Photon drag at the junction between metal and 2d semiconductor

Dmitry Svintsov; Zhanna Devizorova

REVIEW 2 major objections 4 minor 17 references

Photon drag at the junction between metal and 2d semiconductor

T0 review · 2 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A metal contact to a 2D semiconductor converts incident light into a photon-drag photovoltage whose p-polarized response survives as the sheet conductivity tends to zero.

desk verdict Clean theory paper with a genuinely new prediction of strong junction photon drag in 2D materials; the main open question is whether nonlocal corrections near the metal edge change the headline numbers. read the letter →

arxiv 2411.14075 v1 pith:7RCFURNB submitted 2024-11-21 cond-mat.mes-hall physics.optics

Dmitry Svintsov , Zhanna Devizorova This is my paper · ORCID

classification cond-mat.mes-hallphysics.optics

keywords photondragmetal-2dsemiconductorjunctionterahertzphotodetectionlightningrodeffectWiener-Hopfdiffractionmomentumtransfercoefficientphotothermoelectrictwo-dimensionalelectrongas

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper argues that photon drag—photocurrent produced when light transfers momentum to charge carriers—does not have to be weak at the contact between a metal and a two-dimensional semiconductor. Diffraction at the metal edge creates strongly nonuniform local fields, and the Lorentz force on induced charges in these fields does not average to zero. Combining an exact diffraction solution with a microscopic force-balance calculation, the authors derive a responsivity $r_{pd}=-2(\alpha_x+\alpha_y)/(\omega e n_{2d})$, where the dimensionless momentum-transfer coefficients $\alpha_x,\alpha_y$ depend only on the normalized 2D conductivity $\eta=2\pi\sigma/c$ and on polarization. For $p$-polarized light, $\alpha_x$ remains finite ($\simeq 0.45$) as $\eta\to0$, because the edge field diverges as $1/\sqrt{\eta(1+\eta)}$; for $s$-polarized light, $\alpha_y\propto \eta\ln\eta^{-1}$. If this is right, contact-induced photon drag can dominate the thermoelectric response at terahertz frequencies, with the ratio set by $\omega\tau_\varepsilon$ for $p$-polarization and no such suppression for $s$-polarization.

What carries the argument

The calculation is carried by three ingredients: (i) the wave-mean-force expression $f_{pd}=\langle\rho E\rangle+c^{-1}\langle j\times B\rangle$, which after time-averaging and using the continuity equation and the local Ohm's law $j_\omega(x)=\sigma_\omega(x)E_\omega(x)$ becomes $\frac{2}{\omega}\mathrm{Im}\{\sigma_\omega[\partial_x E_x E_x^*-\partial_x E_y^*E_y]\}$; (ii) the exact Wiener-Hopf diffraction spectra for the local fields, Eqs. (14) and (16), obtained from factorized 2D dielectric functions $\varepsilon_p(q)=1+\eta\sqrt{k_0^2-q^2}/k_0$ and $\varepsilon_s(q)=1+\eta k_0/\sqrt{k_0^2-q^2}$; and (iii) the momentum balance plus thermal balance equations that separate the photon-drag voltage from the thermoelectric voltage. The singular behavior enters through the edge field $E_x(0)=E_0/\sqrt{\eta(1+\eta)}$, which keeps $\eta|E_x|^2$ finite as $\eta\to0$, and through the long-range $e^{ik_0x}/\sqrt{x}$ cylindrical wave whose logarithmic divergence in the drag integral is cut off at distance $\sim\lambda_0/\eta$.

What would settle it

A direct check: measure the zero-bias photovoltage at a metal-graphene junction under focused p-polarized terahertz illumination while a back gate tunes the sheet density and hence $\eta$ over at least a decade. The theory predicts a response that tracks $1/n_{2d}$ with $\alpha_x\simeq0.45$ essentially independent of $\eta$; observation of a strong $\eta$-dependent deviation, or of an $\alpha_x$ that vanishes with $\eta$, would rule out the local-field drag mechanism described here. For s-polarization, the signature is the superlinear $\alpha_y\propto \eta\ln(1/\eta)$ growth, which should be absent if nonlocal corrections dominate.

Watch

Extended reading notes

Core claim

At a straight interface between a perfect metal and a 2D electron system, the open-circuit photovoltage from photon drag is $V_{pd}=-(2/\omega e n_{2d})\int_0^\infty \mathrm{Im}\{\sigma_\omega[\partial_x E_x E_x^*-\partial_x E_y^* E_y]\}\,dx$, and for normal incidence the responsivity factorizes into a universal $1/(\omega e n_{2d})$ prefactor times the sum of momentum-transfer coefficients $\alpha_x+\alpha_y$. The $p$-polarized coefficient stays nonzero in the zero-conductivity limit because the singular edge field concentrates the drag force in a narrow region of width $\sim\eta\lambda_0$; the $s$-polarized coefficient is dominated by the long cylindrical wave emitted by the half-plane and scales as $\eta\ln(1/\eta)$. The same expression shows that the ordinary bulk photon drag is smaller by a factor $\eta' k_x L$, so the junction effect removes both conventional smallness parameters: photon momentum and low absorbance.

Load-bearing premise

The derivation assumes that the current at each point responds locally to the electric field, $j_\omega(x)=\sigma_\omega(x)E_\omega(x)$; near the contact for small $\eta$ the field changes over a length $\sim\eta\lambda_0$, which can be shorter than the electron mean free path or screening length, so nonlocal spatial-dispersion corrections could shift the value of $\alpha_x$ and the predicted scaling.

Editorial extensions

If this is right

At terahertz frequencies, junction photon drag can dominate the hot-carrier thermoelectric response for $p$-polarized light whenever $\omega\tau_\varepsilon\gtrsim1$, which is typical for wavelengths of about 30 $\mu$m and shorter.
For $s$-polarized light the photovoltage is essentially pure photon drag, since the thermoelectric contribution at the edge is small and $\alpha_y$ remains positive.
The responsivity contains no factor of photon momentum or small absorbance: the prefactor $2/(\omega e n_{2d})$ alone gives tens of $\mu$V cm$^2$/W at 1 THz and $n_{2d}=10^{11}$ cm$^{-2}$.
The theory applies to any 2D conductor describable by a local dynamic conductivity, including graphene, semiconductor quantum wells, and transition-metal dichalcogenides.
Plasmonic resonances do not resonantly enhance the drag: the plasmon quality factor multiplies the dissipative conductivity, so the momentum-transfer coefficients remain smooth across the complex-$\eta$ plane.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Editorial inference: because the drag force is proportional to $\mathrm{Im}\,\sigma_\omega$ and the field profile is set by both $\eta'$ and $\eta''$, measuring the photovoltage with focused light at both polarizations gives separate access to the real and imaginary parts of the sheet conductivity without patterning a separate antenna.
Editorial inference: the same mechanism should contribute to the DC photoresponse of contacted 2D detectors usually fitted by plasma-wave or hot-carrier rectification, so polarization-resolved contact-illumination measurements could isolate this contact drag from those channels.
Editorial inference: the local-Ohm's-law assumption can be relaxed by replacing $\sigma_\omega(x)$ with a nonlocal conductivity kernel; since the $p$-polarized drag is generated within $\sim\eta\lambda_0$ of the edge, the first nonlocal corrections are expected when this length becomes comparable to the electron mean free path or screening length.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The paper does something solid: it takes the exact Wiener–Hopf diffraction spectra at a metal–2DES junction and combines them with a transparent photon-drag transport derivation. The result is a clear, testable prediction that the junction drag photovoltage is not suppressed by the small photon momentum, with distinctive scaling laws: α_x stays finite (~0.45) as η→0 for p-polarization, and α_y ~ η ln(1/η) for s-polarization. The comparison with thermoelectric response, giving a ratio of order ωτ_ε for p-polarization, is a useful rule of thumb. The authors are also honest about the main assumptions, which is a plus.

The real soft spot is the locality assumption near the metal edge. The derivation uses j = σE everywhere, but the p-polarization drag is dominated by a near-edge region of width l ~ ηλ_0. For small η in realistic THz graphene, that width is comparable to or smaller than the electron mean free path. The paper acknowledges the assumption but does not estimate what nonlocal corrections do to α_x ≈ 0.45. This is not a fatal flaw, but it means the numerical value and possibly the η→0 limit are less secure than the text suggests. A second, milder issue is the claim that s-polarization photon drag always dominates thermoelectric effect. That rests on a local-heating approximation in which field at the junction sets the temperature rise; but heat generated over the larger strip where the s-polarized field is non-zero can diffuse to the junction, so the comparison deserves a more careful treatment.

The citation pattern is fine. The field spectra come from earlier work by the same group, but those are parameter-free exact solutions, not fitted hacks. The derivation is analytic and detailed enough for independent reimplementation. This is a good theory paper for people working on THz photodetection, photocurrent mapping, and photon drag in 2D materials. It deserves a serious referee; the concerns I raised are addressable in revision but do not invalidate the central idea.

Referee Report

2 major / 4 minor

Summary. The manuscript develops a theory of photon drag at the junction between a metal and a two-dimensional electron system (2DES). The authors combine exact Wiener-Hopf diffraction spectra for the local electromagnetic fields at a metal-2DES edge with a microscopic transport-theory expression for the ponderomotive force on the 2D carriers. Their central result, Eq. (18), is a photovoltage responsivity r_pd = -2/(omega e n_2d)(alpha_x + alpha_y), where the dimensionless momentum-transfer coefficients alpha_i depend only on the normalized 2D conductivity eta = 2*pi*sigma/c and on polarization. For p-polarized light, alpha_x approaches a finite constant (~0.45) as eta -> 0, which the authors attribute to the dynamic lightning-rod field singularity at the edge; for s-polarized light, alpha_y scales as eta ln(1/eta), arising from a long-range cylindrical wave emitted by the metal half-plane. The paper also compares the junction photon drag with the contact thermoelectric effect, concluding that for p-polarization the ratio is set by omega*tau_epsilon and for s-polarization photon drag dominates.

Significance. If the central prediction is correct, the paper identifies a qualitatively new route to terahertz photodetection: junction photon drag is not suppressed by the small free-photon momentum or by the small absorbance of typical 2D materials, and it can exceed the thermoelectric response in common contact geometries. The derivation from the ponderomotive force, Eqs. (3)-(13), is clean and internally consistent, and the use of parameter-free Wiener-Hopf diffraction spectra from Refs. 33 and 34, with no fitted parameters, is a genuine strength. The two scaling laws (alpha_x -> const and alpha_y ~ eta ln eta^{-1}) are falsifiable predictions that can be tested in photocurrent-mapping experiments. However, the universality of these predictions rests on assumptions whose breakdown scales are not quantified, in particular the locality of the Ohm's law in the singular near-edge region and the treatment of the logarithmic divergence in the s-polarization channel.

major comments (2)

[Section II.A and Eq. (21)] The locality assumption j_omega(x) = sigma_omega(x) E_omega(x) is load-bearing for the p-polarization result. The text states that for small eta the p-polarized field diverges at the edge as E_x(0) ~ E_0/sqrt(eta(1+eta)) and varies over a length l ~ eta*lambda_0. For eta ~ 10^-2 (graphene at THz frequencies) and lambda_0 = 30-100 micrometers, l is roughly 0.3-1 micrometer, which is comparable to or shorter than the electron mean free path in high-mobility 2D systems at low temperature. In this regime a q-dependent conductivity sigma(q,omega) modifies both the field profile and the integral in Eq. (19), so the numerical value alpha_x ~ 0.45 and its claimed eta -> 0 limit are not established. The manuscript acknowledges the locality assumption but provides no estimate of the breakdown scale. Please quantify the nonlocal correction, for example by comparing q ~ 1/l with the inverse mean free path, or clearly state the parameter regime in which the universal value of alpha_x is expected to hold.
[Section III, s-polarization scaling paragraph] The claim that alpha_y depends only on eta and polarization is complicated by the logarithmic divergence described for s-polarization. The text states that the integral (19) diverges logarithmically at large distances and is cut off by finite absorption in the 2DES at L ~ lambda_0/eta, but this cutoff is not derived. In a finite sample of length L_sd < lambda_0/eta, the coefficient will depend on ln(L_sd/lambda_0) or on the actual absorption length, so the abstract's statement that the momentum-transfer coefficient depends only on eta and polarization is not universal. A finite-length expression for alpha_y(L_sd), or an explicit statement that the scaling requires L_sd >> lambda_0/eta, is needed to make the s-polarization prediction usable for experiments.

minor comments (4)

[Section II.B] In the sentence introducing Eqs. (12)-(13), "Demoting the Seebeck coefficient" should read "Denoting the Seebeck coefficient".
[Section III] The word "superliner" should be "superlinear" in the discussion of the s-polarization scaling.
[Fig. 1 caption] The second bullet in the caption describes the s-polarized case (E0 parallel to the junction), but the text labels it as "For p-polarized incident wave"; this should be corrected to s-polarized.
[Eq. (21)] Equation (21) as typeset appears as E_x(0) = E_0 sqrt(eta(1+eta)), which contradicts the surrounding text stating that the field diverges as eta -> 0. The intended expression is presumably E_x(0) = E_0 / sqrt(eta(1+eta)); the typesetting should be corrected.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation: the central α(η) scalings are computed from parameter-free Wiener-Hopf field spectra; only a mild same-group citation is present.

full rationale

The paper's central claim—r_pd = -2/(ω e n2d)(αx+αy) with αx tending to a finite constant and αy ∝ η ln(1/η) at small η—is obtained by substituting the Fourier spectra of the local fields, Eqs. (14) and (16), into the independently derived momentum-transfer integral, Eq. (19). No parameter is fitted to the target quantity; αi is computed from the field solution, not defined into existence by the claimed result. The field spectra are quoted from Refs. 33 and 34, which are by the same group, but those are exact Wiener-Hopf solutions of Maxwell's equations for a step junction with local conductivity; their assumptions (local Ohm's law, stepwise carrier density) do not include the value of α, and the solutions are parameter-free and externally checkable. The photovoltage formula also overlaps with Ref. 11, but that is a prior independent result by other authors and is explicitly generalized to confined 2DES. The only substantive caveat is the locality assumption j=σE near the singular edge, stated in Sec. II.A, which is a correctness risk about nonlocal corrections rather than a circular step. Thus no load-bearing input reduces to the output by construction; the score of 2 reflects the mild same-author citation of the diffraction solution, not an actual circular reduction.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The paper introduces no fitted free parameters; η, n2d, and τε are material inputs. The central claim rests on several stated modeling assumptions, most notably the locality of the current-field relation near the singular edge, the truncated angular-harmonic closure, the borrowed Wiener-Hopf field spectra, and a local thermal model for the thermoelectric comparison.

assumptions (5)

domain assumption Locality of the current-field relation j_ω(x)=σ_ω(x)E_ω(x), i.e., no spatial dispersion.
Stated in Section II.A before Eq. (3); required for Eq. (4). The p-polarization drag is dominated by the near-edge region where the field varies on scale l~ηλ0, which can be shorter than the electron mean free path, making this assumption load-bearing.
domain assumption Truncation of the second-order distribution function to angular harmonics 0 and 1; the stress tensor reduces to scalar pressure.
Invoked in Section II.B to obtain Eqs. (6) and (7); requires strong electron-electron collisions or dominant low-angle scattering. Affects the relation between photovoltage and force density.
domain assumption Open-circuit condition with a perfect metallic contact (n(x<0)→∞) and photovoltage detected between the contact and the 2DES bulk.
Used to derive Eqs. (12) and (13); assumes the photovoltage at an individual contact can be isolated, for example by focused illumination as discussed in Section IV.
domain assumption The exact diffraction field spectra (14) and (16) from Refs. 33,34 describe the local fields at a sharp metal-2DES junction.
The paper states it borrows these results in Section II. The central scaling laws inherit every approximation in those Wiener-Hopf solutions, including zero-thickness metal, local conductivity, and semi-infinite geometry.
domain assumption Thermal balance with local energy relaxation time τε, Eq. (8), for estimating the thermoelectric photovoltage.
Used in Section IV to obtain Eq. (24) and the ratio r_pte/r_pd≈ωτε; the local-heating approximation may understate nonlocal heating for s-polarization.

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Cite this review

Pith. "Pith review of Photon drag at the junction between metal and 2d semiconductor." pith.science (2026). https://pith.science/paper/7RCFURNB

@misc{pith2026241114075,
  author       = {Pith},
  title        = {Pith review of: Photon drag at the junction between metal and 2d semiconductor},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7RCFURNB}},
  note         = {Machine review of arXiv:2411.14075}
}

abstract

Photon drag represents a mechanism of photocurrent generation wherein the electromagnetic (EM) field momentum is transferred directly to the charge carriers. It is believed to be small by the virtue of low photon momentum compared to the typical momenta of the charge carriers. Here, we show that photon drag becomes particularly strong at the junctions between metals and 2d materials, wherein highly non-uniform local EM fields are generated upon diffraction. To this end, we combine an exact theory of diffraction at 'metal-2d material' junctions with microscopic transport theory of photon drag, and derive the functional dependences of the respective photovoltage on the parameters of EM field and 2d system. The voltage responsivity appears inversely proportional to the electromagnetic frequency $\omega$, the sheet density of charge, and a dimensionless momentum transfer coefficient $\alpha$ which depends only on 2d conductivity in units of light speed $\eta = 2\pi \sigma/c$ and light polarization. For $p$-polarized incident light, the momentum transfer coefficient appears finite even for vanishingly small 2d conductivity $\eta$, which is a consequence of dynamic lightning rod effect. For $s$-polarized incident light, the momentum transfer coefficient scales as $\eta \ln \eta^{-1}$, which stems from long-range dipole radiation of a linear junction. A simple estimate shows that the ratio of thermoelectric and photon drag photovoltages at the junction for $p$-polarization is roughly $\omega\tau_\varepsilon$, where $\tau_\varepsilon$ is the energy relaxation time, while for $s$-polarization the photon drag always dominates over the thermoelectric effect.

Figures

Figures reproduced from arXiv: 2411.14075 by the authors.

**Figure 2.** FIG. 2. Photon drag at metal-2d semiconductor interface [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** FIG. 3. Momentum transfer coefficients at metal-2DES junc [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

17 extracted references · 17 canonical work pages

[1]

1 (A)], electromagnetic diﬀraction gives rise to the local z-component of electric ﬁeld

For p-polarized incident wave [ B0 is directed along the junction, Fig. 1 (A)], electromagnetic diﬀraction gives rise to the local z-component of electric ﬁeld. This components induces the charge density ρ(t) ∝ Ez via the dynamic ﬁeld ef- fect. The x-component of the ﬁeld drags the induces charges longitudinally, which results in photocurrent. For p-polar...

work page
[4]

We consider the most practical case of monochromatic waves, E(t) = Eω e−iωt + h .c., and similarly for other time-dependent quantities

are relevant to the p- and s-polarizations of the incident wave, respectively. We consider the most practical case of monochromatic waves, E(t) = Eω e−iωt + h .c., and similarly for other time-dependent quantities. The charge and current den- sities in that case can be expressed with continuity equa- tion and Ohm’s law: −iωρω + (∇, jω ) = 0 , jω = σω Eω ,...

work page
[5]

(3) The superscript ‖ implies taking only the x and y com- ponents of the respective vector, it stems from the two- dimensional character of the current density

we ﬁnd, after some simpliﬁcations: fpd = 2 ω Im σω {( ∇‖ Eω ) E∗‖ ω − [E‖ ω × [∇×E∗ ω ]] } . (3) The superscript ‖ implies taking only the x and y com- ponents of the respective vector, it stems from the two- dimensional character of the current density. Further simpliﬁcations are possible if all ﬁelds do not depend on 3 the coordinate y along the junctio...

work page
[6]

Similarly, the drag photocurrent can appear as the unidirectional surface plasmons are propagating along the conductor

work page
[7]

Such photocurrent is often marked as ’plasmon drag’10, though the underlying electromagnetic forces are the same as in photon drag

Launching of such unidirectional plasmons is achieved with specially designed asymmetric couplers, the simplest example being the metal grating lacking the inversion center above the 2d semiconduc- tor 8,9. Such photocurrent is often marked as ’plasmon drag’10, though the underlying electromagnetic forces are the same as in photon drag. Taking a detailed ...

work page
[8]

At this stage, we assume that all angular harmonics of the second-order dc distribution function, except for the zeroth and the ﬁrst ones, are damped

has no limits of applicability, it can become useful for the evaluation of photocurrent if only the functional forms of momentum vector Pi and stress tensor Π (2) ij are speciﬁed. At this stage, we assume that all angular harmonics of the second-order dc distribution function, except for the zeroth and the ﬁrst ones, are damped. This occurs either for str...

work page
[11]

(27) We observe that ’ordinary’ photon drag diﬀers from the ’junction drag’ by factors of η′ (absorbance factor) and kxLsd (light momentum factor)

to the ﬁeld E ∝ eikxx, we ﬁnd r(0) pd = − 2 ωen2d η′(kxL) |Ex|2 + |Ey|2 |E0|2 ∼ η′(kxL)rpd. (27) We observe that ’ordinary’ photon drag diﬀers from the ’junction drag’ by factors of η′ (absorbance factor) and kxLsd (light momentum factor). The former is well below unity for graphene and most quantum wells. The latter is below unity for sub-wavelength devi...

work page
[13]

for photon drag photovoltage supple- mented by expressions of the local electric ﬁelds ( 14,16) form the necessary building blocks for numerical evalua- tions. The results can be cast in a transparent form by introducing the photovoltage responsivity of the junction per incident light intensity rpd = VpdZ0/(2E2 0), where Z0 = 4π/c is the free-space impeda...

work page

Show all 17 references

[14]

7 All our consideration was based on assumption that the photovoltage at an individual metal contact (say, source) can be isolated from the photovoltage at the drain

and ( 12) combined with simulations of local electric ﬁelds. 7 All our consideration was based on assumption that the photovoltage at an individual metal contact (say, source) can be isolated from the photovoltage at the drain. It means that the incident radiation should be fo...
[16]

We attempted to formulate the theory in terms of high- frequency 2d conductivity σω , independent of its micro- scopic nature

The resulting ’con- tact drag photovoltage’ does not contain typical small- ness parameters associated with low photon momentum and low absorbance by (most) two-dimensional systems. We attempted to formulate the theory in terms of high- frequency 2d conductivity σω , independe...
[17]

( A1) is possible

Alternatively, a direct numerical evaluation us- ing Eq. ( A1) is possible. When dealing with q-values on the real axis (which is suﬃcient for all calculations), we rewrite Eq. A1 as: ε± (q) = √ ε(q)× exp   ± +∞∫ 0 ln ε (q + v) − ln ε (q − v) 2πiv dv    . (A4) The conven...

1970 arXiv
[19]

This results in αx = |Epl|2 |E0|2 { Reη × Qpl − Imη 2 } , (23) where Qpl = Reqp pl/Imqp pl is the quality factor of 2D plas- mons

and evaluating the respective momentum transfer coeﬃcient. This results in αx = |Epl|2 |E0|2 { Reη × Qpl − Imη 2 } , (23) where Qpl = Reqp pl/Imqp pl is the quality factor of 2D plas- mons. The above simple calculation explains that plas- monic Q-factor (beneﬁting from low dis...
[21]

(25) As the momentum transfer coeﬃcient αx ∼ 1, we observe that the only parameter governing the ratio of PTE and PD photovoltages is ωτε

for local ﬁeld, and assuming real conductivity, we ﬁnd rpte = 2τε en2d = ωτε αx rpd. (25) As the momentum transfer coeﬃcient αx ∼ 1, we observe that the only parameter governing the ratio of PTE and PD photovoltages is ωτε. The energy relaxation time τε varies between hundreds...
[33]

The diﬀerence in eﬀective dielectric functions in s- and p- polarizations results in diﬀerent plasmon dispersion laws

In the Fourier space, they can be seen as sin- gularities of E(q) appearing provided ε(q) = 0. The diﬀerence in eﬀective dielectric functions in s- and p- polarizations results in diﬀerent plasmon dispersion laws. For p-polarization the plasmons exist for inductive 2DES conduc...
[42]

In the far infrared range ( λ0 = 10 µm), we estimate ωτε ≫ 1 even for the shortest energy relaxation time τε = 0.1 ps

Therefore, the junction photon drag can readily exceed the thermoelectric eﬀect, at least at terahertz fre- quencies. In the far infrared range ( λ0 = 10 µm), we estimate ωτε ≫ 1 even for the shortest energy relaxation time τε = 0.1 ps. More accurate estimates of thermoelectri...
[43]

Relative polarity of carriers in the screening layer and in the 2DES bulk aﬀects the photo- electric eﬀects

In the simplest approximation, the metal-induced carrier den- sity can be considered as constant in the screening layer of length lj ∼ 100 nm. Relative polarity of carriers in the screening layer and in the 2DES bulk aﬀects the photo- electric eﬀects. Dissimilar doping ( p − n...
[44]

Evaluation of photo- voltages in this realistic situation can be based on general expressions (

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [1]

1 (A)], electromagnetic diﬀraction gives rise to the local z-component of electric ﬁeld

For p-polarized incident wave [ B0 is directed along the junction, Fig. 1 (A)], electromagnetic diﬀraction gives rise to the local z-component of electric ﬁeld. This components induces the charge density ρ(t) ∝ Ez via the dynamic ﬁeld ef- fect. The x-component of the ﬁeld drags the induces charges longitudinally, which results in photocurrent. For p-polar...

work page

[2] [4]

We consider the most practical case of monochromatic waves, E(t) = Eω e−iωt + h .c., and similarly for other time-dependent quantities

are relevant to the p- and s-polarizations of the incident wave, respectively. We consider the most practical case of monochromatic waves, E(t) = Eω e−iωt + h .c., and similarly for other time-dependent quantities. The charge and current den- sities in that case can be expressed with continuity equa- tion and Ohm’s law: −iωρω + (∇, jω ) = 0 , jω = σω Eω ,...

work page

[3] [5]

(3) The superscript ‖ implies taking only the x and y com- ponents of the respective vector, it stems from the two- dimensional character of the current density

we ﬁnd, after some simpliﬁcations: fpd = 2 ω Im σω {( ∇‖ Eω ) E∗‖ ω − [E‖ ω × [∇×E∗ ω ]] } . (3) The superscript ‖ implies taking only the x and y com- ponents of the respective vector, it stems from the two- dimensional character of the current density. Further simpliﬁcations are possible if all ﬁelds do not depend on 3 the coordinate y along the junctio...

work page

[4] [6]

Similarly, the drag photocurrent can appear as the unidirectional surface plasmons are propagating along the conductor

work page

[5] [7]

Such photocurrent is often marked as ’plasmon drag’10, though the underlying electromagnetic forces are the same as in photon drag

Launching of such unidirectional plasmons is achieved with specially designed asymmetric couplers, the simplest example being the metal grating lacking the inversion center above the 2d semiconduc- tor 8,9. Such photocurrent is often marked as ’plasmon drag’10, though the underlying electromagnetic forces are the same as in photon drag. Taking a detailed ...

work page

[6] [8]

At this stage, we assume that all angular harmonics of the second-order dc distribution function, except for the zeroth and the ﬁrst ones, are damped

has no limits of applicability, it can become useful for the evaluation of photocurrent if only the functional forms of momentum vector Pi and stress tensor Π (2) ij are speciﬁed. At this stage, we assume that all angular harmonics of the second-order dc distribution function, except for the zeroth and the ﬁrst ones, are damped. This occurs either for str...

work page

[7] [11]

(27) We observe that ’ordinary’ photon drag diﬀers from the ’junction drag’ by factors of η′ (absorbance factor) and kxLsd (light momentum factor)

to the ﬁeld E ∝ eikxx, we ﬁnd r(0) pd = − 2 ωen2d η′(kxL) |Ex|2 + |Ey|2 |E0|2 ∼ η′(kxL)rpd. (27) We observe that ’ordinary’ photon drag diﬀers from the ’junction drag’ by factors of η′ (absorbance factor) and kxLsd (light momentum factor). The former is well below unity for graphene and most quantum wells. The latter is below unity for sub-wavelength devi...

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[8] [13]

for photon drag photovoltage supple- mented by expressions of the local electric ﬁelds ( 14,16) form the necessary building blocks for numerical evalua- tions. The results can be cast in a transparent form by introducing the photovoltage responsivity of the junction per incident light intensity rpd = VpdZ0/(2E2 0), where Z0 = 4π/c is the free-space impeda...

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