Hydrodynamic electron flow through a quantum Hall bar with chiral edge channels

Transport and collective behavior of quantum devices

Geometry across long and short times

At long times, transport in a metal is dominated by itinerant charge and the Drude response. At short times, interband motion and the quantum geometry of states near the Fermi surface re-enter. We develop a single geometric description that separates these channels and identifies spectral-weight ratios as lattice-scale probes.

Long and short time linear response of metals: a geometric approach (2026).

Long- and short-time response of continuum and lattice metals in the time and frequency domains

Hidden scales from lattice interference

Quantum geometry is not an abstract correction to band dispersion. Interband dipole fluctuations introduce new length and time scales that control dielectric response, optical absorption, collective motion, and the robustness of superconductivity. Our Perspective organizes these effects around the separation of scales that makes geometry experimentally visible.

Quantum geometry and the hidden scales in materials (Nature Reviews Physics, 2026).

Lattice interference creates a hidden quantum-geometric length scale in a material

Collective flow remembers the wavefunction

With the Basov Laboratory and collaborators, we use terahertz spacetime metrology to follow plasmons in mono- and bilayer graphene. The measured Drude weight exceeds the non-interacting value, especially at low density, showing that pseudospin dynamics of Dirac electrons can directly reshape a collective mode.

Plasmon dynamics in graphene (2026).

Preprint panel showing measured graphene plasmon propagation and its dispersion

Kinetic inductance as a pairing probe

Mary and collaborators in Kin Chung Fong's Quantum Wave-Matter group use microwave kinetic inductance to measure the penetration depth of the Weyl semimetal MoTe2. Power-law temperature dependence together with the nonlinear Meissner effect provides complementary evidence for nodal superconductivity.

Observing unconventional superconductivity via kinetic inductance in Weyl semimetal MoTe2 (2025).

Preprint result panels showing kinetic-inductance signatures of nodal superconductivity in Weyl-semimetal Td-MoTe2

The instantaneous response as a generating function

We formulate a time-dependent quantum geometric tensor for the zero-point motion of bound electrons. Its successive time derivatives organize conductivity sum rules and recover the optical mass, orbital angular momentum, dielectric response, and other geometric observables within one gauge-invariant framework.

Instantaneous response and quantum geometry of insulators (PNAS, 2025).

Published schematic of instantaneous quantum-geometric response in an insulator

Quantum geometry across material platforms

Our review with Jiabin Yu, Andrei Bernevig, Enrico Rossi, Päivi Törmä, and Bohm-Jung Yang connects quantum geometry to optical response, Landau levels, fractional Chern phases, superfluid weight, spin stiffness, excitons, and electron-phonon coupling.

Quantum geometry in quantum materials (npj Quantum Materials, 2025).

Figure 3 from the review Quantum geometry in quantum materials, showing geometric effects across material platforms

Measuring the metric in a step

A direct quantum-metric observable is hidden by energy denominators in ordinary conductivity. We show that relaxation from a constrained equilibrium implements the needed frequency integral: with the right step-like electric field, the response is directly proportional to the Brillouin-zone-integrated quantum metric.

Framework to measure quantum metric from step response (Physical Review Letters, 2025).

Published schematic showing how step response measures the integrated quantum metric

Geometric stiffness in an exciton condensate

In an interlayer exciton condensate, counterflow rigidity acquires a geometric contribution inherited from the underlying bands. The result connects quantum metric to a collective response and to the phase coherence of a directly testable many-body state.

Geometric stiffness in interlayer exciton condensates (Physical Review Letters, 2024).

Published figure showing the quantum-geometric contribution to interlayer exciton-condensate stiffness

Capacitance measures occupied-state geometry

Capacitance is not only an electrostatic property. In an insulator, polarization records the spread and geometry of the occupied quantum states, turning a familiar response coefficient into a probe of wavefunction structure.

The quantum geometric origin of capacitance in insulators (Nature Communications, 2024).

Published figure showing the quantum-geometric contribution to capacitance in an insulator

Hydrodynamic electron flow

With Shahal Ilani’s group and collaborators, we used local Hall-field imaging and kinetic theory to distinguish ballistic transport from viscous electron flow in graphene. The transverse electric field changes character across the crossover and exposes the formation of Poiseuille flow.

Visualizing Poiseuille flow of hydrodynamic electrons
Nature 576, 75–79 (2019).

Local imaging reveals how electron flow changes from ballistic motion at low temperature to a hydrodynamic profile once electron-electron collisions dominate. The measured Hall field provides a spatial marker of this crossover.

Published Hall-field profiles distinguishing ballistic and hydrodynamic electron flow in graphene

Ballistic and hydrodynamic magnetotransport in narrow channels
Physical Review B 100, 245305 (2019).

Weak-field magnetotransport separates ballistic and hydrodynamic motion through the curvature of the transverse electric field. The theory also identifies boundary peaks that appear when transport becomes nonlocal.

Published figure comparing transverse electric-field profiles and classical trajectories across ballistic and hydrodynamic transport regimes