Our Research
Enigma of two-dimensional melting in a disordered environment
We study melting in a two-dimensional system of classical and quantum particles with short-range interactions in disordered environments. The clean system validates the conventional two-step melting described by KTHNY theory, with an exotic phase (called hexatic phase) intervening between the solid and the liquid. This picture gets significantly modified in the presence of disorder. Impurities in a random distribution of pinning centers force a hexatic-like low-temperature phase to extend up to zero temperature, which transits into the liquid at a single melting temperature. In contrast, pinning centers located at randomly chosen sites of a perfect crystal of the clean system anchor a solid at low temperatures, which undergoes a direct transition to the liquid at corresponding critical temperature. Thus, the two-step melting is lost in either case of disorder. Addressing dynamics across melting, we will demonstrate intriguing signatures of cooperative motion of particles in string-like paths found at low temperatures. Such motional footprints are being realized in equilibrium phases for the first time! We also explore their repercussions on various spatio-temporal correlations.
We also study quantum melting in a two-dimensional system of interacting "Boltzmann" quantum particles in clean and randomly pinned systems at zero temperature. The melting is driven by tuning the density of particles. Upon increasing the density from a minimal value, we find the system undergoes from a disordered liquid to an ordered solid state, which melts back to a disordered liquid state again at a large critical density, realizing a re-entrant quantum melting. The melting is tracked by the onset of positional and bond-orientational orders and from the peaks of their corresponding susceptibilities, whose behavior rules out any intervening hexatic phase. The implication of our findings in light of recent experiments are being investigated.
Reference:
Phys. Rev. E 109, L062101 (2024)
arXiv:2411.15654 (2024)
Paradigm For Superconducting Vortices with Non-metallic Cores
When a pristine and conventional type-II superconductor (SC) is exposed to an orbital magnetic field, the Abrikosov vortex lattice forms. These vortices feature a metallic core and define the standard paradigm of "vortices." Here, we show that many SCs of interest, beyond "pristine" or "conventional," depart from the above truism and often feature vortices with non-metallic cores. We study the phenomena associated with unconventional vortices, focusing primarily on the following three cases:
(a) A conventional type-II SC under simultaneous perturbations of disorder and magnetic field: For weak disorder, the critical field for suppressing the superconducting energy gap matches the critical field HC at which the superfluid density collapses. However, these two critical fields diverge from each other with increasing disorder, creating a large pseudogap region. Our phase diagram explains the disappearance of the celebrated Caroli-de Gennes-Matricon peak in the local density of states at the vortex cores of disordered SCs. We explore how spatial inhomogeneities evolve as a function of disorder and magnetic field. We also compare our predictions with those of a recent experiment. We have been carrying out similar exercises for unconventional SCs.
(b) A strongly correlated d-wave SC in the presence of an orbital field: The strong electronic repulsion at low doping promotes the formation of Mott insulating vortex cores, and consistently, the local density approaches half-filling in the core region. We show a non-monotonic variation of the vortex size as a function of doping in contrast with weak coupling descriptions. This causes an enhancement of the vortex region in the underdoped limit. The Mott-insulating vortex core has prominent effects on the local density of states, and our finding sheds light on the tunneling spectroscopic measurements in the vortex phase of cuprate superconductors.
(c) Charge modulation in the vortex halo of a SC: When an orbital magnetic field suppresses superconductivity, forming periodic vortices, subdominant orders can emerge in the vortex cores. Rather than competing with superconductivity, we find that the emergent charge order within the halo of a vortex makes superconductivity more robust by enhancing the upper critical field. We show that the spectral signatures from the Caroli-de Gennes-Matricon (CdGM) bound states in vortex cores track the charge modulation. The CdGM-like peak is found to shift toward the gap edge and oscillate from particle-to-hole bias from site to site, signaling charge modulation.
Please refer:
Phys. Rev. B 107, L140502 (2023)
Phys. Rev. B 111, 134519 (2025)
arXiv:2506.11195 (2025)
Interplay of superconductivity and competing orders in strongly correlated quantum matter: Novel aspects from non-equilibrium quenches
When a complex quantum material is suddenly pushed out of equilibrium, say, by a rapid change in temperature or coupling, it doesn't return to balance in a simple, uniform way. Instead, it often develops textures: islands of symmetry-broken order, fluctuating domains, and tangled patterns of charge modulation and/or pairing as observed in pump-probe experiments. These inhomogeneities are intimately connected to how the system relaxes, but they are averaged out in most of the current descriptions. Understanding these effects is the key to unlocking new ways to manipulate quantum matter. We are investigating how spatial inhomogeneities emerge and evolve during quantum quenches in conventional and strongly correlated superconductors, using a real-space, real-time self-consistent framework combined with von Neumann dynamics.
Please refer:
Reference Link
Tripartite Interplay of charge order and superconductivity in doped transition metal dichalcogenides
Transition metal dichalcogenides (TMDs) are a family of layered materials with ultra-high tunability, through doping, pressure, strain etc. There is a surge in the research interests involving TMDs, because they can be exfoliated to monolayer, yielding a true two-dimensional system like graphene, albeit more interesting due to stronger spin-orbit coupling in TMDs, for studying topological phases. They provide opportunities not only for testing fundamental physics in lower dimensions, but also open up possibilities of exciting applications to nano-devices. TMDs exhibit a unique combination of truly monolayer two-dimensional (2D) materials with the additional possibility of strong spin-orbit coupling that can lead to topological signatures, among other features. We are exploring the tripartite interplay of electronic correlations, inhomogeneities arising from disorder, and the topological effects from spin-orbit coupling on the correlated phases of TMDs.
Please refer:
Reference Link