We construct quantum systems of many interacting electrons, one two-dimensional layer at a time. By tuning their structure, sometimes during the measurement itself, and their environment with fields and neighboring layers, we study the collective behavior that emerges.
Designer universes
How an electron moves through a solid is set by its surroundings: which atoms the solid contains, how those atoms are arranged, and the symmetries of that arrangement. Carbon shows how much this matters. Stacked in sheets as graphite, it conducts along its layers and shears apart easily. Locked into a three-dimensional network as diamond, it becomes a hard, transparent insulator. Isolated as a single sheet, graphene, it hosts electrons that behave as though they have no mass.
Atomically thin crystals let us choose all three ingredients ourselves. We peel single layers from bulk crystals such as graphite, boron nitride and transition-metal dichalcogenides, then stack them in any order and at any angle. A small twist between two layers produces a moiré pattern, a new periodic landscape roughly ten nanometers across or larger, made by hand. Each stack is a small designer universe, with rules that nature never assembled.
Quantum materials go a step further. When electrons interact strongly with one another, or when the geometry and topology of their wavefunctions matter, the whole system can do things no single electron can. They can carry current with zero resistance as a superconductor, order into a magnet, or host excitations that carry a fraction of an electron charge. These emergent states are the focus of our lab.
A guiding question
To what degree can the complete order parameter of a superconductor be reconstructed?
In a superconductor, electrons bind into pairs. The order parameter describes that pairing: how strongly electrons pair as a function of their direction of motion, and how the quantum-mechanical phase of the pairs changes around the Fermi surface. It is central to every theory of superconductivity, yet experiments rarely measure it completely. Two superconductors can have similar energy gaps and still differ in their phase structure, and that difference decides whether the pairing is conventional, unconventional or topological. Topological superconductors are sought as building blocks for quantum bits protected from noise.
Layered materials make this question newly accessible, because the pairing can be tuned while it is measured: by the density of electrons, by an applied electric field, and by the twist between layers. The same question applies to twisted semiconductors, graphene multilayers and other layered superconductors, touching on each of the directions below.
When do interactions and topology produce superconductivity?
In certain stacks of graphene layers, and in twisted semiconductors, the electrons' kinetic energy drops to the point that their mutual repulsion begins to dominate. The result is a crowded phase diagram: correlated insulators, magnetism in the electrons' spin and valley, superconductivity, and fractional Chern insulators, in which electrons without any applied magnetic field form a state with fractionally charged excitations. Gate electrodes above and below the device set the density of electrons and the electric field, moving a single device across this phase diagram.
We ask which of these neighboring states superconductivity grows out of, and whether a superconductor next to a topological state can inherit some of its topology. We measure with low-temperature electrical transport and with thermodynamic measurements of the chemical potential, which quantify the energy cost of adding each electron to the system.
Selected published work 6 papers
- Cascade of isospin phase transitions in Bernal-stacked bilayer graphene at zero magnetic field , Nature Physics (2022)
- Superconductivity and strong interactions in a tunable moiré quasicrystal , Nature (2023)
- Magic-angle helical trilayer graphene , Science Advances (2023)
- Topological bands and correlated states in helical trilayer graphene , Nature Physics (2025)
- Highly tunable junctions and non-local Josephson effect in magic-angle graphene tunnelling devices , Nature Nanotechnology (2021)
- Tuning Ising superconductivity with layer and spin–orbit coupling in two-dimensional transition-metal dichalcogenides , Nature Communications (2018)
What happens at the interface between two crystals, and how does it change with twist?
Most experiments on twisted materials fix the twist angle when the device is built, so studying how a property depends on twist means making a new device for every angle. In our scanning van der Waals microscope (SVM), one crystal is mounted on the tip of a scanning-probe cantilever and pressed against a second crystal on the sample stage. The probe then rotates, so the twist angle between the two crystals is tunable in a single device. Force feedback holds the crystals in contact, and electrodes on both sides of the interface measure how electrons tunnel across it, how charge redistributes between the two layers, and how the interface resists sliding, each as a continuous function of twist.
The SVM belongs to the same family of instruments as the quantum twisting microscope introduced by Shahal Ilani's group in 2023. Ours is built on a force-sensing cantilever platform and operates at room temperature, and a millikelvin version is under construction.
The SVM also serves our guiding question. A tunneling electrode rotating above a superconductor can sample its energy gap along different directions of electron motion, and a superconducting electrode in the same geometry can serve as a phase reference. Together these offer a route toward both the amplitude and the phase of the order parameter.
We are looking for students who enjoy designing and building instruments, especially electronics, ML/AI-assisted control software, and automated materials-handling hardware.
We are also looking for a postdoc with prior experience designing cryogenic scanning probe instrumentation.
Background: our earlier work on tunneling between 2D layers 3 papers
- Magnitude of the current in 2D interlayer tunneling devices , Journal of Physics: Condensed Matter (2018)
- Theory of resonant tunneling in bilayer-graphene/hexagonal-boron-nitride heterostructures , Applied Physics Letters (2015)
- Theory of graphene–insulator–graphene tunnel junctions , Journal of Vacuum Science & Technology B (2014)
Can we tune interactions from outside the material?
Electrons in a two-dimensional layer still live in three dimensions. They can feel their surroundings. Nearby metals and dielectrics screen the repulsion between them. Neighboring crystals can also introduce spin–orbit coupling and weak local strain through lattice relaxations. That makes the environment a second set of controls.
We use high-permittivity van der Waals dielectrics to modify screening in graphene multilayers. We study how that screening changes electric-field-induced phase transitions and whether it can tune superconductivity. We plan to use nearby metallic gates for stronger screening and, in the future, suspended devices to explore the weak-screening limit.
How we measure
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Electrical transport:
resistance and the Hall effect as functions of carrier density, electric field, magnetic field and temperature.
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Chemical potential and compressibility:
capacitance-based measurements of the energy needed to add electrons, a thermodynamic view of each electronic state.
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Tunneling spectroscopy:
the energy-resolved density of states, including superconducting gaps.
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The scanning van der Waals microscope:
interfaces whose twist angle and contact are controlled during the measurement.
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Cryogenic platforms:
a dilution refrigerator reaching 7 mK and a variable-temperature cryostat reaching 1.4 K, each with a 12 T superconducting magnet.
See our facilities for the instruments behind these measurements.
Joining the lab
Students in the lab build their own devices from start to finish: isolating atomically thin crystals, assembling them layer by layer with polymer stamps, patterning electrodes by electron-beam lithography, and measuring the finished devices near absolute zero. Many also build instruments. All students write the software that runs our measurements and analysis.
Current openings and how to apply are on our prospective students and postdocs page . Meet the current group on our people page .
Collaborations
We work with experimental and theory groups in Toronto, across Canada and around the world. We are part of the department's Quantum Condensed Matter Physics group , and Toronto has a large quantum community, including the Centre for Quantum Information and Quantum Control and the Centre for Quantum Materials .
Where we are heading
Over the next decade we aim to move from exploring the parameter space of quantum materials and discovering quantum states in layered materials to engineering them to generate certain properties on demand. Interfaces tuned continuously, measurements of both the amplitude and the phase of superconducting pairing, and control of interactions through the environment all point toward designing topological superconductors and confirming them directly, the kind of states quantum technologies protected by topology will need.