Non-Hermitian Physics in Mesoscopic Electron Transport Through Coupled Quantum Dots

Abstract We investigate electron mesoscopic transport in a three-terminal setup with coupled quantum dots and a magnetic flux. By mapping the original transport problem into a non-Hermitian Hamiltonian form, we study the interplay between the coherent couplings between quantum dots, the magnetic flux, and the dissipation due to the tunnel coupling with the reservoirs. We explore the emergence of exceptional points (EPs) and their impact on the charge transport, particularly, the chiral currents. We further analyze the effective Hamiltonian to identify conditions under which EPs arise and the role of parity-time ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="script">P</mml:mi> <mml:mi mathvariant="script">T</mml:mi> </mml:mrow> </mml:math> ) symmetry. These EPs are shown to govern the spectral singularities and dramatically affect the dynamical behavior of chiral currents. We also show that the transmission function in the Landauer formula can be expressed in simpler forms using the non-Hermitian eigenstates. By examining the transmission function, we establish the relationship between <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="script">P</mml:mi> <mml:mi mathvariant="script">T</mml:mi> </mml:mrow> </mml:math> symmetry, EPs, and peaks in the transmission spectrum. Our findings could provide a deeper understanding of non-Hermitian quantum effects in electron tranpsort phenomena, offering valuable insights for the design of tunable non-Hermitian chiral quantum devices with engineered transport properties.