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The ground-state density of states of the half-filled Falicov-Kimball modelcontains a charge-density-wave gap. At finite temperature, this gap is notimmediately closed, but is rather filled in by subgap states. For a specificcombination of parameters, this leads to a stable phase where the system is inan ordered charge-density-wave phase, but there is high density of states atthe Fermi level. We show that this property can be, in finite dimensions,traced to a crossing of sharp states resulting from the single particleexcitations of the localized subsystem. The analysis of the inverseparticipation ratio points to a strong localization in the discussed regime.However, the pronounced subgap density of states can still lead to a notableincrease of charge transport through a finite size system. We show this byfocusing on the transmission in heterostructures where a Falicov-Kimball systemis sandwiched between two metallic leads.

Gapless regime in the charge density wave phase of the finite dimensional Falicov-Kimball model