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"Young, A. F."
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Tunable interacting composite fermion phases in a half-filled bilayer-graphene Landau level
Various fractional quantum Hall phases are observed in a new generation of bilayer-graphene-based van der Waals heterostructures, including an even-denominator state predicted to harbour non-Abelian anyons.
Graphene sandwich fills quantum phase gaps
In the past decade, graphene has emerged as an important platform for discovering exotic phases that can arise in the fractional quantum Hall regime. In this regime, electrons confined to two dimensions are subjected to high magnetic fields and the strong interactions form composite quasiparticles. Andrea Young and colleagues have developed an exceptionally high-quality platform for such studies. They encapsulate bilayer graphene in hexagonal boron nitride and sandwich the structure between graphite electronic gates. As a result, they can clearly resolve various fractional quantum Hall phases, including a sought-after 'even-denominator' state, which refers to the fraction of filling of the so-called Landau states that arise in a magnetic field and that are associated with plateaus of quantized conductance. This phase is of particular interest as it is predicted to harbour non-Abelian anyons as emergent quasiparticles, which have topological properties that could be used for storing quantum information.
Non-Abelian anyons are a type of quasiparticle with the potential to encode quantum information in topological qubits protected from decoherence
1
. Experimental systems that are predicted to harbour non-Abelian anyons include p-wave superfluids, superconducting systems with strong spin–orbit coupling, and paired states of interacting composite fermions that emerge at even denominators in the fractional quantum Hall (FQH) regime. Although even-denominator FQH states have been observed in several two-dimensional systems
2
,
3
,
4
, small energy gaps and limited tunability have stymied definitive experimental probes of their non-Abelian nature. Here we report the observation of robust even-denominator FQH phases at half-integer Landau-level filling in van der Waals heterostructures consisting of dual-gated, hexagonal-boron-nitride-encapsulated bilayer graphene. The measured energy gap is three times larger than observed previously
3
,
4
. We compare these FQH phases with numerical and theoretical models while simultaneously controlling the carrier density, layer polarization and magnetic field, and find evidence for the paired Pfaffian phase
5
that is predicted to host non-Abelian anyons. Electric-field-controlled level crossings between states with different Landau-level indices reveal a cascade of FQH phase transitions, including a continuous phase transition between the even-denominator FQH state and a compressible composite fermion liquid. Our results establish graphene as a pristine and tunable experimental platform for studying the interplay between topology and quantum criticality, and for detecting non-Abelian qubits.
Journal Article
Massive Dirac Fermions and Hofstadter Butterfly in a van der Waals Heterostructure
van der Waals heterostructures constitute a new class of artificial materials formed by stacking atomically thin planar crystals. We demonstrated band structure engineering in a van der Waals heterostructure composed of a monolayer graphene flake coupled to a rotationally aligned hexagonal boron nitride substrate. The spatially varying interlayer atomic registry results in both a local breaking of the carbon sublattice symmetry and a long-range moiré superlattice potential in the graphene. In our samples, this interplay between short-and long-wavelength effects resulted in a band structure described by isolated superlattice minibands and an unexpectedly large band gap at charge neutrality. This picture is confirmed by our observation of fractional quantum Hall states at ±5/3 filling and features associated with the Hofstadter butterfly at ultrahigh magnetic fields.
Journal Article
Direct measurement of discrete valley and orbital quantum numbers in bilayer graphene
The high magnetic field electronic structure of bilayer graphene is enhanced by the spin, valley isospin, and an accidental orbital degeneracy, leading to a complex phase diagram of broken symmetry states. Here, we present a technique for measuring the layer-resolved charge density, from which we directly determine the valley and orbital polarization within the zero energy Landau level. Layer polarization evolves in discrete steps across 32 electric field-tuned phase transitions between states of different valley, spin, and orbital order, including previously unobserved orbitally polarized states stabilized by skew interlayer hopping. We fit our data to a model that captures both single-particle and interaction-induced anisotropies, providing a complete picture of this correlated electron system. The resulting roadmap to symmetry breaking paves the way for deterministic engineering of fractional quantum Hall states, while our layer-resolved technique is readily extendable to other two-dimensional materials where layer polarization maps to the valley or spin quantum numbers.
The phase diagram of bilayer graphene at high magnetic fields has been an outstanding question, with orders possibly between multiple internal quantum degrees of freedom. Here, Hunt et al. report the measurement of the valley and orbital order, allowing them to directly reconstruct the phase diagram.
Journal Article
Evidence for a spin phase transition at charge neutrality in bilayer graphene
A quantum phase transition from an antiferromagnetic to a ferromagnetic state is now measured in graphene bilayers. This observation supports the idea that bilayer graphene can sustain counter-propagating spin-polarized edge modes in analogy to the quantum spin Hall effect seen in topological insulators.
The quantum spin Hall effect is characterized by spin-polarized counter-propagating edge states
1
,
2
,
3
. It has been predicted that this edge state configuration could occur in graphene when spin-split electron- and hole-like Landau levels are forced to cross at the edge of the sample
4
,
5
,
6
. In particular, a quantum-spin-Hall analogue has been predicted in bilayer graphene with a Landau level filling factor
ν
= 0 if the ground state is a spin ferromagnet
7
. Previous studies have demonstrated that the bilayer
ν
= 0 state is an insulator in a perpendicular magnetic field
8
,
9
,
10
,
11
,
12
,
13
,
14
, although the exact nature of this state has not been identified. Here we present measurements of the
ν
= 0 state in a dual-gated bilayer graphene device in a tilted magnetic field. We map out a full phase diagram of the
ν
= 0 state as a function of experimentally tunable in-plane magnetic field and perpendicular electric field. At large in-plane magnetic field we observe a quantum phase transition to a metallic state with conductance of the order of 4
e
2
/
h
, consistent with predictions for the ferromagnet.
Journal Article
Intrinsic quantized anomalous Hall effect in a moiré heterostructure
Quantum anomalous Hall effect—the appearance of quantized Hall conductance at zero magnetic field—has been observed in thin films of the topological insulator Bi 2 Se 3 doped with magnetic atoms. The doping, however, introduces inhomogeneity, reducing the temperature at which the effect occurs. Two groups have now observed quantum anomalous Hall effect in intrinsically magnetic materials (see the Perspective by Wakefield and Checkelsky). Serlin et al. did so in twisted bilayer graphene aligned to hexagonal boron nitride, where the effect enabled the switching of magnetization with tiny currents. In a complementary work, Deng et al. observed quantum anomalous Hall effect in the antiferromagnetic layered topological insulator MnBi 2 Te 4 . Science , this issue p. 900 , p. 895 ; see also p. 848 Transport measurements indicate quantized Hall conductance without a magnetic field. The quantum anomalous Hall (QAH) effect combines topology and magnetism to produce precisely quantized Hall resistance at zero magnetic field. We report the observation of a QAH effect in twisted bilayer graphene aligned to hexagonal boron nitride. The effect is driven by intrinsic strong interactions, which polarize the electrons into a single spin- and valley-resolved moiré miniband with Chern number C = 1. In contrast to magnetically doped systems, the measured transport energy gap is larger than the Curie temperature for magnetic ordering, and quantization to within 0.1% of the von Klitzing constant persists to temperatures of several kelvin at zero magnetic field. Electrical currents as small as 1 nanoampere controllably switch the magnetic order between states of opposite polarization, forming an electrically rewritable magnetic memory.
Journal Article
Electrical switching of magnetic order in an orbital Chern insulator
Magnetism typically arises from the joint effect of Fermi statistics and repulsive Coulomb interactions, which favours ground states with non-zero electron spin. As a result, controlling spin magnetism with electric fields—a longstanding technological goal in spintronics and multiferroics
1
,
2
—can be achieved only indirectly. Here we experimentally demonstrate direct electric-field control of magnetic states in an orbital Chern insulator
3
–
6
, a magnetic system in which non-trivial band topology favours long-range order of orbital angular momentum but the spins are thought to remain disordered
7
–
14
. We use van der Waals heterostructures consisting of a graphene monolayer rotationally faulted with respect to a Bernal-stacked bilayer to realize narrow and topologically non-trivial valley-projected moiré minibands
15
–
17
. At fillings of one and three electrons per moiré unit cell within these bands, we observe quantized anomalous Hall effects
18
with transverse resistance approximately equal to
h
/2
e
2
(where
h
is Planck’s constant and
e
is the charge on the electron), which is indicative of spontaneous polarization of the system into a single-valley-projected band with a Chern number equal to two. At a filling of three electrons per moiré unit cell, we find that the sign of the quantum anomalous Hall effect can be reversed via field-effect control of the chemical potential; moreover, this transition is hysteretic, which we use to demonstrate non-volatile electric-field-induced reversal of the magnetic state. A theoretical analysis
19
indicates that the effect arises from the topological edge states, which drive a change in sign of the magnetization and thus a reversal in the favoured magnetic state. Voltage control of magnetic states can be used to electrically pattern non-volatile magnetic-domain structures hosting chiral edge states, with applications ranging from reconfigurable microwave circuit elements to ultralow-power magnetic memories.
Non-volatile electrical switching of magnetic order in an orbital Chern insulator is experimentally demonstrated using a moiré heterostructure and analysis shows that the effect is driven by topological edge states.
Journal Article
Even-denominator fractional quantum Hall states at an isospin transition in monolayer graphene
In monolayer graphene, the two inequivalent sublattices of carbon atoms combine with the electron spin to give electrons a nearly fourfold degenerate internal isospin. At high magnetic fields, the isospin degeneracy increases the already large intrinsic degeneracy of the two-dimensional Landau levels, making low-disorder graphene systems a versatile platform for studying multicomponent quantum magnetism. Here, we describe magnetocapacitance experiments of ultraclean monolayer graphene devices in which a hexagonal boron nitride substrate breaks the symmetry between carbon sublattices. We observe a phase transition in the isospin system, which is marked by unusual transitions in odd-denominator fractional quantum Hall states for filling factors ν near charge neutrality and by the unexpected appearance of incompressible even-denominator fractional quantum Hall states at ν = ±1/2 and ν = ±1/4. We propose a scenario in which the observed states are multicomponent fractional quantum Hall states incorporating correlations between electrons on different carbon sublattices, associated with a quantum Hall analogue of the Néel-to-valence bond solid transition that occurs at charge neutrality.
Journal Article
Author Correction: Even-denominator fractional quantum Hall states at an isospin transition in monolayer graphene
In the version of this Article originally published, the sketch of ‘PSP’ in Fig. 1a was incorrect; it has now been replaced. Please see the correction note to compare the original and corrected figure.
Journal Article