Prototypical many-body signatures in transport properties of semiconductors

Resistance saturation in semi-conducting polyacetylene molecular wires

“…This saturation phenomenon has first been discussed [ 23 ] for correlated narrow-gap semiconductors [ 25 ], such as Kondo insulators. In these periodic bulk systems, the low-temperature regime is dominated by intra-band transitions [ 24 ]: For a band endowed with a quasi-particle lifetime and weight Z , the Kubo conductivity (without vertex corrections) can be expressed analytically as [ 85 ] with the unit cell volume V , the intra-band group velocity with in the Brillouin zone and derivatives of the digamma function evaluated at , where . The characteristic temperature that delimits the resistivity saturation regime encoded in the Kubo Eq.…”

“…More sophisticated approximations further include dynamical renormalizations, either limited to low-energies via the quasi-particle weight [ 37 ], or account for the full frequency dependence, e.g., within GW , [ 38 – 40 ] Anderson impurity calculations [ 41 – 44 ], dynamical mean-field theory [ 45 , 46 ] or its extensions [ 47 – 50 ]. Such approaches can describe correlation phenomena at all energy scales, including site-selective Mott physics [ 51 – 54 ] and temperature-dependent phenomena [ 23 , 24 , 55 – 59 ], and have been successfully applied to describe the electronic [ 47 , 53 , 57 , 60 – 64 ] and transport [ 21 , 22 , 38 – 40 , 51 , 52 , 54 – 56 , 58 , 65 – 70 ] properties of molecular and nanoscopic systems.…”

“…Using the Kubo formula, it was recently shown [ 23 , 24 ] that finite lifetimes of charge carriers can lead to non-trivial transport phenomena in bulk correlated narrow-gap semiconductors [ 25 ]. From this perspective, it is interesting to ask how quasi-particle incoherence manifests in transport through semiconducting nanoscopic systems.…”

LinReTraCe: The linear response transport centre

“…A quantum mechanical description of transport using Kubo's linear response theory [42] overcomes these artefacts by correctly treating effects of finite lifetimes (incoherence) of charge carriers [1,2,43].…”

“…The unique feature of LinReTraCe is the treatment of thermal and lifetime broadening on an equal footing [1-3], while still incurring numerical costs as low as semi-classical Boltzmann approaches in the relaxation-time approximation. We exploit that linearizing the dynamics of many-body renormalizations (self-energy) allows for a semi-analytical (instead of numerical) evaluation of leading contributions in Kubo's linear response theory [1,2,4]. LinReTraCe's principle input are electronic excitation energies and associated quasi-particle weights and lifetimes, as well as optical transition matrix elements.…”