It is a routine exercise to map individual Fermi surfaces in a multiband system by isolating different frequencies in SdH oscillations ( 31), and one can, indeed, measure the Berry’s phase of individual bands ( 26). Here, we stress the fact that the Berry’s phase of the two bands is not additive ( 1). Moreover, we show the continuous variation of Berry’s phase–induced quantum oscillation phase shift, as a function of gate voltage ( V BG), in an inversion symmetry broken system close to the Dirac band edge. The phase switches sharply from π to −π as the Fermi level is tuned from below the Dirac bandgap to above it. The phase shift of the quadratic band SdH oscillations depends on the position of the Fermi level in the coexisting Dirac band. The unusual phase shifts are found in measured Shubnikov–de Haas (SdH) oscillations of a quadratic band in a multiband system-the ABA-trilayer graphene. In particular, we reveal how the quantum oscillations of a massive quadratic band (with a constant and trivial Berry’s phase) can acquire nontrivial (±π) phase shifts that are gate tunable.
Here, we unveil a new phase shift for quantum oscillations that appears in multi–Fermi surface metals. Tracking these quantum oscillation phase shifts has emerged as a powerful probe for topological materials ( 26– 30). This is visible in oscillations of both resistance and thermodynamic quantities like magnetization. As a result, quantum oscillations of a closed Fermi surface can acquire phase shifts-a direct result of the Berry’s phase of electrons ( 3). In the presence of a magnetic field ( B), the (quantized) size of closed cyclotron orbits depends on both the magnetic flux threading the orbits and the Berry’s phase of electrons. The value of the Berry’s phase of electrons as they encircle a single, closed Fermi surface can be used as a litmus test for topological bands: π indicates a nontrivial band ( 18– 22), whereas 2π indicates a massive quadratic band ( 23– 25). In anomalous Hall metals, the Berry’s phase on the Fermi surface determines the (unquantized part of the) anomalous Hall conductivity ( 15, 16) nontrivial π Berry’s phase enforces the absence of backscattering in topological materials ( 17).
A prominent example is the Berry’s phase ( 12– 14).
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