Science - USA (2020-05-22)

sciencemag.org SCIENCE

and Bose-Einstein condensates. These soli-
tary waves do not necessarily have special
interaction properties.
In a different research direction, it was
shown ( 4 ) that topological properties and
invariants could be used to explain the in-
teger quantum Hall effect. As an external
magnetic field is gradually increased, the
conductivity in materials such as gallium
arsenide heterostructures decreases by
quantized jumps. The field
of topological insulators in
electromagnetic media can be
traced to 2008, when topolog-
ically protected modes were
theoretically identified in
suitably constructed material
permittivity ( 5 ). By using me-
dia that break time-reversal
symmetry, linear edge waves
were found that propagate
unidirectionally and possess
nontrivial topological invari-
ants (Chern numbers).
The first experimental ob-
servation of a topologically
protected mode in an elec-
tromagnetic system found
that localized edge waves
could propagate in suitable
magnetic media that break
time-reversal symmetry ( 6 ). These linear
magneto-optical waves propagated unidirec-
tionally without backscatter from defects.
The topology here is spectral in nature and
is different from spatial topology observed
in dark solitons and vortices.
A few years later, a photonic system was
constructed ( 7 ) that broke time-reversal
symmetry by creating a helical rotation of
the lattice waveguides in the propagation
direction. The media vary periodically in
the direction of propagation, and models
of this system involve wave equations with
coefficients that share this periodicity. The
mathematician Gaston Floquet studied
differential equations with periodic coef-
ficients, so this system is referred to as a
Floquet topological insulator.
All of these systems are linear. A non-
linear waveguide system was proposed in
( 8 ) that exhibits a similar type of cyclo-
tronic motion, as has now been observed
by Mukherjee and Rechtsman (see the first
figure). From a mathematical perspective,
the model used to describe both systems
consists of a discrete nonlinear Schrödinger
(NLS) equation in two spatial dimensions,
with periodic coefficients in the propaga-
tion variable. One-dimensional solitons in
uniform waveguides, but without topology,
were theoretically predicted in ( 9 ) and ob-
served a decade later ( 10 ). They were sub-
sequently observed in two-dimensional

uniform waveguides ( 11 ). These uniform

systems are modeled by one- and two-

dimensional discrete NLS equations with

constant coefficients.

Researchers have theoretically predicted

the existence of solitons ( 12 ) on the bound-

ary edge of the helically varying waveguides

used in the experiments of ( 7 ). The linear

topology and the unidirectional propaga-

tion through defects appear to be naturally

inherited by the nonlinear

soliton modes (see the second

figure). We anticipate future

research that will continue to

examine how the presence of

topology affects the behavior

of solitons.

An aspect of the work of

Mukherjee and Rechtsman

indicates the extent to which

waveguide fabrication has

progressed. Early fabricated

optical structures created

waveguides with uniform fea-

tures in the late 1990s. This

approach was extended to

waveguides with helical struc-

ture in the longitudinal direc-

tion with femtosecond laser

writing techniques in ( 7 ). The

waveguides used in the pres-

ent study are engineered so that during one

period, each waveguide couples to its nearest

neighbors sequentially and one at a time. All

sorts of truly complex waveguides that could

demonstrate noteworthy wave features can

now be constructed, so this observation of

topological solitons is likely to be one of

many more. j

REFERENCES AND NOTES

1. S. Mukherjee, M. C. Rechtsman, Science 368 , 856
   (2020).


2. M. J. Ablowitz, Nonlinear Dispersive Waves (Cambridge
   Univ. Press, 2011).


3. N. J. Zabusky, M. D. Kruskal, Phys. Rev. Lett. 15 , 240
   (1965).


4. D. J. Thouless, M. Kohmoto, M. P. Nightingale, M. den Nijs,
   Phys. Rev. Lett. 49 , 405 (1982).


5. F. D. M. Haldane, S. Raghu, Phys. Rev. Lett. 100 , 013904
   (2008).


6. Z. Wang, Y. Chong, J. D. Joannopoulos, M. Soljačić,
   Nature 461 , 772 (2009).


7. M. C. Rechtsman et al., Nature 496 , 196 (2013).


8. Y. Lumer, Y. Plotnik, M. C. Rechtsman, M. Segev, Phys.
   Rev. Lett. 111 , 243905 (2013).


9. D. N. Christodoulides, R. I. Joseph, Opt. Lett. 13 , 794
   (1988).


10. H. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, J.
    S. Aitchison, Phys. Rev. Lett. 81 , 3383 (1998).


11. J. W. Fleischer, M. Segev, N. K. Efremidis, D. N.
    Christodoulides, Nature 422 , 147 (2003).


12. M. J. Ablowitz, C. W. Curtis, Y.-P. Ma, Phys. Rev. A 90 ,
    023813 (2014).

ACKNOWLEDGMENTS

Supported by Air Force Office of Scientific Research grant

FA9550-19-1-0084.

10.1126/science.abb5162

INSIGHTS | PERSPECTIVES

GRAPHIC: JOSHUA BIRD/

SCIENCE

By Brande B. H. Wulff^1 and

Jonathan D. G. Jones^2

E

very year, infection of wheat by the

fungus Fusarium graminearum re-

sults in losses of ~28 million metric

tons of wheat grain ( 1 ), valued at $5.6

billion. The fungus reduces yields but

also contaminates harvests with tri-

chothecene toxins such as deoxynivalenol

(DON; also called vomitoxin because of its

effects on mammals) that render grain too

poisonous to use. The disease is becoming

more prevalent because of increasing culti-

vation of maize (also a host for the fungus)

and reduced tillage (ploughing) agriculture,

which promotes fungal survival on last sea-

son’s plant debris. On page 844 of this issue,

Wang et al. ( 2 ) reveal the molecular identity

of the Fusarium head blight 7 (Fhb7) gene,

which encodes a glutathione S-transferase

that detoxifies DON. This gene was acquired

through a “natural” fungus-to-plant gene

transfer in a wild wheat relative. This natu-

rally occurring genetically modified (GM)

wheat strain is therefore exempt from regu-

lation and can be grown directly by farmers.

Annual yield losses due to Fusarium

head blight are second only to leaf rust

( 1 ). Despite screening thousands of wheat

lines, little resistance to Fusarium has been

found. Wild grassy relatives of wheat, how-

ever, represent a rich source of genetic di-

versity, which has long been mined for re-

sistance genes by interspecific crossing. The

Fhb7 gene was introduced into wheat from

tall wheat grass (Thinopyrum ponticum)

and provides major, semidominant resis-

tance ( 2 ), unlike most Fusarium resistance

in wheat, which is typically conferred by

polygenic minor-effect genes that are diffi-

cult for breeders to track ( 3 ).

The identification of Fhb7 by Wang et al.

reveals an enzyme that detoxifies DON by

PLANT BIOLOGY

Breeding a

fungal gene

into wheat

(^1) John Innes Centre, Norwich Research Park, Norwich,
UK.^2 The Sainsbury Laboratory, University of East Anglia,
Norwich Research Park, Norwich, UK. Email: brande.wulff@
jic.ac.uk; [email protected]
An ancient cross-kingdom
gene transfer enables wheat
resistance to a fungal toxin
Defect
Undeterred by
defects
A topological edge soliton
localized along the boundary
of a waveguide array cannot
reflect backward and instead
propagates around a defect.
822 22 MAY 2020 • VOL 368 ISSUE 6493
Published by AAAS