Injection Current in Physics & Engineering

• Injection current is a transport phenomenon where externally injected carriers, momentum, or angular momentum create measurable current responses in various systems.
• It spans diverse applications including secure communications, superconducting devices, plasma accelerators, photovoltaic effects, and spintronics.
• Research covers methodologies and simulations quantifying injection levels, control parameters, and countermeasures against current-based attacks.

Injection current denotes a family of transport phenomena in which a current is established by an externally imposed injection process, or, in nonlinear optics, by asymmetric photoexcitation of carriers. In contemporary literature the term spans active electrical injection into communication channels and superconducting films, beam-current formation in plasma accelerators, dc charge injection in bulk photovoltaic effects, and pure spin-current generation in spintronic and low-dimensional systems (Chen et al., 2015, Kogan et al., 2014, Hue et al., 2023, Arora et al., 2021, Panday et al., 2018). The shared motif is not a single microscopic mechanism, but the introduction of carriers, momentum, or angular momentum into a system such that a measurable current or current-like response is generated, modulated, or inferred.

1. Scope and domain-specific meanings

In the cited literature, “injection current” is not monosemous. It refers to externally driven electrical current in some fields, to the current of an injected witness bunch in accelerator physics, and to a nonlinear optical dc response in condensed matter. This variety is substantial enough that the meaning is usually fixed by context.

Domain	Injection process	Representative quantity
Secure communication	Gaussian current injected into a KLJN channel	Eve’s success probability $P_E$
Superconducting and semiconductor devices	Current or carriers injected into a bank, base, or cathode	Phase profile, $J_c$, $I_{C,\max}$
Plasma and beam physics	Density-downramp, pulsed cathode, or helicity injection	$J_w$, SCL current density, 3D perturbing field
Bulk photovoltaic transport	Optical interband excitation under broken symmetry	Injection-current tensor or current rate
Spin transport	Electrical or optical spin-current injection	Spin current density, DW velocity
Correlated 1D transport	Leviton injection from an STM tip	$\bar I(x)$, $S^{\rm ex}(x)$

In secure-key hardware, the current is deliberately imposed by an adversary; in Josephson and bipolar devices it is an engineered control parameter; in plasma and vacuum electronics it is the transported or transport-limited beam current; in nonlinear optics it is a second-order or interference-enabled dc response; and in spintronics it is often a pure spin current rather than a charge current (Chen et al., 2015, Kogan et al., 2014, Xia et al., 2024, Hue et al., 2023, Pei et al., 19 Dec 2025, Fukuzawa et al., 2023).

2. Electrical injection as attack mechanism and control variable

In the KLJN secure key exchange, the current injection attack is an active invasive attack in which Eve injects a Gaussian current $I_{\text{inj}}(t)$ with the same bandwidth as the channel noises, and during each bit exchange period measures the cross-correlations

$$p_a=\langle I_{\text{inj}}(t) I_{\text{ch,Alice}}(t)\rangle,\qquad p_b=\langle I_{\text{inj}}(t) I_{\text{ch,Bob}}(t)\rangle.$$

Because the injected current divides according to the current divider rule, more current flows toward the lower resistance $R_L$ than toward $R_H$. Eve therefore evaluates $J_c$0, guessing LH if $J_c$1 and HL otherwise. LTSPICE simulations with an RG58 cable model, $J_c$2, $J_c$3, a $J_c$4 s bit exchange period, 10,000 key bits, $J_c$5, and 250 Hz noise bandwidth found $J_c$6, $J_c$7, and $J_c$8 for injected currents equal to $J_c$9, $I_{C,\max}$0, and $I_{C,\max}$1 of the channel current RMS value, respectively; larger injection therefore produced larger information leakage (Chen et al., 2015). The same work reported two countermeasures. Instantaneous current comparison in the ideal system, and current-plus-voltage comparison against an accurate cable model in the practical system, detect the attack and lead Alice and Bob to discard the bit. A simple privacy-amplification scheme based on XOR-ing adjacent bits reduced $I_{C,\max}$2 from $I_{C,\max}$3 to $I_{C,\max}$4 after one pass and $I_{C,\max}$5 after two passes for the $I_{C,\max}$6 injection case (Chen et al., 2015).

In thin-film Josephson junctions, injected current is a designed actuator rather than an attack variable. For a half-infinite strip of width $I_{C,\max}$7, the self-field is neglected and the sheet-current stream function satisfies $I_{C,\max}$8. With source and sink at arbitrary edge positions, conformal mapping yields an analytic current distribution and an associated phase field. The phase produced by a source–sink pair is

$I_{C,\max}$9

so the phase change is proportional to the injected current and is spatially tunable through the injector geometry. In this setting, injection current is a means of continuously managing the phase distribution at the junction and of realizing behaviors associated with artificial $J_w$0-$J_w$1 structures (Kogan et al., 2014).

A related engineering usage appears in selective-injection GaN heterojunction bipolar transistors. There the base is patterned into thin and thick p-GaN stripes, SiO$J_w$2 blocks electron injection into the thick-base regions, and regrown emitter material is placed only above the thin stripes. Minority-carrier electron injection is thereby confined to the thin p-GaN base, while majority-carrier holes for base current are injected from adjacent thick p-GaN regions. The reported device reached $J_w$3 with $J_w$4, versus $J_w$5 and $J_w$6 for the planar control, and the stated purpose of the selective-injection geometry was to decouple the usual trade-off between base resistance and current gain (Xia et al., 2024).

3. Injected beam current in plasma, vacuum, and startup plasmas

In electron-driven plasma wakefield acceleration, density-downramp injection creates a witness bunch by elongating the plasma bubble at a sharp density transition. The injected witness current is reported to be essentially independent of the absolute downramp length once the ramp is steep enough for trapping; the dominant control parameter is instead the effective current

$J_w$7

For sufficiently short drivers, the witness current scales linearly with this parameter, $J_w$8, while for longer drivers a correction appears: $J_w$9 The downramp therefore sets the threshold for injection, but not the plateau value of the injected current once trapping occurs (Hue et al., 2023).

In a planar vacuum diode with time-variant pulsed injection, the relevant injected current is the cathode emission profile $\bar I(x)$0 imposed during $\bar I(x)$1. One-dimensional PIC simulations with VORPAL considered constant, linearly increasing, linearly decreasing, symmetric triangular, and quadratic-ramp profiles. For time-invariant injection the steady limit is the Child–Langmuir law,

$\bar I(x)$2

while the constant short-pulse limit is given by Valfells’ formula. For time-variant profiles, the maximum average current density normalized to the constant-pulse short-pulse limit can be substantially larger when $\bar I(x)$3; the reported enhancement reaches about $\bar I(x)$4–$\bar I(x)$5 times for linear ramps and as high as $\bar I(x)$6 times for the quadratic ramp, then approaches unity as $\bar I(x)$7 (Huang et al., 10 Feb 2026). The stated physical picture is temporal localization of charge closer to the cathode near the end of the pulse, reducing cumulative space-charge repulsion.

In local helicity injection plasmas, the injected current stream is modeled as a helical filament whose magnetic field is calculated with the Biot–Savart law,

$\bar I(x)$8

M3D-C1 calculations for Pegasus-III found substantial flux-surface degradation in all modeled cases, with the onset of overlapping magnetic structures and large-scale surface deformation beginning at $\bar I(x)$9. Rotation produced partial screening of the $S^{\rm ex}(x)$0 perturbation in both single-fluid and two-fluid models, and the two-fluid case showed stronger suppression near the edge. A refined stream model with spatial spreading or oscillatory motion reproduced magnetic power profiles better than a rigid filament model (Schaefer et al., 6 Nov 2025).

4. Injection current as a bulk photovoltaic charge response

In nonlinear optical transport, injection current is a bulk photovoltaic dc current produced by asymmetric population of states during interband optical transitions. In strained twisted bilayer graphene with broken sublattice symmetry, the injection-current rate under circularly polarized light was written as

$S^{\rm ex}(x)$1

with $S^{\rm ex}(x)$2. The central geometric quantity is the interband Berry curvature dipole

$S^{\rm ex}(x)$3

The reported mechanism requires both hBN-induced $S^{\rm ex}(x)$4 breaking and strain-induced $S^{\rm ex}(x)$5 breaking; the resulting injection current is controlled by light helicity, has pronounced THz response, and is tunable by chemical potential. The reported nonlinear susceptibility associated with the response reaches $S^{\rm ex}(x)$6, and the sign flips when the chemical potential is moved from one side of charge neutrality to the other (Arora et al., 2021).

In ferroelectric monolayer GeS, GeSe, SnS, and SnSe, the injection-current response tensor is $S^{\rm ex}(x)$7. For point group mm2, the dominant component is $S^{\rm ex}(x)$8, corresponding to current perpendicular to the spontaneous in-plane polarization. The response is maximal for circularly polarized light and zero for linearly polarized light, with peak bulk-effective values between $S^{\rm ex}(x)$9 and $I_{\text{inj}}(t)$0 in the visible spectrum. Compression along the polar axis can increase the injection current or change its sign, so strain acts as a direct control parameter and the current itself becomes a probe of crystal structure and polarization state (Panday et al., 2018).

A distinct optical-injection setting is two-color coherent current injection in moderate-angle twisted bilayer graphene. There the current arises from quantum interference between one-photon absorption of $I_{\text{inj}}(t)$1 light and two-photon absorption of $I_{\text{inj}}(t)$2 light, and the rate of a general observable $I_{\text{inj}}(t)$3 includes a coherent term $I_{\text{inj}}(t)$4. The spectra divide into three regimes for undoped twisted bilayer graphene: a low-energy linear-dispersion regime described by a renormalized Fermi velocity, a middle regime around the Van Hove singularity with fine structure, and a high-energy regime where the response approaches that of uncoupled graphene layers. The two-photon carrier injection diverges in the middle regime because of double resonant transitions, whereas the current injection is suppressed at the Van Hove singularity itself because the injected electrons there have zero group velocity (Zheng et al., 2021).

5. Spin-current injection and spin photogalvanic responses

In GaAs bulk and quantum wells, pure spin current injection by quantum interference and control uses phase-locked $I_{\text{inj}}(t)$5 and $I_{\text{inj}}(t)$6 laser pulses to interfere one-photon and two-photon excitation pathways. The injected spin-current density is

$I_{\text{inj}}(t)$7

with average velocity

$I_{\text{inj}}(t)$8

Because $I_{\text{inj}}(t)$9 and $$p_a=\langle I_{\text{inj}}(t) I_{\text{ch,Alice}}(t)\rangle,\qquad p_b=\langle I_{\text{inj}}(t) I_{\text{ch,Bob}}(t)\rangle.$$0, the paper concluded that $$p_a=\langle I_{\text{inj}}(t) I_{\text{ch,Alice}}(t)\rangle,\qquad p_b=\langle I_{\text{inj}}(t) I_{\text{ch,Bob}}(t)\rangle.$$1, and that the density of injected pure spin current increases monotonically with the excitation laser intensities. The reported experiments agreed with Fermi’s-golden-rule calculations and did not show the non-monotonic behavior predicted by strong-field many-body models in the measured range (Ruzicka et al., 2010).

In graphene with Rashba spin-orbit coupling, linearly polarized light at normal incidence injects a pure spin current without magnetic field and without net charge current. The spin-current operator is

$$p_a=\langle I_{\text{inj}}(t) I_{\text{ch,Alice}}(t)\rangle,\qquad p_b=\langle I_{\text{inj}}(t) I_{\text{ch,Bob}}(t)\rangle.$$2

and the injection rate is

$$p_a=\langle I_{\text{inj}}(t) I_{\text{ch,Alice}}(t)\rangle,\qquad p_b=\langle I_{\text{inj}}(t) I_{\text{ch,Bob}}(t)\rangle.$$3

The response vanishes for circularly polarized light and is maximized for linearly polarized light; the spin current flows perpendicular to the polarization axis, with spin polarization parallel to it. The reported spin-current polarization reaches as high as $$p_a=\langle I_{\text{inj}}(t) I_{\text{ch,Alice}}(t)\rangle,\qquad p_b=\langle I_{\text{inj}}(t) I_{\text{ch,Bob}}(t)\rangle.$$4 for photon frequencies comparable to the Rashba frequency (Rioux et al., 2014).

In the Janus altermagnet Fe$$p_a=\langle I_{\text{inj}}(t) I_{\text{ch,Alice}}(t)\rangle,\qquad p_b=\langle I_{\text{inj}}(t) I_{\text{ch,Bob}}(t)\rangle.$$5SSeO, linearly polarized light generates a spin injection current rather than a charge current. The dc response is

$$p_a=\langle I_{\text{inj}}(t) I_{\text{ch,Alice}}(t)\rangle,\qquad p_b=\langle I_{\text{inj}}(t) I_{\text{ch,Bob}}(t)\rangle.$$6

and for the [100] Néel-axis configuration the independent injection components include $$p_a=\langle I_{\text{inj}}(t) I_{\text{ch,Alice}}(t)\rangle,\qquad p_b=\langle I_{\text{inj}}(t) I_{\text{ch,Bob}}(t)\rangle.$$7, $$p_a=\langle I_{\text{inj}}(t) I_{\text{ch,Alice}}(t)\rangle,\qquad p_b=\langle I_{\text{inj}}(t) I_{\text{ch,Bob}}(t)\rangle.$$8, $$p_a=\langle I_{\text{inj}}(t) I_{\text{ch,Alice}}(t)\rangle,\qquad p_b=\langle I_{\text{inj}}(t) I_{\text{ch,Bob}}(t)\rangle.$$9, and $R_L$0. The dominant reported value is $R_L$1 at $R_L$2, while $R_L$3 compressive strain enhances the peak to $R_L$4 at $R_L$5. The effect is switchable by rotating the magnetization direction and by strain engineering, and the paper explicitly distinguished the injection component from the smaller shift-spin-current contribution (Pei et al., 19 Dec 2025).

Spin-current injection is also used as a dynamical actuator. In noncollinear antiferromagnets such as Mn$R_L$6Ir and Mn$R_L$7Sn, the texture angle $R_L$8 obeys a driven dissipative sine-Gordon equation containing a spin-current term $R_L$9, with $R_H$0 generated by the spin Hall effect. The domain-wall velocity was derived as

$R_H$1

and estimated to reach around $R_H$2 in Mn$R_H$3Ir for electric current density around $R_H$4 (Yamane et al., 2019). In a different geometry, a remote spin-polarized CPP injection through a nanocontact displaced a domain wall in a nanostripe by an exchange-spring mechanism; the cited simulations used current densities of order $R_H$5, corresponding to currents as low as $R_H$6, and found displacements of several hundred nanometers (Skirdkov et al., 2013). Local injection of pure spin current into an electrically disconnected ferromagnet/normal-metal sandwich was further shown to generate closed-loop electric currents obeying

$R_H$7

with long-range spin-accumulation tails that cross over to $R_H$8 for thick ferromagnetic overlayers (Bazaliy et al., 2016).

6. Minimal excitation, high-injection diagnostics, and theoretical caveats

Not every injected current is characterized primarily by its magnitude. In a metallic single-wall carbon nanotube described as a non-chiral Luttinger liquid, periodic Lorentzian voltage pulses applied to an STM tip inject Levitons. The average current $R_H$9 and noise $J_c$00 were computed with nonequilibrium Keldysh Green functions, and the excess noise

$J_c$01

was proved to vanish exactly whenever the injected charge per period $J_c$02 is an integer. This extends minimal-injection physics to a strongly correlated one-dimensional non-chiral system. The same calculation showed that time-dependent current profiles are reshaped by Andreev-like reflections at nanotube–lead interfaces, even though the minimal-excitation criterion survives (Fukuzawa et al., 2023).

In electron-beam-induced-current measurements, the phrase “high injection regime” denotes a distinct but related limit in which the total electron–hole generation rate exceeds the rate at which carriers can be extracted. The analytic model gives

$J_c$03

or, in 3D,

$J_c$04

Above this threshold, charge accumulation screens the built-in field, the EBIC profile broadens, the maximum collection efficiency decreases, and the maximum shifts away from the junction (Haney et al., 2014). In this usage, injection current is inseparable from extraction limits and nonlinear screening.

A methodological controversy appears in theoretical studies of bulk photovoltaic injection current. Numerical and perturbative analyses of one-dimensional models and first-principles calculations for BaTiO$J_c$05 found that time-dependent Hartree, time-dependent Hartree–Fock, and time-dependent Kohn–Sham mean-field schemes can produce a dc current after irradiation by linearly polarized light, whereas the independent-particle approximation does not. The paper identified this mean-field injection current as an artifact of population imbalance generated by unphysical self-excitation pathways, and concluded that investigations of many-body effects on shift current and injection current must be conducted carefully in mean-field schemes because of contamination by unphysical dc current (Sato et al., 2023). By contrast, linearly polarized-light spin injection is explicitly reported as symmetry-allowed in graphene with Rashba coupling and in Janus Fe$J_c$06SSeO (Rioux et al., 2014, Pei et al., 19 Dec 2025). This suggests that the caveat concerns specific mean-field descriptions of charge injection current rather than a general prohibition on linearly polarized injection phenomena.