TY - BOOK

T1 - Models for a quantum atomic chain coupled to a substrate

AU - Abdelwahab Mohammed, Anas Omer

N1 - Doctoral thesis

PY - 2018

Y1 - 2018

N2 - One-dimensional correlated conductors are described by the Luttinger liquid theory.Recently, several systems of atomic wires on semiconducting substrates have been re-ported to host some of the Luttinger liquid properties but without any explanation of theinfluence of the substrate on the one-dimensional electrons. This thesis addresses thisissue by investigating two approaches for modeling wire-substrate systems.The first model consists of an asymmetric 2-leg ladder system with one leg describedusing a Hubbard chain and an other leg described by a one-dimensional electron gas.The two-legs are connected by nearest-neighbor inter-leg hopping. This model revealedrich physics through the different phases that are uncovered as a function of the Hubbardinteraction and the rung hopping at half filling. These phases include a Luttinger liquidat very weak interchain hopping, a Kondo-Mott insulator at moderate interchain hoppingor strong Hubbard interaction and a spin-gapped paramagnetic Mott insulator at inter-mediate values of the rung hopping and the interaction. The last phase is a correlatedband insulator for large rung hopping. This model is found insufficient to represent wire-substrate systems but it is useful, as a minimal model, to study coexistence and proximityeffects of different quasi-long-range orders that could be relevant in higher-dimensions.The second approach presents the successful construction of a suitable model forwire-substrate systems. The modeling is started by constructing a lattice Hamiltonianfor a one-dimensional quantum wire on a three-dimensional substrate. This model ismapped onto an effective two-dimensional lattice using the Lanczos algorithm and then itis approximated by narrow ladder models that can be investigated using well-establishedmethods for one-dimensional correlated quantum systems, such as the density-matrixrenormalization group. The validity of this approach is investigated using a wire withnoninteracting electrons as well as a correlated wire with a Hubbard electron-electronrepulsion. The narrow ladder models capture the low-energy physics of wires on semi-conducting substrates using at least 3-leg ladders. They accurately reproduce the quasi-one-dimensional excitations of the full three-dimensional model.This approach can be extended to investigate other features such as electron-phononcoupling, spin-orbit coupling, etc. It is also suitable for comparisons with experimentsand first-principles calculations.

AB - One-dimensional correlated conductors are described by the Luttinger liquid theory.Recently, several systems of atomic wires on semiconducting substrates have been re-ported to host some of the Luttinger liquid properties but without any explanation of theinfluence of the substrate on the one-dimensional electrons. This thesis addresses thisissue by investigating two approaches for modeling wire-substrate systems.The first model consists of an asymmetric 2-leg ladder system with one leg describedusing a Hubbard chain and an other leg described by a one-dimensional electron gas.The two-legs are connected by nearest-neighbor inter-leg hopping. This model revealedrich physics through the different phases that are uncovered as a function of the Hubbardinteraction and the rung hopping at half filling. These phases include a Luttinger liquidat very weak interchain hopping, a Kondo-Mott insulator at moderate interchain hoppingor strong Hubbard interaction and a spin-gapped paramagnetic Mott insulator at inter-mediate values of the rung hopping and the interaction. The last phase is a correlatedband insulator for large rung hopping. This model is found insufficient to represent wire-substrate systems but it is useful, as a minimal model, to study coexistence and proximityeffects of different quasi-long-range orders that could be relevant in higher-dimensions.The second approach presents the successful construction of a suitable model forwire-substrate systems. The modeling is started by constructing a lattice Hamiltonianfor a one-dimensional quantum wire on a three-dimensional substrate. This model ismapped onto an effective two-dimensional lattice using the Lanczos algorithm and then itis approximated by narrow ladder models that can be investigated using well-establishedmethods for one-dimensional correlated quantum systems, such as the density-matrixrenormalization group. The validity of this approach is investigated using a wire withnoninteracting electrons as well as a correlated wire with a Hubbard electron-electronrepulsion. The narrow ladder models capture the low-energy physics of wires on semi-conducting substrates using at least 3-leg ladders. They accurately reproduce the quasi-one-dimensional excitations of the full three-dimensional model.This approach can be extended to investigate other features such as electron-phononcoupling, spin-orbit coupling, etc. It is also suitable for comparisons with experimentsand first-principles calculations.

U2 - 10.15488/9107

DO - 10.15488/9107

M3 - Doctoral thesis

CY - Hannover

ER -