Abstract

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 vF = v sqrt(1−β2), implying that the low-energy density of states, the thermodynamic density of states, and the quantum capacitance all scale as (1−β2)−1 as |β|→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−β2)−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.

Abstract

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 vF = v sqrt(1−β2), implying that the low-energy density of states, the thermodynamic density of states, and the quantum capacitance all scale as (1−β2)−1 as |β|→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−β2)−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.

Abstract

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 vF = v sqrt(1−β2), implying that the low-energy density of states, the thermodynamic density of states, and the quantum capacitance all scale as (1−β2)−1 as |β|→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−β2)−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.

Abstract

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 vF = v sqrt(1−β2), implying that the low-energy density of states, the thermodynamic density of states, and the quantum capacitance all scale as (1−β2)−1 as |β|→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−β2)−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.