Vibronic Ground-State Degeneracies and the Berry Phase: A Continuous Symmetry Perspective

Abstract

We develop a geometric construction to prove the inevitability of the electronic ground-state (adiabatic) Berry phase for a class of Jahn-Teller models with maximal continuous symmetries and N > 2 intersecting electronic states. Given that vibronic ground-state degeneracy in JT models may be seen as a consequence of the electronic Berry phase, and that any JT problem may be obtained from the subset we investigate in this letter by symmetry-breaking, our arguments reveal the fundamental origin of the vibronic ground-state degeneracy of JT models.The Jahn-Teller (JT) theorem [1, 2] is a cornerstone of condensed matter and chemical physics; it enunciates that adiabatic electronically degenerate states of symmetric nonlinear molecules are unstable with respect to symmetry-breaking distortions of the molecular geometry (unless the degeneracy is protected by time-reversal symmetry). Given this statement, one might be tempted to loosely extrapolate that molecular quantum state degeneracies are generally unstable. This is, however, an incorrect conclusion: It is interesting that a large class of JT models exhibit robust vibronic ground-state degeneracies [3][4][5][6][7][8][9][10][11][12][13]. Thus, there is a counterintuitive flavor to the JT theorem: vibronic degeneracies can be born at the expense of the breakdown of their electronic counterparts [10,11]. These degeneracies leave distinctive signatures in the chemical dynamics of JT systems which are sometimes immune to degeneracy-breaking perturbations [13,14]. The goal of this letter is to explain the fundamental reason for the emergence of degenerate vibronic ground-states in JT models.Vibronic ground-state degeneracy (VGSD) in JT models appears frequently when linear vibronic couplings dominate [10,11] (for a recent proposal of direct noninterferometric experimental verification of VGSD, see e.g., [15,16]), although there are exceptions [17][18][19][20]. More specifically, there exists a particular class of JT models for which VGSD is guaranteed to exist whenever the adiabatic approximation with inclusion of Berry phase effects [22,23]) is valid [10,11,24]. These are the JT systems containing continuous symmetries and all possible couplings between JT active modes and a single electronically degenerate multiplet (at the reference geometry for a description of the JT effect, from now on denoted by JT center ) [3,4,[24][25][26][27][28][29], the simplest and most famous example being the linear E ⊗ e model (we use the standard convention where the electronic irreducible representation (irrep) is given by a capital letter and the vibrational irrep is given by a lowercase) which displays an exotic SO(2) (circular) symmetry in its potential energy surface [3,11]. The most complex spinless example is the SO(5)-invariant model of the icosahedral JT problem H ⊗ (g ⊕ 2h), which contains all possible JT active modes associated with the electronic H quintuplet [9,10,29,30]. On the other hand, the linearized H ⊗ h model has SO(3) symmetry [31], but it does not include the cou...

On the Nature of Geometric and Topological Phases in the Presence of Conical Intersections

“…The electron–nuclear dynamics of interest in this work is initiated in the ground state of a Jahn–Teller model, which has been extensively studied with respect to geometric phase effects in the past. − We use the E ⊗ e Jahn–Teller Hamiltonian recently explored by Valahu et al (details in section SI1 of the Supporting Information). The experimental setup of ref consists of a mixed-qudit-boson encoding in which both electronic and motional degrees of freedom are described.…”

Continuous vibronic symmetries in Jahn–Teller models

“…Because the existence and properties of the trough are independent of the reduced vibronic coupling constant and vibrational frequency, the Berry phase in the spinless models of table 1 is robust with respect to both changes in the fundamental parameters of these models which preserve their fundamental symmetry, and perturbations that break the symmetry, but do not induce new ground-state esis in low-energy regions of the JT APES. More recently, we employed the theory described here to show that the Berry phase and the associated vibronic ground-state degeneracy of the JT models here discussed follow straightforwardly from the results of sections 3.2.1 and 3.2.2 without any lengthy computation [70]. Briefly, the argument relies on the fact that the trough spectrum (equation ( 26)) implies that the electronic ground-state at any geometry in this subspace can be mapped onto the normal vector of a sphere.…”

“…This sphere provides a double-valued representation of the vibrational configuration space (which is topologically equivalent to RP N as proved in section 3.2.2), such that its antipodal points correspond to the same trough geometry. Parallel transport of a normal vector at a point to its antipodal on the sphere reverses its direction, hence implying a −1 Berry phase for the electronic ground-state [70].…”

Nonadiabatic phenomena in molecular vibrational polaritons

“…Recently efforts have been made to study the vibrational strong coupling (VSC) within one molecular electronic state [27,29,36,37,39,40,46]. In this regime experiments focus on the cavity-induced manipulation of chemical reactions in the ground electronic state or studying the effects of vibrational polaritons in solid and liquid phase inside infrared (IR) Fabry-Pérot cavities [28,[30][31][32][33][34][35].…”