Paving the Way Towards 1D Helical Conductors with Fractional Quantum Statistics

In a letter published in the February 2017 issue of Nature Nanotechnology, Ben Hunt and his collaborators at the Massachusetts Institute of Technology, the University of California Santa Barbara, and the National Institute for Materials Science in Tsukuba, Japan describe how they engineered a graphene electron–hole bilayer device into a helical 1-dimensional (1D) conductor and characterized its transport properties. In a helical 1D conductor, electrons moving in opposite directions also have opposite spin polarizations, and such helical states can be obtained by combining two quantum Hall (QH) edge states with opposite spins and opposite momenta relative to the magnetic field (i.e. opposite chiralities).

To simultaneously realize those quantum Hall edge states with opposite spins and chiralities, the authors combined the properties of graphene (high electron and hole mobility and electron–hole symmetry) to that of a bilayer system in which a perpendicular electric field can induce different filling of each layer.

The authors therefore built a device consisting of two layers of graphene that are twisted with respect to each other (Left figure: two graphene layers with a relative twist angle θ). The twist causes the layers to have a reduced interlayer coupling relative to the “natural” (Bernal) stacking of bilayer graphene.

At a magnetic field of 1 T, a quantum Hall plateau sequence double that of monolayer graphene was observed, which indicated that the layers were degenerate. In fact, the misalignment induced only a very weak coupling that could not lift the degeneracy of the layers, and the system could therefore be modelled as two parallel conductors.

When a net voltage of zero is applied to the layers such that they are overall charge neutral, the conductance of the system is also zero: we have an insulating state similar to that observed in neutral monolayer graphene. If, however, a perpendicular electric field is applied while the system remains charge neutral, the top layer can be populated with electrons and the bottom layer will be left with an equal number of holes, naturally realizing QH states with opposite chirality in the top and bottom layers because of the opposite response of electrons and holes to the magnetic field. Moreover, in monolayer graphene, the state with a filling factor ±1 is thought to be spin polarized. Therefore, if the twisted bilayer graphene device behaves as two individual layers, it should be possible to create a pair of helical edge states with opposite chiralities and opposite spin polarizations by realizing coexisting ν = 1 and ν = −1 states. 

My colleagues at MIT came up with this ingenious way of producing helical edge states from two decoupled graphene layers, and then they proved their idea worked with a series of powerful transport experiments,” says Hunt. “I was thrilled to be able to make a contribution to the experiment by using capacitance measurements to help prove that the unique helical states they observe really are edge states.”

Characterizing the transport properties

The authors explored the transport properties of their device for different filling factors (Figure 2). Their measurements show that the (±1,∓1) filling state is conducting when the total applied voltage is zero, whereas other filling states are not. Moreover, backscattering between the two layers is nearly absent in the (±1,∓1) states, resulting in the measured conductive plateau.

LEFT: CONDUCTANCE MAP; THE (±1,∓1) STATE IS DEPICTED BY DASHED LINE; RIGHT: MAP OF POSSIBLE FILLING FACTOR COMBINATIONS

In addition, the non-local voltage response shows that the non-local resistance is exceptionally large, indicating that the (±1,∓1) states are neither normal chiral edge states nor diffusive conductors. In fact, the strong non-local resistance of the (±1,∓1) states signifies that current flows predominantly along the edge, with both forward and backward propagating modes equilibrating at the electrodes to give a voltage drop. The authors therefore conclude that at this filling factor, conduction occurs through a pair of QH edge states with opposite chiralities, and the result is a pair of helical edge states in the (±1,∓1) electron–hole bilayer.

Finally, the authors probed the low-field regime of the (±1,∓1) states. At a magnetic field, 1.5 T, the non-local resistance sharply increases from its initial value when no magnetic field is applied. This sharp increase is interpreted as the onset of conduction in the helical edge states at 1.5 T, a comparatively low field that is encouraging for future efforts to engineer topological superconductivity in this helical conductor.

Not only is this behavior encouraging, but also building 1D helical conductors from QH edge states would offer the possibility to extending the system to fractional edge states--in fact, the authors have observed the fractional QH effect in the high-quality devices. Those fractional QH states pave the way towards realizing a fractional quantum spin Hall state and go one step further towards fractional generalizations of Majorana fermions as a key component of fault-tolerant quantum information processing devices.