Illustrations by Lucy Reading-Ikkanda August 2020, ScientificAmerican.com 53through, I saw that it was actually only partially solved. Yet one
of those partial breakthroughs had led to a Fields Medal, one of
the highest honors in mathematics, in 2006, and the other would
earn one four years later. In this company, it was clear the prob-
lem I was tasked with solving was no ordinary quandary. I con-
sidered carefully if I could solve such a question within a year.
The reason for the time limit is that a postdoc in math or physics
usually lasts two years. At the end of your first year, if you have
done great research, you may apply to top universities for a ten-
ure-track professorship. If your research is good but not great,
you may apply for a second postdoc or look for a less competitive
tenure-track position. If you have nothing to show after your first
year, there is always Wall Street.
Still, the idea of backing out now, without even trying to attack
the problem, was difficult to swallow. For a person growing up in
Spata, a small town outside of Athens, Greece, big dreams were
unusual. My dad grew up in the same house I did. He played soc-
cer and got into fights. When he eventually dropped out of high
school, his dad offered him a position at the local grocery store.
My father refused. Despite being a dropout, he had ambition. He
interned at the local real-estate agency and learned the ropes of
buying and selling land. Later, he went back to school to get his
GED at my mother’s insistence. Down the line, when my older
brother, Nikos, brought home his first-grade report card, my
father cried with happiness when he realized that his son was a
good student. Nikos and I would go on to compete at the Inter-
national Mathematical Olympiad, an honor afforded to six high
school students from each country every year. Then, one after the
other, Nikos, I and my younger brother, Marios, traded high
school in Athens for college at the Massachusetts Institute of
Technology in Cambridge—a rare accomplishment for any fami-
ly, let alone one of modest means, and a testament to my parents.
I thought that if they could perform miracles, maybe I could, too.
So, in the fall of 2008, I began working on problem number two,
aiming, as the list put it, to “formulate the theory of the integer
quantum Hall effect, which explains the quantization of the Hall
conductance, so that it applies also for interacting electrons in
the thermodynamic limit.”
The integer quantum Hall effect has a long history. The orig-
inal Hall effect was discovered in 1879 by Edwin H. Hall, a stu-
dent at Johns Hopkins University. Young Hall had decided to chal-
lenge a claim made by the father of electromagnetism, James
Clerk Maxwell. In his 1873 Treatise on Electricity and Magnetism,
Maxwell confidently declared that, in the presence of a magnet-
ic field, a conducting material with current flowing through it
will bend because of the magnetic force on the material, not on
the current. Maxwell concluded that “when a constant magnet-
ic force is made to act on the system ... the distribution of the
current will be found to be the same as if no magnetic force were
in action.” To test the idea, Hall ran current across a thin leaf of
gold placed in a magnetic field perpendicular to its surface and
noticed that his galvanometer (an instrument used to detect small
currents) registered a current, which implied a voltage (electric
potential) in a direction perpendicular to that of the current’s
original path. He concluded that the magnetic field was pushing
the electrons in the current toward one edge of the conductor,
permanently changing their distribution on the surface of the
material. Maxwell was wrong. This unexpected charge buildup
along the conductor’s edges became known as the Hall voltage.The quantum Hall effect was first observed nearly a century
later, on February 5, 1980, in Grenoble, France, by German exper-
imental physicist Klaus von Klitzing. His aim was to study the Hall
effect more carefully under ultralow temperatures and high mag-
netic fields. He was looking for small deviations from the expect-
ed effect in certain two-dimensional semiconductors, the materi-
als underlying all modern transistors. In particular, he was trying
to measure the Hall resistance, a quantity proportional to the Hall
voltage. What he observed was astonishing: the Hall resistance
was quantized! Let me explain. As the strength of the magnetic
field increased, the resistance between the edges of the material
would stay exactly the same, until the field got high enough. Then,
the resistance would jump to a new value instead of climbing up
steadily the way Hall had originally observed—and all known phys-
ics at the time predicted. Even more surprisingly, the values of the
Hall conductance, the inverse of the Hall resistance, were precise
integer multiples of a quantity intimately related to the fine-struc-
ture constant, a fundamental constant of nature that describes the
strength of the electromagnetic interaction between elementary
charged particles. The integer quantum Hall effect was born.Von Klitzing’s discovery was remarkable, not least of all
because the fine-structure constant was supposed to describe
aspects of the quantum realm that were too fine-grained for any
macroscopic phenomenon, such as the Hall conductance, to be
able to probe, let alone define with incredible precision. Yet not
only did the Hall conductance capture an essential aspect of the
microscopic world of quantum physics, it did so with impossible
ease. The integer plateaus of the Hall resistance appeared irre-
spective of variations in the size, the purity or even the particular
type of semiconducting material used in the experiment. It was
as if a symphony of a trillion trillion electrons maintained their
collective quantum tune across vast atomic distances without they xzOriginal Hall EffectOriginal direction
Magnetic field of currentDeflected
chargesQuantum Hall EffectMagnetic FieldHall Resistance© 2020 Scientific American © 2020 Scientific American