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

Harper - Hofstadter problem for 2 D electron gas with k - linear Rashba spin - orbit coupling

– The Harper-Hofstadter problem for two-dimensional electron gas with Rashba spin-orbit coupling subject to periodic potential and perpendicular magnetic field is studied analytically and numerically. The butterfly-like energy spectrum, spinor wave functions as well as the spin density and average spin polarization are calculated for actual parameters of semiconductor structure. Our calculation...

An algebraic semi-classical approach to Bloch electrons in a magnetic field

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...

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...

Berry phase, hyperorbits, and the Hofstadter spectrum: Semiclassical dynamics in magnetic Bloch bands.

We have derived a new set of semiclassical equations for electrons in magnetic Bloch bands. The velocity and energy of magnetic Bloch electrons are found to be modified by the Berry phase and magnetization. This semiclassical approach is used to study general electron transport in a DC or AC electric field. We also find a close connection between the cyclotron orbits in magnetic Bloch bands and...