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TT: Fachverband Tiefe Temperaturen
TT 86: Correlated Electrons: Method Development
TT 86.3: Vortrag
Freitag, 22. März 2024, 10:00–10:15, H 3007
Engineering effective nearest neighbor hopping — •Nico Leumer — DIPC, San Sebastian, Spain
The complexity of condensed matter in general implies the need for simple effective models that are still capable of describing the real world physics accurately. One approach is based on non-interacting tight-binding (TB) models, where we restrict Hamiltonians typically to onsite energies and nearest-neighbor (nn) hopping terms since next nearest neighbor (nnn) hoppings are deemed unimportant. However, has it ever come to your mind that nnn processes can be willingly engineered to dominate their nn cousins?
Theory demonstrated recently that onsite and nn hopping t1 are sufficient to realize effective nnn hoppings t2 [1]. Here, the key feature is the ability to tune t1/t2 such that the strong nnn regime t2≫ t1 becomes in fact accessible. Contrary to its potentially "unrealistic" appearance on first glance, this procedure of generating nnn hoppings was already successfully applied [2], actually without experimentalist’s awareness.
In my contribution, I present how nnn hoppings emerge from a free particle Hamiltonian featuring only onsite and nn terms. Further, I state why onsite terms are essential in reaching the strong t2 limit. The nnn hoppings are not only a curiosity, they also imply the presence of in general complex wavevectors and the existence of degenerate (finite) energy eigenvalues at well-defined parameter constraints.
[1] N. G. Leumer, J. Phys. A: Math. Theor. 56 435202 (2023)
[2] K. Qian et.al., Phys. Rev. Research 5, L012012 (2023)
Keywords: Engineering tunable next nearest neighbor hopping; Complex wavevectors