Anomalous Transport at Band Edges

Explore the intricacies of anomalous transport at band edges in this 32-minute lecture by Manas Kulkarni from PCS Institute for Basic Science. Delve into the fascinating world of non-Hermitian matrices and their symmetries in open quantum systems. Examine how the spectrum of a one-dimensional tight-binding chain with periodic on-site potential can be analyzed using transfer matrices. Discover the unique symmetry these non-Hermitian matrices possess, similar to parity-time symmetry, and learn about their transitions across exceptional points. Investigate the correlation between exceptional points of the transfer matrix and band edges of the spectrum. Uncover the subdiffusive scaling of conductance with system size when the system is connected to zero-temperature baths at both ends, particularly when the chemical potential of the baths matches the band edges. Explore the universal existence of a dissipative quantum phase transition as the chemical potential is tuned across any band edge, regardless of the periodic potential details or the number of bands in the underlying lattice. Gain insights into this phenomenon's uniqueness in the presence of baths and its absence otherwise.