Hyperbolic metamaterial (HMM) alternately stacked by graphene and silicon carbide (SiC) is proposed to theoretically study near-field radiative heat transfer. Heat transfer coefficients (HTCs) are calculated using the effective medium theory (EMT). We observe that HMMs can exhibit better heat transfer characteristic than graphene-covered SiC bulks when appropriate SiC thickness and chemical potentials of graphene are selected. Transfer matrix method (TMM) is also employed to calculate HTC between HMMs with thicker SiC, given the invalidity of EMT in this case. We deduce that with increasing SiC thickness, HTC first increases rapidly and then decreases slowly when it reaches maximum value. HTC is high for graphene with small chemical potential. Results may benefit applications of thermophotovoltaic devices.

References

1.
Ben-Abdallah
,
P.
, and
Biehs
,
S.-A.
,
2014
, “
Near-Field Thermal Transistor
,”
Phys. Rev. Lett.
,
112
(
4
), p.
044301
.
2.
Ilic
,
O.
,
Jablan
,
M.
,
Joannopoulos
,
J. D.
,
Celanovic
,
I.
, and
Soljačić
,
M.
,
2012
, “
Overcoming the Black Body Limit in Plasmonic and Graphene Near-Field Thermophotovoltaic Systems
,”
Opt. Express
,
20
(
10
), pp.
A366
A384
.
3.
Lim
,
M.
,
Jin
,
S.
,
Lee
,
S. S.
, and
Lee
,
B. J.
,
2015
, “
Graphene-Assisted Si-InSb Thermophotovoltaic System for Low Temperature Applications
,”
Opt. Express
,
23
(
7
), pp.
A240
A253
.
4.
Jin
,
S.
,
Lim
,
M.
,
Lee
,
S. S.
, and
Lee
,
B. J.
,
2016
, “
Hyperbolic Metamaterial-Based Near-Field Thermophotovoltaic System for Hundreds of Nanometer Vacuum Gap
,”
Opt. Express
,
24
(
6
), pp.
A635
A649
.
5.
Messina
,
R.
, and
Ben-Abdallah
,
P.
,
2013
, “
Graphene-Based Photovoltaic Cells for Near-Field Thermal Energy Conversion
,”
Sci. Rep.
,
3
(
1
), p.
1383
.
6.
Kittel
,
A.
,
Müller-Hirsch
,
W.
,
Parisi
,
J.
,
Biehs
,
S.-A.
,
Reddig
,
D.
, and
Holthaus
,
M.
,
2005
, “
Near-Field Heat Transfer in a Scanning Thermal Microscope
,”
Phys. Rev. Lett.
,
95
(
22
), p.
224301
.
7.
De Wilde
,
Y.
,
Formanek
,
F.
,
Carminati
,
R.
,
Gralak
,
B.
,
Lemoine
,
P. A.
,
Joulain
,
K.
,
Mulet
,
J. P.
,
Chen
,
Y.
, and
Greffet
,
J. J.
,
2006
, “
Thermal Radiation Scanning Tunnelling Microscopy
,”
Nature
,
444
(
7120
), pp.
740
743
.
8.
Challener
,
W. A.
,
Peng
,
C.
,
Itagi
,
A. V.
,
Karns
,
D.
,
Peng
,
W.
,
Peng
,
Y.
,
Yang
,
X.
,
Zhu
,
X.
,
Gokemeijer
,
N. J.
,
Hsia
,
Y.-T.
,
Ju
,
G.
,
Rottmayer
,
R. E.
,
Seigler
,
M. A.
, and
Gage
,
E. C.
,
2009
, “
Heat-Assisted Magnetic Recording by a Near-Field Transducer With Efficient Optical Energy Transfer
,”
Nat. Photonics
,
3
(
4
), pp.
220
224
.
9.
Stipe
,
B. C.
,
Strand
,
T. C.
,
Poon
,
C. C.
,
Balamane
,
H.
,
Boone
,
T. D.
,
Katine
,
J. A.
,
Li
,
J.-L.
,
Rawat
,
V.
,
Nemoto
,
H.
,
Hirotsune
,
A.
,
Hellwig
,
O.
,
Ruiz
,
R.
,
Dobisz
,
E.
,
Kercher
,
D. S.
,
Roberson
,
N.
,
Albrecht
,
T. R.
, and
Terris
,
B. D.
,
2010
, “
Magnetic Recording at 1.5 Pb m-2 Using an Integrated Plasmonic Antenna
,”
Nat. Photonics
,
4
(
7
), pp.
484
488
.
10.
Dai
,
S.
,
Ma
,
Q.
,
Andersen
,
T.
,
Mcleod
,
A. S.
,
Fei
,
Z.
,
Liu
,
M. K.
,
Wagner
,
M.
,
Watanabe
,
K.
,
Taniguchi
,
T.
,
Thiemens
,
M.
,
Keilmann
,
F.
,
Jarillo-Herrero
,
P.
,
Fogler
,
M. M.
, and
Basov
,
D. N.
,
2015
, “
Subdiffractional Focusing and Guiding of Polaritonic Rays in a Natural Hyperbolic Material
,”
Nat. Commun.
,
6
, p.
6963
.
11.
Polder
,
D.
, and
Van Hove
,
M.
,
1971
, “
Theory of Radiative Heat Transfer Between Closely Spaced Bodies
,”
Phys. Rev. B
,
4
(
10
), pp.
3303
3314
.
12.
Volokitin
,
A. I.
, and
Persson
,
B. N. J.
,
2007
, “
Near-Field Radiative Heat Transfer and Noncontact Friction
,”
Rev. Mod. Phys.
,
79
(
4
), pp.
1291
1329
.
13.
Biehs
,
S.-A.
,
Tschikin
,
M.
, and
Ben-Abdallah
,
P.
,
2012
, “
Hyperbolic Metamaterials as an Analog of a Blackbody in the Near Field
,”
Phys. Rev. Lett.
,
109
(
10
), p.
104301
.
14.
Kajihara
,
Y.
,
Kosaka
,
K.
, and
Komiyama
,
S.
,
2011
, “
Thermally Excited Near-Field Radiation and Far-Field Interference
,”
Opt. Express
,
19
(
8
), pp.
7695
7704
.
15.
Liu
,
X. L.
,
Wang
,
L. P.
, and
Zhang
,
Z. M.
,
2015
, “
Near-Field Thermal Radiation: Recent Progress and Outlook
,”
Nanoscale Microscale Thermophys. Eng.
,
19
(
2
), pp.
98
126
.
16.
Lenert
,
A.
,
Bierman
,
D. M.
,
Nam
,
Y.
,
Chan
,
W. R.
,
Celanović
,
I.
,
Soljačić
,
M.
, and
Wang
,
E. N.
,
2014
, “
A Nanophotonic Solar Thermophotovoltaic Device
,”
Nat. Nanotechnol.
,
9
(
2
), pp.
126
130
.
17.
Ottens
,
R. S.
,
Quetschke
,
V.
,
Wise
,
S.
,
Alemi
,
A. A.
,
Lundock
,
R.
,
Mueller
,
G.
,
Reitze
,
D. H.
,
Tanner
,
D. B.
, and
Whiting
,
B. F.
,
2011
, “
Near-Field Radiative Heat Transfer Between Macroscopic Planar Surfaces
,”
Phys. Rev. Lett.
,
107
, p.
014301
.
18.
Francoeur
,
M.
,
Mengüç
,
M. P.
, and
Vaillon
,
R.
,
2008
, “
Near-Field Radiative Heat Transfer Enhancement Via Surface Phonon Polaritons Coupling in Thin Films
,”
Appl. Phys. Lett.
,
93
(
4
), p.
043109
.
19.
Basu
,
S.
,
Yang
,
Y.
, and
Wang
,
L.
,
2015
, “
Near-Field Radiative Heat Transfer Between Metamaterials Coated With Silicon Carbide Thin Films
,”
Appl. Phys. Lett.
,
106
(
3
), p.
033106
.
20.
Dai
,
J.
,
Dyakov
,
S. A.
, and
Yan
,
M.
,
2015
, “
Enhanced Near-Field Radiative Heat Transfer Between Corrugated Metal Plates: Role of Spoof Surface Plasmon Polaritons
,”
Phys. Rev. B
,
92
(
3
), p.
035419
.
21.
Volokitin
,
A. I.
, and
Persson
,
B. N. J.
,
2011
, “
Near-Field Radiative Heat Transfer Between Closely Spaced Graphene and Amorphous SiO2
,”
Phys. Rev. B
,
83
(
24
), p.
241407
.
22.
Svetovoy
,
V. B.
,
van Zwol
,
P. J.
, and
Chevrier
,
J.
,
2012
, “
Plasmon Enhanced Near-Field Radiative Heat Transfer for Graphene Covered Dielectrics
,”
Phys. Rev. B
,
85
(
15
), p.
155418
.
23.
Ilic
,
O.
,
Jablan
,
M.
,
Joannopoulos
,
J. D.
,
Celanovic
,
I.
,
Buljan
,
H.
, and
Soljačić
,
M.
,
2012
, “
Near-Field Thermal Radiation Transfer Controlled by Plasmons in Graphene
,”
Phys. Rev. B
,
85
(
15
), p.
155422
.
24.
Song
,
J.
, and
Cheng
,
Q.
,
2016
, “
Near-Field Radiative Heat Transfer Between Graphene and Anisotropic Magneto-Dielectric Hyperbolic Metamaterials
,”
Phys. Rev. B
,
94
(
12
), p.
125419
.
25.
Zhang
,
R. Z.
,
Liu
,
X. L.
, and
Zhang
,
Z. M.
,
2015
, “
Near-Field Radiation Between Graphene-Covered Carbon Nanotube Arrays
,”
AIP. Adv.
,
5
(
5
), p.
053501
.
26.
Zhao
,
Q.
,
Zhou
,
T.
,
Wang
,
T.
,
Liu
,
W.
,
Liu
,
J.
,
Yu
,
T.
,
Liao
,
Q.
, and
Liu
,
N.
,
2017
, “
Active Control of Near-Field Radiative Heat Transfer Between Graphene-Covered Metamaterials
,”
J. Phys. D: Appl. Phys.
,
50
(
14
), p.
145101
.
27.
Zhou
,
T.
,
Song
,
C.-C.
,
Wang
,
T.-B.
,
Liu
,
W.-X.
,
Liu
,
J.-T.
,
Yu
,
T.-B.
,
Liao
,
Q.-H.
, and
Liu
,
N.-H.
,
2017
, “
Enhancement of Near-Field Radiative Heat Transfer Via Multiple Coupling of Surface Waves With Graphene Plasmon
,”
AIP. Adv.
,
7
(
5
), p.
055213
.
28.
Yang
,
Y.
, and
Wang
,
L.
,
2017
, “
Electrically-Controlled Near-Field Radiative Thermal Modulator Made of Graphene-Coated Silicon Carbide Plates
,”
J. Quant. Spectros. Radiat. Transfer
,
197
, pp.
68
75
.
29.
Joulain
,
K.
,
Drevillon
,
J.
, and
Ben-Abdallah
,
P.
,
2010
, “
Noncontact Heat Transfer Between Two Metamaterials
,”
Phys. Rev. B
,
81
(
16
), p.
165119
.
30.
Francoeur
,
M.
,
Basu
,
S.
, and
Petersen
,
S. J.
,
2011
, “
Electric and Magnetic Surface Polariton Mediated Near-Field Radiative Heat Transfer Between Metamaterials Made of Silicon Carbide Particles
,”
Opt. Express
,
19
(
20
), pp.
18774
18788
.
31.
Liu
,
D.
,
Das
,
A.
, and
Park
,
W.
,
2017
, “
Direct Modeling of Near Field Thermal Radiation in a Metamaterial
,”
Opt. Express
,
25
(
11
), pp.
12999
13009
.
32.
Liu
,
X. L.
,
Zhang
,
R. Z.
, and
Zhang
,
Z. M.
,
2014
, “
Near-Field Radiative Heat Transfer With Doped-Silicon Nanostructured Metamaterials
,”
Int. J. Heat Mass Transfer
,
73
, pp.
389
398
.
33.
Guo
,
Y.
,
Cortes
,
C. L.
,
Molesky
,
S.
, and
Jacob
,
Z.
,
2012
, “
Broadband Super-Planckian Thermal Emission From Hyperbolic Metamaterials
,”
Appl. Phys. Lett.
,
101
(
13
), p.
131106
.
34.
Biehs
,
S.-A.
,
Tschikin
,
M.
,
Messina
,
R.
, and
Ben-Abdallah
,
P.
,
2013
, “
Super-Planckian Near-Field Thermal Emission With Phonon-Polaritonic Hyperbolic Metamaterials
,”
Appl. Phys. Lett.
,
102
(
13
), p.
131106
.
35.
Biehs
,
S.-A.
, and
Ben-Abdallah
,
P.
,
2017
, “
Near-Field Heat Transfer Between Multilayer Hyperbolic Metamaterials
,”
Z. Naturforsch
,
72
(
2
), pp.
115
127
.
36.
Liu
,
X. L.
,
Zhang
,
R. Z.
, and
Zhang
,
Z. M.
,
2013
, “
Near-Field Thermal Radiation Between Hyperbolic Metamaterials: Graphite and Carbon Nanotubes
,”
Appl. Phys. Lett.
,
103
(
21
), p.
213102
.
37.
Moncada-Villa
,
E.
,
Fernández-Hurtado
,
V.
,
García-Vidal
,
F. J.
,
García-Martín
,
A.
, and
Cuevas
,
J. C.
,
2015
, “
Magnetic Field Control of Near-Field Radiative Heat Transfer and the Realization of Highly Tunable Hyperbolic Thermal Emitters
,”
Phys. Rev. B
,
92
(
12
), p.
125418
.
38.
Liu
,
X. L.
, and
Zhang
,
Z. M.
,
2015
, “
Giant Enhancement of Nanoscale Thermal Radiation Based on Hyperbolic Graphene Plasmons
,”
Appl. Phys. Lett.
,
107
(
14
), p.
143114
.
39.
Shi
,
K.
,
Bao
,
F.
, and
He
,
S.
,
2017
, “
Enhanced Near-Field Thermal Radiation Based on Multilayer Graphene-hBN Heterostructures
,”
ACS Photonics
,
4
(
4
), pp.
971
978
.
40.
Zhao
,
B.
,
Guizal
,
B.
,
Zhang
,
Z. M.
,
Fan
,
S.
, and
Anterzza
,
M.
,
2017
, “
Near-Field Heat Transfer Between Graphene/hBN Multilayers
,”
Phys. Rev. B
,
95
(
24
), p.
245437
.
41.
Demichelis
,
F.
,
Pirri
,
C. F.
, and
Tresso
,
E.
,
1992
, “
Influence of Doping on the Structural and Optoelectronic Properties of Amorphous and Microcrystalline Silicon Carbide
,”
J. Appl. Phys.
,
72
(
4
), pp.
1327
1333
.
42.
Hu
,
L.
, and
Chui
,
S. T.
,
2002
, “
Characteristics of Electromagnetic Wave Propagation in Uniaxially Anisotropic Left-Handed Materials
,”
Phys. Rev. B
,
66
(
8
), p.
085108
.
43.
Wu
,
H.
,
Huang
,
Y.
, and
Zhu
,
K.
,
2015
, “
Near-Field Radiative Transfer Between Magneto-Dielectric Uniaxial Anisotropic Media
,”
Opt. Lett.
,
40
(
19
), pp.
4532
4535
.
44.
Sreekanth
,
K.
,
De Luca
,
A.
, and
Strangi
,
G.
,
2013
, “
Negative Refraction in Graphene-Based Hyperbolic Metamaterials
,”
Appl. Phys. Lett.
,
103
(
2
), p.
023107
.
45.
Zhang
,
R. Z.
, and
Zhang
,
Z. M.
,
2017
, “
Validity of Effective Medium Theory in Multilayered Hyperbolic Materials
,”
J. Quant. Spectrosc. Radiat. Transfer
,
197
, pp.
132
140
.
46.
Vakil
,
A.
, and
Engheta
,
N.
,
2011
, “
Transformation Optics Using Graphene
,”
Science
,
332
(
6035
), pp.
1291
1294
.
47.
Falkovsky
,
L. A.
,
2008
, “
Optical Properties of Graphene
,”
J. Phys.: Conf. Ser.
,
129
(
1
), p.
012004
.
48.
Gan
,
C. H.
,
2012
, “
Analysis of Surface Plasmon Excitation at Terahertz Frequencies With Highly Doped Graphene Sheets Via Attenuated Total Reflection
,”
Appl. Phys. Lett.
,
101
(
11
), p.
111609
.
49.
Palik
,
E. D.
,
1998
,
Handbook of Optical Constants of Solids
,
Academic Press
,
New York
.
50.
Basu
,
S.
, and
Wang
,
L.
,
2013
, “
Near-Field Radiative Heat Transfer Between Doped Silicon Nanowire Arrays
,”
Appl. Phys. Lett.
,
102
(
5
), p.
053101
.
51.
Liao
,
Q.-H.
,
Song
,
C.-C.
,
Wang
,
T.-B.
,
Zhang
,
D.-J.
,
Liu
,
W.-X.
,
Yu
,
T.-B.
, and
Liu
,
N.-H.
,
2017
, “
Modulation of the Electromagnetic Local Density of States in Graphene-Based Hyperbolic Metamaterials
,”
J. Appl. Phys.
,
122
(
19
), p.
193101
.
52.
Zhan
,
T.
,
Shi
,
X.
,
Dai
,
Y.
,
Liu
,
X.
, and
Zi
,
J.
,
2013
, “
Transfer Matrix Method for Optics in Graphene Layers
,”
J. Phys.: Condens. Matter
,
25
(
21
), p.
215301
.
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