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Quantised Conductance Resistance Standard

Testing the accuracy and reliability of quantised conductance in thoroughly average commodity electronics.

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Quantised conductance is a phenomenon seen in quantum point contacts also known as quantum nanowires. It refers to the fact that when a wire is sufficiently narrow and short the conductance through it will go to some multiple of the conductance quantum. As you change the properties of the conductor rather than getting a continuous change in conductance you instead will switch between the conductor allowing different numbers of states.

This project aims to reliable measure quantum conductance in commodity electronics components and hopefully use it as a standard (which should be independent of temperature and other factors) to measure some resistors.

In a sufficiently narrow conductor confinement of electrons leads to a certain number of allowed quantum channels. Much in the same manner as in conventional waveguides. Of course, unlike in a waveguide, electrons are subject to scattering events so if you want to see the effects of the quantisation a narrow conductor which is a lot shorter than the mean free path of the electrons. These extremely short conductors can be realised through the use of an STM probe, GaAs/AlGaAs heterostructures, or during conductance breaking events.

The conductance breaking events are the jankiest method but also the most possible to realise cheaply at home. It's pretty easy to set up a circuit where you can see the effect using a scope and a couple of gold wires. If you want something a bit more reliable and reproducible you can use a relay.

Still, no matter what you do the entire process is still pretty janky, so this first part of this project is to see how reliable the measurement can be made using only components that you might have on your own benches. This isn't as trivial as you might imagine. Sometimes there won't be any events, sometimes you might get heaps of noise because the electron transport isn't completely ballistic for some reason, sometimes there'll be multiple nanowires at the same time, and sometimes you'll only get the first level which for later purposes isn't enough.

Still, given a reliable and reasonably precise setup I want to see if I can use it to measure resistors. Given that you can measure multiples of the conductance quantum G0, which is nice and constant reference (indepedent of temperature, mechanical stress, and other factors that can affect resistors):

then you can account for an other pesky resistance in the circuit and even start to account for small non-linearities in whatever ADC you're using if the results are good enough.

  • Science not Tools

    kirrent06/18/2016 at 07:32 0 comments

    Putting together the tiny about of hardware for this project I've been thinking about what I really want to do with it. Really, measuring resistors using a micro isn't that exciting as a project. Measuring physical constants using common components is a lot more interesting. Actually, the conductance quantum is related to one of the most accurately measured constants of physics, the fine structure constant (https://en.wikipedia.org/wiki/Fine-structure_constant). The relation is:

    The magnetic permeability is a defined constant (so, you know, pretty high accuracy) so I suppose you could even try to get a good measure for the speed of light.

    All in all, I think it'd be a lot more fun to make a circuit I can sit downstairs that doesn't do anything but try to determine the conductance quantum.

  • Choosing Components

    kirrent04/16/2016 at 10:37 0 comments

    I want to reiterate before going over the parts I want to use that part of the point of this project is to use cheap and cheerful components. At least partially because I enjoy the idea of seeing obviously quantum phenomena without spending a lot of money.

    The first important thing to consider is the choice of contact mechanism. When you're only doing a few trials a couple of wires or a switch is fine, but I want to get reliability from a huge number of trials so a relay is the only choice. The choice of contact is a little bit more involving. The small amount of literature on measuring contact breaking QC shows that copper and silver work but aren't ideal, there's nothing I could find on silver alloys, and from my small experience and the literature gold works the best. Gold plated relays aren't the most common but cheap on the few websites I checked.

    Measuring the current is a little interesting. Normally you might think to hook up a transimpedance amplifier into a proper ADC however the capacitance of the entire system should be tiny. I'm not sure if the trace capacitance, some coupling with the relay coil, or the ADC sample capacitance are the largest but they're all tiny. With such a small time constant I'll just be measuring voltage across a resistor.

    I should clarify that there's no requirement for any sort of high accuracy resistor. In fact, because I'm lazy and can't think of any other easy way to rescale for testing a nice wide range of resistors I'm going to use a digital pot to vary range. It might also help during contact breaking events to reduce the effect of constant error in the ADC on ever smaller measurements.

    Seeing as this is going to be a prototype, and a simple one at that, and I might want to iterate lots I'll just be doing the entire thing on veroboard with a Teensy and its delicious 13 ENOB ADC.

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