My research in theoretical condensed matter physics focuses on two central themes: (i) superconductivity and (ii) quantum criticality. Below is a list of projects I have worked on within these subjects.
I. Superconductivity
- Fluctuation theory of superconductors.
The above Feynman diagrams give the ultraclean fluctuation response in the normal-state of a Fermi superfluid. They are gauge invariant, have no Meissner effect, and the total electrical conductivity, in this ultra-clean limit, is due to only the final diagram. The first diagram is known as "Aslamazov-Larkin", the second diagram is known as "Maki-Thompson", and the third and fourth diagrams are referred to as the "Density of states" contribution. Phys. Rev. B 98, 184504 (2018). - Eliashberg theory of superconductivity:
Eliashberg theory is an electron-phonon theory of superconductivity that incorporates a dynamical pairing function.
These are the self-consistent equations (in diagrammatic form) for Eliashberg theory. Phys. Rev. B 104, 014513 (2021). The pairing gap (phi) is frequency dependent, and this results in very interesting behaviour in the limit of weak electron-phonon interactions.
In particular, differences between weak-coupling Eliashberg theory and BCS theory can be found in the respective electrical conductivities, which is shown in the above figure. Commun. Phys. 6, 54 (2023). - Fulde-Ferrell superconductors:
Fulde-Ferrell (FF) and Larkin-Ovchinnikov (LO) superconductors have finite centre of mass momentum Cooper pairs. This type of inhomogeneous pairing usually occurs in the presence of an external magnetic field or a chemical potential imbalance between different spin species. Collective modes have important contributions in the superfluid response of such inhomogeneous systems.
This Feynman diagram shows one of the self-consistent equations to determine the collective modes (amplitude and phase modes) of a Fulde-Ferrell superfluid. Phys. Rev. B 95, 214501 (2017).
II. Spin liquids
- Three-dimensional quantum electrodynamics (QED3):
Spin liquids involve entanglement, fractionalization, and other many-body effects. The abelian spin liquid is a phase of matter described by gapless spinons interacting with a U(1) gauge field. This theory is known as QED3, and it forms a phase from which other spin liquid or antiferromagnetic states can emerge at the transition point.
The phase transition from an abelian spin liquid to a Z2 spin liquid is descirbed by QED3--Gross-Neveu Yukawa. The above Feynman diagrams arise in the computation of the correlation exponent for this theory. PRB 99, 195135 (2019). - Monopole operators in QED3--Gross-Neveu Yukawa:
In continuum free space, Maxwell's theory of electromagnetism contains a vector potential which takes values on the real line. On a lattice, however, the vector potential is periodic, and so one can incorporate gauge-invariant additions of integer multiples of 2pi to the vector potential. This leads to the notion of flux-insertion (or monopole) operators. These operators are important as they can potentially render a phase transition unstable. Thus, studying their scaling dimensions is an important problem to consider. PRX 12, 031012 (2022).
