Shigeru Kanemitsu

Negative capacitance (NC) has been reported across a wide range of physical systems, yet its interpretation has remained fragmented due to the absence of a unified conceptual framework. Existing explanations—spanning ferroelectric free‑energy curvature, tunneling transport, plasmonic resonances, and electronic compressibility—have often been treated as unrelated or even contradictory. This review resolves these inconsistencies by demonstrating that all manifestations of NC arise from —non‑synchronization—between external excitation and internal response. We classify NC into three fundamental categories: temporal mismatch, originating from delays or inertia in charge or polarization dynamics; spatial mismatch, caused by nonuniform field or mode distributions; and quantitative mismatch, resulting from intrinsic parameter reversal such as negative curvature or negative compressibility. Despite their diverse physical origins, these mechanisms share the same mathematical signature (C_eff=∂Q/∂V< 0). Organizing NC within this unified framework clarifies long‑standing ambiguities, connects previously isolated research fields, and establishes a systematic foundation for engineering NC in electronic, photonic, and quantum devices. The framework further highlights tunnel‑current‑induced NC as a distinct single‑particle mechanism, expanding the scope of NC beyond ferroelectricity and collective modes. Overall, this work positions NC not as a singular anomaly but as a universal response class emerging from the interplay between excitation and internal dynamics.

Through theoretical analysis, we demonstrate that a capacitor modeled as a parallel combination of a resistance (R) and a capacitance (C), with a current–voltage characteristic I = I (E), exhibits a volatile negative capacitance effect when the condition I′(E) > I (E) is satisfied. In contrast, ordinary dielectric capacitors satisfy I′(E) < I (E), resulting in the accumulation of free charge on the plates and a positive capacitance. When the capacitive component becomes negligible and only resistance remains, I′(E) = I (E) and which corresponds to Ohm’s law. We fabricated two-electrode structures with nanometer-scale spacing using multi-walled carbon nanotubes (MWCNTs) and Si crystals as electrode materials. Experimental measurements confirmed the presence of negative capacitance, in agreement with theoretical predictions. Unlike ferroelectric-origin negative capacitance, this mechanism arises from the I − V characteristics between electrodes. We further show that this negative capacitance can be equivalently represented as an inductance in a circuit, enabling its use as a two-dimensional inductor without electromagnetic interaction. Circuit-level integration and broader applications are anticipated.

In this paper we will be concerned with zeta-symmetry—the functional equation for the (Riemann) zeta-function (equivalents to which are called modular relations)—and reveal the reason why so many results are intrinsic to PFE (Partial Fraction Expansion) for the cotangent function. The hidden reason is that the cotangent function (as a function in the upper half-plane, say) is the polylogarithm function of order 0 (with complex exponential argument), and therefore it shares properties intrinsic to the Lerch zeta-function of order 0. Here we view the Lerch zeta-function defined in the unit circle as a zeta-function in a wider sense, as a function defined in the upper and lower half-planes. As evidence, we give a plausibly most natural proof of Ramanujan’s formula, including the eta transformation formula as a consequence of the modular relation via the cotangent function, speculating the reason why Ramanujan had been led to such a formula. Other evidence includes the pre-Poisson summation formula as the pick-up principle (which in turn is a generalization of the argument principle).

Institute of Mathematics of the Czech Academy of Sciences