Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review Letters

Conductivity between Luttinger Liquids in the Confinement Regime and c -Axis Conductivity in the Cuprate Superconductors

David G. Clarke, Steven P. Strong, P. W. Anderson

Published May 29, 1995• 63 citations
Publisher

Abstract

We calculate the interliquid conductivity for Luttinger liquids, within the so-called ``confinement'' regime where interliquid hopping is completely incoherent. We argue that the interliquid conductivity behaves as ${\ensuremath{\sigma}}_{\ensuremath{\perp}}(\ensuremath{\omega})\ensuremath{\sim}{\ensuremath{\omega}}^{4\ensuremath{\alpha}}$, where $\ensuremath{\alpha}$ is the Luttinger liquid exponent. We discuss the effect of finite temperature, which is found to introduce a coherent weight into the conductivity. These results are in good agreement with experimental measurements of the frequency dependent normal state $c$-axis conductivity in the high-temperature superconductors YB${\mathrm{a}}_{2}$C${\mathrm{u}}_{3}$O ${}_{7\ensuremath{-}\ensuremath{\delta}}$ and La ${}_{2\ensuremath{-}x}$Sr ${}_{x}$Cu${\mathrm{O}}_{4}$.

DOI
10.1103/physrevlett.74.4499

Related papers

Confinement and transverse conductivity in coupled Luttinger liquids

Sylvain Capponi, Didier Poilblanc, Frédéric Mila

One-particle interchain hopping in a system of coupled Luttinger liquids is investigated using exact diagonalizations techniques. First, the two-chain problem of spinless fermions is studied in order to see the behavior of the band splitting as a function of the exponent $\ensuremath{\alpha}$ which characterizes the one-dimensional (1D) Luttinger liquid. Moderate intrachain interactions can lead to a strong reduction of this splitting. The onset of the confinement within the individual chains (defined by a vanishing splitting) seems to be governed by $\ensuremath{\alpha}$. We give numerical evidence that interchain coherent hopping can be totally suppressed for $\ensuremath{\alpha}\ensuremath{\sim}0.4$ or even smaller $\ensuremath{\alpha}$ values. The transverse conductivity is shown to exhibit a strong incoherent part. Even when coherent interchain hopping is believed to occur (at small $\ensuremath{\alpha}$ values), it is shown that the coherent Drude weight is always significantly smaller than the incoherent weight. Implications for the optical experiments in quasi-1D organic or high-${T}_{c}$ superconductors are outlined.

arXiv:cond-mat/9608004•Physical review. B, Condensed matter•Dec 15, 1996•11 citations

New evidence for `confined coherence' in weakly coupled Luttinger liquids

David G. Clarke, Steven P. Strong

On the basis of a calculation of the exact interliquid hopping rate and an approximate single particle Green's function, we present new evidence for the existence of a phase of relevant but incoherent inter-Luttinger liquid transport. This phase of ``confined coherence'' occurs when the Luttinger liquid exponent alpha satisfies alpha_c

arXiv:cond-mat/9607141•Journal of Physics Condensed Matter•May 12, 1997•2 citations

Single particle hopping between luttinger liquids: A spectral function approach

David G. Clarke, Steven P. Strong

We present a pedagogical account of our approach to the problem of Luttinger liquids coupled by interliquid single particle hopping. It is shown that the key issue is that of coherence/incoherence of interliquid hopping, and not of relevance/irrelevance in a renormalization group sense. A clear signal of coherence, present in the case of coupled Fermi liquids, is absent for Luttinger liquids, and we argue for the existence of an incoherent regime when the interliquid hopping rate is sufficiently small. The problem is relevant to any sufficiently anisotropic, strongly correlated metal, and in particular to understanding the anomalous c-axis conductivity in the cuprate superconductors, and the physics of the quasi-1D organic conductors.

arXiv:cond-mat/9510168•Ferroelectrics•Mar 1, 1996•7 citations

Frequency-temperature crossover in the conductivity of disordered Luttinger liquids

Bernd Rosenow, Andreas Glatz, Thomas Nattermann

The temperature $(T)$ and frequency $(\ensuremath{\omega})$ dependent conductivity of weakly disordered Luttinger liquids is calculated in a systematic way both by perturbation theory and from a finite temperature renormalization group (RG) treatment to leading order in the disorder strength. Whereas perturbation theory results in $\ensuremath{\omega}∕T$ scaling of the conductivity, such scaling is violated in the RG treatment. We also determine the nonlinear field dependence of the conductivity, whose power law scaling is different from that of temperature and frequency dependence.

arXiv:cond-mat/0610426•Physical Review B•Oct 10, 2007•4 citations

Tunneling density of states, pair correlation, and Josephson current in spin-incoherent Luttinger-liquid/superconductor hybrid systems

Dagim Tilahun, Gregory A. Fiete

We study a hybrid system consisting of a spin-incoherent Luttinger liquid adjoined at one or both ends to a superconductor. We find that the tunneling density of states diverges at low energies and exhibits a universal frequency dependence independent of the strength of the interactions in the system. We show that in spite of exponentially decaying pair correlations with distance into the spin-incoherent Luttinger liquid, the Josephson current remains robust. Compared to the zero temperature Luttinger-liquid case, there is a factor of 2 reduction in the critical current and a halving of the period in the phase difference between the superconductors. We hope these results motivate a class of experiments in the spin-incoherent regime of one-dimensional systems.

arXiv:0706.3418•Physical Review B•Apr 18, 2008•6 citations

Transport in a spin-incoherent Luttinger liquid

Gregory A. Fiete, Karyn Le Hur, Leon Balents

We theoretically investigate transport in a spin-incoherent one-dimensional electron system, which may be realized in quantum wires at low-electron density and finite temperature. Both the pure and disordered cases are considered, both in finite wires and in the thermodynamic limit. The effect of Fermi-liquid leads attached to the finite-length system is also addressed. In the infinite system, we find a phase diagram identical to that obtained for a spinless Luttinger liquid, provided we make the identification $g=2{g}_{c}$, where $g$ is the interaction parameter in a spinless Luttinger liquid and ${g}_{c}$ is the interaction parameter of the charge sector of a Luttinger-liquid theory for electrons with spin. For a finite-length wire attached to Fermi-liquid leads, the transport depends on the details of the disorder in the wire. A simple picture for the crossover from the spin-incoherent regime to the spin-coherent regime as the temperature is varied is also discussed, as well as some physical implications.

arXiv:cond-mat/0505186•Physical Review B•Sep 13, 2005•33 citations
We calculate the interliquid conductivity for Luttinger liquids, within the so-called ``confinement'' regime where interliquid hopping is completely incoherent. We argue that the interliquid conductivity behaves as \ensuremathσ\ensuremath⊥(\ensuremathω)\ensuremath∼\ensuremathω4\ensuremathα{\ensuremath{\sigma}}_{\ensuremath{\perp}}(\ensuremath{\omega})\ensuremath{\sim}{\ensuremath{\omega}}^{4\ensuremath{\alpha}}\ensuremathσ\ensuremath⊥​(\ensuremathω)\ensuremath∼\ensuremathω4\ensuremathα, where \ensuremathα\ensuremath{\alpha}\ensuremathα is the Luttinger liquid exponent. We discuss the effect of finite temperature, which is found to introduce a coherent weight into the conductivity. These results are in good agreement with experimental measurements of the frequency dependent normal state ccc-axis conductivity in the high-temperature superconductors YBa2{\mathrm{a}}_{2}a2​Cu3{\mathrm{u}}_{3}u3​O 7\ensuremath−\ensuremathδ{}_{7\ensuremath{-}\ensuremath{\delta}}7\ensuremath−\ensuremathδ​ and La 2\ensuremath−x{}_{2\ensuremath{-}x}2\ensuremath−x​Sr x{}_{x}x​CuO4{\mathrm{O}}_{4}O4​.
One-particle interchain hopping in a system of coupled Luttinger liquids is investigated using exact diagonalizations techniques. First, the two-chain problem of spinless fermions is studied in order to see the behavior of the band splitting as a function of the exponent $\ensuremath{\alpha}$ which characterizes the one-dimensional (1D) Luttinger liquid. Moderate intrachain interactions can lead to a strong reduction of this splitting. The onset of the confinement within the individual chains (defined by a vanishing splitting) seems to be governed by $\ensuremath{\alpha}$. We give numerical evidence that interchain coherent hopping can be totally suppressed for $\ensuremath{\alpha}\ensuremath{\sim}0.4$ or even smaller $\ensuremath{\alpha}$ values. The transverse conductivity is shown to exhibit a strong incoherent part. Even when coherent interchain hopping is believed to occur (at small $\ensuremath{\alpha}$ values), it is shown that the coherent Drude weight is always significantly smaller than the incoherent weight. Implications for the optical experiments in quasi-1D organic or high-Tc{T}_{c}Tc​ superconductors are outlined.
We present a pedagogical account of our approach to the problem of Luttinger liquids coupled by interliquid single particle hopping. It is shown that the key issue is that of coherence/incoherence of interliquid hopping, and not of relevance/irrelevance in a renormalization group sense. A clear signal of coherence, present in the case of coupled Fermi liquids, is absent for Luttinger liquids, and we argue for the existence of an incoherent regime when the interliquid hopping rate is sufficiently small. The problem is relevant to any sufficiently anisotropic, strongly correlated metal, and in particular to understanding the anomalous c-axis conductivity in the cuprate superconductors, and the physics of the quasi-1D organic conductors.
The temperature (T)(T)(T) and frequency $(\ensuremath{\omega})$ dependent conductivity of weakly disordered Luttinger liquids is calculated in a systematic way both by perturbation theory and from a finite temperature renormalization group (RG) treatment to leading order in the disorder strength. Whereas perturbation theory results in $\ensuremath{\omega}∕T$ scaling of the conductivity, such scaling is violated in the RG treatment. We also determine the nonlinear field dependence of the conductivity, whose power law scaling is different from that of temperature and frequency dependence.
We study a hybrid system consisting of a spin-incoherent Luttinger liquid adjoined at one or both ends to a superconductor. We find that the tunneling density of states diverges at low energies and exhibits a universal frequency dependence independent of the strength of the interactions in the system. We show that in spite of exponentially decaying pair correlations with distance into the spin-incoherent Luttinger liquid, the Josephson current remains robust. Compared to the zero temperature Luttinger-liquid case, there is a factor of 2 reduction in the critical current and a halving of the period in the phase difference between the superconductors. We hope these results motivate a class of experiments in the spin-incoherent regime of one-dimensional systems.
We theoretically investigate transport in a spin-incoherent one-dimensional electron system, which may be realized in quantum wires at low-electron density and finite temperature. Both the pure and disordered cases are considered, both in finite wires and in the thermodynamic limit. The effect of Fermi-liquid leads attached to the finite-length system is also addressed. In the infinite system, we find a phase diagram identical to that obtained for a spinless Luttinger liquid, provided we make the identification g=2gcg=2{g}_{c}g=2gc​, where ggg is the interaction parameter in a spinless Luttinger liquid and gc{g}_{c}gc​ is the interaction parameter of the charge sector of a Luttinger-liquid theory for electrons with spin. For a finite-length wire attached to Fermi-liquid leads, the transport depends on the details of the disorder in the wire. A simple picture for the crossover from the spin-incoherent regime to the spin-coherent regime as the temperature is varied is also discussed, as well as some physical implications.