = \langle \phi(0,t) - \phi(L,t)\rangle_t,$5–$\Delta U = \langle \phi(0,t) - \phi(L,t)\rangle_t,$6 range. A perpendicular magnetic field provides an additional tuning knob via magnetoplasmon coupling (Delgado-Notario et al., 28 Nov 2025).

A plausible implication is that graphene makes gate-dependent THz photocurrent spectroscopy unusually sensitive to band-structure class itself: the same cavity geometry distinguishes Dirac and Schrödinger carriers through how resonances move in the $\Delta U = \langle \phi(0,t) - \phi(L,t)\rangle_t,$7 plane.

5. Miniband, gap, and threshold spectroscopy in graphene superstructures

Gate-dependent THz photocurrent spectroscopy has also been used to interrogate miniband structure directly. In graphene/hBN moiré superlattices, a dual-gate geometry tunes the Fermi level through the main Dirac point and secondary Dirac points, while THz frequencies from $\Delta U = \langle \phi(0,t) - \phi(L,t)\rangle_t,$8 to $\Delta U = \langle \phi(0,t) - \phi(L,t)\rangle_t,$9 provide photon energies of $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$00–$$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$01. At each frequency, the zero-bias photocurrent $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$02 is recorded at $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$03, and the responsivity follows

$$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$04

In a simple intraband model, the low-temperature low-doping scaling becomes

$$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$05

linking the gate dependence directly to valley degeneracy and Fermi velocity (Delgado-Notario et al., 22 Jul 2025).

This gate sweep resolves two regimes. In the off-resonance regime, when the radiation energy is smaller than the gap values, intraband rectification dominates and produces a bipolar $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$06 that changes sign at each Dirac point and vanishes far from them. In perfectly aligned devices, the intraband responsivity near the secondary Dirac point greatly exceeds that at the main Dirac point, with

$$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$07

and experimental $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$08–$$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$09 at $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$10. Above-gap excitations change the lineshape qualitatively: interband photocurrent dips appear exactly at $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$11, revealing inversion-breaking gaps and avoided crossings. The reported values include $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$12 for a valence-band secondary Dirac point at $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$13, $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$14 at a conduction-band secondary Dirac point in $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$15 devices, $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$16 in $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$17 devices, and local gaps $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$18–$$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$19 near a conduction-band secondary Dirac point. Tight-binding and shift-conductivity simulations reproduce the sign reversals and confirm gap values $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$20–$$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$21 (Delgado-Notario et al., 22 Jul 2025).

A related but distinct form of gate spectroscopy appears in nonlinear THz edge photocurrents in graphene. In Hall-bar graphene/hexagonal-BN devices under a back gate, the Fermi energy obeys

$$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$22

with $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$23. The edge photogalvanic current contains a Drude-like intraband term and a direct interband term,

$$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$24

with different saturation laws and different gate dependences. Direct transitions switch on when $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$25 at small $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$26, so sweeping $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$27 tunes the Pauli-blocking edge through a fixed THz photon energy. The paper states that by fitting $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$28 with the two-channel model one simultaneously obtains the Fermi-level map $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$29, the electron and hole relaxation times $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$30, the electron temperature $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$31, and the characteristic energy scales $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$32 and Pauli-block thresholds (Candussio et al., 2021).

These examples clarify a central point: in gate-dependent THz photocurrent spectroscopy, “spectroscopy” need not mean frequency sweep alone. A fixed-frequency experiment can become spectroscopic when the gate shifts the Fermi level, carrier type, or miniband occupation through an optical threshold.

6. Nanoscale waveform sampling and cryogenic quantum sensing

In terahertz scanning tunneling microscopy, the “gate” is the intrinsic nonlinearity of the tunnel junction itself. Under a static bias $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$33, a THz pulse acts like a transient bias

$$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$34

with field-enhancement factor $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$35, so the instantaneous tunneling current is

$$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$36

Li et al. introduced a two-pulse coherent scan in which a strong gate pulse and a weak probe pulse generate a lock-in-detected photocurrent

$$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$37

When the gating filter is much shorter than the probe waveform, this reduces to direct sampling of the near-field waveform. The gate pulse produced a strongly gated current burst of $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$38 FWHM; the local fields reached $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$39; and line scans across a single Au atom cluster yielded a full-width-half-maximum of $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$40. The same method retrieved carrier-envelope phase shifts introduced by a custom metamaterial CEP shifter and enabled point-to-point local THz time-domain spectroscopy imaging (Li et al., 2023).

At cryogenic temperatures, graphene Josephson junctions provide a different gate-dependent THz photocurrent spectroscopy platform. The reported devices used monolayer graphene encapsulated between hBN layers, with naturally cracked NbSe$$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$41 contacts forming a clean $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$42 graphene weak link and a bottom graphite gate swept from $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$43 to $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$44. Under low-intensity illumination at $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$45, $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$46, and $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$47, the key effect was radiation-induced heating and suppression of the critical current. Under current bias, the photovoltage was defined as

$$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$48

and the responsivity and thermal-fluctuation NEP were extracted from

$$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$49

At $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$50 the paper reports, for three gate voltages, $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$51 at $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$52, $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$53 at $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$54, and $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$55 at $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$56; corresponding responsivities of $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$57, $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$58, and $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$59; and $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$60, $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$61, and $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$62. Near the local neutrality point, hysteretic current-voltage characteristics persisted up to $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$63, which the authors identify as a potential route toward single-photon THz detection beyond millikelvin temperatures (Zhou et al., 1 Apr 2026).

These two implementations occupy opposite ends of the spatial and thermodynamic spectrum. THz-STM converts the tunnel junction into a sub-200 fs nanoscale gate for waveform sampling, whereas graphene Josephson junctions convert a gate-tuned superconducting weak link into a cryogenic calorimetric detector. In both cases, the gate sweep determines which aspect of the THz field becomes observable.

7. Interpretive issues, misconceptions, and technological significance

One misconception is that helicity-sensitive THz photocurrents in transistors are simply another manifestation of the standard Dyakonov–Shur response. The dual-grating-gate HEMT experiments explicitly separate these regimes: at $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$64 the microwave measurements recover the standard Dyakonov–Shur $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$65 response, whereas the helicity-dependent dynamics are identified as unique to the DGG ratchet geometry at THz frequencies (Faltermeier et al., 2015).

A second misconception is that gate dependence only modulates the overall magnitude of the photoresponse. The literature here shows several stronger statements. In DGG HEMTs, dual-gate bias acts as a tunable symmetry-breaking element that selects and amplifies specific polarization and ratchet-driven photocurrent channels. In graphene superlattices, unequal subgrating voltages can invert the current over the entire back-gate range and maximize it by more than an order of magnitude. In short-gate Dyakonov–Shur devices, sub-optimal gate placement can substantially decrease the detection efficiency. In moiré superlattices, gate sweeps reveal tiny inversion-breaking global and local energy gaps that are inaccessible by conventional electrical or optical techniques (Faltermeier et al., 2015, Olbrich et al., 2015, Riolo et al., 16 Jan 2025, Delgado-Notario et al., 22 Jul 2025).

A third misconception is that useful THz photocurrent spectroscopy must be resonant. The corpus shows both resonant and off-resonant modes of operation. Off-resonance regimes include intraband ratchets, Seebeck thermoratchets, Pauli-blocking edge spectroscopy, and the moiré-superlattice regime where enhanced zero-bias responsivities arise due to lower Fermi velocities and specific valley degeneracies. Resonant regimes include Dyakonov–Shur plasma waves, Fabry–Pérot plasmons, and magnetoplasmons. This suggests that gate-dependent THz photocurrent spectroscopy should be understood as a broad spectroscopic methodology rather than as a single resonant detector principle (Olbrich et al., 2015, Tomadin et al., 2013, Delgado-Notario et al., 28 Nov 2025, Delgado-Notario et al., 22 Jul 2025).

The application landscape follows directly from these distinctions. The DGG HEMT work provides a proof of principle for all-electric detection of the radiation’s polarization state and identifies potential for resonant plasmonic enhancement, enabling high-responsivity, fast THz polarimeters and imaging arrays. Plasmonic FETs offer compact room-temperature spectrometers covering $$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$66–$$s_0 = |E_x|^2 + |E_y|^2,\quad s_1 = |E_x|^2 - |E_y|^2,\quad s_2 = E_x E_y^* + E_x^* E_y,\quad s_3 = i (E_x E_y^* - E_x^* E_y).$$67. Graphene TeraFET magnetoplasmonics enables magnetically programmable, frequency-selective photonics. THz-STM generalizes to local THz-TDS imaging across arbitrary surfaces. Graphene Josephson junctions point toward broadband cryogenic radiation sensing and, potentially, single-photon THz detection. Moiré superlattices are presented as promising material platforms for advanced, sensitive and low-noise terahertz detection applications (Faltermeier et al., 2015, Liu et al., 2020, Delgado-Notario et al., 28 Nov 2025, Li et al., 2023, Zhou et al., 1 Apr 2026, Delgado-Notario et al., 22 Jul 2025).

A plausible synthesis is that the field is converging on a unified experimental idea: a THz excitation is converted into dc transport by a nonlinear electronic element, while the gate sweep supplies the spectroscopic axis. Depending on architecture, that axis resolves polarization state, cavity mode index, carrier type, Berry-curvature-driven interband response, local waveform phase, or thermal switching threshold.