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• W1760746 abstract "This thesis is on the effect of electron-electron interactions on the transport properties in two cases: (A) Finite length clean quantum wires and (B) point-like constrictions. In both situations, the system is connected adiabatically to noninteracting leads. The main difference between the two cases is that the finite length quantum wire has approximately translational symmetry and the pointlike constriction does not. Therefore the electron-electron interaction have to conserve momentum in the case of finite quantum wires (A), but not for point-like constrictions (B). In both cases, the change in conductance G and thermopower S due to interactions are considered. Common for both cases is that without interactions the conductance is 2e 2 h times the number of modes and the thermopower is exponentially suppressed at low temperatures T , i.e. ∝ e−TF/T (TF being the Fermi temperature). This thesis present three main effects of interactions: • (A) In a single mode quantum wire two-particle interactions cannot change the distribution of electrons due to momentum and energy conservation. Therefore multi-mode wires are considered and we find that the interaction induced resonances in the conductance and thermopower at particular values of the Fermi level (i.e. gate voltage). The magnetic field splitting of the resonances provide a unique signature of the effect. • (A) Three-particle collisions in a single-mode finite wire can change the electron distribution, but the contribution to the conductance and thermopower turns out to be exponentially suppressed in temperature to lowest order in the interaction. However, several interesting properties of the tree-particle scattering rate are found. • (B) For a point-like constriction, two-particle scattering can change the current even for a single-mode. Therefore a weak interaction V0 changes the current as I(T, V )/V ≃ 2e2 h − α|V0|T 2 − γ|V0|V 2 and the thermopower as S ∝ |V0|T 3 for low temperature T and/or small bias V (α and γ being constants). Furthermore, the noise is reduced compared to the single-particle case. In a large magnetic field, the interaction among electrons of equal spin suppress the low-temperature corrections to the transport properties by two extra powers of temperature. The conductance versus temperature (for B = 0) beyond the perturbative regime was found in a self-consistent 2nd order approach. Based on numerical results, we conjecture that the conductance approach ∼ e/h for higher temperatures, however, still lower than TF. These results are all in qualitative agreement with experimental studies on the 0.7 anomaly in quantum point contacts. On the technical side, the Boltzmann equation approach is used for the finite quantum wires whereas the Green’s function approach is used for the point-like constriction. In both cases, the regime of weak interactions are studied using perturbation theory to second order in the interaction." @default.
• W1760746 created "2016-06-24" @default.
• W1760746 creator A5067975704 @default.
• W1760746 creator A5082558495 @default.
• W1760746 date "2007-01-01" @default.
• W1760746 modified "2023-09-27" @default.
• W1760746 title "Electron-Electron Interactions in Quantum Point Contacts and Finite Quantum Wires" @default.
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