Phonon Shift Current: Mechanisms & Applications

• Phonon shift current is a zero-bias dc photocurrent generated by the coherent excitation of polar phonons in noncentrosymmetric crystals without creating electron–hole pairs.
• It arises from inversion symmetry breaking and strong electron–phonon coupling, where geometric phase effects and Berry connections govern the shift in electronic polarization.
• Experimental studies in ferroelectric materials like BaTiO₃ reveal that THz-driven soft phonon excitation produces robust photocurrents, validating the geometric current framework.

Phonon shift current denotes a family of zero-bias dc current phenomena in which phonons enter the microscopic role ordinarily associated with optical interband excitation in the bulk photovoltaic effect (BPVE). In the most direct usage, coherent excitation of a polar phonon in a noncentrosymmetric crystal generates a dc photocurrent without creating electron–hole pairs; in related usages, propagating phonons dynamically break inversion symmetry, or a frozen-in ferroelectric soft mode statically produces the noncentrosymmetric electronic structure that supports a large shift current. This multiplicity of definitions suggests that the topic is best organized around the common ingredients of inversion breaking, electron–phonon coupling, and geometric charge displacement rather than around a single model (Okamura et al., 2022, Morimoto et al., 21 Aug 2025, Ogata et al., 13 Mar 2026, Tan et al., 10 Jul 2025).

1. Geometric origin and relation to conventional shift current

In conventional BPVE, illumination of a noncentrosymmetric crystal generates a dc current in the bulk without an applied bias. The canonical microscopic mechanism is the electronic shift current, a second-order nonlinear response,

$$J^a = \sigma^{abc}(\omega)\,E^b(\omega)\,E^c(-\omega),$$

with nonzero $\sigma^{abc}$ only when inversion symmetry is broken. Microscopically, the current is governed by a shift vector,

$$R_{nm}^a(\mathbf{k}) = \partial_{k_a} \arg r_{nm}^b(\mathbf{k}) - \left[A_n^a(\mathbf{k}) - A_m^a(\mathbf{k})\right],$$

constructed from the phase of the interband matrix element and the Berry connections of the participating bands. In ferroelectrics, the same Berry-phase structure that underlies macroscopic polarization also controls the shift vector, which is why the literature repeatedly connects phonon shift current to changes in electronic polarization rather than to semiclassical carrier drift (Okamura et al., 2022).

A central reformulation defines phonon shift current as a second-order optical dc current generated when light excites polar phonons in an electron–phonon coupled, noncentrosymmetric crystal. In that formulation no real electron–hole pairs are created; instead, optically excited phonons carry electric polarization through their coupling to electrons, and the current follows the polarization-change relation $J=dP/dt$. The leading contribution is therefore not a transport current of photoexcited carriers, but a geometric current associated with the steady-state change of polarization under phonon excitation (Morimoto et al., 21 Aug 2025).

2. Microscopic formulations in electron–phonon coupled systems

A minimal microscopic construction uses a ferroelectric Rice–Mele-type framework,

$$H = H_{\text{el}} + H_{\text{ph}} + H_{\text{el-ph}},$$

in which inversion breaking is encoded in the electronic tight-binding sector and a soft phonon coordinate $Q$ modulates the electronic parameters through electron–phonon coupling $g$. In that setting the phonon-induced nonlinear conductivity obeys the scaling

$\sigma^{(2)} \propto \frac{g^2}{E_{\text{ph}}},$

and can be written in a geometric form proportional to the phonon linear conductivity $\sigma^{(1)}$ times a shift vector $R$. The small phonon energy $\sigma^{abc}$0 of a soft mode is therefore itself an enhancement mechanism, which is why THz soft phonons can yield a response comparable to that of electronic interband transitions at eV scales (Okamura et al., 2022).

A later diagrammatic treatment reexamined the problem through gauge invariance and the Ward–Takahashi identity. There the second-order phonon shift current near resonance takes the form

$\sigma^{abc}$1

and the effective phonon Hamiltonian is written as

$\sigma^{abc}$2

with $\sigma^{abc}$3 and $\sigma^{abc}$4. In this language each optically created phonon carries a definite polarization $\sigma^{abc}$5, and the dc current is the rate of polarization injection. The same analysis estimates

$\sigma^{abc}$6

so phonon shift current is typically smaller than electronic shift current by an energy-scale ratio, although soft modes make the suppression less severe (Morimoto et al., 21 Aug 2025).

The heat-current analog, termed shift heat current, uses the same geometric structure but weights the response by the electronic heat carried per transition. For two-band, time-reversal-symmetric systems,

$\sigma^{abc}$7

When this formalism is applied to electron–phonon coupled systems, even if only phonons are excited by the external field, the amplitude of the shift heat current is determined by the electronic energy scale rather than the phonon energy scale. That result sharply distinguishes phonon-driven geometry from a picture in which the phonon sector itself would carry the primary shift vector (Onishi et al., 2022).

3. Soft-phonon bulk photovoltaic effect in ferroelectric BaTiO$\sigma^{abc}$8

The clearest experimental realization of phonon shift current is the THz-driven BPVE in ferroelectric BaTiO$\sigma^{abc}$9. BaTiO$$R_{nm}^a(\mathbf{k}) = \partial_{k_a} \arg r_{nm}^b(\mathbf{k}) - \left[A_n^a(\mathbf{k}) - A_m^a(\mathbf{k})\right],$$0 is a prototypical displacement-type ferroelectric with a tetragonal, noncentrosymmetric $$R_{nm}^a(\mathbf{k}) = \partial_{k_a} \arg r_{nm}^b(\mathbf{k}) - \left[A_n^a(\mathbf{k}) - A_m^a(\mathbf{k})\right],$$1 phase below $$R_{nm}^a(\mathbf{k}) = \partial_{k_a} \arg r_{nm}^b(\mathbf{k}) - \left[A_n^a(\mathbf{k}) - A_m^a(\mathbf{k})\right],$$2 K and a large electronic band gap $$R_{nm}^a(\mathbf{k}) = \partial_{k_a} \arg r_{nm}^b(\mathbf{k}) - \left[A_n^a(\mathbf{k}) - A_m^a(\mathbf{k})\right],$$3 eV. The reported THz pulses had center photon energy and bandwidth both of order $$R_{nm}^a(\mathbf{k}) = \partial_{k_a} \arg r_{nm}^b(\mathbf{k}) - \left[A_n^a(\mathbf{k}) - A_m^a(\mathbf{k})\right],$$4 meV, three orders of magnitude smaller than the band gap, so electronic interband absorption was negligible and the observed current had to originate from phonon excitation and electron–phonon coupling (Okamura et al., 2022).

Two soft modes were emphasized.

Mode	Driving polarization	Dominant response
Relaxational mode	$$R_{nm}^a(\mathbf{k}) = \partial_{k_a} \arg r_{nm}^b(\mathbf{k}) - \left[A_n^a(\mathbf{k}) - A_m^a(\mathbf{k})\right],$$5	$$R_{nm}^a(\mathbf{k}) = \partial_{k_a} \arg r_{nm}^b(\mathbf{k}) - \left[A_n^a(\mathbf{k}) - A_m^a(\mathbf{k})\right],$$6
Slater mode	$$R_{nm}^a(\mathbf{k}) = \partial_{k_a} \arg r_{nm}^b(\mathbf{k}) - \left[A_n^a(\mathbf{k}) - A_m^a(\mathbf{k})\right],$$7	$$R_{nm}^a(\mathbf{k}) = \partial_{k_a} \arg r_{nm}^b(\mathbf{k}) - \left[A_n^a(\mathbf{k}) - A_m^a(\mathbf{k})\right],$$8

Experimentally, zero-bias photocurrent was observed at room temperature for both modes. Reversing the ferroelectric polarization reversed the current sign, while a multidomain state with zero net polarization gave vanishing photocurrent. The signal vanished in the centrosymmetric paraelectric phase, scaled quadratically as $$R_{nm}^a(\mathbf{k}) = \partial_{k_a} \arg r_{nm}^b(\mathbf{k}) - \left[A_n^a(\mathbf{k}) - A_m^a(\mathbf{k})\right],$$9, appeared only during illumination, and showed step-like integrated charge with bias independence up to fields corresponding to more than $J=dP/dt$0 V/cm. These features excluded drift and diffusion of mobile carriers and identified the current as a genuine BPVE driven by coherent soft-phonon excitation.

The mode dependence was pronounced. Using the absorption-normalized measure $J=dP/dt$1, proportional to $J=dP/dt$2, the THz response for the Slater mode was about $J=dP/dt$3 times larger than for the relaxational mode, consistent with its much larger oscillator strength. The phonon-driven BPVE was also comparable in magnitude to the electronic interband BPVE under near-gap ultraviolet excitation. First-principles calculations for the Slater mode reproduced the sign and magnitude trends, and showed that $J=dP/dt$4 from the phonon could be comparable to, or larger than, the electronic contribution near the band edge. In this realization, phonon shift current is not a secondary correction to a carrier-photocurrent picture; it is the primary nonlinear current channel.

4. Dynamically broken inversion and other phonon-driven zero-bias currents

A broader literature uses closely related language for dc currents driven by propagating or scattering phonons rather than by optically excited $J=dP/dt$5 polar modes. In metals and one-dimensional charge-density-wave systems on a piezoelectric substrate, a surface acoustic wave was shown microscopically to generate a zero-bias current through second-order response to deformation and piezoelectric potentials. There the underlying electronic system can be centrosymmetric, but the propagating phonon with finite $J=dP/dt$6 dynamically breaks inversion symmetry. The current is dissipative, odd in $J=dP/dt$7, proportional in the metallic limit to $J=dP/dt$8, and in the CDW model appears only below the transition temperature where the gap $J=dP/dt$9 is nonzero (Ogata et al., 13 Mar 2026).

Another related mechanism is the thermal generation of shift electric current in noncentrosymmetric quantum wells. There a hot electron gas relaxes toward the phonon bath by emission or absorption of lattice phonons, and each inelastic electron–phonon scattering event produces a real-space shift of the Bloch wave packet. The net dc current is therefore driven by the imbalance between emission and absorption when $$H = H_{\text{el}} + H_{\text{ph}} + H_{\text{el-ph}},$$0, rather than by photon absorption itself. In the zinc-blende quantum-well setting analyzed there, the current is symmetry-controlled, proportional to the temperature mismatch, and vanishes in higher-symmetry orientations such as 001.

Disorder introduces yet another variant. In a noncentrosymmetric one-dimensional Anderson insulator, the photocurrent under uniform illumination was found to form only in the presence of electron–phonon coupling; without phonon-assisted dissipation it decays exponentially with system size. With phonons, however, the photocurrent remains robust even when the random-potential scale exceeds the bandwidth, whereas local illumination or relaxation only through electrodes makes the current decay exponentially (Ishizuka et al., 2020).

Chiral-phonon-induced current in helical crystals is geometrically adjacent but not identical. There the rotational motion of atoms is treated adiabatically, and the time-averaged current along the helical axis is finite in the metallic phase but vanishes in the insulating phase, while the in-plane current has zero time average because of threefold rotation space-time symmetry. The insulating cancellation is traced to a Chern number in the combined $$H = H_{\text{el}} + H_{\text{ph}} + H_{\text{el-ph}},$$1 parameter space, making the phenomenon closer to an adiabatic Berry-phase pump than to a conventional second-order BPVE tensor (Yao et al., 2022).

These cases show that the label “phonon shift current” is sometimes applied narrowly to phonon-driven BPVE and sometimes more broadly to phonon-induced zero-bias currents with shift-like real-space displacement. This suggests a terminological boundary rather than a sharp physical discontinuity.

5. Static ferroelectric phonons, topology, and material realizations

In some materials the relevant phonon does not need to be dynamically excited: a frozen-in ferroelectric distortion can be the essential ingredient that makes a giant shift current possible. EuAuBi is a concrete example. A centrosymmetric paraelectric $$H = H_{\text{el}} + H_{\text{ph}} + H_{\text{el-ph}},$$2 structure hosts an unstable $$H = H_{\text{el}} + H_{\text{ph}} + H_{\text{el-ph}},$$3 mode at $$H = H_{\text{el}} + H_{\text{ph}} + H_{\text{el-ph}},$$4 THz; freezing in that soft mode yields the polar $$H = H_{\text{el}} + H_{\text{ph}} + H_{\text{el-ph}},$$5 phase. First-principles calculations gave a spontaneous polarization of $$H = H_{\text{el}} + H_{\text{ph}} + H_{\text{el-ph}},$$6–$$H = H_{\text{el}} + H_{\text{ph}} + H_{\text{el-ph}},$$7, a switching barrier of $$H = H_{\text{el}} + H_{\text{ph}} + H_{\text{el-ph}},$$8 meV/f.u., carrier concentration of order $$H = H_{\text{el}} + H_{\text{ph}} + H_{\text{el-ph}},$$9 cm$Q$0, and total electron–phonon coupling constant $Q$1. The ferroelectric $Q$2 mode descending from the unstable $Q$3 mode contributes only about $Q$4 of the total electron–phonon coupling, consistent with the decoupled electron mechanism. In that static polar state the computed shift current reaches $Q$5, and its sign reverses under polarization reversal. In this usage, “phonon shift current” refers to a phonon-driven structural distortion that establishes the electronic geometry for a giant, switchable shift current, rather than to a dynamically excited phonon current (Tan et al., 10 Jul 2025).

Trigonal Se and Te provide a different topological context. Their occupied electronic bands require an essential band representation $Q$6 and exhibit a $Q$7 Zak phase, which identifies the one-dimensional Se/Te chain as a chiral Su–Schrieffer–Heeger chain. In Se quantum wells the calculated shift-current components reach approximately $Q$8 and $Q$9 near $g$0 eV. The same work also found that the phonon spectrum is unconventional, with three separated phonon-band groups assigned to $g$1, $g$2, and $g$3, implying obstructed phonon states on the (0001) surface. The paper explicitly does not compute a phonon shift current in the strict sense, but it identifies a material setting in which large electronic shift current and nontrivial phonon topology coexist (Zhang et al., 2022).

6. Many-body renormalization, competing mechanisms, and present scope

Many-body theory sharpens the distinction between phonon-generated and phonon-renormalized shift currents. In an excitonic formulation of BPVE, shift current originates from a light-induced shift of charge centers to many-body excited states, and the many-body shift vector is expressed through a sum rule over nearly degenerate optically active excitons. Exciton–phonon coupling then enters through exciton–phonon self-energies, which broaden and shift the excitonic resonances and reduce the many-body shift vector at higher temperature. In that framework phonons do not create a new current mechanism; they reshape an electronic or excitonic shift current through renormalization and decoherence (Lai et al., 2024).

A separate and experimentally important phonon-related contribution is ballistic current. A first-principles perturbative theory for intrinsic phonon-assisted ballistic current in BaTiO$g$4 found a magnitude comparable to shift current, and the total spectrum, shift plus ballistic, agreed well with measured photocurrents. This is a critical conceptual boundary: a phonon-related dc photocurrent in a noncentrosymmetric crystal need not be a shift current, even when it belongs to the broader BPVE phenomenology (Dai et al., 2020).

The heat-current extension further broadens the framework. Shift heat current is controlled by the same shift vector as charge shift current, depends directly on chemical potential, and in electron–phonon coupled systems remains governed by an electronic energy scale even when only phonons are resonantly driven (Onishi et al., 2022). Together with the gauge-invariant Ward–Takahashi construction of phonon shift current, this points to a coherent organizing principle: observable phonon-driven shift-type responses require broken inversion symmetry, phonon modes that strongly modulate electronic polarization, and a relaxation structure compatible with extracting a dc component (Morimoto et al., 21 Aug 2025).

Accordingly, phonon shift current is best regarded not as a single formula but as a geometric category of phonon-mediated dc responses. Its most restrictive meaning is the coherent, bias-free BPVE generated by resonant excitation of polar phonons without real electron–hole creation. Its broader usage encompasses dynamically inversion-breaking acoustic-phonon transport, phonon-enabled shift currents in localized systems, and frozen ferroelectric phonon distortions that imprint the noncentrosymmetric electronic structure required for large switchable BPVE.