We study thermoelectric power under strong magnetic field (TPM) in carbon nanotubes (CNTs) and quantum wires (QWs) of nonlinear optical, optoelectronic, and related materials. The corresponding results for QWs of III-V, ternary, and quaternary compounds form a special case of our generalized analysis. The TPM has also been investigated in QWs of II-VI, IV-VI, stressed materials, n-GaP, p-PtSb2, n-GaSb, and bismuth on the basis of the appropriate carrier dispersion laws in the respective cases. It has been found, taking QWs of n-CdGeAs2, n-Cd3As2, n-InAs, n-InSb, n-GaAs, n-Hg1xCdxTe, n-In1xGaxAsyP1y lattice-matched to InP, p-CdS, n-PbTe, n-PbSnTe, n-Pb1xSnxSe, stressed n-InSb, n-GaP, p-PtSb2, n-GaSb, and bismuth as examples, that the respective TPM in the QWs of the aforementioned materials exhibits increasing quantum steps with the decreasing electron statistics with different numerical values, and the nature of the variations are totally band-structure-dependent. In CNTs, the TPM exhibits periodic oscillations with decreasing amplitudes for increasing electron statistics, and its nature is radically different as compared with the corresponding TPM of QWs since they depend exclusively on the respective band structures emphasizing the different signatures of the two entirely different one-dimensional nanostructured systems in various cases. The well-known expression of the TPM for wide gap materials has been obtained as a special case under certain limiting conditions, and this compatibility is an indirect test for our generalized formalism. In addition, we have suggested the experimental methods of determining the Einstein relation for the diffusivity-mobility ratio and the carrier contribution to the elastic constants for materials having arbitrary dispersion laws.

1.
S.
Iijima
,
Nature (London)
354
,
56
(
1991
).
2.
V. N.
Popov
,
Mater. Sci. Eng., R.
43
,
61
(
2004
).
3.
J.
Sandler
,
M. S. P.
Shaffer
,
T.
Prasse
,
W.
Bauhofer
,
K.
Schulte
, and
A. H.
Windle
,
Polymer
40
,
5967
(
1999
).
4.
D.
Qian
,
E. C.
Dickey
,
R.
Andrews
, and
T.
Rantell
,
Appl. Phys. Lett.
76
,
2868
(
2000
).
5.
J.
Kong
,
N. R.
Franklin
,
C. W.
Zhou
,
M. G.
Chapline
,
S.
Peng
,
K. J.
Cho
, and
H. J.
Dai
,
Science
287
,
622
(
2000
).
6.
W. A.
Deheer
,
A.
Chatelain
, and
D.
Ugarte
,
Science
270
,
1179
(
1995
).
7.
A. G.
Rinzler
,
J. H.
Hafner
,
P.
Nikolaev
,
L.
Lou
,
S. G.
Kim
,
D.
Tomanek
,
P.
Nordlander
,
D. T.
Olbert
, and
R. E.
Smalley
,
Science
269
,
1550
(
1995
).
8.
A. C.
Dillon
,
K. M.
Jones
,
T. A.
Bekkedahl
,
C. H.
Kiang
,
D. S.
Bethune
, and
M. J.
Heben
,
Nature (London)
386
,
377
(
1997
).
9.
C.
Liu
,
Y. Y.
Fan
,
M.
Liu
,
H. T.
Cong
,
H. M.
Cheng
, and
M. S.
Dresselhaus
,
Science
286
,
1127
(
1999
).
10.
P.
Kim
and
C. M.
Lieber
,
Science
286
,
2148
(
1999
).
11.
D.
Srivastava
,
Nanotechnology
8
,
186
(
1997
).
12.
C.
Ke
and
H. D.
Espinosa
,
Appl. Phys. Lett.
85
,
681
(
2004
).
13.
J. W.
Kang
and
H. J.
Hwang
,
Nanotechnology
15
,
1633
(
2004
);
J.
Cumings
and
A.
Zettl
,
Science
289
,
602
(
2000
).
[PubMed]
14.
S. J.
Tans
,
M. H.
Devoret
,
H. J.
Dai
,
A.
Thess
,
R. E.
Smalley
,
L. J.
Geerligs
, and
C.
Dekker
,
Nature (London)
386
,
474
(
1997
).
15.
S. J.
Tans
,
A. R. M.
Verschueren
, and
C.
Dekker
,
Nature (London)
393
,
49
(
1998
).
16.
P.
Avouris
,
Acc. Chem. Res.
35
,
1026
(
2002
).
17.
P. G.
Collins
,
A.
Zettl
,
H.
Bando
,
A.
Thess
, and
R. E.
Smalley
,
Science
278
,
100
(
1997
).
18.
R. H.
Baughman
,
A. A.
Zakhidov
, and
W. A.
de Heer
,
Science
297
,
787
(
2002
).
19.
Z.
Yao
,
H. W. C.
Postma
,
L.
Balents
, and
C.
Dekker
,
Nature (London)
402
,
273
(
1999
).
20.
S. J.
Tans
,
A. R. M.
Verschueren
, and
C.
Dekker
,
Nature (London)
393
,
49
(
1998
).
21.
T.
Rueckes
,
K.
Kim
,
E.
Joselevich
,
G. Y.
Tseng
,
C. L.
Cheung
, and
C. M.
Lieber
,
Science
289
,
94
(
2000
).
22.
A.
Bachtold
,
P.
Hadley
,
T.
Nakanish
, and
C.
Dekker
,
Science
294
,
1317
(
2001
).
23.
H.
Sasaki
,
Jpn. J. Appl. Phys.
19
,
94
(
1980
).
24.
P. M.
Petroff
,
A. C.
Gossard
,
R. A.
Logan
, and
W.
Weigmann
,
Appl. Phys. Lett.
41
,
635
(
1982
).
25.
I.
Miller
,
A.
Miller
,
A.
Shahar
,
U.
Koren
, and
P. J.
Corvini
,
Appl. Phys. Lett.
54
,
188
(
1989
).
26.
F.
Sols
,
M.
Macucci
,
U.
Ravaioli
, and
K.
Hess
,
Appl. Phys. Lett.
54
,
350
(
1989
).
27.
C. S.
Lent
and
D. J.
Kirkner
,
J. Appl. Phys.
67
,
6353
(
1990
).
28.
C. S.
Kim
,
A. M.
Satanin
,
Y. S.
Joe
, and
R. M.
Cosby
,
Phys. Rev. B
60
,
10962
(
1999
).
29.
S.
Midgley
and
J. B.
Wang
,
Phys. Rev. B
64
,
153304
(
2001
).
30.
T.
Sugaya
,
J. P.
Bird
,
M.
Ogura
,
Y.
Sugiyama
,
D. K.
Ferry
, and
K. Y.
Jang
,
Appl. Phys. Lett.
80
,
434
(
2002
).
31.
B.
Kane
,
G.
Facer
,
A.
Dzurak
,
N.
Lumpkin
,
R.
Clark
,
L.
PfeiKer
, and
K.
West
,
Appl. Phys. Lett.
72
,
3506
(
1998
).
32.
C.
Dekker
,
Phys. Today
52
,
22
(
1999
).
33.
A.
Yacoby
,
H. L.
Stormer
,
N. S.
Wingreen
,
L. N.
Pfeiffer
,
K. W.
Baldwin
, and
K. W.
West
,
Phys. Rev. Lett.
77
,
4612
(
1996
).
34.
Y.
Hayamizu
,
M.
Yoshita
,
S.
Watanabe
,
H. A. L.
Pfeiker
, and
K.
West
,
Appl. Phys. Lett.
81
,
4937
(
2002
).
35.
S.
Frank
,
P.
Poncharal
,
Z. L.
Wang
, and
W. A.
Heer
,
Science
280
,
1744
(
1998
).
36.
I.
Kamiya
,
I. I.
Tanaka
,
K.
Tanaka
,
F.
Yamada
,
Y.
Shinozuka
, and
H.
Sakaki
,
Physica E (Amsterdam)
13
,
131
(
2002
).
37.
A. K.
Geim
,
P. C.
Main
,
N.
LaScala
,
L.
Eaves
,
T. J.
Foster
,
P. H.
Beton
,
J. W.
Sakai
,
F. W.
Sheard
,
M.
Henini
, and
G.
Hill
,
Phys. Rev. Lett.
72
,
2061
(
1994
).
38.
A. S.
Mel’nikov
and
V. M.
Vinokur
,
Nature (London)
415
,
60
(
2002
).
39.
K.
Schwab
,
E. A.
Henriksen
,
J. M.
Worlock
, and
M. L.
Roukes
,
Nature (London)
404
,
974
(
2000
).
40.
L.
Kouwenhoven
,
Nature (London)
403
,
374
(
2000
).
41.
S.
Komiyama
,
O.
Astafiev
,
V.
Antonov
, and
H.
Hirai
,
Nature (London)
403
,
405
(
2000
).
42.
E.
Paspalakis
,
Z.
Kis
,
E.
Voutsinas
, and
A. F.
Terziz
,
Phys. Rev. B
69
,
155316
(
2004
).
43.
J. H.
Jefferson
,
M.
Fearn
,
D. L. J.
Tipton
, and
T. P.
Spiller
,
Phys. Rev. A
66
,
042328
(
2002
).
44.
J.
Appenzeller
,
C.
Schroer
,
T.
Schapers
,
A.
Hart
,
A.
Froster
,
B.
Lengeler
, and
H.
Luth
,
Phys. Rev. B
53
,
9959
(
1996
).
45.
J.
Appenzeller
and
C.
Schroer
,
J. Appl. Phys.
87
,
3165
(
2000
).
46.
P.
Debray
,
O. E.
Raichev
,
M.
Rahman
,
R.
Akis
, and
W. C.
Mitchel
,
Appl. Phys. Lett.
74
,
768
(
1999
).
47.
P. M.
Solomon
,
Proc. IEEE
70
,
489
(
1982
);
T. E.
Schlesinger
and
T.
Kuech
,
Appl. Phys. Lett.
49
,
519
(
1986
).
48.
H.
Heiblum
,
D. C.
Thomas
,
C. M.
Knoedler
, and
M. I.
Nathan
,
Appl. Phys. Lett.
47
,
1105
(
1985
).
49.
O.
Aina
,
M.
Mattingly
,
F. Y.
Juan
, and
P. K.
Bhattacharyya
,
Appl. Phys. Lett.
50
,
43
(
1987
).
50.
I.
Suemune
and
L. A.
Coldren
,
IEEE J. Quantum Electron.
24
,
1778
(
1988
).
51.
D. A. B.
Miller
,
D. S.
Chemla
,
T. C.
Damen
,
J. H.
Wood
,
A. C.
Burrus
,
A. C.
Gossard
, and
W.
Weigmann
,
IEEE J. Quantum Electron.
21
,
1462
(
1985
).
52.
J.
Hajdu
and
R.
Landwher
,
Springer Ser. Solid-State Sci.
57
,
97
(
1985
).
53.
K.
von Klitzing
,
Rev. Mod. Phys.
58
,
519
(
1986
).
54.
K. P.
Ghatak
and
S. N.
Biswas
,
J. Appl. Phys.
70
,
299
(
1991
).
55.
B.
Mitra
and
K. P.
Ghatak
,
Phys. Lett. A
141
,
81
(
1989
).
57.
F. M.
Peeters
and
P.
Vasilopoulos
,
Phys. Rev. B
46
,
4667
(
1992
).
58.
K. P.
Ghatak
,
M.
Mitra
,
B.
Goswami
, and
B.
Nag
,
Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. B: Nonlinear Opt.
16
,
167
(
1996
).
59.
I. M.
Tsidilkovskii
,
Band Structures of Semiconductors
(
Pergamon
,
London
,
1982
).
60.
S. K.
Biswas
,
A. R.
Ghatak
,
A.
Neogi
,
A.
Sharma
,
S.
Bhattacharya
, and
K. P.
Ghatak
,
Physica E (Amsterdam)
36
,
163
(
2007
).
61.
S. P.
Zelenim
,
A. S.
Kondratev
, and
A. E.
Kuchma
,
Sov. Phy. Semicond.
16
,
355
(
1982
).
62.
K. P.
Ghatak
and
B.
Nag
,
Nanostruct. Mater.
2
,
14
(
1995
).
63.
B. M.
Askerov
,
N. F.
Gashimzade
, and
M. M.
Panakhov
,
Sov. Phys. Solid State
29
,
456
(
1987
).
64.
J. L.
Shay
and
J. W.
Wernik
,
Ternary Chalcopyrite Compounds: Growth, Electronic Properties and Applications
(
Pergamon
,
London
,
1975
).
65.
G. P.
Chuiko
,
Sov. Phys. Semicond.
15
,
739
(
1981
).
66.
E. K.
Arushanov
,
A. F.
Knyazev
,
A. N.
Nateprov
, and
S. I.
Radautsan
,
Sov. Phys. Semicond.
15
,
828
(
1981
).
67.
S. I.
Radautsan
,
E. K.
Arushanov
,
A. N.
Nateprov
, and
G. P.
Chuiko
,
Cadmium Arsenide and Phosphide
(
Shtiintsa
,
Kishinev
,
1976
) (in Russian).
68.
I. W.
Rowe
and
J. L.
Shay
,
Phys. Rev.
83
,
451
(
1971
).
69.
I. J.
Hopfdeld
,
Phys. Chem. Solids
15
,
97
(
1960
).
J. L.
Shay
and
B.
Tell
,
Surf. Sci.
37
,
748
(
1973
).
71.
B. Kh.
Mamedov
and
E. O.
Osmanov
,
Sov. Phys. Semicond.
5
,
1120
(
1972
).
72.
O. V.
Emelyanenko
,
F. P.
Kesamanly
,
I. K.
Polushina
, and
V. A.
Skripkin
,
Sov. Phys. Semicond.
5
,
304
(
1971
).
73.
S. D.
Chemla
,
F. R.
Beglay
, and
L. R.
Byer
,
IEEE J. Quantum Electron.
10
,
71
(
1974
).
74.
H.
Kildal
,
Phys. Rev.
10
,
B5082
(
1974
).
75.
G. P.
Chuiko
and
N. N.
Chuiko
,
Sov. Phys. Semicond.
15
,
739
(
1981
);
K. P.
Ghatak
and
S. N.
Biswas
,
Proc. SPIE
1484
,
146
(
1991
).
76.
R.
Bisaro
,
G.
Laurencin
,
A.
Friederich
, and
M.
Razeghi
,
Appl. Phys. Lett.
40
,
978
(
1982
).
77.
R. C.
Alferness
,
C. H.
Joyner
,
M. D.
Divino
,
M. J. R.
Martyak
, and
L. L.
Buhl
,
Appl. Phys. Lett.
49
,
125
(
1986
).
78.
T. E.
Bell
,
IEEE Spectrum
20
,
38
(
1983
).
79.
P. Y.
Lu
,
C. H.
Wang
,
C. M.
Williams
,
S. N. G.
Chu
, and
C. M.
Stiles
,
Appl. Phys. Lett.
49
,
1372
(
1986
).
80.
N. R.
Taskar
,
I. B.
Bhat
,
K. K.
Parat
,
D. H.
Terry Ehsani
, and
S. K.
Gandhi
,
J. Vac. Sci. Technol. A
7
,
281
(
1989
).
81.
E.
Weiss
and
N.
Mainzer
,
J. Vac. Sci. Technol. A
7
,
391
(
1989
).
82.
F.
Koch
,
Springer Series in Solid State Sciences
(
Springer-Verlag
,
Berlin
,
1984
), Vol.
53
.
83.
D. H.
Jaw
,
D. S.
Caoand
, and
G. B.
Stringfellow
,
J. Appl. Phys.
69
,
2552
(
1991
).
84.
M. L.
Timmons
,
S.
Bedair
,
M. R. J.
Markunas
, and
J. A.
Hutchby
,
Proceedings of the 16th IEEE Photovoltaic Specialists Conferences
(
IEEE
,
San Diego
,
1982
), p.
666
.
85.
M. K.
Lee
,
D. S.
Wu
, and
H. H.
Tung
,
J. Appl. Phys.
62
,
3209
(
1987
).
86.
K. P.
Ghatak
and
S.
Bhattacharya
,
J. Appl. Phys.
102
,
073704
(
2007
).
87.
S.
Adachi
,
J. Appl. Phys.
53
,
8775
(
1982
).
88.
S. I.
Radaustan
,
V. I.
Morozava
,
A. F.
Knyazev
,
L. S.
Koval
,
E. K.
Arushanov
, and
A. N.
Nataprov
,
Sov. Phys. Semicond.
19
,
691
(
1985
).
89.
M. A.
Herman
and
M.
Pessa
,
J. Appl. Phys.
57
,
2671
(
1985
).
90.
K.
Sakamoto
and
Y.
Okabe
,
J. Appl. Phys.
23
,
444
(
1986
).
91.
T.
Nguyen Duy
,
J.
Meslage
, and
G.
Pichard
,
J. Cryst. Growth
72
,
490
(
1985
).
92.
D. H.
Chow
and
T. C.
Mc Gill
,
Appl. Phys. Lett.
48
,
1485
(
1986
).
93.
J. J.
Hopfield
,
J. Appl. Phys.
32
,
2277
(
1961
).
94.
J. O.
Dimmock
, in
The Physics of Semimetals and Narrow Gap Compounds
, edited by
D L.
Carter
and
R. T.
Bates
(
Pergamon
,
Oxford
,
1971
), p.
319
.
95.
D. G.
Seiler
,
B. D.
Bajaj
, and
A. E.
Stephens
,
Phys. Rev. B
16
,
2822
(
1977
);
K. P.
Ghatak
and
B.
Mitra
,
Phys. Scr.
46
,
182
(
1992
).
96.
G. J.
Rees
,
Physics of Compounds
, in
Proceedings of the 13th International Conference
, edited by
F. G.
Fumi
(
North Holland
,
Amsterdam
,
1976
), p.
1166
.
97.
D.
Shoenberg
,
Proc. R. Soc. London, Ser. A
170
,
341
(
1939
).
98.
B.
Abeles
and
S.
Mieboom
,
Phys. Rev.
101
,
544
(
1956
).
99.
B.
Lax
,
J. G.
Mavroides
,
H. J.
Ziegeer
, and
R.
Keyes
,
Phys. Rev. Lett.
5
,
241
(
1960
).
100.
M.
Maltz
and
M. S.
Dresselhaus
,
Phys. Rev. B
2
,
2877
(
1970
).
101.
M.
Cankurtaran
,
M.
Celik
, and
T.
Alper
,
J. Phys. F: Met. Phys.
16
,
853
(
1986
).
102.
103.
R. J.
Dinger
and
A. W.
Lawson
,
Phys. Rev. B
3
,
253
(
1971
).
104.
J. A.
Koch
and
J. D.
Jensen
,
Phys. Rev.
184
,
643
(
1969
).
105.
J.
Rose
and
R.
Schuchardt
,
Phys. Status Solidi B
117
,
213
(
1983
).
106.
S.
Takaoka
,
H.
Kawamura
,
K.
Murse
, and
S.
Takano
,
Phys. Rev. B
13
,
1428
(
1976
).
107.
J. W.
McClure
and
K. H.
Choi
,
Solid State Commun.
21
,
1015
(
1977
).
108.
X.
Yang
and
J.
Ni
,
Phys. Rev. B
72
,
195426
(
2005
);
D.
Kahn
and
J. P.
Lu
,
Phys. Rev. B
60
,
6535
(
1999
).
109.
B. R.
Nag
,
Electron Transport in Compound Semiconductors
(
Springer-Verlag
,
Berlin
,
1980
).
110.
P. R.
Emtage
,
Phys. Rev.
138
,
A246
(
1965
).
111.
D. G.
Seiler
,
W. M.
Beeker
, and
L. M.
Roth
,
Phys. Rev. B
1
,
764
(
1970
).
112.
W.
Szuszkiewicz
,
Phys. Status Solidi B
79
,
691
(
1977
).
113.
P. T.
Landsberg
,
Eur. J. Phys.
2
,
213
(
1981
), and references cited therein.
114.
115.
H.
Kroemer
,
IEEE Trans. Electron Devices
25
,
850
(
1978
);
S.
Mukherjee
,
S. N.
Mitra
,
P. K.
Bose
,
A. R.
Ghatak
,
A.
Neogi
,
J. P.
Banerjee
,
A.
Sinha
,
M.
Pal
,
S.
Bhattacharya
, and
K. P.
Ghatak
,
J. Comput. Theor. Nanosci.
4
,
550
(
2007
).
116.
R. W.
Keyes
,
IBM. J. Res. Dev.
5
,
266
(
1961
)
117.
K. P.
Ghatak
,
S.
Bhattacharya
,
S. K.
Biswas
,
A.
Dey
, and
A. K.
Dasgupta
,
Phys. Scr.
75
,
820
(
2007
).
118.
O.
Madelung
,
Semiconductors: Data Handbook
, 3rd ed. (
Springer
,
Berlin
,
2004
);
M.
Kriechbaum
,
P.
Kocevar
,
H.
Pascher
, and
G.
Bauer
,
IEEE J. Quantum Electron.
24
,
1727
(
1988
).
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