We are interested in multiple aspects of topology and symmetry in quantum systems. See below some research directions.

Classification of topological matter

Topological phases appear in many forms and shapes. We strive for a exhaustive understanding of the topology of condensed matter systems, studying novel phases, novel invariants and boundary signatures.

Disordered topological matter

Dirt and impurities are unavoidable in real physical systems. They break translation symmetry and invalidate Bloch's theorem. But can we still find order in disorder? Are there topological invariants that subside these harsh conditions?

Electron hydrodynamics

In different environments, electrons move through materials in drastically different ways. Sometimes, they can move like fluids through water pipes. But this is not so common, it requires a balance between electron-impurity and electron-electron scattering that can happen in certain temperature ranges in high-mobility materials like graphene. We study aspects of the transitions in transport regimes with changing conditions.


Quantum interference and spectroscopy

Quantum states are characterized by how they transform under the symmetries of materials, which implies strict constraints in how they interfere with each other, scatter from impurities or respond to local spectroscopic probes. We study how we can detect the symmetry and topological nature of quantum states in solid-state experiments.


Topological defects

Topology reflects how the collection of filled electrons transform under the symmetries of the crystal. They can often show robust vortices in momentum space, robust to any local perturbation in the material. How do we see these topological objects? By looking at real space lattice defects. Dislocations, edges, disclinations, vacancies. Lattice defects in topological materials bind robust electronic modes with unusual properties. 


Topological materials

Searching for new topological materials, with robust electron states ideal for physical applications requires a combined understanding of solid state chemistry, physics, and group theory. We adopt an interdisciplinary approach to find common threads between available materials and understand the mechanisms that bring about nontrivial topology in nature.

Topological quantum computation

Spatially confining topological bound states such as Majorana states or chiral modes in quantum devices implies creating quantum states that are unperturbed by local environment perturbations. This means a substantial decrease in quantum decoherence that haunts quantum computation technologies. We utilize topological materials to propose new robust quantum devices.


Twisted 2D materials

More is different? Yes! Two sheets of graphene behave completely differently than each one separately, with its physical properties immensely tunable with the layer mismatch. We study the topological nature of the resulting band structure of twisted graphene and other Van der Waals materials, and the resulting effects on electron-electron correlations and disorder scattering.


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For details and inquiries, don't hesitate to contact us.

> Postdocs: There are currently no funded open positions in the group. External funding opportunities are available externally: Simons Society of FellowsMarie Curie Global Fellowship, L'Oréal USA For Women in Science, contact me for joint applications.

> Graduate students: Apply and follow instructions through the Columbia graduate program

> Undergraduate students: We invite motivated Columbia undergraduates to join our research group for summer projects.