Enhancing superconductivity in bulk β−Bi2Pd by negative pressure induced by quantum electronic stress

An effective way to enhance the critical temperature (${T}_{c}$) of bulk superconductivity (SC) is employing external pressure accompanied with or without phase transitions. However, the variations of ${T}_{c}$ are not always ``positively'' proportional to the pressure even in the same superconducting phase. There exist a class of bulk superconductors such as $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{B}{\mathrm{i}}_{2}\mathrm{Pd}$, whose ${T}_{c}$ will be suppressed by pressure starting from the atmospheric pressure. Then the pressure approach of enhancing SC becomes invalid because it is impossible to apply a negative pressure. Here we demonstrate that quantum electronic stress (QES) induced by electronic doping affords a general approach to further enhance ${T}_{c}$ of such kinds of bulk superconductors without causing phase transition. Our first-principles calculations show that electron doping gives rise to a negative QES acting as an effective ``negative'' pressure, which expands the lattice of $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{B}{\mathrm{i}}_{2}\mathrm{Pd}$. Consequently, it leads to an increase of electronic density of states at the Fermi level and softening of phonon vibration modes, which in turn enhances the strength of electron-phonon coupling. Conversely, the same concept also explains the experimental reports of pressure and hole-type substitution suppressed SC of bulk $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{B}{\mathrm{i}}_{2}\mathrm{Pd}$, which unifies the effects of pressure and chemical substitution into the same theoretical framework of QES tuning SC. We also envision that surface QES induced by quantum confinement may play an important role in affecting the ${T}_{c}$ of epitaxial superconductors, such as the experimentally reported $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{B}{\mathrm{i}}_{2}\mathrm{Pd}$ thin films.