Fractonic View of Folding and Tearing Paper: Elasticity of Plates Is Dual to a Gauge Theory with Vector Charges.

We offer a fractonic perspective on a familiar observation-a flat sheet of paper can be folded only along a straight line if one wants to avoid the creation of additional creases or tears. Our core underlying technical result is the establishment of a duality between the theory of elastic plates and a fractonic gauge theory with a second rank symmetric electric field tensor, a scalar magnetic field, a vector charge, and a symmetric tensor current. Bending moment and momentum of the plate are dual to the electric and magnetic fields, respectively. While the flexural waves correspond to the quadratically dispersing photon of the gauge theory, a fold defect is dual to its vector charge. Crucially, the fractonic condition constrains the latter to move only along its direction, i.e., the fold's growth direction. By contrast, fracton motion in the perpendicular direction amounts to tearing the paper.

Surprises in the t-J Model: Implications for Cuprates.

Many strongly correlated systems, such as the cuprate superconductors, have the interesting physics of low dimensionality and hence enhanced fluctuation effects. We perform an analysis of the t-J model in the slave boson formulation which accounts for strong correlations, focusing on fluctuation effects that have hitherto not received the attention they deserve. We find several interesting results including the instability of the d-wave superconducting state to internal phase fluctuations giving way to a time reversal broken d+is^{*} superconductor at low doping. This offers an explanation for some recent experimental findings in the cuprate superconductors, including the observation of nodeless superconductivity at low doping. We also suggest further experiments that can validate our claims. On a broader perspective, this work points to the importance of considering fluctuation effects in other two-dimensional strongly correlated systems opening up a plethora of possibilities.

Topological Insulators in Amorphous Systems.

Much of the current understanding of topological insulators, which informs the experimental search for topological materials and systems, is based on crystalline band theory, where local electronic degrees of freedom at different crystal sites hybridize with each other in ways that produce nontrivial topology. Here we provide a novel theoretical demonstration of realizing topological phases in amorphous systems, as exemplified by a set of sites randomly located in space. We show this by constructing hopping models on such random lattices whose gapped ground states are shown to possess nontrivial topological nature (characterized by Bott indices) that manifests as quantized conductances in systems with a boundary. Our study adds a new dimension, beyond crystalline solids, to the search for topological systems by pointing to the promising possibilities in amorphous solids and other engineered random systems.

Quantized edge modes in atomic-scale point contacts in graphene.

The zigzag edges of single- or few-layer graphene are perfect one-dimensional conductors owing to a set of gapless states that are topologically protected against backscattering. Direct experimental evidence of these states has been limited so far to their local thermodynamic and magnetic properties, determined by the competing effects of edge topology and electron-electron interaction. However, experimental signatures of edge-bound electrical conduction have remained elusive, primarily due to the lack of graphitic nanostructures with low structural and/or chemical edge disorder. Here, we report the experimental detection of edge-mode electrical transport in suspended atomic-scale constrictions of single and multilayer graphene created during nanomechanical exfoliation of highly oriented pyrolytic graphite. The edge-mode transport leads to the observed quantization of conductance close to multiples of G0 = 2e2/h. At the same time, conductance plateaux at G0/2 and a split zero-bias anomaly in non-equilibrium transport suggest conduction via spin-polarized states in the presence of an electron-electron interaction.

Cooling a band insulator with a metal: fermionic superfluid in a dimerized holographic lattice.

A cold atomic realization of a quantum correlated state of many fermions on a lattice, eg. superfluid, has eluded experimental realization due to the entropy problem. Here we propose a route to realize such a state using holographic lattice and confining potentials. The potentials are designed to produces a band insulating state (low heat capacity) at the trap center, and a metallic state (high heat capacity) at the periphery. The metal "cools" the central band insulator by extracting out the excess entropy. The central band insulator can be turned into a superfluid by tuning an attractive interaction between the fermions. Crucially, the holographic lattice allows the emergent superfluid to have a high transition temperature - even twice that of the effective trap temperature. The scheme provides a promising route to a laboratory realization of a fermionic lattice superfluid, even while being adaptable to simulate other many body states.

Continuum theory of edge states of topological insulators: variational principle and boundary conditions.

We develop a continuum theory to model low energy excitations of a generic four-band time reversal invariant electronic system with boundaries. We propose a variational energy functional for the wavefunctions which allows us to derive natural boundary conditions valid for such systems. Our formulation is particularly suited for developing a continuum theory of the protected edge/surface excitations of topological insulators both in two and three dimensions. By a detailed comparison of our analytical formulation with tight binding calculations of ribbons of topological insulators modelled by the Bernevig-Hughes-Zhang (BHZ) Hamiltonian, we show that the continuum theory with a natural boundary condition provides an appropriate description of the low energy physics.

Nature and properties of a repulsive Fermi gas in the upper branch of the energy spectrum.

We generalize the Noziéres-Schmitt-Rink method to study the repulsive Fermi gas in the absence of molecule formation, i.e., in the so-called "upper branch." We find that the system remains stable except close to resonance at sufficiently low temperatures. With increasing scattering length, the energy density of the system attains a maximum at a positive scattering length before resonance. This is shown to arise from Pauli blocking which causes the bound states of fermion pairs of different momenta to disappear at different scattering lengths. At the point of maximum energy, the compressibility of the system is substantially reduced, leading to a sizable uniform density core in a trapped gas. The change in spin susceptibility with increasing scattering length is moderate and does not indicate any magnetic instability. These features should also manifest in Fermi gases with unequal masses and/or spin populations.

Competition between antiferromagnetic and superconducting states, electron-hole doping asymmetry, and fermi-surface topology in high temperature superconductors.

We investigate the asymmetry between electron and hole doping in a 2D Mott insulator and the resulting competition between antiferromagnetism (AFM) and d-wave superconductivity (SC), using variational Monte Carlo calculations for projected wave functions. We find that key features of the T=0 phase diagram, such as critical doping for SC-AFM coexistence and the maximum value of the SC order parameter, are determined by a single parameter eta which characterizes the topology of the "Fermi surface" at half filling defined by the bare tight-binding parameters. Our results give insight into why AFM wins for electron doping, while SC is dominant on the hole-doped side. We also suggest using band structure engineering to control the eta parameter for enhancing SC.

Edge state magnetism of single layer graphene nanostructures.

We study edge state magnetism in graphene nanostructures using a mean field theory of the Hubbard model. We investigate how the magnetism of the zigzag edges of graphene is affected by the presence of other types of terminating edges and defects. By a detailed study of both regular shapes, such as polygonal nanodots and nanoribbons, and irregular shapes, we conclude that the magnetism in zigzag edges is very robust. Our calculations show that the zigzag edges that are longer than three to four repeat units are always magnetic, irrespective of other edges, regular or irregular. We, therefore, clearly demonstrate that the edge irregularities and defects of the bounding edges of graphene nanostructures do not destroy the edge state magnetism.

Electric-field induced instabilities and morphological phase transitions in soft elastic films.

We investigate the morphological transitions of surface patterns induced in a soft elastic film in the presence of an applied electric field by the linear stability analysis and simulations. The surface patterns emerge beyond a critical strength of the electric field and the pattern length scale is always nearly three times the film thickness, regardless of the precise pattern morphology and other physical parameters. Interestingly, the simulations show that the precise pattern morphology depends strongly on the film and the field parameters and can be classified into three broad morphological phases: columns, stripes, and cavities. By tuning the electric field and the gap distance, we show that transitions from one morphological phase to another can be induced as described by a morphological phase diagram for this phenomenon. We also study the conditions under which the transitions can be "glassy" or "hysteretic." In addition to uncovering the rich physics underlying these nearly two-dimensional morphological phase transitions, our simulations also suggest experiments and applications of this phenomenon in mesopatterning. In particular, simulations demonstrate the possibility of controlling the pattern morphology and alignment by using the electric-field induced instability in soft elastic films. Unlike the short range adhesive interactions which cannot be varied, the use of an electric field allows far greater flexibility in modulation and control of the pattern morphology and its height.

Factors influencing deformation stability of binary glasses.

A possible mechanism of strain accommodation in large deformation of glasses is crystallization; deformation stability is a measure of the resistance of glasses to crystallization. We study the effect of atomic size ratio and atomic stiffness parameter (related to the curvature of the interatomic potential) on deformation stability of binary glasses using molecular static simulations. The deformation stability of a glass is found to increase with increasing atomic size ratio and magnitude of the atomic stiffness, which is proportional to the bulk modulus of the pure crystalline system, as well as the ratio of atomic stiffnesses of constituent atoms. To understand the role of the above parameters on deformation stability, misfit energies of randomly substituted solid solution fcc crystals and glasses are compared for various atomic size ratios and atomic stiffness values. Unlike in fcc solid solution, the misfit energy of binary glasses is found to be insensitive to the atomic size ratio. It is also found that the packing fraction of glasses is insensitive to the atomic size ratio, consistent with the above result. Beyond a critical atomic size ratio, the misfit energy of fcc solid solution exceeds the energy of the glass, thus making the amorphous state completely stable to deformation induced crystallization. Our analysis shows that critical atomic size ratio decreases with increasing atomic stiffness which leads to an increase in the deformation stability of glasses.

Electronic phase separation and other novel phenomena and properties exhibited by mixed-valent rare-earth manganites and related materials.

Transition metal oxides, such as the mixed-valent rare-earth manganites Ln(1-x)AxMnO3 (Ln, rare-earth ion, and A, alkaline-earth ion), show a variety of electronic orders with spatially correlated charge, spin and orbital arrangements, which in turn give rise to many fascinating phenomena and properties. These materials are also electronically inhomogeneous, i.e. they contain disjoint spatial regions with different electronic orders. Not only do we observe signatures of such electronic phase separation in a variety of properties, but we can also observe the different 'phases' visually through different types of imaging. We discuss various experiments pertaining to electronic orders and electronic inhomogeneities in the manganites and present a discussion of theoretical approaches to their understanding. It is noteworthy that the mixed-valent rare-earth cobaltates of the type Ln(1-x)AxCoO3 also exhibit electronic inhomogeneities just as the manganites.

Coulomb interactions and nanoscale electronic inhomogeneities in manganites.

We study electronic inhomogeneities in manganites using simulations on a microscopic model with Coulomb interactions amongst two electronic fluids-one localized (polaronic), the other extended-and dopant ions. The long range Coulomb interactions frustrate phase separation induced by the large on site repulsion between the fluids. A single phase ensues which is inhomogeneous at a nanoscale, but homogeneous on mesoscales, with many features that agree with experiments. This, we argue, is the origin of nanoscale inhomogeneities in manganites, rather than phase competition or disorder effects.

Resonance energy transfer from a fluorescent dye to a metal nanoparticle.

A quantum mechanical theory of the rate of excitation energy transfer from a fluorescent dye molecule to the surface plasmonic modes of a spherical metal nanoparticle is presented. The theory predicts the distance dependence of the transfer rate to vary as 1/d(sigma), with sigma=3-4 at intermediate distances, in partial agreement with the recent experimental results. Förster's 1/d(6) dependence is recovered at large separations. The predicted rate exhibits nontrivial nanoparticle size dependence, ultimately going over to an asymptotic, a(3) size dependence. Unlike in conventional fluorescence resonance energy transfer, the orientational factor is found to vary between 1 and 4.

Effect of strain on the thermal conductivity of solids.

We present a systematic study of the effect of strain (equivalent to uniform pressure) on the thermal conductivity of an insulating solid. Following a theoretical analysis that uncovers the dependence of the thermal conductivity on temperature and strain, we present classical molecular dynamics calculations of the thermal conductivity. We find that the molecular dynamics results closely match the theoretical result.

Electronic phase separation in correlated oxides: the phenomenon, its present status and future prospects.

Many transition metal oxide materials of high chemical purity are not necessarily monophasic. Thus, single crystals of chemically pure rare earth manganites and cobaltates of the general formula Ln(1-x)A(x)MO(3) (Ln=rare earth metal, A=alkaline earth metal, M=Mn, Co) exhibit the phenomenon of electronic phase separation wherein "phases" of different electronic and magnetic properties coexist. Such phase separation, the length scale of which can vary anywhere between a few nanometers to microns, gives distinct signatures in X-ray and neutron diffraction patterns, electrical and magnetic properties, as well as in NMR and other spectroscopies. While the probe one employs to investigate electronic phase separation depends on the length scale, it is noteworthy that direct imaging of the inhomogeneities has been accomplished. Some understanding of this phenomenon has been possible on the basis of some of the theoretical models, but we are far from unraveling the varied aspects of this new phenomenon. Herein, we present the highlights of experimental techniques and theoretical approaches, and comment on the future outlook for this fascinating phenomenon.