For the first time, a research group at the University of Electro-Communications has succeeded in rigorously determining the energy of solid-state electrons quantized by a magnetic field.
The energy of electrons in metals and semiconductors is quantized by a magnetic field.The electronic state in a solid is determined by F. Bloch's theory created in 1928, and the electronic state when a magnetic field is applied in a vacuum (not in a solid) is the LD created in 1930. Obtained by Landau's theory.However, the electronic state when a "magnetic field" is applied to a "solid" cannot be simply combined with Bloch's theory and Landau's theory, and it has been difficult to calculate accurately even in modern times.
On the other hand, as the relativistic effect (effect of the interaction between the spin of an electron and its orbital motion) in solid electrons has attracted attention in recent years and has been actively studied, the rigorous calculation of quantization energy in a magnetic field It is said that methods have come to be required.
Under these circumstances, the researchers have succeeded in developing a method for calculating quantization energy by applying "matrix mechanics".We began by analyzing in detail the equations derived by JM Luttinger and W. Korn in 1955 that balance the periodic potential and the magnetic field in solids.The Luttinger-Corn equation is very complex and could not be solved in general (except in a simplified special case), but as a result of searching for a mathematical method to solve it, matrix mechanics is possible. I found that.
Using the method completed based on this discovery, the calculation of the semiconductor PbTe, whose relativistic effect has recently become a problem, overturns the conventional wisdom that the relativistic effect fluctuates greatly depending on the magnetic field. The phenomenon became clear, and it became possible to understand the observed values, which were different from the conventional theory, without any contradiction.
This method can be applied to various substances and is expected to deepen the understanding of the relativistic effect.
Paper information:[Physical Review Letters] Nonperturbative Matrix Mechanics Approach to Spin-Split Landau Levels and the g Factor in Spin-Orbit Coupled Solids
