A layered form of graphene shows a rare semimetal state with balanced electrons and holes that becomes a topological insulator when exposed to moderate magnetic fields.
(Nanowerk Spotlight) Semimetals attract attention because they occupy a narrow space between metal and insulator. In a metal, electrons move freely. In an insulator, electrons stay localized. A semimetal sits between these limits and has only a slight overlap of conduction and valence bands. This overlap allows electrons and positively charged holes to move at the same time.
Such systems have supported giant magnetoresistance in materials like tungsten ditelluride and bismuth, fluidlike electron transport in graphene, and phases where electrons and holes bind together.
Topological semimetals add to this picture by hosting band crossings that do not vanish under small disturbances. These features have made semimetals central to efforts to understand how symmetry, electronic structure, and interactions shape unusual states of matter.
But it has remained difficult to produce a semimetal that combines electrons and holes with strong interactions, topological properties, and broken time reversal symmetry in a stable and tunable form.
Layered forms of graphene have moved this field forward. When several graphene sheets are arranged in a rhombohedral pattern, the stacking shifts each layer slightly relative to the one below it.
Rhombohedral graphene is defined by this three-layer repeating pattern. It changes the low energy electronic structure so that the outer layers host very flat bands. A flat band means slow electrons, and slow electrons interact more strongly. Rhombohedral multilayer graphene has therefore revealed correlated insulating behavior, spontaneous symmetry breaking, and unconventional superconductivity.
When this type of graphene is placed on a transition metal dichalcogenide, it can also receive strong spin orbit coupling. Spin orbit coupling ties an electron’s spin to its motion. In the Ising form relevant here, the spin prefers to point perpendicular to the plane and becomes linked to the valley degree of freedom. Valleys are the two distinct momentum space corners where graphene’s low energy electrons reside.
As the number of graphene layers grows, higher order hopping terms reshape the flat band through a trigonal warping effect. This effect creates a semimetal with small electron and hole pockets that can be tuned with an electric field. That tunability makes rhombohedral multilayer graphene a strong candidate for realizing semimetals that break time reversal symmetry. A clear example of such a state, especially one that remains ungapped, had not been firmly identified.
A study in Advanced Materials (“Spin–Orbit‐Driven Quarter Semimetals in Rhombohedral Graphene”) fills this gap. It examines rhombohedral pentalayer graphene in contact with a thin layer of tungsten diselenide. The device is fully encapsulated by hexagonal boron nitride and controlled by top and bottom gates that adjust carrier density and electric displacement field.
Within this platform, the paper’s authors identify a semimetal at charge neutrality in which only one of the four possible spin and valley flavors remains active. This single flavor carries both electrons and holes. Transport measurements also reveal broken time reversal symmetry. The paper refers to this regime as a quarter semimetal. When a moderate magnetic field is applied, the same system transitions into a Chern insulator with Chern number equal to negative five.
The authors begin by mapping the resistance of the device as a function of carrier density and displacement field. They find an insulating layer antiferromagnetic state at small displacement field. In this state, electrons with opposite spins occupy opposite outer layers, while the overall fourfold spin valley degeneracy is preserved. At larger positive and negative displacement fields, the device enters layer polarized insulating phases. Between these insulating states lie metallic regions where the band structure changes.
A small electric field breaks the symmetry between the outer layers. Two of the four spin valley flavors then gain a small overlap between conduction and valence bands. This creates a semimetal. When tungsten diselenide is present, its Ising type spin orbit coupling splits the valley energies. One valley moves up in energy and the other moves down. At charge neutrality, the Fermi level crosses only one of the four original flavors. This produces the quarter semimetal, which carries electrons and holes that share a single spin and valley flavor.
Quantum oscillation measurements support this picture. At high density and zero displacement field, the oscillations show a fourfold degeneracy. When the device is tuned into the quarter metal regime, the pattern reveals a singlefold degeneracy instead. This reduction confirms that only one flavor sector participates in transport.
The Hall and longitudinal resistivities at charge neutrality display the behavior of a compensated semimetal. The Hall signal bends strongly with magnetic field and changes sign, and the longitudinal resistivity depends roughly on the square of the field. These features indicate that electrons and holes are both present.
The authors apply a two-carrier model, which treats electrons and holes as separate carriers with their own densities and mobilities. The fits yield densities of about 1.0×10¹¹ per square centimeter at low temperature and mobilities near 1.0×10⁴ square centimeters per volt second. As temperature falls, both carrier densities decrease while both mobilities increase. This matches the expectations for small electron and hole pockets.
The Hall response also contains an anomalous term that remains at zero field and produces a hysteresis loop. This signals internal magnetization. In the quarter semimetal, electrons and holes are valley polarized and carry orbital magnetic moments that arise from Berry curvature. Berry curvature describes how the phase of an electron’s wavefunction changes across momentum space and can create an effect similar to a magnetic field in that space. When spin orbit coupling lifts the valley degeneracy, the system favors one valley and breaks time reversal symmetry.
The anomalous Hall term shows a peak as temperature decreases. It grows as thermal fluctuations weaken from about 1.0×10¹ kelvin, then falls again at lower temperature. The paper explains this behavior as a balance between stronger magnetic order at low temperature and the reduced density of valley polarized carriers that carry the orbital moments.
A stronger magnetic field turns the quarter semimetal into a Chern insulator. Spin orbit coupling ties spin to valley, so the magnetic field shifts the valley energies in opposite directions through a valley Zeeman effect. One valley undergoes band inversion and the other becomes more strongly gapped.
At fields above about 8.0×10⁻¹ tesla, the Hall resistance rises sharply. Around 1.5×10⁰ tesla it forms a plateau near the value h divided by 5e², which signals a Chern number of negative five. The positions of resistance minima and Hall plateaus follow the expected relation between carrier density and magnetic field. In this insulating regime, the Hall resistance increases with cooling and then saturates, which is consistent with a stable energy gap.
The strength of the proximity induced spin orbit coupling depends on the twist angle between graphene and tungsten diselenide. Theory predicts strong coupling when the two crystals are misaligned by about 1.5×10¹ to 2.0×10¹ degrees.
The devices used in the study fall within this range. The authors compare their results to earlier work with tungsten disulfide and argue that tungsten diselenide helps stabilize the quarter semimetal in this geometry.
This work shows that rhombohedral pentalayer graphene with proximity induced spin orbit coupling can host a ferromagnetic semimetal built from a single spin valley flavor and that this semimetal can become a high Chern number insulator under moderate magnetic fields. The material platform combines tunable band structure, strong interactions, and flexible topology in a controlled way. These features create a setting suited for studying correlated electron hole phases, hydrodynamic transport, and fractional quantum anomalous Hall states that can emerge from semimetallic ground states.
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