Research

Emergent phases often occur when electronic kinetic energy is comparable to Coulomb interactions. One way to identify material systems that host these phases is by achieving localization of electronic wavefunctions due to the geometric frustration inherent in the crystal structure, leading to flat electronic bands. Recently, such efforts have uncovered a variety of exotic phases in two-dimensional (2D) kagome lattices and three-dimensional (3D) pyrochlore lattices, including magnetic order, time-reversal symmetry breaking charge order, nematicity, and superconductivity. Many such phases occur due to a cooperation between correlations and topology in flat band systems known as Obstructed Correlated Phases. Therefore, it is crucial to search for materials that can exhibit these functional properties. 

The T-symmetry broken charge density wave ordered phase or the DW_t phase is an example of an Obstructed Correlated Phase (OCP) that emerges due to a cooperation between topological obstruction and strong correlations.  Here the spin and charge degrees of freedom are entwined by topology.

The question of whether and how topological phases can be defined in the absence of a quasiparticle picture is an outstanding problem. A suitable and extreme platform where this occurs is when the single particle Green's function vanishes (zeros of the Green's function).  We recently introduced a framework to diagnose topology in strongly correlated electron systems, particularly focusing on Mott insulators . We were able to  define a Green's function Berry curvature, which is frequency-dependent, and demonstrated that this approach can identify topological phases even when traditional methods fail. The key result is the quantization of Berry flux at the zeros of the Green’s function, providing a new way to classify topological phases in correlated materials. This method opens the door for computational searches for topological materials, particularly those with strong electron correlations.

Spatially uniform superconducting (SC) order formed from Cooper pairs with zero center-of-mass momentum is the energetically favored ground state in the conventional theory of Bardeen, Cooper and Schrieffer (BCS).   On the other hand, a non-uniform order with non-zero center-of-mass momentum Cooper pair can occur in the presence of explicit time-reversal symmetry breaking from an external magnetic field. Such a modulated order parameter can also be realized in the presence of time-reversal symmetry; termed  pair-density waves (PDWs), these states are generated spontaneously and posited to exist in a variety of systems, including kagome lattice materials and high-temperature cuprate superconductors. Currently, there is no known robust and generic mechanism, numerical or analytical, for why such modulated pairing is favored over a homogeneous superconductor spontaneously.  This is despite widespread experimental evidence for fluctuating and static pair density waves in cuprates, Kagome metals and transition metal dichalcogenides. Some of our recent works have attempted to address mechanisms for non-uniform superconductivity both static and fluctuating

We recently investigated the role of shot noise Fano factor in understanding the properties of strongly correlated metals, specifically focusing on the heavy fermion compound YbRh₂Si₂. We developed a theoretical framework using the Boltzmann-Langevin equation to describe shot noise in diffusive metals under strong electron correlations. Our findings revealed that the observed suppression of the Fano factor in experiments suggests a loss of quasiparticles, challenging traditional quasiparticle descriptions in these systems. The study opens avenues for further exploration of shot noise as a diagnostic tool to characterize correlated metals like the Weidemann-Franz Law

A key consequence of Dirac monopoles  in an electronic band structure is obstruction to superconducting pairing -- lack of a smooth representation of the superconducting  gap function across the Brillouin zone. This occurs despite the existence of topologically trivial bands that dominate the superfluid density. Iron superconductors (FeSCs) such as Fe(Se,Te),  LiFeAs and CaKFe$_4$As$_4$ are known to exhibit intriguing topological properties such as surfaces states, hinge modes and possibly Majorana fermions. Several of these properties can occur due to Dirac monopoles in the electronic structure.  One of the objectives of this project is to explore the character of the low-energy excitations, pairing symmetry and derive other experimental consequences to superconductivity in the presence of non-abelian monopole obstruction in Iron based superconductors. 

Recent proton irradiation experiments (M. Leroux et al., (2018)) on the cuprate superconductor La2-xBaxCuO4 (LBCO)  observe a disorder induced increase in $T_c$ even when the transition temperature of the proximate charge density wave (CDW) is unaffected by the presence of irradiation. This observation cannot be explained by standard theories of $T_c$ enhancement via disorder as they all rely on competition between two different mean field phases. Recently, my work on enhancing superconducting $T_c$ via glassy behavior (https://journals.aps.org/prb/abstract/10.1103/PhysRevB.99.144523) and dissipation shows a possible and interesting manner in which one can raise $T_c$ without requiring a `tug-of-war' -like scenario between two competing phases. This opens up a new avenue to enhance superconductivity via collective disorder and lots of intriguing problems on the interplay between superconductivity and glassy phases of matter can now be addressed.

Instabilities of the Fermi Surface, like superconductivity and density waves, are well-known in condensed matter physics. Our recent work (Phys. Rev. B 2020, 2021) explores instabilities on a Luttinger Surface, where zeros of the many-body Green function occur. Unlike Fermi surface pairing, we find a zero-temperature superconducting transition with a non-zero attractive potential, occurring at a critical interaction strength. The "normal state" is a non-Fermi liquid (NFL) with a power-law van-Hove singularity, and in strong coupling, the fluctuation thermodynamics of the NFL phase resemble models with gravity duals, such as Sachdev-Ye-Kitaev (SYK) models.

These results suggest that order-parameter fluctuations link Mott physics with SYK-like models. This connection raises questions about electron diffusion near the NFL-SC quantum critical point on a Luttinger surface, the impact of scalar impurities on electronic transport, and whether cuprate transport phenomena, like fractional $\omega^{-2/3}$ behavior in optical conductivity, can be explained by pair fluctuations on Luttinger surfaces.

 The 11 Iron chalcogenide family, especially FeSe, has shown many intriguing electronic and thermodynamic properties. Amongst these is the recently observed large zero temperature residual specific heat in ultra-clean samples of FeSeS. This phenomenon cannot be explained by point or line nodes as their co-dimensinality with the original fermi surface is non-zero. A couple years ago,  researchers  proposed that  multiband  unconventional  superconductors could exhibit Bogoliubov Fermi surfaces, defined as finite areas of the normal state Fermi surface left ungapped in the superconducting state, provided time reversal symmetry is broken.  While this research  focussed  primarily  on  the  realization  of  such  states  in  higher  total  spin  pair  systems,  a similar phenomenon should appear in multiband systems with spin-1/2 pairs, e.g.  the iron-based superconductors, in the presence of spin-orbit coupling (see our recent work on these ``Ultranodal" superconductors https://arxiv.org/abs/1903.00481).  Such a state can lead to finite residual Sommerfeld coefficient in the zero temperature limit, as for a disordered nodal superconductor, but occurring even in the pure case. Another possibility is phase related frustration effects in multiband systems which can linger at the lowest temperatures; the thermodynamic properties of such a system needs further investigation. 

Ultrafast time-resolved pump-probe X-ray/optical spectroscopy has recently emerged as a powerful tool for probing ground states and their excitations. A few years ago, in collaboration with the Beijing group (IOP), we demonstrated (Physical Review B, 92(14), 140504) that the phase of coherent phonon oscillations can detect pairing symmetry in superconductors. Specifically, we found that a sign-changing gap function in the Brillouin zone causes a $\pi$ phase jump in Iron pnictides. However, nematic fluctuations present in the pnictide phase diagram could complicate this picture. Our goal is to use pump-probe coherent phonon experiments to explore the interplay between nematicity, unconventional superconductivity, and other collective modes. The first step involves understanding how charged nematic fluctuations independently couple to phonons, which can be modeled as a system of coupled, driven harmonic oscillators. This coupling could significantly impact the phase behavior of coherent phonons in the presence of unconventional superconductivity.

Twisted bilayer systems are created by rotating one layer of an AB stacked bilayer around a specific lattice point. Earlier studies have shown that bilayer graphene with a small twist angle exhibits an insulating state at certain densities and superconductivity with a dome shape similar to that seen in copper-oxide and iron-based materials. This occurs near the so-called "first magic angle," making it remarkable that the high Tc phase diagram can be reproduced from two non-interacting sheets of carbon. Key questions include the nature of the superconductivity and insulating state, and how two non-interacting systems can create a complex phase diagram with strongly correlated phases. In a recent paper (Nano Letters, 2018), we argued that the insulating state might be a Wigner crystal rather than the initially proposed Mott insulator, but the effects of pressure, temperature, and magnetic field remain unresolved. Since then many other exotic platforms for studying twisted bilayer systems have been proposed including Transition Metal Dichalcogenides which are continuing to be explored. 

Exploring exotic superconductivity near topological states of matter is a promising research area. Recently, more topological materials, like line-nodal semimetals and nodal knot semimetals, have been proposed, but their electronic, transport, and optical properties remain largely unexplored. Building on our recent work on d-wave superconductivity on the surface of a line-nodal semimetal (Physical Review B, 95, 140202), we aim to study the impact of link and knot invariants on impurity-bound states in these topological phases near superconductivity. Additionally, new methods like entanglement entropy could help characterize these topological behaviors.

QPI pattern for a d-wave superconductor on the surface of a linenodal semimetal