Novel electronic states seen in graphene

A simple system made from two sheets of graphene has been converted from an insulator to a superconductor. The finding holds promise for opening up studies of an unconventional form of superconductivity.
Eugene J. Mele is in the Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.

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In two papers in Nature, Cao et al.1,2 report the discovery of new electronic ground states in twisted bilayer graphene — a pair of single-atom-thick sheets of carbon atoms, stacked with their honeycomb lattices rotated out of alignment. The authors interpret one of these states2 as a correlated Mott insulator, a non-conducting state produced by strong repulsive interactions between electrons. The other1 is a superconductor, a state of zero electrical resistance produced by effective attractive interactions between electrons. The insulator turns into the superconductor when a small number of charge carriers are added to the graphene. This connection between the states is unlikely to be a coincidence — as Sherlock Holmes might have commented, “the universe is rarely so lazy”.

Cao et al. show that the stacking of graphene sheets allows access to a new family of materials with electronic behaviours that are exquisitely sensitive to the atomic alignment between the layers, which affects interlayer electron motion. This finding might surprise physicists, because electronic behaviour is usually dominated by whichever of the associated processes has the largest energy scale. But, in this case, there’s a conundrum: the energy associated with electron motion between atoms within a layer is of the order of electronvolts, whereas the energy for electron motion between layers3 is, at most, hundreds of millielectronvolts.

The resolution to this conundrum is a matter of symmetry. Well-prepared, single layers of graphene are highly ordered systems whose electronic properties are determined by a subtle symmetry, which is encoded in a solid-state version of the Dirac equation describing low-energy excitations. These excitations are sensitive to interlayer couplings that alter the symmetries of the stack.

Interactions between electrons in these excitations can produce forms of matter generically described as being strongly correlated. A well-reasoned strategy for discovering such forms of matter has been to restrict intralayer electron motion by applying a strong magnetic field4. This generates narrow electron energy bands (Landau levels) in which electron–electron repulsion can control the physics of the graphene bilayer.

Cao et al. have taken a simpler tack to discover strongly correlated states. They used the rotational misalignment of graphene sheets to tune twisted bilayer graphene into a regime in which interactions between electrons can dominate the electronic states of the system. Such rotational misalignment forces the electronic band structures in the two sheets out of alignment and enlarges the bilayer’s unit cell (the smallest repeating unit of the crystal lattice) (Fig. 1a). For large rotations, the first effect completely dominates, and electron motion between layers is suppressed by a kinematic barrier5.

Figure 1 | The effects of rotation in twisted bilayer graphene. a, When a graphene bilayer is twisted so that the top sheet is rotated out of alignment with the lower sheet, the unit cell (the smallest repeating unit of the material’s 2D lattice) becomes enlarged. For large rotations, the electronic band structures of the two graphene sheets are also rotated out of alignment (not shown). b, For small rotation angles, a ‘moiré’ pattern is produced in which the local stacking arrangement varies periodically. Cao et al.1,2 have observed that, for rotation angles of less than 1.05°, regions in which the atoms are directly above each other (the lighter regions in the pattern) form narrow electron energy bands, in which electron ‘correlation’ effects are enhanced. This results in the generation of a non-conducting state2 (a Mott insulator), which can be converted into a superconducting state1 if charge carriers are added to the graphene system.

However, at very low rotation angles, a moiré pattern is produced by the misaligned lattices (Fig. 1b); the unit cell is greatly enlarged and so the effects of this come into play6,7. The misalignment of the band structure essentially disappears, and theory predicts that the low-energy electronic states are completely reconstructed7. Coupling between electrons in the different layers becomes strong, and new narrow bands emerge at certain ‘magic’ rotation angles below 1.05° when the bilayer system is close to charge neutrality. Electrons in these narrow bands are found mainly in regions of the moiré pattern in which the atoms are stacked directly above each other (the light regions in Fig. 1b). In these circumstances, the bilayer can be thought of as a synthetic, triangular lattice of weakly coupled quantum dots (tiny semiconductor particles that bind electronic states) with a residual tunnelling of electrons between them6.

Cao et al. fabricated twisted bilayer graphene so that the sheets are rotated at magic angles, and accumulated or depleted charge carriers in the system to study how the charge-transport properties of the system depend on the filling of the energy bands. The authors observed2 strong insulating behaviour when each unit cell of the synthetic lattice contained four charge carriers, a density that corresponds to complete filling of the bands. Intriguingly, they also find evidence for additional insulating states at lower densities in which the number of carriers per unit cell is an integer, but for which the narrow energy bands of the system are fractionally occupied. This suggests that the additional states are Mott insulating states, in which free motion of the carriers is prevented by their mutual repulsion, producing gridlock on the lattice. Mott insulators are a strongly correlated, non-conducting form of matter.

“Increasing the temperature at which superconductivity occurs could have phenomenal technological applications”

Even more intriguing is what happens when charge carriers are added to the Mott-insulator states associated with half-full unit cells of the synthetic lattice. The authors observe1 that the system enters a state that has zero electrical resistance below a critical temperature of approximately 1.7 kelvin, in a phase change known as a Berezinskii–Kosterlitz–Thouless transition, thus forming a 2D superconductor. This transition temperature is remarkably high, given the very low carrier density achieved in these measurements (1011 charge carriers per square centimetre). The high transition temperature and the apparent connection to correlated insulating states invites comparison of this superconducting state to that of a family of ‘unconventional’ superconductors8, which also have a close relationship with other strongly correlated electronic ground states. Twisted bilayer graphene might therefore be a useful experimental system in which to investigate the mechanism of unconventional superconductivity.

In the meantime, Cao and colleagues’ discoveries will stimulate a wave of activity as scientists seek to unwind the microscopic basis for the reported striking phenomena. The findings also demonstrate the promise of using twisted bilayer graphene as a flexible and tunable platform in which correlated electronic phenomena can be readily observed, and possibly even engineered and exploited9.

Nature 556, 37-38 (2018)


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