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arXiv:cond-mat/0007349 · Physical review. B, Condensed matter

Sliding phases via magnetic fields

Shivaji L. Sondhi, Kun Yang

Published Jan 11, 2001• 83 citations
arXivHTMLPDF

Abstract

We show that three-dimensional ``sliding'' analogs of the Kosterlitz-Thouless phase, in stacked classical two-dimensional $\mathrm{XY}$ models and quantum systems of coupled Luttinger liquids, can be enlarged by the application of a parallel magnetic field, which has the effect of increasing the scaling dimensions of the most relevant operators that can perturb the critical sliding phases. Within our renormalization-group analysis, we also find that for the case of coupled Luttinger liquids, this effect is interleaved with the onset of the integer quantum Hall effect for weak interactions and fields. We comment on experimental implications for a conjectured smectic metal phase in the cuprates.

DOI
10.1103/physrevb.63.054430

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We show that three-dimensional ``sliding'' analogs of the Kosterlitz-Thouless phase, in stacked classical two-dimensional XY\mathrm{XY}XY models and quantum systems of coupled Luttinger liquids, can be enlarged by the application of a parallel magnetic field, which has the effect of increasing the scaling dimensions of the most relevant operators that can perturb the critical sliding phases. Within our renormalization-group analysis, we also find that for the case of coupled Luttinger liquids, this effect is interleaved with the onset of the integer quantum Hall effect for weak interactions and fields. We comment on experimental implications for a conjectured smectic metal phase in the cuprates.
Materials consisting of a stack of “two-dimensional” layers that exhibit 2D power-law order in the absence of coupling between layers include systems as diverse as layered magnets, DNA-lipid complexes, and coupled Luttinger liquids. It is common belief that these systems exhibit “three-dimensional” order whenever there is a nonvanishing interlayer coupling. However, with appropriately chosen interlayer gradient couplings between layers, they can exhibit unusual equilibrium “Sliding Phases” characterized by 2D-like power-law correlations. After reviewing the various types of sliding phases that can occur, this paper will discuss in detail the properties of the simplest sliding phases, the sliding xy phases in three-dimensional stacks of planar xy models. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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 systems of coupled spin-gapped and gapless Luttinger liquids. First, we establish the existence of a sliding Luttinger liquid phase for a system of weakly coupled parallel quantum wires, with and without disorder. It is shown that the coupling can stabilize a Luttinger liquid phase in the presence of disorder. We then extend our analysis to a system of crossed Luttinger liquids and establish the stability of a non-Fermi-liquid state: the crossed sliding Luttinger liquid phase. In this phase the system exhibits a finite-temperature, long-wavelength, isotropic electric conductivity that diverges as a power law in temperature T as $\stackrel{\ensuremath{\rightarrow}}{T}0.$ This two-dimensional system has many properties of a true isotropic Luttinger liquid, though at zero temperature it becomes anisotropic. An extension of this model to a three-dimensional stack exhibits a much higher in-plane conductivity than the conductivity in a perpendicular direction.
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 electronic phase competition in a strongly correlated system of three coupled spinless Luttinger liquids—one of the simplest models where topologically nontrivial chiral orders may be realized. We study the problem as a coupled sine-Gordon model, using a perturbative renormalization group (RG) approach. In contrast with counterparts with fewer fermionic species, here the scaling procedure generates off-diagonal contributions to the phase stiffness matrix, which require both rescaling as well as large rotations of the bosonic fields. These rotations, generally non-abelian in nature, introduce a coupling between different interaction channels even at the tree-level order in the coupling constant scaling equations. We study competing phases in this system, taking into account the aforementioned rotations, and determine its critical behaviour in a variety of interaction parameter regimes where perturbative RG is possible. The phase boundaries are found to be of the Berezinskii–Kosterlitz–Thouless type, and we specify the parameter regimes where symmetry breaking between the three flavours of bosonic fields, orders involving different flavours, and chiral orders may be observed. Our approach and findings may be relevant for understanding phases and transitions at high magnetic fields in semimetals such as bismuth featuring three Fermi pockets.