arXiv:cond-mat/0501132 · Physical Review B

Temperature-dependent spin susceptibility in a two-dimensional metal

Victor M. Galitski, Andrey V. Chubukov, S. Das Sarma

Published May 11, 2005• 20 citations

Abstract

We consider a two-dimensional electron system with Coulomb interaction between particles at a finite temperature $T$. We show that the dynamic Kohn anomaly in the response function at $2{k}_{F}$ leads to a nonanalytic, linear-in-$T$ correction to the spin susceptibility, $\ensuremath{\delta}\ensuremath{\chi}(T)=aT$, the same as in systems with short-range interaction. We show that the singularity of the Coulomb interaction at $q=0$ does not invalidate the expansion of the prefactor $a$ in powers of ${r}_{s}$, but makes the expansion nonanalytic.

DOI: 10.1103/physrevb.71.201302

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arXiv:cond-mat/0501132 · Physical Review B

Temperature-dependent spin susceptibility in a two-dimensional metal

Victor M. Galitski, Andrey V. Chubukov, S. Das Sarma

Published May 11, 2005• 20 citations

arXiv HTML PDF

Abstract

We consider a two-dimensional electron system with Coulomb interaction between particles at a finite temperature

T

. We show that the dynamic Kohn anomaly in the response function at

2{k}_{F}

leads to a nonanalytic, linear-in-

T

correction to the spin susceptibility,

\ensuremath{\delta}\ensuremath{\chi}(T)=aT

, the same as in systems with short-range interaction. We show that the singularity of the Coulomb interaction at

q=0

does not invalidate the expansion of the prefactor

a

in powers of

{r}_{s}

, but makes the expansion nonanalytic.

DOI: 10.1103/physrevb.71.201302

Related papers

Nonanalytic behavior of the spin susceptibility in clean Fermi systems

D. Belitz, T. R. Kirkpatrick, Thomas Vojta

The wave vector and temperature-dependent static spin susceptibility, ${\mathrm{\ensuremath{\chi}}}_{\mathrm{s}}$(Q,T), of clean interacting Fermi systems is considered in dimensions 1\ensuremath{\leqslant}d\ensuremath{\leqslant}3. We show that at zero temperature ${\mathrm{\ensuremath{\chi}}}_{\mathrm{s}}$ is a nonanalytic function of |Q|, with the leading nonanalyticity being |Q${\mathrm{|}}^{\mathrm{d}\mathrm{\ensuremath{-}}1}$ for 13, and ${\mathbf{Q}}^{2}$ ln |Q| for d=3. For the homogeneous spin susceptibility we find a nonanalytic temperature dependence ${\mathrm{T}}^{\mathrm{d}\mathrm{\ensuremath{-}}1}$ for 13. We give qualitative mode-mode coupling arguments to that effect, and corroborate these arguments by a perturbative calculation to second order in the electron-electron interaction amplitude. The implications of this, in particular for itinerant ferromagnetism, are discussed. We also point out the relation between our findings and established perturbative results for one-dimensional systems, as well as for the temperature dependence of ${\mathrm{\ensuremath{\chi}}}_{\mathrm{s}}$(Q=0) in d=3.The wave vector and temperature-dependent static spin susceptibility, ${\mathrm{\ensuremath{\chi}}}_{\mathrm{s}}$(Q,T), of clean interacting Fermi systems is considered in dimensions 1\ensuremath{\leqslant}d\ensuremath{\leqslant}3. We show that at zero temperature ${\mathrm{\ensuremath{\chi}}}_{\mathrm{s}}$ is a nonanalytic function of |Q|, with the leading nonanalyticity being |Q${\mathrm{|}}^{\mathrm{d}\mathrm{\ensuremath{-}}1}$ for 13, and ${\mathbf{Q}}^{2}$ln |Q| for d=3. For the homogeneous spin susceptibility we find a nonanalytic temperature dependence ${\mathrm{T}}^{\mathrm{d}\mathrm{\ensuremath{-}}1}$ for 13. We give qualitative mode-mode coupling arguments to that effect, and corroborate these arguments by a perturbative calculation to second order in the electron-electron interaction amplitude. The implications of this, in particular for itinerant ferromagnetism, are discussed. We also point out the relation between our findings and established perturbative results for one-dimensional systems, as well as for the temperature dependence of ${\mathrm{\ensuremath{\chi}}}_{\mathrm{s}}$(Q=0) in d=3.

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Logarithmic temperature contributions to long-wavelength spin susceptibility from particle-particle scattering

B. Sriram Shastry, Subodh R. Shenoy

Based on a second-order perturbation calculation with a $\ensuremath{\delta}$-function interaction, Geldart and Rasolt have recently shown that the long-wavelength static spin susceptibility is nonanalytic in $T$ at low temperatures. We find the nonanalyticity is suppressed by the summation of particle-particle scattering terms to all orders. Commonly held analyticity assumptions regarding the long-wavelength and low-temperature behavior of the susceptibility are thus not invalidated. We suggest that for the nonuniform susceptibility, a Kohn-Luttinger-Ward-like equivalence between the zero- and low-temperature perturbation series exists between classes of terms, rather than order by order.Based on a second-order perturbation calculation with a $\ensuremath{\delta}$-function interaction, Geldart and Rasolt have recently shown that the long-wavelength static spin susceptibility is nonanalytic in $T$ at low temperatures. We find the nonanalyticity is suppressed by the summation of particle-particle scattering terms to all orders. Commonly held analyticity assumptions regarding the long-wavelength and low-temperature behavior of the susceptibility are thus not invalidated. We suggest that for the nonuniform susceptibility, a Kohn-Luttinger-Ward-like equivalence between the zero- and low-temperature perturbation series exists between classes of terms, rather than order by order.

Physical review. B, Condensed matterSep 1, 19791 citation

We consider a two-dimensional electron system with Coulomb interaction between particles at a finite temperature

T

. We show that the dynamic Kohn anomaly in the response function at

2{k}_{F}

leads to a nonanalytic, linear-in-

T

correction to the spin susceptibility,

\ensuremath{\delta}\ensuremath{\chi}(T)=aT

, the same as in systems with short-range interaction. We show that the singularity of the Coulomb interaction at

q=0

does not invalidate the expansion of the prefactor

a

in powers of

{r}_{s}

, but makes the expansion nonanalytic.

{\mathbf{Q}}^{2}

ln |Q| for d=3. For the homogeneous spin susceptibility we find a nonanalytic temperature dependence ${\mathrm{T}}^{\mathrm{d}\mathrm{\ensuremath{-}}1}$ for 13. We give qualitative mode-mode coupling arguments to that effect, and corroborate these arguments by a perturbative calculation to second order in the electron-electron interaction amplitude. The implications of this, in particular for itinerant ferromagnetism, are discussed. We also point out the relation between our findings and established perturbative results for one-dimensional systems, as well as for the temperature dependence of ${\mathrm{\ensuremath{\chi}}}_{\mathrm{s}}$(Q=0) in d=3.

{T}^{2}

term in the specific heat, linear-in-

T

terms in the effective mass and in the uniform spin susceptibility ${\ensuremath{\chi}}_{s}(Q=0,T),$ and

|Q|

term in ${\ensuremath{\chi}}_{s}(Q,T=0).$ The existence of these terms has been the subject of recent controversy, which is resolved in this paper. We present exact expressions for all nonanalytic terms to second order in a generic interaction

U(Q)

and show that the nonanalytic terms originate exclusively from forward- and backward-scattering of particles with zero total momentum.

{T}^{2}

term in the specific heat, linear-in-

T

terms in the effective mass and in the uniform spin susceptibility ${\ensuremath{\chi}}_{s}(Q=0,T),$ and

|Q|

U(Q)

and show that the nonanalytic terms originate exclusively from forward- and backward-scattering of particles with zero total momentum.

T

term we use angular harmonics in the Cooper channel, because for each harmonic the interaction amplitude is renormalized independently. We observe, that as a consequence of strong renormalizations in the Cooper ladder, the temperature derivative of the spin susceptibility may change its sign at low temperatures.

T

at low temperatures. We find the nonanalyticity is suppressed by the summation of particle-particle scattering terms to all orders. Commonly held analyticity assumptions regarding the long-wavelength and low-temperature behavior of the susceptibility are thus not invalidated. We suggest that for the nonuniform susceptibility, a Kohn-Luttinger-Ward-like equivalence between the zero- and low-temperature perturbation series exists between classes of terms, rather than order by order.