TY - JOUR

T1 - Effective narrow ladder model for two quantum wires on a semiconducting substrate

AU - Abdelwahab, Anas

AU - Jeckelmann, Eric

N1 - Funding Information: We would like to thank T. Shirakawa for fruitful discussions on the BL algorithm. This work was done as part of the Research Units Metallic nanowires on the atomic scale: Electronic and vibrational coupling in real world systems (FOR1700) of the German Research Foundation (DFG) and was supported by Grant No. JE 261/1-2. The DMRG calculations were carried out on the cluster system at the Leibniz University of Hannover.

PY - 2021/6/2

Y1 - 2021/6/2

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85108023812&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.103.245405

DO - 10.1103/PhysRevB.103.245405

M3 - Article

VL - 103

JO - Physical Review B

JF - Physical Review B

SN - 2469-9950

IS - 24

M1 - 245405

ER -