Research Highlights

Topological phases of Mott Insulators

The Hubbard operators are a powerful framework for analyzing topological phases in strongly correlated electrons. In Mott insulators, strong repulsive interactions prevent electron motion, which splits electrons into holon and doublon excitations. Topologically nontrivial behavior can arise when the doublon band of one orbital inverts with the holon band of another, resulting in a nontrivial winding of the Green’s function poles around the Brillouin zone, as illustrated in the accompanying animation. According to the bulk-boundary correspondence, such topological poles are associated with conducting edge states. Conversely, zeros in the Green’s function reflect the composite nature of the electronic degrees of freedom in a Mott insulator. When these zeros exhibit nontrivial winding across the Brillouin zone, a gapless, charge-neutral edge mode emerges, indicating an insulating boundary. This work is published in Physical Review B.

Vortex charge modulation enhances superconductivity

In superconductors, magnetic fields can create vortices that locally destroy the electron pairs responsible for superconductivity. The vortex cores generally behave like normal metals. However, the charge around vortices can form periodic patterns when the system is near a charge density wave state. Rather than competing with superconductivity, these charge modulations help protect it, allowing superconductivity to persist under stronger magnetic fields. This unexpected mechanism suggests a new way to enhance superconductivity in materials such as cuprates, flat-band moiré systems, and transition metal dichalcogenides. It also suggests mechanisms to enhance an important metric, the upper critical field, for designing superconducting magnets. Preprint.

Charge density waves as modulated Mott insulators

Understanding the behavior of complex materials, especially those where electrons interact strongly with each other, remains a major challenge. To tackle this, we developed a new approach that allows us to study how these systems behave when they are not uniform. Our method focuses on solving the local parts of the system exactly and uses a well-established technique to handle how electrons move. With this, we discovered a range of patterns that emerge when some electrons are removed (a process known as doping), including regions with alternating rich and poor concentrations of electrons. These patterns, known as charge-density waves, become less pronounced as more electrons are removed. Our work provides a clearer, more precise way to study these patterns and offers new insights into how and why they form. This work is published in Physical Review B.

Chiral to nematic superconductivity in 4Hb-TaS2

Most superconductors behave in a simple, uniform way that’s well explained by standard BCS theory. However, some rare materials show more complex superconducting behavior that breaks these expectations. In this study, we explore the unusual superconductor 4Hb-TaS2 using advanced microscopy and transport measurements. We discover directional patterns in its superconducting properties, including a two-fold symmetric critical field, suggesting a state that breaks rotational symmetry, known as nematic superconductivity. At the same time, we observe round, symmetric vortex cores, which seems contradictory. To resolve this, we develop a theoretical model that rules out conventional explanations and shows a competition between two types of superconductivity: a dominant chiral state and a weaker nematic state that appears near the transition to the normal phase. Our work provides strong evidence for two-component superconductivity in 4Hb-TaS₂ and reveals a transition from nematic to chiral behavior. This work is published in Nature Communications.

Insulating vortex cores in disordered superconductors

In typical superconductors, magnetic fields break superconductivity by creating vortex-like structures with metallic centers. As the field increases, these vortices multiply and overlap, turning the material into a metal. But a different process occurs in disordered superconductors: vortices with insulating centers form, and superconductivity fades in stages. The superconductor loses its long-range phase coherence and energy gap at separate field strengths, revealing an unusual insulating state where electron pairs survive strong magnetic fields in an insulating phase. The resulting phase diagram uncovers an array of intriguing phenomena, including gigantic magnetoresistance peaks of disordered superconducting films and the disappearance of key spectral features inside vortices. This work is published in Physical Review B (Letters).

Emergent superconductivity upon disordering a charge density wave

This study reveals how disorder affects the coexistence of superconductivity and charge density wave (CDW) order in a conventional BCS superconductor. As disorder increases, long-range CDW order breaks down, giving rise to domain walls—regions where charge modulations lose phase coherence. Remarkably, we find that these domain walls become favorable sites for the emergence of superconductivity, suggesting that disorder-induced inhomogeneity can promote superconducting order in systems with competing phases. This work is published in Physical Review B.

Proximity-induced charge density wave in a metallic system

In metal superconductor hybrid systems, the leaking of Cooper pairs to the metallic region induces superconducting correlations in a metal. Similarly, when a metal is placed in contact with a charge density wave CDW, periodic charge modulations can emerge in the metal due to the tunneling of finite-momentum particle-hole pairs from the CDW region. Upon hole-doping the metallic region, these initially commensurate modulations evolve into incommensurate patterns characterized by regular phase shifts. This CDW proximity effect has recently been observed in TaS₂/graphene heterostructures, highlighting a new route for engineering electronic order in layered materials.  This work is published in Physical Review B.

Distinguishing pair density wave states from the pairing modulations

The complex relationship between superconductivity and charge density waves (CDWs) gives rise to two intriguing possibilities. In one scenario, the presence of a CDW order makes superconducting pairing modulate spatially, while still maintaining an overall average pairing. In a more exotic alternative, the CDW and superconducting orders combine to form pair density wave (PDW), where the superconducting pairs themselves are modulated in space but the average pairing strength is zero. Distinguishing between these two states is difficult using standard experimental techniques. To address this, we performed theoretical calculations involving Josephson junctions and developed specific predictions that can help identify the correct scenario. Notably, we found that in the PDW case, the ac-Josephson current may display multiple frequency components—a signature not present in the simpler coexistence case. This work is published in Physical Review B.