Research

Overview

I study the collective behavior of a statistically large number of particles in a setting where their quantum nature dominates the physics. More specifically, I am interested in the topological phases of matter and phase transitions involving them. Topological phases are states of matter with a finite energy gap for excitations and cannot be deformed to a trivial product state without a phase transition. My research focuses on the physics of phases that fundamentally involve quenched disorder (impurities at random locations) and/or interactions between particles such as Coulomb repulsion.

Quantum Hall to Insulator Transitions

Quantum Hall effect is one of the earliest topological phenomenon to be discovered in experiments and recognized so. It is observed in a system composed of electrons confined to two-dimensions moving under the influence of a large perpendicular magnetic field. During my Ph.D., I worked on the theory of phase transitions between quantum Hall and insulating phases. They are a set of paradigmatic quantum critical points between topologically non-trivial and trivial phases. Both interactions and disorder are important, making it challenging but a fundamental open problem in condensed matter physics.

We proposed an alternate dual description of such transitions using the framework of composite-fermion theory. The composite-fermion is an emergent particle obtained by binding an even number of vortices to an electron. A significant result of our construction is that all abelian quantum Hall transitions are in the same universality class - a conjecture rooted in experiments but had so far eluded theoretical understanding. Further, the dynamics are crucially altered by the Coulomb repulsion between electrons. Future research in this field would be focused on studying the regime where the conductivities are close to the quantum scale, i.e. σ ~ e²/h.

Phase transitions out of FQH states

We have recently found a phase transition in the first Landau level between a Laughlin-like FQH state and a stripe phase that contains periodic modulations of the electron density. The transition is continuous and takes place between a topologically ordered and a conventionally ordered state. It is tuned by introducing anisotropy, for example, by tilting the magnetic field towards the plane of electrons. Previous experiments are consistent with this scenario, however, a more conclusive evidence could be provided by future numerical simulations under realistic conditions.

Our study is motivated by a broad question: what continuous transitions can occur out of the topologically ordered states to other topological and/or conventional spontaneous symmetry breaking phases? Previously, a spontaneous phase change from a FQH to nematic state has been proposed to take place upon tuning the interactions between electrons. Obtaining the critical scaling properties of these transitions remains an exciting future problem for both theory and experiment.

Excitations of Quantum Hall Phases

More recently, I have been interested in the dynamical properties of topological phases that go beyond the ground state physics. Using state of the art time-evolution techniques based on matrix-product states, we computed the neutral excitation spectra of quantum Hall phases. For example, at the celebrated Laughlin fractional quantum Hall state obtained at filling fraction ν=1/3, we found dipole-like excitations called magneto-rotons that are bound states of charge e/3 and -e/3 quasi-particles.

Our main achievement was at ν=1/2 where, for the first time, we confirmed the emergence of low-energy composite-fermions to a quantitative degree, going beyond the previous qualitative studies. Moreover, we have found multiple low energy excitations at ν=2/5 making it a richer fractional quantum Hall state compared to the one at ν=1/3. In future, it would be interesting to look at non-abelian phases such as the Moore-Read state where an exotic supersymmetry, between the bosonic roton and the neutral fermion, could emerge at long wavelengths. Moreover, how interactions affect the dynamics near the integer quantum Hall to insulator transition in the presence of disorder, is an exciting avenue to explore.