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I would like to know if anyone knows of a material where the conductivity drops when the current increases? Usually, it's the opposite.

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  • $\begingroup$ Welcome to our site! $\endgroup$
    – Camps
    Aug 27 '20 at 10:27
  • $\begingroup$ What? I thought it was almost always the opposite: Current increase -> increase scattering -> lower conductivity. $\endgroup$
    – user14717
    Aug 28 '20 at 17:39
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This also occurs in traditional (filament) light bulbs.

The filament resides in an evacuated glass envelope, backfilled with a percentage of inert gas, to prevent oxidization and immediate failure. The filament is constructed of a fine tungsten (likely alloy) wire, wrapped into a microscopically-tight spiral, then this wrapped again into a slightly larger spiral. The double-wrapping greatly increases the effective length, and thus the total electrical resistance. The length is specifically chosen to be compatible with various standard supply voltages (120v, 240v etc.) The diameter of the filament is also responsible for the "power" of the lamp, with larger diameters making more light (and using more energy.)

The moment a light switch is thrown, the bulb appears as a low resistance (high conductance) as the filament is cold. This causes a large current to flow for a very short amount of time, which quickly heats the filament to red-hot. As the temperature increases, the filament becomes more resistive (less conductive) and the temperature-increase-rate slows. Eventually (perhaps 0.1s) later, this rate drops to zero, and the bulb is glowing white-hot in an equilibrium state.

Addition: I think most (if not all) pure metals exhibit this behavior (decreasing conductance / increasing resistance with increasing temperature.) Such is termed a "PTC" or positive temperature coefficient of resistance. As the atoms heat up, they are forced to expand, increasing the inter-atom distance, which makes them less electrically conductive. Tungsten is used for lamps due to it's extremely high melting point, which allows a wider range of operation, up to the white-hot point which few other materials can survive.

Semi-conductor materials (such as atomically doped silicon used in practically all computer systems today) tend to have NTC or negative temperature coefficients, meaning they become more conductive at higher temperatures. Thus "heat sinking" (keeping them cool) is needed for dense integrated circuits today.

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    $\begingroup$ Thank you very much for this very interesting answer. I was not aware that tungsten had these properties! Is this the case for other materials too? $\endgroup$
    – henry
    Aug 28 '20 at 12:54
  • $\begingroup$ most (all?) metalls do this, especially pure elements. the alloy nichrome (and constantan) are notable for not doing this much. $\endgroup$
    – Jasen
    Aug 28 '20 at 23:54
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This occurs in superconductors. In the simplest version (called type-I BCS superconductors) there is a resistanceless state at low temperature, magnetic field, and current density. When the current density is raised over a critical value, a transition into a state with finite resistance occurs. This was discovered by Kamerlingh Onnes in the 1910s in mercury. In other types of superconductors, the details may be more complex, but the central point of a resistanceless state disappearing at high current density remains.

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    $\begingroup$ @NikeDattani Thanks. Didn't realize it's been that long since my last answer. I've participated in two workshops this month, so my activity here was reduced to lurking in the background. $\endgroup$
    – Anyon
    Aug 27 '20 at 17:29
  • $\begingroup$ And workshops these days consume double the energy that they used to, since everything is online. No worries about being busy. I was going to ask you though if you know anything about this question, or know anyone in the field that might be able to answer: mattermodeling.stackexchange.com/q/689/5. Since you were the hero that came to the rescue when we had questions about the Heisenberg model and Ising model, and this is another "model Hamiltonian" question more for "condensed-matter physics theorists" rather than "computational quantum chemists", I thought you might be the one to ask? $\endgroup$ Aug 27 '20 at 18:19
  • $\begingroup$ Thanks a lot for your answer! This is very interesting. Do you know of any other material that shows this property at normal temperatures? $\endgroup$
    – henry
    Aug 28 '20 at 12:56

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