Mean--field stability for the junction of quasi 1D systems with Coulomb interactions

Abstract

Junctions appear naturally when one studies surface states or transport properties of quasi one dimensional materials such as carbon nanotubes, polymers and quantum wires. These materials can be seen as 1D systems embedded in the 3D space. In this article, we first establish a mean--field description of reduced Hartree--Fock type for a 1D periodic system in the 3D space (a quasi 1D system), the unit cell of which is unbounded. With mild summability condition, we next show that a quasi 1D system in its ground state can be described by a mean--field Hamiltonian. We also prove that the Fermi level of this system is always negative. A junction system is described by two different infinitely extended quasi 1D systems occupying separately half spaces in 3D, where Coulombic electron-electron interactions are taken into account and without any assumption on the commensurability of the periods. We prove the existence of the ground state for a junction system, the ground state is a spectral projector of a mean--field Hamiltonian, and the ground state density is unique.

References in corpus (24)

• Topological Insulators
• Optoelectronics with electrically tunable PN diodes in a monolayer dichalcogenide
• Solar-energy conversion and light emission in an atomic monolayer p-n diode
• Quantum thermal transport in nanostructures
• Quantum transport in carbon nanotubes
• A new approach to the modelling of local defects in crystals: the reduced Hartree-Fock case
• Topological invariants of edge states for periodic two-dimensional models
• Existence of a stable polarized vacuum in the Bogoliubov-Dirac-Fock approximation
• Self-consistent solution for the polarized vacuum in a no-photon QED model
• The Local Density Approximation in Density Functional Theory
• Adiabatically switched-on electrical bias in continuous systems, and the Landauer-Buttiker formula
• A positive density analogue of the Lieb-Thirring inequality
• Energy Cost to Make a Hole in the Fermi Sea
• A variational approach to dislocation problems for periodic Schrödinger operators
• A mathematical formulation of the random phase approximation for crystals
• Schrödinger operator with a junction of two 1-dimensional periodic potentials
• Adiabatic non-equilibrium steady states in the partition free approach
• Bound States for Nano-Tubes with a Dislocation
• Surface Gap Soliton Ground States for the Nonlinear Schrödinger Equation
• The reduced Hartree-Fock model for short-range quantum crystals with defects
• Absolute continuity of the spectrum for periodically modulated leaky wires in ${\mathbb{R}}^3$
• Landauer-Büttiker and Thouless conductance
• Conductance and absolutely continuous spectrum of 1D samples
• Crystalline conductance and absolutely continuous spectrum of 1D samples