Electrons and bursting waterworks

Abstract

The Expert Opinion is written by a distinguished scientist and presents his/her personal view on important and relevant new results of research, highlighting their significance and putting the work into perspective for a broader audience. Please send comments to pss@wiley-vch.de A yearly ritual before the winter returns is the emptying of the waterworks outside our homes. It is a well-known fact that water, when it freezes, expands, usually with destructive consequences for the waterworks, that is to say, if we have forgotten to empty them. The freezing of water is a typical example of a phase transition. When water turns into ice, the so-called chemical potential of the water molecules changes, causing fewer molecules to occupy the same amount of space.Electrons in a metal usually form some kind of liquid. Unlike water molecules, each electron carries a small amount of charge and, due to the spin, also a small amount of magnetic moment. The charge and the spin allow the electrons to order in a large diversity of states of matter, such as ferromagnets, superconductors, antiferromagnets, etc. Electrons can even crystallize, thus prohibiting the conduction of electrical currents, a phenomenon which is known as Wigner crystallization. These forms of ordering disappear when we warm up the electrons to a characteristic temperature, the so-called transition temperature, T c . Just as for the water/ice transition, the chemical potential of the electrons changes at T c [1]. That such a change should take place is firmly rooted in a set of fundamental equations of thermodynamics, the so-called Ehrenfest relations [2]. Accordingly, the temperature dependence of the electron chemical potential is directly related to dT c /dn, where n is the density of the electrons. This means that just like for the water in the waterworks, the electron density wants to change when a phase transition occurs: the electrons try to spill over the boundaries of the material in which they are contained! A water pipe has only two options: Either it is strong enough to sustain the pressure of the compressed ice, or it bursts. For electrons in a solid this is different: When the electron liquid begins to expand, a charge layer builds up on the sample surface, giving rise to an electric field which exactly balances the change in chemical potential [3]. Hence the sample does not burst, but instead the charge at the surface changes. This causes a change of the electrical fields outside the sample which, in principle, can be measured. Earlier attempts to measure these small changes of electric field were either utilizing a vibrating capacitance bridge [4], or electrochemical cells [5,6]. The disadvantage of the former is that it requires very clean and stable sample surfaces, which is only possible under ultra high vacuum conditions. For the latter method the sample must be immersed in an aqueous solution during the measurements, which imposes considerable limitations on the possible range of substances and temperatures.Recently Matlak and Pietruszka...

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