Strain-Induced Landau Levels in Arbitrary Dimensions with an Exact Spectrum

Abstract

Certain non-uniform strain applied to graphene flakes has been shown to induce pseudo-Landau levels in the single-particle spectrum, which can be rationalized in terms of a pseudo-magnetic field for electrons near the Dirac points. However, this Landau level structure is in general approximate and restricted to low energies. Here we introduce a family of strained bipartite tight-binding models in arbitrary spatial dimension d and analytically prove that their entire spectrum consists of perfectly degenerate pseudo-Landau levels. This construction generalizes the case of triaxial strain on graphene's honeycomb lattice to arbitrary d; in d = 3 our model corresponds to tetraxial strain on the diamond lattice. We discuss general aspects of pseudo-Landau levels in arbitrary d.

Pseudo-electromagnetic fields in 3D topological semimetals

“…Pseudo-electromagnetic fields emerge in graphene, Weyl and Dirac semimetals. However, they are not restricted to low energy relativistic systems [27]; any momentum-spacedependent field in principle can be treated as a pseudofield. Thus, we expect that more systems can show effects of emergent pseudo-fields.…”

Collapse of Landau levels in Weyl semimetals

“…This is the case for example of the torsional strain discussed in [11] or the tetra-axial strain in the diamond lattice of ref. [16]. Other strain configurations easier to implement experimentally will be fully affected by the effect.…”

“…Strain engineering can give rise to pseudo LL in these 3D materials, nice examples are provided in refs. [11,13] and a general analysis of strain induced LL in any dimension has been presented in [16].…”

The induced by an electromagnetic field coexistence of types I and II spectra in Weyl semimetals

“…Recently, these pseudo-fields have been studied in WSMs 33 . The different topological effects induced by such fields have been investigated in 34 – 39 . The DoS oscillations and Shubnikov-de Haas effect caused by a pseudo-magnetic field were investigated in 36 .…”