Polarity is a matter of perspective

The polarity of charge carriers — positive or negative — is found to depend on the direction from which you look.

Whenever an electrical current is flowing, one of the most basic questions one can ask is: is the current being carried by positive charges or negative charges? After all, a current flowing to the right can correspond either to a collection of positive charges (‘p-type’ conduction) moving rightward or to negative charges (‘n-type’) moving leftward. In this way materials can be classified according to a basic dichotomy, the p-type or n-type polarity. For some materials the question of polarity is complicated by the presence of multiple coexisting electronic energy bands, but, writing in Nature Materials, Bin He and co-workers1 have shown that even a material comprising a single band can display both p-type and n-type behaviour simultaneously. Most strikingly, they show that whether the material looks p- or n-type can depend on which direction the current is flowing. This direction-dependent polarity could lead us to radically reconsider what is possible for electrical and heat flow in materials.

Electrons within a crystalline material are arranged in bunches of electronic energy levels called bands. Since two electrons cannot occupy the same quantum state, a band fills up in much the same way as packing balls into a box. Electrons buried deep within a band scarcely move; as a result, the dynamical properties of metals are dominated by those electrons in the uppermost filled energy levels. Mapping out the momenta of these uppermost electrons defines a Fermi surface, which takes the form of some particular geometric shape when drawn in the space of the three momentum coordinates (Fig. 1). Crucially, the concavity or convexity of this Fermi surface determines whether the carriers that move along it are p- or n-type (Fig. 1a,b).

Fig. 1: The goniopolar effect.

a,b, The polarity of carriers in a single-band metal depends on the geometry of the Fermi surface. When a Fermi surface is concave (a), it corresponds to p-type conduction. When it is convex (b), n-type conduction ensues. Here the shaded region corresponds to the region in momentum space occupied by electrons; kx and ky are the wavectors. c,d, In a goniopolar material, the Fermi surface is concave in some directions and convex in others (c). This is analogous to how a carved block (d) can look like the letter P from one perspective and the letter N from another.

The polarity of a material can be diagnosed experimentally by a few simple tests. Among the most reliable is to examine the thermopower, which is the generation of a voltage difference across the material when a temperature difference is applied. Hotter charge carriers tend to diffuse faster, which causes them to pile up on the cold side, so that the sign of the resulting voltage reflects the sign of the carrier. Of course, if a material has multiple bands with differing polarity then the thermoelectric effect can become more complicated, particularly if the diffusion constant of carriers depends on direction2. But single-band materials, where there is only one band composing the Fermi surface, are usually thought of as simple, with a definite polarity: p-type or n-type. The authors’ finding, then, that a single band can look p-type or n-type, depending on which way the current flows, is remarkable.

The key insight suggested by the authors is to imagine a geometric shape for the Fermi surface that can look either concave or convex in profile, depending on which direction you look at it from. Imagine, for example, a hyperboloid with a slightly rounded top, similar to what is shown in Fig. 1c. When seen from the side, this hyperboloid has the profile of an hourglass and casts a concave shadow, which would suggest p-type conduction. However, when seen from along its axis, it has a convex, circular profile, suggesting n-type behaviour.

This surprising and simple geometric observation leads the authors to suggest a phenomenon that they dub ‘goniopolarity’, (from the greek γωνια, meaning angle). They study this effect in the layered crystalline material NaSn2As2 and find striking evidence for a direction-dependent carrier sign. Most notably, the thermopower in NaSn2As2 is positive in the concave direction, and negative in the convex direction.

The authors put their results through an extensive battery of sanity checks. For example, they measure a very small Nernst effect (transverse thermopower in the presence of a magnetic field), which suggests the presence of only a single band, since multiple bands contribute additively to the Nernst effect3. They also measure the thermal conductivity, and find no sign of strong anisotropy that could mimic the goniopolar effect in thermopower. Further, theoretical calculations of the band structure of NaSn2As2 show that it indeed has aspects of mixed-direction concavity/convexity and only a single band.

The implications of goniopolarity largely remain to be seen, but it is interesting to consider what it might mean for the ubiquity of applications that require p–n junctions — interfaces between p-type and n-type materials that are essential components of digital logic circuits, photovoltaic technologies, and solid-state heaters, coolers, and thermometers. The existence of a goniopolar effect implies that one could make such a junction not from two diverse materials, whose interface is often complicated, but from two samples of the exact same material rotated with respect to one another.

Even without making junctions, one can imagine using the goniopolar effect together with a recent theoretical proposal for generating perpendicular heat flow4,5,6. Since the sign of the thermopower is direction-dependent (say, positive in the x direction and negative in the z direction), flowing an electrical current in the x + z direction generates a heat current that has a component in the perpendicular xz direction. Generating such perpendicular heat flow usually requires a magnetic field, but for goniopolar materials it can seemingly be achieved in a single (and single-band) material without any applied field (albeit only for specific directions of current flow). One can now imagine constructing simple, solid-state heaters and refrigerators without any junctions, which operate by running an electrical current parallel to the object from which they are heating or cooling.


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Correspondence to Justin C. W. Song.

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Skinner, B., Song, J.C.W. Polarity is a matter of perspective. Nat. Mater. 18, 532–533 (2019).

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