So let's start with what is the
classical
Hall Effect discovered by Edwin Hall at
Johns Hopkins University in the
nineteenth century.
So when you have an ordinary
piece of metal, let's say a wire or a
sheet of metal, in order to drive
current through it because it has
electrical resistance if it's not
superconducting you need a
push. You need to push the electrons
through it with an electric field and that
requires having a voltage drop from one side of the wire
to the other and the electric field
points in the direction that the current
is flowing.
Edwin Hall discovered that if you put
a very strong magnetic field
perpendicular to that
direction of the current flow, the
electrons would
get pushed sideways by what's called the
Lorentz force,
a velocity dependent force that pushes
the electron
at right angles to the velocity in right
angles to the
magnetic field. It pushes the electrons
off to one side
and a voltage drop appears now at right
angles to the current following
and that's called the Hall voltage. So this
phenomenon is used in sensing magnetic
fields, is used in your
automobile for, in,
what used to be the distributor.
Now an electronic circuit that uses
these
Hall sensors and it has a number of
other practical uses.
The quantum Hall effect takes place
in a very thin layer
of electrons essentially a
two-dimensional
sheet of electrons or electron gas in a
very strong perpendicular magnetic field
when the system is cool down near
absolute 0
and it was discovered that
independent of all the
microscopic details and the size and
shape of the sample and exactly what the
sample was made of and
where any dirt and imperfections
in the sample nevertheless when you've put
a certain current through the
sample you got a certain voltage.
The ratio of that Hall voltage to the
current
as units of electrical resistance,
ohms, and it was discovered that
you got a universal value
for that ratio and
that resistance is called the
quantized Hall resistance discovered by
Klaus von Klitzing and it's
twenty-five thousand eight hundred
and twelve point 8-0 ohms approximately
and its value is actually given by the
ratio of two
fundamental constants planks constant
divided by the electron charge squared.
Completely universal and fundamental
even though it's taking this phenomenon,
is taking place in a
dirty, not very perfect, handmade,
human-made sample. So that was a
huge surprise. Then there was a
second huge surprise
that some of the, it's possible to see
fractional quantum numbers in
this system and under other special
circumstances where the electron
interactions are important.
So this lead to a
huge advance in our theoretical
understanding of how
a large system of interacting
electrons can form a
surprisingly subtle and complex quantum
ground state. Further progress
after that
lead to the realization that there could
be even more complicated
quantum states containing
kind of, quantum
defects, quantum vortices where there
were little loops of current flowing around
and people realize that those
objects could actually be used to form
quantum bits
and the way you would change the
state of those quantum bits
is to berate, physically move them
around each other to braid them
around each other and the mere act
of moving one particle around the other
changes the state of this particle
and so if there exists a,
an idea for what's called a
topological
quantum computer in which
the, you would use these
objects and braid them around to do the
operations.
A reason this is an interesting idea is I
mentioned earlier that
quantum systems are very sensitive
to small perturbations and noise and imperfections,
but this particular quantum state,
type of state, is very robust against that.
You can make
local perturbations at any spot in the
system
and nothing happens to the quantum state
because the information is kind of
spread out in kind of holographic way it
spread out and shared amongst many of
these particles
and you can't, no local perturbations can
destroy that information.
So the hope is that this would be very
robust against
noise and decoherence.
Experimentally it's very, very
challenging and
people are beginning, they've definitely
have seen these
vortex objects, they have
started to move them around each other.
There is some
evidence that you can see these
fractional statistics and non abelian
statistics the fancy words for these
changes in state when you
braid one around the other but it still
very, very early days and
the physics has not yet been really
clearly demonstrated experimentally but
again it's too early to say it's not
going to work
for any any piece of hardware.
