If the extracted oscillatory frequency (SdH) is more than 1000 T,so what are the chances we can get the Non-trivial Berry phase with such a high frequency ? I will really appreciate if someone responds or suggest some related material .
I think you are confusing the SdH frequency with emergent field arising form certain band topologies. The magnitude of SdH frequency is purely dependent on the size of the cross-sectional area of the Fermi surface. By applying magnetic field each fermi pocket is quantized by Landau levels. As field increases, the high-index Landau levels cross the Fermi level and get unpopulated leading to an oscillation in magneto-resistance which is commonly known is Shubnikov de Haas (SdH) oscillation. Eventually at a certain field all the electrons condense into the lowest Landau level. This field defines the frequency of the SdH oscillations. For example, a SdH frequency of 1000 T means, you need an external filed of 1000 T to reach this limit. Regardless of this frequency, the Fermi pocket itself may carry a non-trivial Berry phase which can be extracted by making a Landau index plot. This plot shows the the inverse of magnetic field (1/B) for each peak in conductivity vs its corresponding Landau level. Depending on where the resulting line intersects with the Landau level axis, the value of Berry phase can be determined. For more information, you can refer to this paper: Article Detection of Berry's Phase in a Bulk Rashba Semiconductor
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