Charge-density wave fluctuation driven composite order in the layered Kagome Metals

The newly discovered kagome metals AV$_3$Sb$_5$ (A = K, Rb, Cs) offer an exciting route to study exotic phases arising due to interplay between electronic correlations and topology. Besides superconductivity, these materials exhibit a charge-density wave (CDW) phase occurring at around 100 K, whose origin still remains elusive. The robust multi-component $2 \times 2$ CDW phase in these systems is of great interest due to the presence of an unusually large anomalous Hall effect. In quasi-2D systems with weak inter-layer coupling fluctuation driven exotic phases may appear. In particular in systems with multi-component order parameters fluctuations may lead to establishment of composite order when only products of individual order parameters condense while the individual ones themselves remain disordered. We argue that such fluctuation-driven regime of composite CDW order may exist in thin films of kagome metals above the CDW transition temperature. We also find that the transition from the composite to individual CDW order is in the $\mathbb{Z}_3$ Potts universality class. Our findings suggest possible presence of exotic phases in the weakly coupled layered kagome metals, more so in the newly synthesized thin films of kagome metals.Comment: 7 pages, 3 figure

Anomalous softening of phonon-dispersion in cuprate superconductors

A softening of phonon-dispersion has been observed experimentally in under-doped cuprate superconductors at the charge-density wave (CDW) ordering wave vector. Interestingly, the softening occurs below the superconducting (SC) transition temperature T$_{c}$, in contrast to the metallic systems, where the softening occurs usually below the CDW onset temperature T$_{\text{CDW}}$. An understanding of the `anomalous' nature of the phonon-softening and its connection to the pseudo-gap phase in under-doped cuprates remain open questions. Within a perturbative approach, we show that a complex interplay among the ubiquitous CDW, SC orders and life-time of quasi-particles associated to thermal fluctuations, can explain the anomalous phonon-softening below T$_{c}$. Furthermore, our formalism captures different characteristics of the low temperature phonon-softening depending on material specificity.Comment: Supplementary include

Incipient loop current order in the under-doped cuprate superconductors

There are growing experimental evidence which indicate discrete symmetry breaking like time-reversal ($\mathcal{T}$), parity ($\mathcal{P}$) and C$_{4}$ lattice rotation in the pseudo-gap state of the under-doped copper-oxide based (cuprate) superconductors. The discrete symmetry breaking manifests a true phase transition to an ordered state. A detailed thermodynamic understanding of these orders can answer various puzzles related to the nature of the transition at the pseudo-gap temperature T$^*$. In this work, we investigate thermodynamic signature of $\mathcal{T-P}$ symmetry breaking considering superconductivity (SC) and bond-density wave (BDW) as two primary orders. The BDW can generate both modulating charge and current densities. This framework takes into account an intricate competition between the ubiquitous charge density wave and SC, which is prominent in various cuprates in the under-doped regime. We demonstrate that within mean-field approach of competing BDW and SC orders, a $\mathcal{T-P}$ breaking ground state of coexisting BDW and SC can be stabilized, provided the BDW itself breaks $\mathcal{T}-\mathcal{P}$. But this ground state ceases to occur at higher temperatures. However, we show that fluctuations in SC and BDW can drive emergence of a new unusual translational symmetry preserving order due to a preemptive phase transition by spontaneously breaking $\mathcal{T-P}$ at a higher temperature before the primary orders set in. We refer this order to be magneto-electric loop current (MELC) order. We present possible nature of phase transition for this new incipient MELC order and discuss some experimental relevance.Comment: To appear in Physical Review

Quantum criticality on a compressible lattice

The stability of a quantum critical point in the $O(N)$ universality class with respect to an elastic coupling, that preserves $O(N)$ symmetry, is investigated for isotropic elasticity in the framework of the renormalization group (RG) close to the upper critical dimension $d=3−ϵ$. With respect to the Wilson-Fisher fixed point, we find that the elastic coupling is relevant in the RG sense for $1≤N≤4$, and the crystal becomes microscopically unstable, i.e., a sound velocity vanishes at a finite value of the correlation length $ξ$. For $N>4$, an additional fixed point emerges that is located at a finite value of the dimensionless elastic coupling. This fixed point is repulsive and separates the flow to weak and strong elastic coupling. As the fixed point is approached the sound velocity is found to vanish only asymptotically as $ξ→∞$ such that the crystal remains microscopically stable for any finite value of $ξ$. The fixed point structure we find for the quantum problem is distinct from the classical counterpart in $d=4−ϵ$, where the crystal always remains microscopically stable for finite $ξ$

Quantum criticality on a compressible lattice

The stability of a quantum critical point in the $O(N)$ universality class with respect to an elastic coupling, that preserves $O(N)$ symmetry, is investigated for isotropic elasticity in the framework of the renormalization group (RG) close to the upper critical dimension $d=3-\epsilon$. If the elastic coupling is relevant in the RG sense, we find that the crystal becomes microscopically unstable, i.e., a sound velocity vanishes, at a finite value of the correlation length $\xi$. If the elastic coupling is irrelevant, an additional fixed point emerges that is located at a finite value of the dimensionless elastic coupling. This fixed point is repulsive and separates the flow to weak and strong elastic coupling. As the fixed point is approached the sound velocity is found to vanish only asymptotically as $\xi \to \infty$ such that the crystal remains microscopically stable for any finite value of $\xi$. The fixed point structure we find for the quantum problem is distinct from the classical counterpart in $d=4-\epsilon$, where the crystal remains always microscopically stable for finite $\xi$.Comment: 12 pages, 11 figure

Electronic Structure and Transport in Correlated and Complex Materials

This dissertation has two parts. The first part provides studies on superconducting systems. The electronic structure and superconducting gaps have been investigated in detail in the multi-orbital iron-based superconducting system with the help of experimental scanning tunneling microscopy results. The results provide quantitative information about the magnitude of the superconducting gaps and hence give important insight to the electron pairing mechanism in these materials. This work also shows that the Josephson current calculation provides a unique pathway to map the spatial variation of the magnitude and phase of the superconducting order parameter in iron-based superconductors in absence of magnetic field and in simple s-wave superconductors in presence of magnetic field. The second part of the dissertation contains study of nano-scale transport networks. This work shows the concept of equivalent resistor in coherent quantum regime through the establishment of Transport Equivalent Networks for various classes of transport networks. This work presents a unique direction for future nano electronics in terms of miniaturization of electronic-circuits

Competitor induced dissipation of carbon quantum dot based hierarchical vesicular self-assembly: A theranostic nanoplatform towards hypercholesterolemia

Hypothesis: Supramolecular self-assembly derived from amphiphilic molecules is one of the prime interests with the motivation to develop new building blocks to create different task-specific self-assemblies. Considering the emergent applicability of these self-aggregates across the globe, it would be necessary to develop an alternate technique for the manufacture of self-aggregates employing novel building blocks. Experiment: With this aim, we synthesized a palmitoyl moiety functionalized carbon quantum dot (FCQD). Interestingly, the synthesized FCQD was found to form a stable amphiphilic inclusion complex (βCD-FCQD) with the ‘host’ β-cyclodextrin (βCD). This amphiphilic βCD-FCQD complex was utilized as a building block to form a hierarchical vesicular self-aggregate (βCD-FCQD vesicle). Findings: This βCD-FCQD vesicle was successfully employed to detect cholesterol. Moreover, cholesterol lowering hydrophilic drug rosuvastatin loaded βCD-FCQD vesicle was found to be potential in regulation of cholesterol. This work is anticipated to encourage the construction of drug loaded self-assembly based formulation to achieve a way out towards graded combined treatment for cholesterol related disorder like hypercholesterolemia

Relating the physical properties of aqueous solutions of ionic liquids with their chemical structures

The physical properties of an aqueous solution of a macromolecule primarily depend on its chemical structure and the mesoscopic aggregates formed by many of such molecules. Ionic liquids (ILs) are the macromolecules that have caught significant research interests for their enormous industrial and biomedical applications. In the present paper, the physical properties, such as density, viscosity, ionic conductivity of aqueous solutions of various ILs, have been investigated. These properties are found to systematically depend on the shape and size of the anion and the cation along with the solution concentration. The ionic conductivity and viscosity behavior of the solutions do not strictly follow the Walden rule that relates the conductivity to the viscosity of the solution. However, the modified Walden rule could explain the behavior. A simple calculation based on the geometry of a given molecule could shed the light on the observed results