I don't know what you think about when you go to sleep but I guess that you probably
don't think about quantum conductance.
And yet, every time you turn off the lights, you are creating a quantum of conductance.
You probably never knew that, so I'm going to explain this to you, but before I get into
the quantum part of things, let me remind you of what conductance normally is.
The conductance is a property of a material that describes its ability to conduct electrical
currents.
So, if you take for example a piece of wire of electrical wire and you attach it to let's
say a battery that produces a voltage across the wire, there will be a current that flows
through the wire and this current will be given by the voltage that you apply to the
wire, times the conductance that we write with the letter G.
The conductance itself can be derived microscopically from an intrinsic property of the material
that's called the conductivity sigma, times the cross section of the wire, the area of
the wire, divided by the length of the wire.
If you look at this, you might be tempted to think that you can keep the same conductance
by shrinking the wire with the same proportions.
So if you make the cross section ten times smaller and the length ten times smaller,
the conductance remains the same and so on.
But in fact there comes a point where this is no longer true, when you make the wire
really really small.
Because when you do so, you need to remind yourself that the electrons that constitute
the electrical currents that you're transporting through the wires are not just little billiard
balls that move through the wire as your classical picture might suggest to you, they are in
fact waves.
They are quantum mechanical waves.
So if you make a really small wire, at some point you reach the limit where the size of
the wire, the width of the wire in particular, becomes comparable to the wavelength lambda
of the electrons travelling through it.
And when this happens, then this wire is no longer just a classical wire, it becomes a
quantum mechanical wave guide in a sense.
And so when this happens, you get conductance that no longer varies in a smooth way depending
on the dimensions of the wire but varies in the quanta.
In steps, in discreet increments of a fundamental quantity of nature that's called the quantum
of conductance, is given by the square of the electrical charge, divided by the plain
constant.
Now, when this happens, the wire has to be very very small and you might think, well,
I never use wires that small.
That's not true.
You do it every time you turn off a light switch.
Think of what a light switch actually is.
It's two metal plates sticking to each other when the switch is closed, and then when you
turn off the lights, you take the two metal plates apart.
But this does not happen instantaneously.
There will be some point where the contact surface between the two plates becomes extremely
small and that's when you create quantum conductance.
So imagine, a light switch as two metal plates that you first press against each other when
you want the light to be on.
But imagine you take a zoom in of this area and you look at what actually happens in there
at a microscopic level.
Well actually, here you have some atoms on one side, they really are attached to the
atoms on the other side and so on.
But as you open the switch, these atoms will be pulled apart and eventually there will
be a point where you will have only one atom between them.
So imagine that this is a good switch so the plates are actually plated in gold.
Gold is of course a very good electrical conductor and it has this peculiar property that when
you pull apart two pieces of gold, it creates a one atom constriction.
The wavelength of an electron in gold is in fact 0.5 nanometres.
And the width of a gold atom is about 0.4 nanometres.
So you see, this actually fulfils the condition to create quantised conductors.
So every time you turn off the light and you break apart the metal plates that touch each
other to let the light be on, you create a quantised value of the conductance between
the plates of the switch.