Non-Hermitian Exceptional Landau Quantization in Electric Circuits

Abstract

Alternating current RLC electric circuits form an accessible and highly tunable platform simulating Hermitian as well as non-Hermitian quantum systems. We propose here a realization of a time-reversal invariant pseudo-magnetic field, enabling the exploration of non-Hermitian physics under external magnetic field. Based on circuit realizations of non-Hermitian Dirac and Weyl systems under magnetic field, we identify the low-energy physics with a generic real energy spectrum from the non-Hermitian relativistic Landau quantization of exceptional points and rings, avoiding the non-Hermitian skin effect and providing a physical example of quasiparticles moving in the complex plane. Realistic detection schemes are designed that can be used to probe the flat energy bands, sublattice polarization, edge states protected by a non-Hermitian sublattice symmetry, and a characteristic nodeless probability distribution.

Non-Hermitian topological metamaterials with odd elasticity

“…The study of topological band theory has been extended to open systems governed by non-Hermitian Hamiltonians , which are realized in classical systems subjected to intrinsic gain and/or loss such as optical , electric [80,[85][86][87][88][89], and acoustic [90,91] structures. In contrast to the ordinary topological band theory, non-Hermitian systems exhibit unique features such as exceptional points, band structure which is sensitive to boundary conditions, and exponentially localized bulk modes ("non-Hermitian skin effect").…”

Non-Hermitian and topological photonics: optics at an exceptional point

“…A Dirac Hamiltonian that deviates from the Hermitian regime is also known to exhibit other interesting effects. To this end, a circuit realization of NH Dirac and Weyl Hamiltonians under the influence of a pseudomagnetic field which is artificially induced by a judicious spatial variation of the circuit elements has been proposed [149]. In this scenario, the combined effect of non-Hermiticity along with the pseudomagnetic field lifts the degeneracy and leads to the emergence of Landau-level-like flat bands in the band structure of the system.…”

Untying links through anti-parity-time-symmetric coupling

“…is the Pauli matrix for spin-1/2 and d − i is the fictitious magnetic field including the real part d = (J cos k + κ cos (2k), J sin k + κ sin (2k), 0) and the imaginary part = (γ , 0, 0) [48,49]. Notably, the quasi-1D lattice and its Bloch Hamiltonian h k are not anti-PT -symmetric.…”