Abstract

We calculate from first principles the high-frequency high-temperature conductivity of metals and find that to dominant order the temperature-dependent collision frequency is given by ν(T) = ν1(T/Tm) + ν2(T/Tm)2, where Tm represents the melting temperature and ν1 and ν2 are independent of T. The origin of the quadratic-temperature term arises from the contribution of the anharmonic ion potential near melting to the phonon spectra.

© 1981 Optical Society of America

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  1. M. Sparks and E. Loh, J. Opt. Soc. Am. 69, 847–858 (1979); J. Opt. Soc. Am. 69, 859–868 (1979).
    [Crossref]
  2. T. Holstein, Phys. Rev. 96, 535 (1954); V. L. Ginzburge and V. P. Silin, Sov. Phys. JETP 2, 46 (1956); P. N. Gurzhi, Sov. Phys. JETP 6, 352, 506 (1958); H. Ehrenriech and H. R. Philipp, Phys. Rev. 128, 1622 (1962).
    [Crossref]
  3. J. Bardeen and D. Pines, Phys. Rev. 99, 1140 (1955); see also J. Bardeen, Encyclopedia of Physics XV (Springer-Verlag, Berlin, 1956).
    [Crossref]
  4. A. Ron, Phys. Rev. 131, 2041 (1963).
    [Crossref]
  5. R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957); A. Ron and N. Tzoar, Phys. Rev. 131(12) (1963); N. Tzoar, Phys. Rev. 132, 202 (1963); A. Ron and N. Tzoar, Phys. Rev. 133A, 1378 (1964).
    [Crossref]
  6. See, for example, M. Sparks and E. Loh, J. Opt. Soc. Am. 69, 847–858 (1979), Figs. 1 and 2.
    [Crossref]
  7. A. P. Miller and B. N. Brockhouse, Can. J. Phys. 49, 704 (1970).
    [Crossref]
  8. See, for example, J. A. Reissland, The Physics of Phonons (Wiley, New York, 1973).
  9. R. C. Shukla and E. R. Muller, Phys. Rev. B 21, 544 (1980). These authors calculated a similar effect to ours for the dc conductivity.
    [Crossref]

1980 (1)

R. C. Shukla and E. R. Muller, Phys. Rev. B 21, 544 (1980). These authors calculated a similar effect to ours for the dc conductivity.
[Crossref]

1979 (2)

1970 (1)

A. P. Miller and B. N. Brockhouse, Can. J. Phys. 49, 704 (1970).
[Crossref]

1963 (1)

A. Ron, Phys. Rev. 131, 2041 (1963).
[Crossref]

1957 (1)

R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957); A. Ron and N. Tzoar, Phys. Rev. 131(12) (1963); N. Tzoar, Phys. Rev. 132, 202 (1963); A. Ron and N. Tzoar, Phys. Rev. 133A, 1378 (1964).
[Crossref]

1955 (1)

J. Bardeen and D. Pines, Phys. Rev. 99, 1140 (1955); see also J. Bardeen, Encyclopedia of Physics XV (Springer-Verlag, Berlin, 1956).
[Crossref]

1954 (1)

T. Holstein, Phys. Rev. 96, 535 (1954); V. L. Ginzburge and V. P. Silin, Sov. Phys. JETP 2, 46 (1956); P. N. Gurzhi, Sov. Phys. JETP 6, 352, 506 (1958); H. Ehrenriech and H. R. Philipp, Phys. Rev. 128, 1622 (1962).
[Crossref]

Bardeen, J.

J. Bardeen and D. Pines, Phys. Rev. 99, 1140 (1955); see also J. Bardeen, Encyclopedia of Physics XV (Springer-Verlag, Berlin, 1956).
[Crossref]

Brockhouse, B. N.

A. P. Miller and B. N. Brockhouse, Can. J. Phys. 49, 704 (1970).
[Crossref]

Holstein, T.

T. Holstein, Phys. Rev. 96, 535 (1954); V. L. Ginzburge and V. P. Silin, Sov. Phys. JETP 2, 46 (1956); P. N. Gurzhi, Sov. Phys. JETP 6, 352, 506 (1958); H. Ehrenriech and H. R. Philipp, Phys. Rev. 128, 1622 (1962).
[Crossref]

Kubo, R.

R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957); A. Ron and N. Tzoar, Phys. Rev. 131(12) (1963); N. Tzoar, Phys. Rev. 132, 202 (1963); A. Ron and N. Tzoar, Phys. Rev. 133A, 1378 (1964).
[Crossref]

Loh, E.

Miller, A. P.

A. P. Miller and B. N. Brockhouse, Can. J. Phys. 49, 704 (1970).
[Crossref]

Muller, E. R.

R. C. Shukla and E. R. Muller, Phys. Rev. B 21, 544 (1980). These authors calculated a similar effect to ours for the dc conductivity.
[Crossref]

Pines, D.

J. Bardeen and D. Pines, Phys. Rev. 99, 1140 (1955); see also J. Bardeen, Encyclopedia of Physics XV (Springer-Verlag, Berlin, 1956).
[Crossref]

Reissland, J. A.

See, for example, J. A. Reissland, The Physics of Phonons (Wiley, New York, 1973).

Ron, A.

A. Ron, Phys. Rev. 131, 2041 (1963).
[Crossref]

Shukla, R. C.

R. C. Shukla and E. R. Muller, Phys. Rev. B 21, 544 (1980). These authors calculated a similar effect to ours for the dc conductivity.
[Crossref]

Sparks, M.

Can. J. Phys. (1)

A. P. Miller and B. N. Brockhouse, Can. J. Phys. 49, 704 (1970).
[Crossref]

J. Opt. Soc. Am. (2)

J. Phys. Soc. Jpn. (1)

R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957); A. Ron and N. Tzoar, Phys. Rev. 131(12) (1963); N. Tzoar, Phys. Rev. 132, 202 (1963); A. Ron and N. Tzoar, Phys. Rev. 133A, 1378 (1964).
[Crossref]

Phys. Rev. (3)

T. Holstein, Phys. Rev. 96, 535 (1954); V. L. Ginzburge and V. P. Silin, Sov. Phys. JETP 2, 46 (1956); P. N. Gurzhi, Sov. Phys. JETP 6, 352, 506 (1958); H. Ehrenriech and H. R. Philipp, Phys. Rev. 128, 1622 (1962).
[Crossref]

J. Bardeen and D. Pines, Phys. Rev. 99, 1140 (1955); see also J. Bardeen, Encyclopedia of Physics XV (Springer-Verlag, Berlin, 1956).
[Crossref]

A. Ron, Phys. Rev. 131, 2041 (1963).
[Crossref]

Phys. Rev. B (1)

R. C. Shukla and E. R. Muller, Phys. Rev. B 21, 544 (1980). These authors calculated a similar effect to ours for the dc conductivity.
[Crossref]

Other (1)

See, for example, J. A. Reissland, The Physics of Phonons (Wiley, New York, 1973).

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Equations (46)

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σ ( ω ) = 1 3 V 0 d τ e i ω τ 0 β d λ j ( τ - λ ) · j ( 0 ) ,
j ( τ ) = e i H τ j e - i H τ
0 = T r { exp [ β ( Ω + μ N - H ) ] 0 } .
e - β Ω = T r { exp [ β ( μ N - H ) ] } ,
j ( 0 ) = e m p p a p + a p ,
σ ( ω ) = i ω p 2 4 π ω + σ 1 ( ω ) ,
σ 1 ( ω ) = 1 3 ω V 0 d τ e i ω τ [ j ( τ ) · , j ( 0 ) ] ,
M ( ω ) = 1 3 V T { j ( u ) · j ( 0 ) } ,
j ( u ) = e H u j ( 0 ) e - H u .
M ( ω n ) = 0 β d u e ω n u M ( u ) ,
ω n = 2 π i n / β ;             n = 0 , ± 1 1 ± 2 ,
σ 1 ( ω ) = 1 i ω M ( ω + i η ) ;             n 0 + .
σ ( ω ) = i ω p 2 4 π ω + 1 i ω M ( ω + i η ) ;             η 0 + .
D k 0 ( α m ) = 1 α m 2 - Ω k 2 ,
α m = 2 π i m / β ;             m = 0 , ± 1 , ± 2 .
D k e - p h ( α m ) = D k 0 ( α m ) + D k 0 ( α m ) V k 2 Q k ( α m ) D k 0 ( α m ) + D k 0 ( α m ) V k 2 Q k ( α m ) D k 0 ( α m ) V k 2 Q k × ( α m ) D k 0 ( α m ) + ,
Q k ( α m ) = 1 V p f p + k / 2 - f p - k / 2 E p + k / 2 - E p - k / 2 - α m .
k ( α m ) = 1 - 4 π e 2 k 2 Q k ( α m ) .
D k ( α m ) = D k 0 ( α m ) 1 - V k 2 Q k ( α m ) k ( α m ) D k 0 ( α m ) .
V k + V k ( 4 π e 2 / k 2 ) Q k ( α m ) k ( α m ) .
V k k ( α m ) ,             V k * k ( α m ) .
ν ( ω ) = 2 3 m n ω 8 π 3 0 d k k 6 V k 2 4 π e 2 P × - + d x [ coth β x 2 - coth β 2 ( x + ω ) ] × Im D k ( x ) Im k - 1 ( x + ω ) .
D k ( x ) = [ ( x + i η ) 2 - Ω k - V k 2 k 2 4 π e 2 1 - k ( x ) k ( x ) ] - 1 ,
V k 2 = ( 4 π e 2 k ) 2 n M ,
ω k 2 c 2 k 2 ,
c 2 = m 3 M v F 2 ,
D k ( x ) = [ ( x + i η ) 2 - ω k 2 ] - 1 .
ν ( ω ) = e 2 6 π m M ω × 0 d k k 4 ω k - + d x [ coth β x 2 - coth β 2 ( x + ω ) ] × Im k - 1 ( x + ω ) [ δ ( x - ω k ) - δ ( x + ω k ) ] .
[ coth β x 2 - coth β 2 ( x + ω ) ] 2 k B T ( 1 x - 1 x + ω ) .
0 d p F ( p ) [ e β ( p - μ ) + 1 ] - 1 ,
F ( p ) = ln m ω * k - k 2 - 2 m p m w * k - k 2 + 2 m p + ( ω - ω ) ,
G ( p ) = 0 p d p F ( p ) ,
0 d p β e β ( p - μ ) ( e β ( p - μ ) + 1 ) 2 G ( p ) ,
ν ( ω ) = 2 3 π e 2 k B T m M ω 0 d k k 4 ω k 2 Im k - 1 ( ω ) ,
D ˜ k ( x ) = [ x 2 - ω k 2 - 2 ω k S k ( x ) ] - 1 ;             x x + i 0 + .
S k ( 1 ) ( x ) = S k ( 1 ) = 2 α , β V α β ( k 1 - k ) u α β .
S k ( 2 ) ( x ) = S k ( 2 ) = 12 { k } coth β ω k 2 V ( 4 ) ( - k , k , k , - k ) ,
S k ( 3 ) ( x ) = - 9 { k 1 } { k 2 } V ( 3 ) ( - k , k 1 , k 2 ) × V ( 3 ) ( k , - k 1 , - k 2 ) δ ( k 1 + k 2 - k ) × [ ( coth β ω k 1 2 - coth β ω k 2 2 ) ( 1 ω k 1 - ω k 2 - x + 1 ω k 1 - ω k 2 + x ) + ( coth β ω k 1 2 + coth β ω k 2 2 ) × ( 1 ω k 1 + ω k 2 - x + 1 ω k 1 + ω k 2 + x ) ] .
ν ( ω ) = 2 3 π 2 ω m M 0 d k k 4 - d x × [ coth β x 1 - coth β 2 ( x + ω ) ] × Im k - 1 ( x + ω ) Im D ˜ k ( x ) ,
ω ˜ k ω k - Δ k T ,
Δ k ( 1 ) = - lim T 1 T Re S k ( ω k ) .
D ˜ k ( x ) [ ( x + i η ) 2 - ω ˜ k 2 ] - 1 .
ν ( ω ) 2 3 π e 2 k B T m M ω 0 d k k 4 ω k 2 ( 1 + 2 Δ k T ω k ) Im k - 1 ( ω ) .
ν ( ω ) = ν 1 ( T T m ) + ν 2 ( T T m ) 2 ,
ν 1 = 2 3 π e 2 k B T m m M ω 0 d k k 4 ω k 2 Im k - 1 ( ω )
ν 2 = 4 3 π e 2 k B T m 2 m M ω 0 d k k 4 ω k 3 Δ k Im k - 1 ( ω ) .