Quantum physics

Electrons in perfect drag


A neat experiment shows that if a current is sent through one of two adjacent conducting layers placed in a strong magnetic field, a quantum effect generates an exactly equal but opposite current in the other layer. See Letter p.481

In a superconductor, electrons travel in pairs and can flow past obstacles without resistance. On page 481 of this issue, Nandi et al.1 demonstrate the existence of a strange analogue of this electronic behaviour in a system of two adjacent conducting layers in which the pairing is instead between an electron in one layer and the absence of an electron in the other layer. This strange form of pairing causes the current in the system to flow without dissipation, as long as the separate currents in each layer are exactly equal in magnitude and opposite in direction. As the physicist Isidor Isaac Rabi once remarked when confronted with an unexpected item from the menu of the delicatessen that is our Universe, “Who ordered that?”.

The 'fluid' model of electricity, developed in the eighteenth century by Benjamin Franklin and others, postulates that electrical charge is a continuous quantity associated with an excess or deficit in the density of some mysterious fluid that smoothly pervades the Universe. This model is perfectly adequate for many practical purposes, but in 1897, J. J. Thomson discovered the electron and concluded that electrical charge is quantized — it occurs in tiny but discrete units carried by elementary particles.

The discreteness of charge is responsible for a phenomenon known as Coulomb drag. To understand what this is, consider two thin metal layers that are separated by an electrically insulating barrier but that are so close to each other that the distance between them (about 10nanometres) is comparable to the distance between individual electrons within each layer (Fig. 1). The electrons in each layer therefore 'see' the graininess of the charge density of the electrons in the other layer. Because of their mutual Coulomb force, electrons in each layer can collide with each other. These collisions cause electrons flowing in one layer (the drive current) to 'drag' the electrons in the other layer, producing a drag current that flows in the same direction as the drive current. An analogous phenomenon occurs when a piece of sandpaper is pushed past another piece: the discrete grains of sand in each sheet produce a mutual friction that drags the second sheet along in the same direction as the first.

Figure 1: Against the current.

Nandi and colleagues' system1 consists of two closely spaced layers of electrons separated by an electrically insulating barrier. The authors show that, by applying a strong magnetic field, the system can be brought into a regime in which the current of electrons in one layer drives the electrons in the other layer to flow in a current that has the same magnitude as the drive current, but the opposite direction. Layer thickness and separation, and the spacing between electrons in each layer, are all about 10 nanometres.

In typical circumstances, the drag current does indeed flow in the same direction as the drive current, but it is much smaller and vanishes as the temperature approaches absolute zero. This is because the mutual drag friction between electron layers is far smaller than the internal friction — that is, the ordinary electrical resistance resulting from the collisions of the electrons with ever-present impurity atoms in each layer. The smallness of the mutual friction is due in part to the fact that, in ordinary metals, the electrons are whizzing about at 1% of the speed of light and don't spend much time near each other during collisions. The disappearance of the drag current at zero temperature is caused by a quantum effect associated with the Pauli exclusion principle, which states that two electrons cannot occupy the same quantum state.

In Nandi and colleagues' experiment, the application of a strong magnetic field perpendicular to the two adjacent conducting layers puts the system in the quantum Hall regime, in which the electrons are forced into small, quantized, circular orbits whose centres drift only slowly. This effectively nullifies the electrons' kinetic energy, leaving the Coulomb interactions to dominate the physics of the system. The microscopic electronic motion in the two layers can thus become strongly correlated, markedly increasing the Coulomb drag current.

It thus seems plausible that the drag current in Nandi and colleagues' experiment could be large, and might even equal the drive current in magnitude. And this is indeed what the authors observe: they detect a drag current that is precisely as large as the drive current. However, the two currents flow in opposite directions. How can that be?

It turns out that our simple sandpaper analogy fails because of quantum effects. The Coulomb interaction energy is lowered if an electron in one layer is paired with a hole (an absence of an electron) in the other layer. The Coulomb attraction between the opposite charges of the electron and the hole produces a quantum-mechanical bound state called an exciton2. An exciton is rather like a hydrogen atom, with the hole replacing the positive charge of the proton. Clearly, when hydrogen atoms move there is no electrical current because the atoms are charge neutral. The same is true here. If all the electrons are bound up in neutral excitons, the sum of the currents in the two layers is zero — no matter which way the excitons are moving.

The story is a bit more subtle than this, however. There are actually two exciton states, denoted 'up' and 'down' according to which layer contains the electron. Quantum mechanically, even if electrons can never tunnel through the insulating barrier to change layers, the two exciton possibilities 'know' about each other, and the lowest-energy exciton state is a quantum superposition of both up and down states at the same time. This superposition can be thought of in chemical-bonding terms as an orbital hybridization in which there is uncertainty about which layer the electron is in.

Crucially, the quantum states of the excitons carrying a current consist of a quantum superposition of an up exciton moving, say, to the left, and a down exciton moving to the right. Although there is still uncertainty about which layer the electron is in, we know that if it is in the upper layer it is moving to the left, and if it is in the lower layer it is moving to the right. As a result, the currents in the two layers are exactly equal in magnitude but opposite in direction. Furthermore, much as in a superconductor, the two currents flow without dissipation. The system prefers to be in this dissipationless state, and so if a current is sent through the drive layer, an exactly equal and opposite drag current automatically appears in the other layer.

Nandi and colleagues' experiment dramatically shows this novel effect of quantum superposition. Although practical applications of the phenomenon are unlikely, it does provide an example of quantum physics that allows the production of something previously considered impossible — namely, an electrical transformer (a device that boosts or reduces voltage) that works with unidirectional (d.c.) current instead of requiring periodically reversing (a.c.) current3.

Finally, if the currents in the two layers are in the form of opposite-handed whirlpools (vortices), something even more bizarre is believed to occur. According to theory4, a new elementary particle emerges — one that has a fractional charge, equal to half that of an electron. But that is a tale for another time.


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Correspondence to Steven M. Girvin.

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Girvin, S. Electrons in perfect drag. Nature 488, 464–465 (2012). https://doi.org/10.1038/488464a

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