Giant piezoelectricity driven by Thouless pump in conjugated polymers

The study addresses whether conjugated (π-bonded) polymers can exhibit giant piezoelectric responses surpassing traditional organic piezoelectrics and approaching or exceeding inorganic ceramics. Conventional high-performance piezoelectrics like PZT offer strong electromechanical coupling but suffer from rigidity, cost, and toxicity (lead). Organic polymers such as PVDF are flexible, low-cost, and biocompatible, but their piezoelectricity arises from local molecular dipoles and typically underperforms relative to inorganic perovskites. Enhancements in inorganic materials often occur near morphotropic phase boundaries (MPB), where competing phases flatten the energy landscape, boosting polarization rotation/extension. Similar ideas have been explored in P(VDF-TrFE) copolymers, yielding modest gains. In contrast, conjugated polymers possess delocalized π-electrons whose polarization is inherently nonlocal and topological in quasi-1D chains. If inversion symmetry is broken, such systems can host ferroelectricity with potentially large electronic polarization changes under strain. The paper proposes that conjugated polymers realize a Thouless pump mechanism for adiabatic charge transport, leading to anomalously large effective charges and enhanced piezoelectricity, especially near a dimerization (Peierls-like) structural phase transition.

• Inorganics (e.g., PZT) show peak piezoelectric responses near MPB due to polarization rotation/extension from flattened free energy surfaces.
• Organic PVDF and P(VDF-TrFE) exhibit ferroelectricity from conformational dipoles, with enhancements upon copolymerization but still an order of magnitude below inorganics.
• Conjugated polymers (e.g., polyacetylene) have been proposed as electronic ferroelectrics due to delocalized π-electrons and nonlocal polarization effects.
• The Rice-Mele model provides a standard framework for 1D ferroelectricity and Thouless adiabatic pumping. Prior theoretical work links topology (Berry phase, Chern numbers) to polar responses in low-dimensional materials (e.g., gapped graphene, valley Chern effects), though in 2D graphene polar responses can be independent of bandgap.
• Quantum anharmonic effects can alter the order of structural transitions in 1D carbon chains, potentially affecting MPB-like divergences but not necessarily topological contributions to polarization.

Modeling: The authors generalize the Rice-Mele 1D tight-binding model to include homogeneous longitudinal strain ε in a diatomic unit cell of length a(ε)=a0(1+ε). Nearest-neighbor hopping modulates with strain and an internal fractional displacement u(ε) (order parameter) through t(e)=t0(1−β ε) and δt(e)=−β(1+ε)u(ε), with β>0 the electron-phonon (e-ph) coupling. The onsite energy alternation Δ≥0 breaks sublattice equivalence. The lattice Hamiltonian includes harmonic nearest-neighbor springs (K) and ionic masses; the electronic Hamiltonian includes hopping and onsite Δ. The equilibrium ū(ε) minimizes the total energy E_tot(u)=E_L(u)+E_e(u). The model exhibits a second-order dimerization transition between a distorted (u≠0) and undistorted (u=0) insulating phase; the gap is E_gap=2√(Δ^2+4(β t u)^2). Strain influences the critical values Δ_c(ε) or β_c(ε).

Polarization and piezoelectricity: Polarization P is computed via the Berry-phase formulation. The longitudinal piezoelectric coefficient C_piezo = dP/dε has two parts: a clamped-ion term (fixed internal coordinate) and an internal-relaxation term proportional to (∂P/∂u)(∂u/∂ε). The effective charge Z* ≡ ∂P/∂u measures how electronic charge follows ionic displacements. Near the second-order critical point, internal strain diverges as ∂u/∂ε ∝ |Δ−Δ_c|^{−1/2} (or |β−β_c|^{−1/2}). A topological argument shows Z* ∝ 1/E_gap in the undimerized phase, leading to large values as the gap shrinks near criticality; specifically Z* ≈ (const)×β/E_gap and in undimerized limit ∼1/Δ.

First-principles simulations: DFT calculations validate model predictions on two substituted polyacetylenes (SPAs): monofluorinated polyacetylene (MFPA; CH–CF repeat) and polymethineimine (PMI; N–CH repeat). All-trans structures are considered. Hybrid range-separated functional LC-ωPBE is used in CRYSTAL with a triple-ζ polarized Gaussian basis; ω=0.4 a0^−1. The long-range exact-exchange mixing parameter c_LR is varied (0–100%) to emulate screened-Coulomb vertex corrections that effectively tune the e-ph coupling β. For each c_LR, structures are optimized; internal coordinate u, band gap, Born effective charges Z* (via Berry-phase finite differences), and piezoelectric coefficients are computed. Strain derivatives ∂u/∂ε are obtained from finite differences at ε≈0.01. Piezoelectric coefficients C_piezo and converse d_piezo are computed including transverse displacements; elastic constant C is obtained from second derivative of total energy vs ε to relate C_piezo and d_piezo (C_piezo d_piezo = C). The model parameters for illustrative plots were also fitted to PBEO calculations on carbyne to demonstrate general behavior.

• Mechanism: Conjugated polymers act as Thouless pumps; adiabatic charge transport around a loop enclosing the metallic point in (Δ, δt) parameter space yields quantized pumped charge and drives anomalously large electronic polar responses. Z* grows as the band gap closes, with Z* ∝ 1/E_gap in the undimerized phase.
• MPB-like enhancement: A second-order dimerization transition produces divergent internal strain response ∂u/∂ε ∝ |Δ−Δ_c|^{−1/2} (or |β−β_c|^{−1/2}), boosting the internal-relaxation contribution to piezoelectricity.
• Combined effect: The total piezoelectric coefficient near criticality is dominated by the internal-relaxation term due to both large ∂u/∂ε and giant Z*. The clamped-ion term is comparatively smaller.
• DFT validation: In MFPA and PMI, varying c_LR tunes the system across a second-order dimerization transition (critical c_LR ≈ 14% for MFPA and ≈ 26% for PMI). Near these critical points, computed carbon effective charges are strongly anomalous, reaching ~30|e| (MFPA) and ~15|e| (PMI). Across a broad c_LR range, carbon Z* values lie between ~5|e| and ~30|e|, even for gaps > 6 eV.
• Piezoelectric response: The computed piezoelectric coefficients are greatly enhanced near the critical points when approached from the dimerized phase; internal-relaxation contribution dominates. Using ab initio Z* and ∂u/∂ε in the model reproduces full DFT piezoelectric values with excellent agreement.
• Comparison to PVDF: Converse piezoelectric coefficients d_piezo of MFPA and PMI exceed those of PVDF, with PMI reaching up to ~6× larger values near the dimerization critical point. PVDF’s response is largely insensitive to exact-exchange fraction, highlighting its different (conformational dipole) mechanism.
• Robustness: While quantum anharmonic effects may alter the order of the structural transition and temper divergences in ∂u/∂ε, the topological origin of the large Z* provides a robust enhancement mechanism. The inverse proportionality to band gap suggests a materials-design rule for maximizing piezoelectricity in conjugated polymers.

The work demonstrates that π-conjugated polymers, when inversion symmetry is broken, can exhibit giant piezoelectricity driven by a Thouless-pump mechanism. Near a second-order dimerization transition (morphotropic-like boundary), the internal strain response diverges and, together with the topological 1/E_gap enhancement of effective charge, yields very large piezoelectric coefficients dominated by internal relaxation. First-principles results on MFPA and PMI confirm both the structural softening and the emergence of strongly anomalous effective charges, significantly outperforming PVDF. The ability to tune the effective e-ph coupling (β) via dielectric screening or chemical substitution (modeled by varying c_LR) provides practical routes to optimize the response. The topological nature of the enhancement, unlike purely structural criticality, is resilient to effects that could otherwise suppress critical divergences (e.g., quantum anharmonicity), making the proposed mechanism relevant and robust for materials design. These findings directly address the research goal by identifying a topological-electronic origin of giant piezoelectricity in organic polymers and establishing tunable control parameters (band gap, β, composition, environment).

The study establishes a topological route to giant piezoelectricity in conjugated polymers: Thouless-pump-driven charge transport leads to anomalously large effective charges inversely proportional to the band gap, while proximity to a second-order dimerization transition adds an MPB-like internal-strain enhancement. DFT calculations on MFPA and PMI corroborate the model, revealing carbon effective charges up to ~30|e| and piezoelectric coefficients surpassing PVDF by as much as sixfold. The results suggest practical design principles: reduce band gaps and enhance e-ph coupling (e.g., via chemical substitution or environmental dielectric screening) while ensuring inversion symmetry breaking. Future work could explore broader SPA families, control of dielectric environments and packing effects, experimental synthesis and poling strategies, and direct measurements of piezoelectric tensors in oriented, crystalline samples. Further theoretical studies including explicit anharmonicity and finite-temperature effects could refine performance predictions and stability windows.

• Mapping of model parameters to specific chemistries is indirect; tuning β via c_LR in hybrid functionals is a proxy for screened Coulomb vertex corrections and may not capture all many-body effects quantitatively.
• The Rice-Mele model simplifies real polymer structures (e.g., focuses on longitudinal displacements, neglects detailed side-group chemistry); although ab initio results include transverse motions, the model comparison omits them.
• Only all-trans chain conformations are considered; polymorphism and disorder in real samples can affect ferroelectric and piezoelectric responses.
• Quantum anharmonic effects may alter the order of the dimerization transition, potentially reducing the divergence of internal strain; while the topological Z* enhancement is robust, the net piezoelectric peak could be tempered.
• Experimental realization of continuous tuning (e.g., substitution fraction) to reach criticality poses challenges; sample crystallinity and orientation complicate direct comparison with experimental PVDF benchmarks.
• Direct experimental validation of giant Z* and the predicted scaling with band gap remains to be demonstrated.