In a one-dimensional electron gas at low enough density, the magnetic (spin) exchange energy $J$ between neighboring electrons is exponentially suppressed relative to the characteristic charge energy, the Fermi energy ${E}_{F}$ . At nonzero temperature $T$ , the energy hierarchy $J⪡T⪡{E}_{F}$ can be reached, and we refer to this as the spin-incoherent Luttinger liquid state. We discuss the Coulomb drag between two parallel quantum wires in the spin-incoherent regime, as well as the crossover to this state from the low-temperature regime by using a model of a fluctuating Wigner solid. As the temperature increases from zero to above $J$ for a fixed electron density, the $2{k}_{F}$ oscillations in the density-density correlations are lost. As a result, the temperature dependence of the Coulomb drag is dramatically altered and nonmonotonic dependence may result. Drag between wires of equal and unequal density are discussed, as well as the effects of weak disorder in the wires. We speculate that weak disorder may play an important role in extracting information about quantum wires in real drag experiments.In a one-dimensional electron gas at low enough density, the magnetic (spin) exchange energy $J$ between neighboring electrons is exponentially suppressed relative to the characteristic charge energy, the Fermi energy ${E}_{F}$. At nonzero temperature $T$, the energy hierarchy $J⪡T⪡{E}_{F}$ can be reached, and we refer to this as the spin-incoherent Luttinger liquid state. We discuss the Coulomb drag between two parallel quantum wires in the spin-incoherent regime, as well as the crossover to this state from the low-temperature regime by using a model of a fluctuating Wigner solid. As the temperature increases from zero to above $J$ for a fixed electron density, the $2{k}_{F}$ oscillations in the density-density correlations are lost. As a result, the temperature dependence of the Coulomb drag is dramatically altered and nonmonotonic dependence may result. Drag between wires of equal and unequal density are discussed, as well as the effects of weak disorder in the wires. We speculate that weak disorder may play an important role in extracting information about quantum wires in real drag experiments.

arXiv:cond-mat/0511715Physical Review BApr 5, 200660 citations

Transport in Luttinger Liquids

Thierry Giamarchi, T. Nattermann, Pierre Le Doussal

arXiv:cond-mat/0403487NATO science series. Series II, Mathematics, physics and chemistryJan 1, 20040 citations

Spin Coulomb drag in a spin-polarized Luttinger liquid

P. Schlottmann

The spin Coulomb drag is a distinctive feature of spin-polarized transport. The current of majority spins can induce a current of minority-spin carriers via the transconductivity. The friction is caused by the Coulomb interaction between up and down spin. This interaction reduces the current but does not change the spin polarization. We calculate the conductivities and the transconductivity for a spin-polarized interacting one-dimensional electron gas with nonmagnetic impurities using the Kubo formalism. Due to the Luttinger-liquid properties, the temperature dependence of the transport correlation functions follow power laws of $T$ with nonuniversal exponents.The spin Coulomb drag is a distinctive feature of spin-polarized transport. The current of majority spins can induce a current of minority-spin carriers via the transconductivity. The friction is caused by the Coulomb interaction between up and down spin. This interaction reduces the current but does not change the spin polarization. We calculate the conductivities and the transconductivity for a spin-polarized interacting one-dimensional electron gas with nonmagnetic impurities using the Kubo formalism. Due to the Luttinger-liquid properties, the temperature dependence of the transport correlation functions follow power laws of $T$ with nonuniversal exponents.

Physical Review BNov 10, 200910 citations

Transport in Luttinger Liquids

Thierry Giamarchi, Thomas Nattermann, Pierre Le Doussal

Springer eBooksJan 1, 20040 citations

Luttinger liquids with curvature: Density correlations and Coulomb drag effect

D. N. Aristov

We consider the effect of the curvature in fermionic dispersion on the observable properties of Luttinger liquid (LL). We use the bosonization technique where the curvature is irrelevant perturbation, describing the decay of LL bosons (plasmon modes). When possible, we establish the correspondence between the bosonization and the fermionic approach. We analyze modifications in density correlation functions due to curvature at finite temperatures, $T$ . The most important application of our approach is the analysis of the Coulomb drag by small momentum transfer between two LLs, which is only possible due to curvature. Analyzing the ac transconductivity in the one-dimensional drag setup, we confirm the results by Pustilnik et al. for $T$ dependence of drag resistivity, ${R}_{12}\ensuremath{\sim}{T}^{2}$ at high and ${R}_{12}\ensuremath{\sim}{T}^{5}$ at low temperatures. The bosonization allows for treating both intra- and interwire electron-electron interactions in all orders, and we calculate exact prefactors in the low- $T$ drag regime. The crossover temperature between the two regimes is ${T}_{1}\ensuremath{\sim}{E}_{F}\ensuremath{\Delta}$, with $\ensuremath{\Delta}$ relative difference in plasmon velocities. We show that $\ensuremath{\Delta}\ensuremath{\ne}0$ even for identical wires, due to lifting of degeneracy by interwire interaction, ${U}_{12}$ , leading to crossover from ${R}_{12}\ensuremath{\sim}{U}_{12}^{2}{T}^{2}$ to ${R}_{12}\ensuremath{\sim}{T}^{5}∕{U}_{12}$ at $T\ensuremath{\sim}{U}_{12}$.We consider the effect of the curvature in fermionic dispersion on the observable properties of Luttinger liquid (LL). We use the bosonization technique where the curvature is irrelevant perturbation, describing the decay of LL bosons (plasmon modes). When possible, we establish the correspondence between the bosonization and the fermionic approach. We analyze modifications in density correlation functions due to curvature at finite temperatures, $T$. The most important application of our approach is the analysis of the Coulomb drag by small momentum transfer between two LLs, which is only possible due to curvature. Analyzing the ac transconductivity in the one-dimensional drag setup, we confirm the results by Pustilnik et al. for $T$ dependence of drag resistivity, ${R}_{12}\ensuremath{\sim}{T}^{2}$ at high and ${R}_{12}\ensuremath{\sim}{T}^{5}$ at low temperatures. The bosonization allows for treating both intra- and interwire electron-electron interactions in all orders, and we calculate exact prefactors in the low-$T$ drag regime. The crossover temperature between the two regimes is ${T}_{1}\ensuremath{\sim}{E}_{F}\ensuremath{\Delta}$, with $\ensuremath{\Delta}$ relative difference in plasmon velocities. We show that $\ensuremath{\Delta}\ensuremath{\ne}0$ even for identical wires, due to lifting of degeneracy by interwire interaction, ${U}_{12}$, leading to crossover from ${R}_{12}\ensuremath{\sim}{U}_{12}^{2}{T}^{2}$ to ${R}_{12}\ensuremath{\sim}{T}^{5}∕{U}_{12}$ at $T\ensuremath{\sim}{U}_{12}$.

arXiv:cond-mat/0702475Physical Review BAug 16, 200735 citations

Transport in Luttinger Liquids

Thierry Giamarchi, Thomas Nattermann, Pierre Le Doussal

Jan 1, 20040 citations

In a one-dimensional electron gas at low enough density, the magnetic (spin) exchange energy

J

between neighboring electrons is exponentially suppressed relative to the characteristic charge energy, the Fermi energy

{E}_{F}

. At nonzero temperature

T

, the energy hierarchy

J⪡T⪡{E}_{F}

can be reached, and we refer to this as the spin-incoherent Luttinger liquid state. We discuss the Coulomb drag between two parallel quantum wires in the spin-incoherent regime, as well as the crossover to this state from the low-temperature regime by using a model of a fluctuating Wigner solid. As the temperature increases from zero to above

J

for a fixed electron density, the

2{k}_{F}

oscillations in the density-density correlations are lost. As a result, the temperature dependence of the Coulomb drag is dramatically altered and nonmonotonic dependence may result. Drag between wires of equal and unequal density are discussed, as well as the effects of weak disorder in the wires. We speculate that weak disorder may play an important role in extracting information about quantum wires in real drag experiments.

T

with nonuniversal exponents.

T

. The most important application of our approach is the analysis of the Coulomb drag by small momentum transfer between two LLs, which is only possible due to curvature. Analyzing the ac transconductivity in the one-dimensional drag setup, we confirm the results by Pustilnik et al. for

T

dependence of drag resistivity, ${R}_{12}\ensuremath{\sim}{T}^{2}$ at high and ${R}_{12}\ensuremath{\sim}{T}^{5}$ at low temperatures. The bosonization allows for treating both intra- and interwire electron-electron interactions in all orders, and we calculate exact prefactors in the low-

T

drag regime. The crossover temperature between the two regimes is ${T}_{1}\ensuremath{\sim}{E}_{F}\ensuremath{\Delta}$, with $\ensuremath{\Delta}$ relative difference in plasmon velocities. We show that $\ensuremath{\Delta}\ensuremath{\ne}0$ even for identical wires, due to lifting of degeneracy by interwire interaction,

{U}_{12}

, leading to crossover from ${R}_{12}\ensuremath{\sim}{U}_{12}^{2}{T}^{2}$ to ${R}_{12}\ensuremath{\sim}{T}^{5}∕{U}_{12}$ at $T\ensuremath{\sim}{U}_{12}$.