Thermodynamic Charge Partition in Accumulation-Layer Heterostructures

TL;DR

This paper presents a thermodynamic framework for understanding charge distribution in accumulation-layer heterostructures, linking capacitance, tunneling, and magnetic effects through a unified theory.

Contribution

It introduces a novel thermodynamic description that separates energetic path selection from geometric capacitance, enabling comprehensive analysis of charge partitioning.

Findings

Differential capacitance, tunnel current, and plateau width are unified as projections of the thermodynamic structure.

Comparison with experimental data supports the model's prediction of charge refilling and screening depth growth under magnetic fields.

Universal master functions allow calculation of the accumulation layer properties across various densities and geometries.

Abstract

We develop a thermodynamic description of accumulation-layer heterostructures in which the induced sheet density is partitioned between the near-interface accumulation-layer charge and a complementary screening charge in the surrounding structure. Treating this partition as the central state variable yields a complete Helmholtz free energy, a corrected locked-branch chemical potential, and a shifted release potential that separates energetic path selection from geometric capacitance. The physical path is selected spectrally: compressible segments remain fully screened, whereas incompressible segments evolve along a locked branch until release is triggered by the relevant gap. Differential capacitance, tunnel current and plateau width then emerge as different projections of the same coupled thermodynamic structure. A canonical two-stage self-consistent Poisson--Schr\"odinger reduction supplies universal master functions for the isolated accumulation layer and master surfaces for its finite-buffer extension, making the theory calculable across density and geometry. Comparison with magnetocapacitance and magnetotunneling data supports a picture in which nearby extended charge refills the accumulation layer and the effective screening depth grows with magnetic field.