Thermodynamic signatures of non-Hermiticity in Dirac materials via quantum capacitance

Non-Hermitian band descriptions capture how loss, gain, and environmental coupling reshape quantum matter, yet most experimental tests rely on wave-based or dynamical probes. Here we establish a new equilibrium route to exceptional physics in Dirac materials: in the weakly non-Hermitian regime, the thermodynamic density of states and the quantum capacitance exhibit a universal equilibrium approach to the exceptional point. In our minimal non-reciprocal graphene model, the hopping imbalance reduces the Dirac velocity as $v_F=v\sqrt{1-β^2}$, implying that the low-energy density of states, the thermodynamic density of states, and the quantum capacitance all scale as $(1-β^2)^{-1}$ as $|β|\to 1^-$. Consequently, at charge neutrality the quantum capacitance remains linear in temperature but with a diverging prefactor, while the inverse response softens linearly on approaching the exceptional point. In a magnetic field, this manifests as a collapse of the Landau-level spacing and a corresponding crowding of thermally active levels. Complementarily, the biorthogonal Bloch states exhibit a Petermann factor $K=(1-β^2)^{-1}$, which isolates the irreducibly non-Hermitian effect of eigenvector non-orthogonality. These results identify quantum capacitance as an experimentally accessible bulk equilibrium probe of effective non-Hermiticity in Dirac materials.

Source: arXiv:2604.14150v1 - http://arxiv.org/abs/2604.14150v1 PDF: https://arxiv.org/pdf/2604.14150v1 Original Link: http://arxiv.org/abs/2604.14150v1