Exact zero-point energy shift in thee⊗(nE),t⊗(nH)many-modes dynamic Jahn-Teller systems at strong coupling

Abstract

We find the exact semiclassical (strong coupling) zero-point energy shifts applicable to the e ⊗ (n E) and t ⊗ (n H) dynamic Jahn-Teller problems, for an arbitrary number n of discrete vibrational modes simultaneously coupled to one single electronic level. We also obtain an analytical formula for the frequency of the resulting normal modes, which has an attractive and apparently general Slater-Koster form. The limits of validity of this approach are assessed by comparison with O'Brien's previous effective-mode approach, and with accurate numerical diagonalizations. Numerical values obtained for t ⊗ (n H) with n = 8 and coupling constants appropriate to C − 60 are used for this purpose, and are discussed in the context of fullerene.

Cooling quasiparticles in A3C60 fullerides by excitonic mid-infrared absorption

“…Once the nuclei defreeze, and the molecular ion can distort, the resulting JT energy E JT strongly competes against exchange J H , since now the quadrupole operators of the t 1u electrons couple with the quadrupole of the H g vibrational modes, but with opposite sign. [3] In C 3− 60 , the JT effect actually prevails over Coulomb exchange, effectively inverting Hund's rules. The real ground state thus becomes the low-spin 2 T 1u multiplet [24][25][26][27][28][29].…”

“…The Coulomb interaction projected onto the t 1u manifold includes a charge repulsion, the Hubbard U ∼ 1 eV, plus a quadrupole-quadrupole electronic interaction providing an intra-molecular Hund's rule exchange J H > 0. The latter splits the twenty possible (t 1u ) 3 configurations of C 3− 60 , assumed at first with nuclei rigidly frozen in their ideal icosahedral positions, as…”

“…Therefore the overall singlet pairing strength g, though still sizeable, is way too small compared to the charging energy of each C 3− 60 to justify by simple arguments why A 3 C 60 are s-wave superconductors. The explanation of this puzzle proposed in [2,3] and vindicated by recent experiments emphasises the crucial role of a parent Mott insulating state where the JT coupling effectively inverts Hund's rules, the molecular ground state therefore turning to spin S = 1/2 rather than S = 3/2 [4]. A S = 1/2 antiferromagnetic insulating phase is indeed the ground state in over-expanded NH 3 K 3 C 60 [5,6] and in Cs 3 C 60 [7] at ambient pressure.…”

“…As a result, the singlet pairing strength g eventually overwhelms the quasiparticle Coulomb pseudopotential and, on approaching the Mott transition, the system is effectively driven towards the top of the universal T c vs. g curve [8], where the critical temperature reaches the maximum possible value at a given non-retarded attraction T MAX c ∼ 0.055 g. Thus, according to the theory of Ref. [3], the peak T c ∼ 38 K reached by Cs 3 C 60 at ∼ 7 kbar [9,10] is actually the highest attainable at equilibrium in fullerides.This equilibrium upper limit has been far surpassed in out-of-equilibrium conditions in a recent remarkable pump-probe experiment on K 3 C 60 [11]. After irradiation by an intense femtosecond infrared pulse between 80 and 200 meV, K 3 C 60 showed a transient regime of some picoseconds where the optical properties looked like those of a superconductor, alas up to a temperature T 200 K, ten times higher than the equilibrium T c ∼ 20 K, see Fig.…”

“…As a result, the singlet pairing strength g eventually overwhelms the quasiparticle Coulomb pseudopotential and, on approaching the Mott transition, the system is effectively driven towards the top of the universal T c vs. g curve [8], where the critical temperature reaches the maximum possible value at a given non-retarded attraction T MAX c ∼ 0.055 g. Thus, according to the theory of Ref. [3], the peak T c ∼ 38 K reached by Cs 3 C 60 at ∼ 7 kbar [9,10] is actually the highest attainable at equilibrium in fullerides.…”