Sample title

Sample Title:with Forced Linebreaka)
A. Author,1, b) B. Author,1, c) and C. Author2, d)1)
2)

Authors’ institution and/or address
Second institution and/or address(Dated: 13 August 2024)

An article usually includes an abstract, a concise summary of the work covered at length in the main body of
the article. It is used for secondary publications and for information retrieval purposes. Valid PACS numbers
may be entered using the \pacs{#1} command.
PACS numbers: Valid PACS appear here
Keywords: Suggested keywords
The “lead paragraph” is encapsulated with the
LATEX quotation environment and is formatted
as a single paragraph before the ﬁrst section
heading. (The quotation environment reverts to
its usual meaning after the ﬁrst sectioning command.) Note that numbered references are allowed in the lead paragraph. The lead paragraphwill only be found in an article being prepared forthe journal Chaos.

I. FIRST-LEVEL HEADING:
THE LINE BREAK WAS FORCED via \\This sample document demonstrates proper use of
REVTEX 4.1 (and LATEX 2ε ) in manuscripts prepared forsubmission to AIP journals. Further information can befound in the documentation included in the distribution
or available at http://authors.aip.org and in the documentation for REVTEX 4.1 itself.
When commands are referred to in this example ﬁle,they are always shown with their required arguments,using normal TEX format. In this format, #1, #2, etc.
stand for required author-supplied arguments to commands. For example, in \section{#1} the #1 stands
for the title text of the author’s section heading, and in\title{#1} the #1 stands for the title text of the paper.
Line breaks in section headings at all levels can be
introduced using \\. A blank input line tells TEX thatthe paragraph has ended.
A.

Second-level heading: FormattingThis ﬁle may be formatted in both the preprint (thedefault) and reprint styles; the latter format may bea) Footnote to title of article.
b) Also at Physics Department, XYZ University.
c) Electronic mail: Second.Author@institution.edu.
d) http://www.Second.institution.edu/˜Charlie.Author.

used to mimic ﬁnal journal output. Either format may
be used for submission purposes; however, for peer review and production, AIP will format the article using
the preprint class option. Hence, it is essential that
authors check that their manuscripts format acceptably
under preprint. Manuscripts submitted to AIP that do
not format correctly under the preprint option may bedelayed in both the editorial and production processes.
The widetext environment will make the text thewidth of the full page, as on page 3. (Note the use the\pageref{#1} to get the page number right automatically.) The width-changing commands only take eﬀect
in twocolumn formatting. It has no eﬀect if preprint
formatting is chosen instead.

1.

Third-level heading: Citations and Footnotes

Citations in text refer to entries in the Bibliography;
they use the commands \cite{#1} or \onlinecite{#1}.
Because REVTEX uses the natbib package of Patrick
Daly, its entire repertoire of commands are available
in your document; see the natbib documentation forfurther details. The argument of \cite is a commaseparated list of keys; a key may consist of letters andnumerals.
By default, citations are numerical;1 author-year citations are an option. To give a textual citation, use\onlinecite{#1}: (Refs. 2–4). REVTEX “collapses”
lists of consecutive numerical citations when appropriate.
REVTEX provides the ability to properly punctuate textual citations in author-year style; this facility works correctly with numerical citations only with natbib’s compress option turned oﬀ. To illustrate, we cite several
together1–3,5 , and once again (Refs. 1, 3–5). Note that,when numerical citations are used, the references were
sorted into the same order they appear in the bibliography.
A reference within the bibliography is speciﬁed with a\bibitem{#1} command, where the argument is the citation key mentioned above. \bibitem{#1} commands
may be crafted by hand or, preferably, generated by using
BibTEX. The AIP styles for REVTEX 4 include BibTEX

Sample title
style ﬁles aipnum.bst and aipauth.bst, appropriate fornumbered and author-year bibliographies, respectively.
REVTEX 4 will automatically choose the style appropriate for the document’s selected class options: the default
is numerical, and you obtain the author-year style byspecifying a class option of author-year.
This sample ﬁle demonstrates a simple use of
BibTEX via a \bibliography command referencing the
aipsamp.bib ﬁle. Running BibTEX (in this case bibtex
aipsamp) after the ﬁrst pass of LATEX produces the ﬁleaipsamp.bbl which contains the automatically formatted \bibitem commands (including extra markup information via \bibinfo commands). If not using BibTEX,
the thebibiliography environment should be used instead.
a. Fourth-level heading is run in. Footnotes are produced using the \footnote{#1} command. Numerical style citations put footnotes into the bibliography6 .
Author-year and numerical author-year citation styles(each for its own reason) cannot use this method. Note:
due to the method used to place footnotes in the bibliography, you must re-run BibTeX every time you change
any of your document’s footnotes.
II.

MATH AND EQUATIONSInline math may be typeset using the $ delimiters.
Bold math symbols may be achieved using the bm package
and the \bm{#1} command it supplies. For instance, abold α can be typeset as $\bm{\alpha}$ giving α. Fraktur and Blackboard (or open face or double struck) characters should be typeset using the \mathfrak{#1} and\mathbb{#1} commands respectively. Both are suppliedby the amssymb package. For example, $\mathbb{R}$gives R and $\mathfrak{G}$ gives G
In LATEX there are many diﬀerent ways to display equations, and a few preferred ways are noted below. Displayed math will center by default. Use the class option
fleqn to ﬂush equations left.
Below we have numbered single-line equations, themost common kind:()|p| + pz
−1/2
χ+ (p) ≲ [2|p|(|p| + pz )], (1)px + ipy∑a }{1 b11234567890abc123αβγδ1234556αβ. (2)A2Note the open one in Eq. (2).
Not all numbered equations will ﬁt within a narrowcolumn this way. The equation number will move down
automatically if it cannot ﬁt on the same line with a
one-line equation:
∑a }
{
1 b
.
ab12345678abc123456abcdef αβγδ1234556αβ 2A(3)When the \label{#1} command is used [cf. input forEq. (2)], the equation can be referred to in text without

2
knowing the equation number that TEX will assign to it.
Just use \ref{#1}, where #1 is the same name that usedin the \label{#1} command.
Unnumbered single-line equations can be typeset using
the \[, \] format:
g+ g+ → g+ g+ g+ g+ . . . , q+ q+ → q+ g+ g+ . . . .
A.

Multiline equations

Multiline equations are obtained by using theeqnarray environment. Use the \nonumber commandat the end of each line to avoid assigning a number:
2
M =igZ(4E1 E2 )1/2 (li2 )−1 δσ1 ,−σ2 (gσe 2 )2 χ−σ2 (p2 )×[ϵj li ϵi ]σ1 χσ1 (p1 ),(4)∑|Mgviol |2 = gS2n−4 (Q2 ) N n−2 (N 2 − 1) 
∑ ∑ 1 1 ∑
× 
cfτ .
S
S
perm 12 12 τ
i<j

(5)

Note: Do not use \label{#1} on a line of a multiline
equation if \nonumber is also used on that line. Incorrectcross-referencing will result. Notice the use \text{#1}for using a Roman font within a math environment.
To set a multiline equation without any equation numbers, use the \begin{eqnarray*}, \end{eqnarray*}format:∑|Mgviol |2 = gS2n−4 (Q2 ) N n−2 (N 2 − 1)
 (
)
∑
∑
1
1
× 
.
S
S
S
S
12
23
n1
12
perm
i<j
To obtain numbers not normally produced by the automatic numbering, use the \tag{#1} command, where #1
is the desired equation number. For example, to get an
equation number of (2.6′ ),g + g + → g + g + g + g + . . . , q + q + → q + g + g + . . . . (2.6′ )A few notes on \tag{#1}. \tag{#1} requires amsmath.
The \tag{#1} must come before the \label{#1}, if any.
The numbering set with \tag{#1} is transparent to theautomatic numbering in REVTEX; therefore, the number
must be known ahead of time, and it must be manually
adjusted if other equations are added. \tag{#1} works
with both single-line and multiline equations. \tag{#1}should only be used in exceptional case - do not use it tonumber all equations in a paper.
Enclosing single-line and multiline equations in\begin{subequations} and \end{subequations} willproduce a set of equations that are “numbered” with letters, as shown in Eqs. (6a) and (6b) below:
∑a }
{
1 b
abc123456abcdef αβγδ1234556αβ 2
,
(6a)
A

Sample title

32
M =igZ(4E1 E2 )1/2 (li2 )−1 (gσe 2 )2 χ−σ2 (p2 )×[ϵi ]σ1 χσ1 (p1 ).

were Eqs. (6).
(6b)
1.

Putting a \label{#1} command right after the\begin{subequations}, allows one to reference all theequations in a subequations environment. For example,
the equations in the preceding subequations environment(
R(d) = gσe 2[ΓZ (3, 21)]σ1[ΓZ (13, 2)]σ1
+ 2
2
2
2
Q12 − MWQ13 − MWTABLE I. This is a narrow table which ﬁts into a text column
when using twocolumn formatting. Note that REVTEX 4 adjusts the intercolumn spacing so that the table ﬁlls the entire
width of the column. Table captions are numbered automatically. This table illustrates left-aligned, centered, and rightaligned columns.
Lefta
1
10
100

Centeredb
2
20
200

Right
3
30
300

a Note a.

Wide equations

The equation that follows is set in a wide format, i.e.,
it spans across the full page. The wide format is reserved
for long equations that cannot be easily broken into fourlines or less:)(+ xW Qe[Γγ (3, 21)]σ1[Γγ (13, 2)]σ1
+ 2
2
2
2
Q12 − MWQ13 − MW).

(7)

Test Figure

FIG. 1. A ﬁgure caption. The ﬁgure captions are automatically numbered.

b Note b.

This is typed to show the output is in wide format. (Since
there is no input line between \equation and this paragraph, there is no paragraph indent for this paragraph.)

III.

CROSS-REFERENCINGREVTEX will automatically number sections, equations, ﬁgure captions, and tables. In order to reference them in text, use the \label{#1} and \ref{#1}
commands. To reference a particular page, use the\pageref{#1} command.
The \label{#1} should appear in a section heading,
within an equation, or in a table or ﬁgure caption. The\ref{#1} command is used in the text where the citation
is to be displayed. Some examples: Section I on page 1,
Table I, and Fig. 1.

IV.

FIGURES AND TABLES

Figures and tables are typically “ﬂoats”; LATEX determines their ﬁnal position via placement rules. LATEX isn’t
always successful in automatically placing ﬂoats where
you wish them.
Figures are marked up with the figure envi-

ronment, the content of which imports the image(\includegraphics) followed by the ﬁgure caption(\caption). The argument of the latter command should
itself contain a \label command if you wish to refer toyour ﬁgure with \ref.
Import your image using either the graphics orgraphix packages. These packages both deﬁne the\includegraphics{#1} command, but they diﬀer in theoptional arguments for specifying the orientation, scaling, and translation of the ﬁgure. Fig. 1 is small enoughto ﬁt in a single column, while Fig. 2 is too wide for asingle column, so instead the figure* environment has
been used.
The analog of the figure environment is table, whichuses the same \caption command. However, you shouldtype your caption command ﬁrst within the table, instead of last as you did for figure.
The heart of any table is the tabular environment,
which represents the table content as a (vertical) sequence of table rows, each containing a (horizontal) sequence of table cells. Cells are separated by the & character; the row terminates with \\. The required argument
for the tabular environment speciﬁes how data are displayed in each of the columns. For instance, a column
may be centered (c), left-justiﬁed (l), right-justiﬁed (r),or aligned on a decimal point (d). (Table II illustrates
the use of decimal column alignment.)
Extra column-spacing may be be speciﬁed as well, al-Sample title

4

Wide Test Figure

FIG. 2. Use the figure* environment to get a wide ﬁgure, spanning the page in twocolumn formatting.

TABLE II. Numbers in columns Three–Five have been aligned
by using the “d” column speciﬁer (requires the dcolumn package). Non-numeric entries (those entries without a “.”) in a“d” column are aligned on the decimal point. Use the “D”
speciﬁer for more complex layouts.
One
one
He
Ca

Two
two
2
Cb

Three
three
2.77234
12537.64

Four
four45672.
37.66345

Five
ﬁve
0.69
86.37

a Some tables require footnotes.

mands are placed after the tabular environment. Examine the LATEX source and output for Tables I and IV
for an illustration.
All AIP journals require that the initial citation of ﬁgures or tables be in numerical order. LATEX’s automatic
numbering of ﬂoats is your friend here: just put eachfigure environment immediately following its ﬁrst reference (\ref), as we have done in this example ﬁle.

ACKNOWLEDGMENTS

b Some tables need more than one footnote.

though REVTEX 4 sets this spacing so that the columns
ﬁll the width of the table. Horizontal rules are typeset using the \hline command. The doubled (or Scotch) rulesthat appear at the top and bottom of a table can beachieved by enclosing the tabular environment within
a ruledtabular environment. Rows whose columns
span multiple columns can be typeset using LATEX’s\multicolumn{#1}{#2}{#3} command (for example, see
the ﬁrst row of Table III).
The tables in this document illustrate various eﬀects.
Tables that ﬁt in a narrow column are contained in atable environment. Table III is a wide table, therefore
set with the table* environment. Lengthy tables mayneed to break across pages. A simple way to allow thisis to specify the [H] ﬂoat placement on the table ortable* environment. Alternatively, using the standard
LATEX 2ε package longtable gives more control over how
tables break and allows headers and footers to be speciﬁed for each page of the table. An example of the use of
longtable can be found in the ﬁle summary.tex that isincluded with the REVTEX 4 distribution.
There are two methods for setting footnotes within atable (these footnotes will be displayed directly below
the table rather than at the bottom of the page or in
the bibliography). The easiest and preferred method isjust to use the \footnote{#1} command. This will automatically enumerate the footnotes with lowercase romanletters. However, it is sometimes necessary to have multiple entries in the table share the same footnote. In thiscase, create the footnotes using \footnotemark[#1] and\footnotetext[#1]{#2}. #1 is a numeric value. Eachtime the same value for #1 is used, the same mark is produced in the table. The \footnotetext[#1]{#2} com-

We wish to acknowledge the support of the authorcommunity in using REVTEX, oﬀering suggestions andencouragement, testing new versions, . . . .

Appendix A: Appendixes

To start the appendixes, use the \appendix command.
This signals that all following section commands refer toappendixes instead of regular sections. Therefore, the\appendix command should be used only once—to set up
the section commands to act as appendixes. Thereafter
normal section commands are used. The heading for asection can be left empty. For example,\appendix\section{}
will produce an appendix heading that says “APPENDIX
A” and\appendix\section{Background}
will produce an appendix heading that says “APPENDIX
A: BACKGROUND” (note that the colon is set automatically).
If there is only one appendix, then the letter “A”
should not appear. This is suppressed by using the starversion of the appendix command (\appendix* in theplace of \appendix).

Appendix B: A little more on appendixes

Observe that this appendix was started by using

Sample title

5

TABLE III. This is a wide table that spans the page width in twocolumn mode. It is formatted using the table* environment.
It also demonstrates the use of \multicolumn in rows with entries that span more than one column.
1
D4h

Ion
K
Mn
Cl
He
Ag

5
D4h

1st alternative(2e) + (2f )(2g)a(a) + (b) + (c) + (d)(8r)a

2nd alternative(4i)(a) + (b) + (c) + (d)
(2g)b
(4j)a
(4k)a

lst alternative(2c) + (2d)
(4e)
(4e)a
(4g)a

2nd alternative(4f )(2a) + (2b)(4h)aa The z parameter of these positions is z ∼ 1 .
4
b This is a footnote in a table that spans the full page width in twocolumn mode. It is supposed to set on the full width of the page, justas the caption does.

TABLE IV. A table with more columns still ﬁts properly ina column. Note that several entries share the same footnote.
Inspect the LATEX input for this table to see exactly how it is
done.
Cu
Ag
Au
Mg
Zn
Cd
Hg
Al
Ga
In
Tl

rc (Å)
0.800
0.990
1.150
0.490
0.300
0.530
0.550
0.230
0.310
0.460
0.480

r0 (Å)
14.10
15.90
15.90
17.60
15.20
17.10
17.80
15.80
16.70
18.40
18.90

κr0
2.550
2.710
2.710
3.200
2.970
3.160
3.220
3.240
3.330
3.500
3.550

Sna
Pbb
Cac
Srd
Lib
Nae
Ke
Rbc
Csd
Bae

rc (Å)
0.680
0.450
0.750
0.900
0.380
0.760
1.120
1.330
1.420
0.960

r0 (Å)
1.870
1.930
2.170
2.370
1.730
2.110
2.620
2.800
3.030
2.460

κr0
3.700
3.760
3.560
3.720
2.830
3.120
3.480
3.590
3.740
3.780

a Here’s the ﬁrst, from Ref. 1.
b Here’s the second.
c Here’s the third.
d Here’s the fourth.
e And etc.

\section{A little more on appendixes}
Note the equation number in an appendix:
E = mc2 .
1.

(B1)

A subsection in an appendix

You can use a subsection or subsubsection in an appendix. Note the numbering: we are now in Appendix B 1.
a.

A subsubsection in an appendix

Note the equation numbers in this appendix, producedwith the subequations environment:
E = mc,
E = mc2 ,E ≳ mc3 .

(B2a)
(B2b)
(B2c)

They turn out to be Eqs. (B2a), (B2b), and (B2c).
1 R. P. Feynman, Phys. Rev. 94, 262 (1954).
2 E. Witten,(2001), hep-th/0106109.

3 A. Einstein, Yu. Podolsky, and N. Rosen, Phys. Rev. 47, 777(1935).
4 N. D. Birell and P. C. W. Davies, Quantum Fields in Curved

Space (Cambridge University Press, 1982).
5 G. P. Berman, Jr. and F. M. Izrailev, Jr., “Stability of nonlinear

modes,” Physica D 88, 445 (1983).
6 Automatically placing footnotes into the bibliography requires

using BibTeX to compile the bibliography.
7 E. B. Davies and L. Parns, “Trapped modes in acoustic waveg-

uides,” Q. J. Mech. Appl. Math. 51, 477–492 (1988).
(McGraw-Hill, New York,
1994) Chap. 7, pp. 654–662, 5th ed.
9 D. E. Knuth, “Fundamental algorithms,”(Addison-Wesley,
Reading, Massachusetts, 1973) Section 1.2, pp. 10–119, 2nd ed.,a full INBOOK entry.
10 J. S. Smith and G. W. Johnson, Philos. Trans. R. Soc. London,
Ser. B 777, 1395 (2005).
11 W. J. Smith, T. J. Johnson, and B. G. Miller, “Surface chemistry
and preferential crystal orientation on a silicon surface,” J. Appl.
Phys. (unpublished).
12 V. K. Smith, K. Johnson, and M. O. Klein, “Surface chemistry
and preferential crystal orientation on a silicon surface,” J. Appl.
Phys. (submitted).
13 U. Ünderwood, N. Ñet, and P. P̄ot, “Lower bounds for wishfulresearch results,” (1988), talk at Fanstord University (A full
UNPUBLISHED entry).
14 M. P. Johnson, K. L. Miller, and K. Smith, personal communication (2007).
15 J. Smith, ed., AIP Conf. Proc., Vol. 841 (2007).
16 W. V. Oz and M. Yannakakis, eds., Proc. Fifteenth Annual, All
ACM Conferences No. 17, ACM (Academic Press, Boston, 1983)
a full PROCEEDINGS entry.
17 Y. Burstyn, “Proceedings of the 5th International Molecular
Beam Epitaxy Conference, Santa Fe, NM,” (2004), (unpublished).
18 B. Quinn, ed., Proceedings of the 2003 Particle Accelerator Conference, Portland, OR, 12-16 May 2005 (Wiley, New York, 2001)
albeit the conference was held in 2005, it was the 2003 conference,and the proceedings were published in 2001; go ﬁgure.
19 A. G. Agarwal, “Proceedings of the Fifth Low Temperature Conference, Madison, WI, 1999,” Semiconductors 66, 1238 (2001).
20 R. Smith, “Hummingbirds are our friends,” J. Appl. Phys. (theseproceedings) Abstract No. DA-01.
21 J. Smith, Proc. SPIE 124, 367 (2007), required title is missing.
22 T. Térriﬁc, “An O(n log n/log log n) sorting algorithm,” Wishful Research Result 7 (Fanstord University, Computer Science
Department, Fanstord, California, 1988) a full TECHREPORT
entry.
8 E. Beutler, “Williams hematology,”Sample title
23 J. Nelson, TWI Report 666/1999 (Jan. 1999) required institution

missing.
24 W. K. Fields, ECE Report No. AL944 (2005) required institution
missing.
25 Y. M. Zalkins, e-print arXiv:cond-mat/040426 (2008).
26 J. Nelson, U.S. Patent No. 5,693,000 (12 Dec. 2005).
27 J. K. Nelson, M.S. thesis, New York University (1999).
28 É. Masterly, Mastering Thesis Writing, Master’s project, Stanford University, English Department (1988), a full MASTERSTHESIS entry.
29 S. M. Smith, Ph.D. thesis, Massachusetts Institute of Technology(2003).
30 S. R. Kawa and S.-J. Lin, J. Geophys. Res. 108, 4201 (2003),
DOI:10.1029/2002JD002268.
31 F. P. Phony-Baloney, Fighting Fire with Fire: Festooning French
Phrases, PhD dissertation, Fanstord University, Department ofFrench (1988), a full PHDTHESIS entry.
32 D. E. Knuth, Seminumerical Algorithms, 2nd ed., The Art ofComputer Programming, Vol. 2 (Addison-Wesley, Reading, Massachusetts, 1981) a full BOOK entry.
33 J. C. Knvth, “The programming of computer art,” Vernier Art
Center, Stanford, California (1988), a full BOOKLET entry.
34 R. Ballagh and C. Savage, “Bose-einstein condensation: fromatomic physics to quantum ﬂuids, proceedings of the 13th physics
summer school,” (World Scientiﬁc, Singapore, 2000) condmat/0008070.
35 W. Opechowski and R. Guccione, “Introduction to the theory ofnormal metals,” in Magnetism, Vol. IIa, edited by G. T. Radoand H. Suhl (Academic Press, New York) p. 105.
36 W. Opechowski and R. Guccione, “Introduction to the theory ofnormal metals,” in Magnetism, Vol. IIa, edited by G. T. Radoand H. Suhl (Academic Press, New York, 1965) p. 105.

6
37 J.

M. Smith, “Molecular dynamics,” (Academic, New York,1980).
38 V. E. Zakharov and A. B. Shabat, “Exact theory of twodimensional self-focusing and one-dimensional self-modulation ofwaves in nonlinear media,” Zh. Eksp. Teor. Fiz. 61, 118–134(1971), [Sov. Phys. JETP 34, 62 (1972)].
39 E. Beutler, in Williams Hematology, Vol. 2, edited by E. Beutler,
M. A. Lichtman, B. W. Coller, and T. S. Kipps (McGraw-Hill,
New York, 1994) 5th ed., Chap. 7, pp. 654–662.
40 R. Ballagh and C. Savage, “Bose-einstein condensation: fromatomic physics to quantum ﬂuids,” in Proceedings of the 13th
Physics Summer School, edited by C. Savage and M. Das (World
Scientiﬁc, Singapore, 2000) cond-mat/0008070.
41 W. Opechowski and R. Guccione, “Introduction to the theory ofnormal metals,” in Magnetism, Vol. IIa, edited by G. T. Radoand H. Suhl (Academic Press, New York, 1965) p. 105.
42 J. M. Smith, in Molecular Dynamics, edited by C. Brown (Academic, New York, 1980).
43 D. D. Lincoll, “Semigroups of recurrences,” in High Speed Computer and Algorithm Organization, Fast Computers No. 23,
edited by D. J. Lipcoll, D. H. Lawrie, and A. H. Sameh (Academic Press, New York, 1977) 3rd ed., Part 3, pp. 179–183, a full
INCOLLECTION entry.
44 A. V. Oaho, J. D. Ullman, and M. Yannakakis, “On notions of
information transfer in VLSI circuits,” in Proc. Fifteenth Annual
ACM, All ACM Conferences No. 17, edited by W. V. Oz and
M. Yannakakis, ACM (Academic Press, Boston, 1983) pp. 133–
139, a full INPROCEDINGS entry.
45 L. Manmaker, The Deﬁnitive Computer Manual, Chips-R-Us,
Silicon Valley, silver ed. (1986), a full MANUAL entry.