Landau–Zener tunnelling in 2D periodic structures in the presence of a gauge field: I. Tunnelling rates

Abstract

We study the interband Landau-Zener tunneling of a quantum particle in the Hall configuration, i.e., in the presence of normal to the lattice plane gauge field (for example, magnetic field for a charged particle) and in-plane potential field (electric field for a charged particle). The interband tunneling is induced by the potential field and for vanishing gauge field is described by the common Landau-Zener theory. We generalize this theory for non-zero gauge field. The depletion rates of low-energy bands are calculated by using semi-analytical method of the truncated Floquet matrix.

Landau–Zener tunnelling in 2D periodic structures in the presence of a gauge field: II. Electric breakdown

“…First, the magnetic field splits Bloch bands into magnetic bands, thus introducing the new energy gaps. According to results of our previous work [1], now the rate of tunneling across the main energy gap ∆ is either smaller or larger than that for B = 0, depending on which magnetic band is initially populated. However, as the first approximation, one can neglect this effect and use the standard Landau-Zener equation to estimate the rate of tunneling.…”

“…This work continues our studies of the Landau-Zener tunneling (LZ-tunneling) for a quantum particle in the Hall configuration [1]. To be certain, here we assume a charged particle in electric and magnetic fields, although the results are equally applied to a neutral particle (for example, an atom in an optical lattice) subject to artificial gauge and potential fields.…”

“…It is well know that a strong electric field induces Landau-Zener transitions (tunneling) across the energy gaps. In our previous work [1] we have shown that these transitions also take place in the presence of a magnetic field and calculated the tunneling rate. Unfortunately, the analytical approach of Ref.…”

“…Unfortunately, the analytical approach of Ref. [1] provides only the rate of tunneling but is incapable to describe dynamics of the system (1) if LZ-tunneling is not negligible. In the present work we study dynamical manifestations of LZ-tunneling by numerically solving the Schrödinger equation with the Hamiltonian (1) and comparing the results with those obtained on the basis of the tight-binding model (tbmodel),…”

Stable Bloch oscillations and Landau-Zener tunneling in a non-Hermitian $\cal{PT}$-symmetric flat band lattice

“…Later on, Bloch oscillations were shown to occur in different periodic systems such as ultracold atoms [7,8], Bose-Einstein condensates in optical lattices [9,10], waveguide arrays [11][12][13], optically induced lattices [14,15], acoustical waves [16] and plasmonic systems [17]. Among the various physical settings, optical systems offer direct visualization of Bloch oscillations [7,10,11,18] and Landau-Zener tunneling [19][20][21][22] both theoretically and experimentally. For example, Bloch oscillations with Landau-Zener tunneling can be used to construct matter-wave beam splitters and Mach-Zehender interferometer [23].…”