Research
Research
Topology and interaction are cornerstones of quantum condensed matter physics. Whether individually, or together, they can lead to novel phases and unconventional responses (to external perturbations) in quantum many-particle systems. In our group, we theoretically study these phenomena in a variety of contexts. Current areas of interest are:
Twisted bilayer graphene and other moiré materials [details]
Unconventional quantum oscillations in insulators [details]
Quasi-flat-band-physics in a class of one-dimensional models [details]
Surface response in topological semimetals [details]
Quantum anomalies in beyond-Weyl systems [details]
Proximity effect in superconductor heterostructures [details]
Interacting ground states of moiré ladders [Phys. Rev. B, arXiv]
Anomalous Chiral Anomaly in Spin-1 Fermionic Systems [Phys. Rev. B, arXiv]
Twisted bilayer graphene (TBG) is formed when two graphene layers are placed on top of each other and mutually rotated by an arbitrary angle. This results in beautiful moiré patterns. The low-energy electronic properties of such systems can vary drastically with the orientation between the layers. For example, although individual layers have linear spectrum, at certain angles of rotation bands become almost flat! This implies that correlations will become strong: Recent experiments have indeed found correlation-driven phases such as superconductivity and Mott-like insulating states. Additionally, these systems also feature nontrivial topological properties. Our goal is to understand the interplay of these factors, and provide a common framework to understand them. The questions go beyond TBG—with the proliferation of new 2D systems in the post-graphene era, this is an area which holds a lot of promise for exciting new physics yet to be discovered.
Recent work: Effect of nonlocal interlayer hopping on wave function in twisted bilayer graphene [arXiv]
It is well known that Landau quantization in a magnetic field leads to discrete energy levels. In metals, as the magnetic field is changed, these levels cross the Fermi level periodically giving rise to oscillations in response functions, both transport (Shubnikov-de Haas) and thermodynamic (de Haas-van Alphen). An insulator, by definition, has no Fermi surface and is not expected to show these oscillations. Yet, with surprising recent observations of quantum oscillations in certain insulators, this canonical understanding has been challenged. We have worked in this direction to show how oscillations can appear without a Fermi surface and have explored the various ways these unconventional oscillations differ from their usual metallic counterparts. These have considered oscillations at the single-particle level. Our current efforts in this direction is to understand the effect of many-body interaction in these unconventional oscillations.
Recent work: Effect of many-body interaction on de Haas-van Alphen oscillations in insulators [arXiv]
We study the moiré ladder, a one-dimensional analogue of moiré superlattices, built from a two-leg ladder with modulated interleg coupling and magnetic flux. It hosts quasi-flat bands with their origin mimicking that of twisted bilayer graphene, but providing a simpler setting to study the interplay of topology, band flattening, and electronic correlations.
Recent work: Interacting ground states of moiré ladders [arXiv]
Topological materials are characterized by some topological invariant in the bulk that leads to nontrivial states on the surface. A question of interest is, what is the response of these surface states to an external electric field? In a topological insulator, because the bulk is gapped, one can directly start with the surface Hamiltonian to answer this question. The procedure, however, fails in topological semimetals, such as Weyl semimetals, where the bulk is not gapped. The goal is to formulate a surface response theory for such systems where the surface cannot be separated a priori from the bulk. We have recently developed a formalism to address this by considering the 3D system to be composed of 2D layers stacked on top of each other. The formalism is rather general and can then be extended to study response in other systems such as topological superconductors.
Recent work: Anomalous surface conductivity of Weyl semimetals [arXiv]
This work aims to understand how the notion of the chiral anomaly extends beyond ideal Weyl systems to more general settings with broken Lorentz symmetry. The goal is to clarify the connection between anomaly, topology, and observable transport when the standard relativistic framework no longer applies.
Recent work: Anomalous Chiral Anomaly in Spin-1 Fermionic Systems [arXiv]
This work aims to understand how superconductivity is modified in heterostructures through proximity and inverse proximity effects. In particular, we explore how symmetry breaking at interfaces can lead to nonreciprocal transport (Josephson diode effect), and how coupling to topological systems such as the SSH chain can suppress or reshape superconducting order near the boundary.
Recent work: Universal route toward a field-free electrically polarity-reversible Josephson diode [arXiv]