Electron-Hole tunneling in momentum space revealed by quantum oscillations
Researchers from the High Field Magnet Laboratory have found evidence for electron-hole tunneling in momentum space in the nodal-line semimetal HfSiS. This specific tunneling phenomenon is revealed in quantum oscillations of the electrical resistance at low temperatures and in high magnetic fields, and can be illustrated as a ‘figure-of-eight orbit’ enclosing one electron and one hole pocket. The observation is a manifestation of Klein tunneling in momentum space though in a regime of partial transmission due to the finite separation between these pockets. This finding suggest that electron-hole tunneling in momentum space is a generic property of semimetals with adjacent electron and hole pockets, provided that the applied magnetic field is strong enough to overcome their k-space separation.
Quantum oscillations are a very powerful tool to determine the Fermi surface of metals, semiconductors and semimetals in the presence of a high magnetic field. For charge carriers subjected to such high fields, the energy levels become quantized and are referred to as Landau bands. If the magnetic field is varied, these bands cross the Fermi energy resulting in oscillations e.g. in the electrical resistance as a function of the magnetic field.
The Fermi surface of HfSiS, a nodal-line semimetal, consists of both hole (α) and electron (β) pockets. In the presence of a magnetic field up to 31 T parallel to the c-axis, quantum oscillations originating both from orbits of individual electron and hole pockets, and from magnetic breakdown between these pockets are observed. These orbits can be visualized in the Fast Fourier Transform (FFT): the peaks in the FFT amplitude correspond to the individual hole pocket (α), its 1st harmonic (2α), the electron pocket (β) and the orbit enclosing one electron and one hole pocket (β-α) in the form of a ‘figure of eight’.
The particular breakdown β-α-orbit enclosing one electron and one hole pocket is a manifestation of ‘Klein tunneling in momentum space’, though in a regime of partial transmission as the pockets are separated. The occurrence of this orbit above a threshold magnetic field, the observed strong dependence of the oscillation amplitude on the field angle with respect to the c-axis and the cyclotron mass of this orbit are in agreement with the theoretical predictions for this novel tunneling phenomenon. Although magnetic breakdown has been extensively studied in simple elements, and in organic metals, this specific type of magnetic breakdown between adjacent electron and hole pockets has been observed for the first time.
Electron-Hole Tunneling Revealed by Quantum Oscillations in the Nodal-Line Semimetal HfSiS,
M.R. van Delft, S. Pezzini, T. Khouri, C.S.A. Müller, M. Breitkreiz, L.M. Schoop, A. Carrington, N.E. Hussey and S. Wiedmann, Physical Review Letters 121 (2018), 256602