We study the stability of the hydrogen molecule interacting with the environment according to the balanced gain and loss energy scheme. We determined the properties of the molecule taking into account all electronic interactions, where the parameters of the Hamiltonian have been computed by using the variational method. The interaction of the hydrogen molecule with the environment was modeled parametrically (γ) with the help of the non-hermitian operator. We have shown that the hydrogen molecule is dynamically unstable. The dissociation time (TD) decreases, if the γ parameter increases (for γ → 0, we get TD → +∞). At the dynamic instability of the hydrogen molecule overlaps its static instability as the coupling constant γ increases. We observed the decrease in the dissociation energy and the existence of the metastable state of the molecule (γMS = 0.659374 Ry). The hydrogen molecule is statically unstable for γ > γD = 1.024638 Ry. One can also observed the PT symmetry breaking effect for the electronic Hamiltonian (γPT = 0.520873 Ry). However, it does not affect the properties of the hydrogen molecule, such as: the electronic Hamiltonian parameters, the phonon and rotational energy, and the values of the electron-phonon coupling constants.

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In the present paper, we analyze the properties of the unbalanced superconducting state on a square lattice with the constant value of the electron-phonon coupling function. We conduct our analysis in the framework of the Eliashberg formalism, explicitly considering k-dependence of the electron and phonon dispersion relations. It is found that the balanced superconducting state does not induce itself in the system due to the high value of the electron effective mass. However, in the unbalanced case the thermodynamic properties of the superconducting condensate can be distinctly different from the predictions of the Bardeen-Cooper-Schieffer theory; when the coupling constant value in the diagonal channel of the self-energy is diminished comparing to the non-diagonal channel. This is due to the reduced dimensionality of the tested system and the strong-coupling effects included in the Eliashberg formalism.

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Recent hydrides-driven advent in the high-pressure phonon-mediated superconductivity motivates research on chemical elements which compound with hydrogen. It is desired that such elements should allow chemical pre-compression of hydrogen to assure the induction of the superconducting phase with the high transition temperature (T ). Herein, we present detailed theoretical insight into the properties of the superconducting state induced under pressure (p) in two of such component elements, namely selenium (Se) and tellurium (Te) at [Formula: see text] GPa and [Formula: see text] GPa, respectively. The assumed external pressure conditions allow us to conduct our analysis just above previously theoretically predicted bcc-fcc structural phase transition of Se and Te, and identify the possible associated discontinuity effect of the critical temperature. In particular, our numerical analysis is conducted within Migdal-Eliashberg formalism, due to the confirmed electron-phonon pairing mechanism and relatively high electron-phonon coupling constant in the materials of interest. We predict that T values in Se and Te equal 8.13 K and 5.96 K, respectively, and mark the highest critical temperature values for these elements within the postulated fcc phase. Additionally, we supplement these results by the estimated maximum values of the superconducting energy band gap and the effective mass of electrons. We predict that all these parameters can be used as a guidelines for experimental observation of the critical temperature discontinuity and the corresponding bcc-fcc phase transition in Se and Te superconductors. Moreover, we show that the thermodynamics of superconducting phase in both elements may exhibit deviations from the conventional estimates of the Bardeen-Cooper-Schrieffer theory, and suggest existence of the strong-coupling and retardation effects. Finally, we note that our results can be also instructive for future screening of chemical elements for applications in superconducting hydrides.