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Instability of sliding Luttinger liquid

V. Fleurov, Kagalovsky, V., Lerner, I.V., I. V. Yurkevich

Published May 10, 2018• 5 citations
OpenAlex

Abstract

We revise a phase diagram for the sliding Luttinger liquid (SLL) of coupled one-dimensional quantum wires packed in two- or three-dimensional arrays in the absence of a magnetic field. We analyse whether physically justifiable (reasonable) inter-wire interactions, i.e. either the screened Coulomb or "Coulomb-blockade" type interactions, stabilise the SLL phase. Calculating the scaling dimensions of the most relevant perturbations (the inter-wire single-particle hybridisation, charge-density wave, and superconducting inter-wire couplings), we find that their combination always destroys the SLL phase for the repulsive intra-wire interaction. However, suppressing the inter-wire tunnelling of repulsive fermions (when the charge-density wave is the only remaining perturbation), one can observe a stability region emerging due to the inter-wire forward scattering interaction.

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We revise a phase diagram for the sliding Luttinger liquid (SLL) of coupled one-dimensional quantum wires packed in two- or three-dimensional arrays in the absence of a magnetic field. We analyse whether physically justifiable (reasonable) inter-wire interactions, i.e. either the screened Coulomb or "Coulomb-blockade" type interactions, stabilise the SLL phase. Calculating the scaling dimensions of the most relevant perturbations (the inter-wire single-particle hybridisation, charge-density wave, and superconducting inter-wire couplings), we find that their combination always destroys the SLL phase for the repulsive intra-wire interaction. However, suppressing the inter-wire tunnelling of repulsive fermions (when the charge-density wave is the only remaining perturbation), one can observe a stability region emerging due to the inter-wire forward scattering interaction.
We revise a phase diagram for the sliding Luttinger liquid (SLL) of coupled one-dimensional quantum wires packed in two- or three-dimensional arrays in the absence of a magnetic field. We analyse whether physically justifiable (reasonable) inter-wire interactions, i.e. either the screened Coulomb or 'Coulomb-blockade' type interactions, stabilise the SLL phase. Calculating the scaling dimensions of the most relevant perturbations (the inter-wire single-particle hybridisation, charge-density wave, and superconducting inter-wire couplings), we find that their combination always destroys the SLL phase for the repulsive intra-wire interaction. However, suppressing the inter-wire tunnelling of repulsive fermions (when the charge-density wave is the only remaining perturbation), one can observe a stability region emerging due to the inter-wire forward scattering interaction.
We study a phase diagram for the sliding Luttinger liquid (SLL) of coupled one-dimensional quantum wires packed in a two-dimensional array in the absence of a magnetic field. We analyse whether the nearest-neighbour inter-wire interactions, stabilise the SLL phase. We construct an analogue of a Su-Schriefer-Heeger (SSH) model (allowing alternating couplings between wires). Calculating the scaling dimensions of the two most relevant perturbations, charge-density wave, and superconducting inter-wire couplings, but excluding the inter-wire single-particle hybridisation, we find a finite stability region for the SLL. It emerges due to the inter-wire forward scattering interaction, and remains stable up to a significant asymmetry between alternating couplings.
We study a phase diagram for the sliding Luttinger liquid (SLL) of coupled one-dimensional quantum wires packed in a two-dimensional array in the absence of a magnetic field. We analyse whether the nearest-neighbour inter-wire interactions, stabilise the SLL phase. We construct an analogue of a Su-Schriefer-Heeger (SSH) model (allowing alternating couplings between wires). Calculating the scaling dimensions of the two most relevant perturbations, charge-density wave, and superconducting inter-wire couplings, but excluding the inter-wire single-particle hybridisation, we find a finite stability region for the SLL. It emerges due to the inter-wire forward scattering interaction, and remains stable up to a significant asymmetry between alternating couplings.
We study systems made of periodic arrays of one-dimensional quantum wires coupled by Coulomb interaction. Using bosonization an interacting metallic fixed point is obtained, which is shown to be a higher-dimensional analog of the Tomonaga-Luttinger liquid, or a sliding Luttinger liquid. This non-Fermi liquid metallic state, however, is unstable in the presence of weak interwire backscatterings, which favor charge density wave states and suppress pairing. Depending on the effective strength of the Coulomb repulsion and the size of interwire spacing, various charge density wave states are stabilized, including Wigner crystal states. Our method allows for the determination of the specific ordering patterns and corresponding energy and temperature scales.
We investigate the effect of both strong and weak potential scattering caused by local impurities and extended (line) defects in the array of Luttinger liquid wires. We find that in both cases a finite range inter-wire interaction stabilises metallic state. Based on calculation of the scaling dimensions of one-particle scattering operators, we construct the phase diagram for low-temperature transport along the array. We find that unlike local impurity case where only conducting and insulating states are realised (metal-insulator transition driven by interactions), the extended line defects may bring the system into a mixed state where conducting or insulating behavior can be observed depending on bare strength of the scatterer (metal-insulator transition driven by disorder).
Using bosonization techniques, we show that strong forward scattering interactions between one-dimensional spinless Luttinger liquids (LL) can stabilize a phase where charge-density wave, superconducting, and transverse single particle hopping perturbations are irrelevant. This new phase retains its LL-like properties in the directions of the chains, but with relations between exponents modified by the transverse interactions, whereas it is a perfect insulator in the transverse direction. The mechanism that stabilizes this phase is strong transverse charge-density wave fluctuations at incommensurate wave vector, which frustrates crystal formation by preventing lock-in of the in-chain density waves.