When Electrons Enter a Moiré Superlattice, They Freeze Into a Wigner Crystal Before They Can Flow

Electrons in a typical conductor are famously chaotic. Add a voltage, and they behave like a gas or a fluid, tumbling past atomic nuclei and colliding into one another as they stream toward the positive terminal.

At low densities, they do the opposite. They stop.

In 1934, Hungarian physicist Eugene Wigner calculated that if you lower the density of an electron gas enough, the electrostatic repulsion between the particles will completely dwarf their kinetic energy. To minimize their total energy, the electrons won't scatter or flow—they will lock into a rigid, periodic triangular array. They freeze into a solid made of pure charge.

For nearly nine decades, "electron ice" remained an elusive theoretical state. Transport measurements had dropped hints, but conventional tools like scanning tunneling microscopes (STMs) routinely destroyed the fragile electronic lattices they tried to measure. The electric field of a standard STM tip acts like a hot poker pushed into a snowflake.

In 2021, a research team led by Feng Wang and Michael Crommie at UC Berkeley and Lawrence Berkeley National Laboratory bypassed that limitation. By placing a graphene sheet above a semiconductor heterostructure to act as a non-invasive sensing layer, they captured direct spatial images showing that electrons inside a moiré superlattice freeze into a Wigner crystal long before reaching densities that permit metallic conduction.

The Architecture of Moiré Confinement

To slow electrons down enough for potential energy to conquer kinetic energy, the Berkeley group constructed a device using transition metal dichalcogenides (TMDs). They stacked an single-atom layer of tungsten disulfide ($\text_2$) over a single-atom layer of tungsten diselenide ($\text_2$).

Because the natural distance between atoms in tungsten disulfide differs slightly from that in tungsten diselenide, overlapping them creates a interference pattern—a moiré superlattice. This long-period pattern produces periodic electrostatic valleys spaced roughly tens of nanometers apart, roughly two orders of magnitude wider than the spacing between the individual atoms in the underlying crystals.

Inside this artificial potential landscape, the effective mass of the electrons increases substantially as they navigate the moiré landscape. Their quantum tunneling from site to site slows to a crawl. The moiré lattice essentially acts as an array of artificial traps.

When the team applied gate voltages to fill these traps at low electron fractions, the particles felt each other’s presence long before filling every available site. Electrostatic repulsion pushed them as far apart from each other as possible. The electrons organized themselves into a repeating, honeycomb-like arrangement.

They weren't bound to nuclear cores. They were bound to each other by pure Coulomb force.

Imaging Without Melting

The primary challenge in proving the existence of a Wigner crystal lies in the measurement apparatus itself. In a traditional scanning tunneling microscope, a sharp metallic tip hovers fractions of a nanometer above a surface, measuring the quantum tunneling current of electrons jumping between the tip and the sample.

When applied to an electron solid, the local electric field from the tip pulls the localized electrons out of their energy minima. The measurement destroys the object.

To solve this, Hongyuan Li and Shaowei Li, co-first authors of the 2021 study, developed a non-invasive sensing technique. They placed a monolayer sheet of graphene directly above the TMD moiré heterostructure, separated by a thin insulating layer of hexagonal boron nitride.

The graphene sheet served as a localized charge detector. Instead of injecting tunneling current directly into the delicate Wigner crystal below, the tip measured minute local charge variations induced in the graphene sheet. The graphene layer acted like photographic paper, holding a shadow image of the electron positions underneath without transferring energy into the underlying lattice.

When the researchers mapped the spatial signal, the output revealed an ordered, periodic lattice of localized charges matching the theoretical predictions for a Wigner crystal.

Measured.

Repulsion Before Conduction

The implications of the experiment extend beyond confirming a 1934 calculation. In standard band theory, a material's conductivity is governed by filling energy bands: empty bands insulate, partially filled bands conduct, and completely filled bands act as band insulators.

In a moiré superlattice under strong electronic interactions, this framework breaks down completely. As gate voltages gradually inject carriers into the device, the system does not smoothly transition into a Fermi liquid metal. Instead, at fractional filling factors—such as one-third or one-half electron per moiré unit cell—the mutual Coulomb repulsion forces the system into an insulating state.

The optical reflection and single-electron charging measurements demonstrated that the energy gap required to break these Wigner states apart is substantial. The electrons deliberately freeze into a rigid, non-conducting phase before reaching the carrier density required to form a conventional metal.

By tuning the back-gate voltage, the Berkeley researchers showed they could systematically melt the electron ice into a liquid phase or freeze it back into a crystal, providing a controlled platform for studying strongly correlated quantum matter without relying on high magnetic fields.

The real power of the TMD moiré platform is its mechanical simplicity. Rather than engineering complex magnetic fields or ultracold atomic traps to force electrons to interact, researchers can align two-dimensional sheets at precise angles, apply a voltage, and watch quantum mechanics do the rest.

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