Quantum physics

Strongly correlated transport

The field-effect transistor underlies microprocessor technology. A version of it has been demonstrated that tunes particle transport from an incoherent regime to a strongly correlated superfluid one. See Letter p.736

The quantum transport of charge is a prominent feature in emerging models for future technologies, from microprocessors in computing to radical ideas for renewable-energy materials. In general, transport describes the motion of matter that has sufficient energy to overcome barriers, in contrast to quantum tunnelling, which occurs directly through barriers. Such transport becomes 'quantum' when the wave-like nature of particles is required to describe the process. There are different types of quantum transport, and devices that turn such flows on and off are called field-effect transistors (FETs)1 and are a mainstay of microprocessor technology. In this issue, Stadler et al.2 demonstrate a micrometre-scale FET that is able to capture the dynamics of quantum transport in a regime called strongly correlated quantum-coherent superfluidity. Their contribution can best be explained by tracking how different FETs can be used to study the dynamics of charge in a progression of transport regimes.

The basic concept of a FET is to use an electric field (gate) to control the transport of electrons or holes (notional particles formed by the absence of electrons) through a narrow channel between two charge reservoirs (source and drain) in a semiconducting material. Quantum mechanics must be used to predict the overall behaviour of the collection of charges, but the motion of each particle amounts to a (biased) random walk. The particles' dynamics is modelled by the semi-classical Boltzmann equation. However, under certain conditions, the wave-like nature of the charges becomes a major feature of transport properties. Then, different scattering paths can interfere like waves, building up constructive and destructive interference patterns, for instance, and the semi-classical Boltzmann equation is no longer correct.

On the edge of this transport regime, a blend of particle and wave-like dynamics is observed. Such partially coherent dynamics is currently being explored3,4,5, for example to efficiently move charges in solar-cell materials and in the latest molecular-electronics devices (Fig. 1a,b). Deeper into the quantum-coherent transport regime, which is facilitated by very cold (near millikelvin) temperatures, the charges pair up into entities called Cooper pairs, their motion becomes weakly correlated (the motion of one pair depends on the motion of the others), and charge flows without resistance. This is the behaviour that underlies the properties of superconductors and their charge-neutral analogues, superfluids. A carefully crafted, cold version of the common FET has been developed for studying coherent-transport dynamics by forming such superconductors in complex oxide layers cooled in conventional dilution refrigerators6 (Fig. 1c).

Figure 1: Quantum transport in field-effect transistors (FETs).

In a solid-state FET, an electrode called a gate, which is usually made of gold, generates an electric field that controls charge transport through a narrow channel between two reservoirs (source and drain). a, Partially coherent transport (orange) between quantum dots underlies a new generation of solar-cell materials3,4, and quantum-dot FETs could be used to control and study the transport dynamics. The dots, which are made of assemblies of atoms (here silicon), are bridged by a small organic molecule and placed on an insulating substrate. The small green atoms connect the molecule to the reservoirs. b, A quantum-interference FET (or QuIET) uses the wave-like nature of the electron (not shown) in different paths (orange arrows) through a single benzene molecule to control charge flow from source to drain5, both of which are made of gold. c, A FET based on a superconductor of electron pairs, formed at the interface of two oxides (lanthanum aluminate and strontium titanate), laid on a conducting substrate, at near-millikelvin temperatures6 can be used to explore coherent transport and quantum-phase transitions. d, Stadler and colleagues2 demonstrate a FET in which a laser beam serves as the device's gate and a magnetic field applied to the FET allows the interactions between ultracold atomic pairs to be tuned.

If the strength of the interactions between Cooper pairs is extreme, they become strongly correlated and the character of the system is fundamentally different. This is the regime of behaviour studied by Stadler and colleagues. The authors' FET is able to capture the dynamics of strongly correlated superfluids7.

Instead of working with charges directly, their apparatus is designed to study the motion of neutral atoms that pair up to make diatomic molecules in place of the Cooper pairs of electrons in a superconductor. Their quantum-coherent FET comprises a source and drain that contain a gas of fermionic lithium atoms (Fig. 1d). Fermions have half-integer spin and are exclusive — that is, identical fermions refuse to be in the same quantum state. Stadler et al. trap their fermionic atoms in laser and magnetic fields, and at sub-microkelvin, ultracold temperatures — 10-million-fold colder than the cosmic microwave background radiation of outer space. Whereas FETs in microprocessors are typically tens of nanometres in size and have charge-carrier velocities approaching 107 centimetres per second, Stadler and colleagues' FET is on the scale of tens of micrometres and operates with transport velocities of between 1 millimetre and a few centimetres per second.

Significantly, the authors' apparatus allows them to tune the attractive atomic interactions over many orders of magnitude, so that the transport behaviour can be made to transition from the weakly correlated dynamics of the superconductors in the cold oxide FETs to the regime of strongly correlated superfluidity in ultracold fermionic atoms. Furthermore, the relatively large size of the authors' FET allows them to view what is actually happening in the transport channel, by means of high-resolution in situ optical imaging. The usual techniques for directly observing atoms, which involve atomic-force microscopy, cannot view such dynamics: we cannot zoom in on a solid-state FET in action.

Strongly correlated quantum behaviour has also been observed in high-energy nuclear-physics experiments8,9,10,11 that create a state of matter known as a quark–gluon plasma, which is thought to have appeared shortly after the Big Bang. It has also been observed in ultracold quantum gases12,13. These two systems fall into the category of extreme quantum matter. Holographic duality14,15,16 (a technique originating from string theory) infers that such strongly interacting quantum systems are mathematically equivalent to weakly curved gravity in one higher spatial dimension than our usual space-time continuum of four dimensions. This extra dimension has the physical effect of acting as a 'zoom' on a quantum system. Holographic duality predicts that these strongly correlated systems approach a perfect fluid, having a ratio of viscosity to entropy density far lower than that of ordinary fluids7.

Stadler et al. thus offer a continuously tunable FET system that not only provides insight into quantum-coherent FET design, but also connects solid-state physics and extreme quantum matter in the new regime of quantum-coherent FET operation.


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Correspondence to Lincoln D. Carr.

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Carr, L., Lusk, M. Strongly correlated transport. Nature 491, 681–682 (2012). https://doi.org/10.1038/491681a

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