[Paper Review] Thermodynamical Signatures of an Excitonic Insulator

B. Bucher, Tuson Park+2 more|ArXiv.org|Feb 22, 2008

Perovskite Materials and Applications1 references3 citations

TL;DR

This paper provides experimental thermodynamic evidence that TmSe₀.₄₅Te₀.₅₅ forms an excitonic insulator ground state under high pressure, where electrons and holes bind into bosonic excitons, confirmed by a sharp change in heat capacity and entropy. The phase transition is first-order, with a large entropy gain from valence fluctuations and phonon binding, supporting a Bose condensate of excitons in an indirect gap semiconductor.

ABSTRACT

In the 1960s speculations arose if a ground state exists in solid state materials with an electron and a hole bound to a pair with their spins added to integer values, i.e. excitons. Here we show that electrons and holes in TmSe0.45Te0.55 do form excitons as the thermodynamical ground state. The formation of a large number of excitons in an indirect gap semiconductor requires momentum conservation by means of phonons and, hence, implies a significant change of the heat capacity of the lattice, as found experimentally. The thermodynamically derived phase diagram sustains a bosonic ground state in condensed matter.

Motivation & Objective

• To establish the existence of an excitonic insulator ground state in TmSe₀.₄₅Te₀.₅₅ using thermodynamic measurements.
• To resolve the long-standing question of whether electron-hole pairs can form a stable, coherent bosonic ground state in condensed matter.
• To determine the thermodynamic signature of exciton formation, particularly through heat capacity and entropy changes.
• To distinguish between competing ground states such as electron-hole liquid or Kondo-like behavior in the presence of strong electron correlation.

Proposed method

• Ac calorimetry was used to measure differential heat capacity on single-crystal TmSe₀.₄₅Te₀.₅₅ under hydrostatic pressure.
• A self-clamping CuBe pressure cell with silicon-based fluid enabled high-pressure measurements up to 14 kbar.
• The heat capacity was derived from the amplitude of the ac temperature oscillation, scaled to the Dulong-Petit limit for absolute estimation.
• Phase transitions were identified by abrupt changes in heat capacity and phase shifts in the thermo-signal.
• Entropy changes were calculated by integrating ΔC/T, with reference to baseline runs to isolate the contribution from the phase transition.
• The pressure dependence of the phase boundary was analyzed using the Clausius-Clapeyron relation to extract ΔS/ΔV and validate thermodynamic consistency.

Experimental results

Research questions

• RQ1 Does the formation of electron-hole pairs in TmSe₀.₄₅Te₀.₅₅ under pressure lead to a thermodynamically stable excitonic insulator phase?
• RQ2 What is the entropy change associated with the phase transition, and can it be attributed to electronic degrees of freedom such as valence fluctuations?
• RQ3 How does the heat capacity and phonon spectrum change upon exciton formation, and what does this imply about the nature of the many-body ground state?
• RQ4 Is the observed first-order transition driven by electronic binding energy or lattice expansion, and how does it compare to latent heat and elastic work?
• RQ5 Can the observed thermodynamic behavior be explained by a Bose condensate of excitons rather than competing phases like electron-hole liquid or Kondo screening?

Key findings

• A sharp first-order phase transition was observed in the heat capacity at approximately 13.5 kbar, coinciding with a discontinuity in thermal conductivity.
• The entropy change upon entering phase B was measured as ΔS ≈ 2.4 J/mol K, with a significant contribution (1.6 J/mol K) from a broad heat capacity tail at low temperatures.
• The spin entropy gain (ΔS_spin ≈ 3.98 J/mol K) from Tm³⁺ to Tm²⁺ valence transition matches the experimental entropy change, supporting a singlet exciton ground state.
• The elastic work required to expand the lattice against pressure (ΔE_elastic ≈ 20 meV/f.u.) greatly exceeds the latent heat (L ≈ 1.7 meV/f.u.), indicating that electronic binding energy, not lattice expansion, drives the transition.
• The large entropy gain and phonon binding at low temperatures are consistent with the formation of a many-body gap due to Bose condensation of excitons.
• The absence of localized electrons in phase B, as shown by Hall effect measurements, rules out a simple charge density wave or localized state, supporting a delocalized excitonic insulator state.