Effective narrow ladder model for two quantum wires on a semiconducting substrate
arXiv:2102.13412 · doi:10.1103/PhysRevB.103.245405
Abstract
We present a theoretical study of two spinless fermion wires coupled to a three dimensional semiconducting substrate. We develop a mapping of wires and substrate onto a system of two coupled two-dimensional ladder lattices using a block Lanczos algorithm. We then approximate the resulting system by narrow ladder models, which can be investigated using the density-matrix renormalization group method. In the absence of any direct wire-wire hopping we find that the substrate can mediate an effective wire-wire coupling so that the wires could form an effective two-leg ladder with a Mott charge-density-wave insulating ground state for arbitrarily small nearest-neighbor repulsion. In other cases the wires remain effectively uncoupled even for strong wire-substrate hybridizations leading to the possible stabilization of the Luttinger liquid phase at finite nearest-neighbor repulsion as found previously for single wires on substrates. These investigations show that it may be difficult to determine under which conditions the physics of correlated one-dimensional electrons can be realized in arrays of atomic wires on semiconducting substrates because they seem to depend on the model (and consequently material) particulars.
References in corpus (17)
- The density-matrix renormalization group
- Evidence for Long-Range Spin Order Instead of a Peierls Transition in Si(553)-Au Chains
- Kondo versus indirect exchange: the role of the lattice and the actual range of RKKY interactions in real materials
- Surface Tomonaga-Luttinger liquid state on Bi/InSb(001)
- Competition between Kondo effect and RKKY physics in graphene magnetism
- Block Lanczos density-matrix renormalization group method for general Anderson impurity models: Application to magnetic impurity problems in graphene
- Atomic scale variation of electron tunneling into a Luttinger liquid ? : High resolution scanning tunneling spectroscopy study on Au/Ge(001)
- Spinless fermions ladders at half filling
- Gold-induced nanowires on the Ge(100) surface yield a 2D, and not a 1D electronic structure
- Ground-state and spectral properties of an asymmetric Hubbard ladder
- Universal scaling behavior of coupled chains of interacting fermions
- Luttinger Liquids: The Basic Concepts
- Correlated atomic wires on substrates. I. Mapping to quasi-one-dimensional models
- Correlated atomic wires on substrates. II. Application to Hubbard wires
- Luttinger liquid and charge-density-wave phases in a spinless fermion wire on a semiconducting substrate
- Block-Lanczos density-matrix renormalization-group approach to spin transport in Heisenberg chains coupled to leads
- Magnetic properties of alternating Hubbard ladders