Energy spectrum of Bloch electrons under checkerboard field modulations

Instantons and the spectrum of Bloch electrons in a magnetic field.

A semiclassical path-integral treatment of the spectrum of a charged particle moving in a twodimensional periodic potential in the presence of a transverse magnetic field is presented. Complex instanton solutions to the Euclidean equations of motion are identified, and it is shown that the dilute-instanton-gas sum reproduces features of the spectrum studied by previous authors. Comparison of th...

Spectrum of 2D Bloch electrons in a periodic magnetic field : algebraic approach

Landau level spectrum of Bloch electrons in a honeycomb lattice

2014 The energy spectrum of a tight-binding honeycomb lattice in the presence of a uniform magnetic field is analysed. The graph of the spectrum over a wide range of rational reduced flux 03A6/03A60 through elementary hexagonal cells is plotted. The energy spectrum is found to have recursive properties similar to those discussed previously on the square and triangular lattices. New features of ...

Weak-field Hall effect and static polarizability of Bloch electrons

Bloch electrons in a magnetic field: why does chaos send electrons the hard Way?

We find that a 2D periodic potential, with different modulation amplitudes in the x and y directions, and a perpendicular magnetic field may lead to a transition to electron transport along the direction of stronger modulation and to localization in the direction of weaker modulation. In the experimentally accessible regime we relate this new quantum transport phenomenon to avoided band crossin...