Electron-hole tunnelling probed in de Haas - van Alphen oscillations in the (double) Dirac semimetal NbTe$_4$

NbTe$_4$ undergoes multiple charge density wave transitions that have attracted great interest in this material for decades. Previous work has shown that the crystal obtains the space group P4/ncc (130) at temperatures below 50K which allows for the existence of eightfold degenerate double Dirac points in the band structure. We provide insights into the electronic structure of this material through density functional theory (DFT) calculations, and a rotation study of de Haas - van Alphen (dHvA) oscillations in the magnetic torque. We find that NbTe$_4$ exhibits magnetic breakdown orbits between electron and hole pockets.