arXiv subjects

Sanjoy K. Sarker

Publications and source records attributed to Sanjoy K. Sarker.

13 recordsLinked to original sources

arXiv2017

Complex Quasi-Two-Dimensional Crystalline Order Embedded in VO$_2$ and Other Crystals

Metal oxides such as VO$_2$ undergo structural transitions to low-symmetry phases characterized by intricate crystalline order, accompanied by rich electronic behavior. We derive a minimal ionic Hamiltonian based on symmetry and local energetics which describes structural transitions involving all four observed phases, in the correct order. An exact analysis shows that complexity results from the symmetry-induced constraints of the parent phase which forces ionic displacements to form multiple interpenetrating groups using low-dimensional pathways and distant neighbors. Displacements within each group exhibit independent, quasi two-dimensional order, which is frustrated and fragile. This selective ordering mechanism is not restricted to VO$_2$: it applies to other oxides which show similar complex order.

cond-mat.mtrl-sci↗

arXiv2017

Spin-charge split pairing in underdoped cuprate superconductors: support from low-$T$ specific heat

We calculate the specific heat of a weakly interacting dilute system of bosons on a lattice and show that it is consistent with the measured electronic specific heat in the superconducting state of underdoped cuprates with boson concentration $ρ\sim x/2$, where $x$ is the hole (dopant) concentration. As usual, the $T^3$ term is due to Goldstone phonons. The zero-point energy, through its dependence on the condensate density $ρ_0(T)$, accounts for the anomalous $T$-linear term. These results support the split-pairing mechanism, in which spinons (pure spin) are paired at $T^*$ and holons (pure charge) form real-space pairs at $T_p < T^*$, creating a gauge-coupled physical pair of charge $+2e$ and concentration $x/2$ which Bose condenses below $T_c$, accounting for the observed phases.

cond-mat.supr-con↗

arXiv2014

An effective Thermodynamic Description of Galactic Haloes

The observation of flat rotation curves in asymptotic region of galaxies implies that the dark matter density profile decreases exponentially with the gravitational potential in this region. It is curious that this behavior is identical to what one would have from a Boltzmann gas in thermal equilibrium. This suggests that an {\it effective} Boltzmann gas description of dark matter is possible for the halo, which follows even though no requirement of thermal equilibrium is assumed for the dark matter particles. We examine some qualitative and quantitative consequences of such an effective description. This is done by studying a simple model that takes into account gravitational self-interactions of dark matter and its gravitational interactions with the baryonic core. Solutions to the dynamics are determined by two parameters, one of which is the ratio of the dark matter mass to the effective temperature of the gas. Crude estimates can be made for these parameters based on observations.

astro-ph.GA↗

arXiv2014

Possible Evidence of Thermodynamic Equilibrium in Dark Matter Haloes

After deducing the density profiles and gravitational potential functions of eight galaxies from the rotation velocity data from THINGS, we find that the density decreases exponentially with the potential in substantial regions of the haloes. Such behavior is in agreement with that of a single-component isothermal Boltzmann gas, and suggests that an effective description in terms of a Boltzmann gas is possible for dark matter in these regions. This could be an indication that dark matter self-interactions are sufficient in strength and number to lead to thermal equilibrium in these regions. We write down the dynamics and boundary conditions for a Boltzmann gas description and examine some of its qualitative and quantitative consequences. Solutions to the dynamical system are determined by three dimensionfull parameters, and provide reasonable fits to the rotational velocity data in the regions where the Boltzmann-like behavior was found. Unlike in the usual approach to curve fitting, we do not assume a specific form for the dark matter density profile and we do not require a detailed knowledge of the baryonic content of the galaxy.

astro-ph.CO↗

arXiv2010

Charge pair hopping and Bose-Einstein condensation in underdoped Mott insulators

Recently, we have solved the long-standing problem of connecting the physics of the Mott insulator to the underdoped regime of the t-J model [PRB 82, 014504, 2010]. We have derived a renormalized Hamiltonian valid for small doping (x) which is characterized by a spin gap, and sublattice preserving hopping by a hole, and by a pair of holes, both accompanied by a spin-singlet backflow. The phase diagram obtained by continuing the spin states from half filling reproduces the phases of the cuprates. Remarkably, confinement of metallic conduction to 2d emerges from the theory (i.e., it is not assumed). Here we show that the Hamiltonian naturally leads to a pairing mechanism in which the pair has a dual character. Its spin part is a spinon singlet which (2d) condenses below T*. The charge part is a real-space holon pair formed at Tp < T*, which undergoes a (3d) Bose-Einstein condensation at Tc < Tp. While neither is observable separately, the combination is, as a well-defined excitation of momentum q, and energy w(q). The mechanism is consistent with the small superfluid density, the decline of Tc at small doping, and the existence of pairs above Tc in cuprates, as indicated by the observation of diamagnetism and Nernst effect.

cond-mat.supr-con↗

arXiv2008

Covalent Molecular Binding in a Susy Background

The Pauli Exclusion principle plays an essential role in the structure of the current universe. However, in an exactly supersymmetric (susy) universe, the degeneracy of bosons and fermions plus the ability of fermions to convert in pairs to bosons implies that the effects of the Pauli principle would be largely absent. Such a universe may eventually occur through vacuum decay from our current positive vacuum energy universe to the zero vacuum energy universe of exact susy. It has been shown that in such a susy universe ionic molecular binding does exist but homonuclear diatomic molecules are left unbound. In this paper we provide a first look at covalent binding in a susy background and compare the properties of the homonuclear bound states with those of the corresponding molecules in our universe. We find that covalent binding of diatomic molecules is very strong in an exact susy universe and the interatomic distances are in general much smaller than in the broken susy universe.

hep-th↗

arXiv2003

Spin-Charge Separation and Kinetic Energy in the t-J Model

I show that spin-charge separation in 2-D t-J model leads to an increase of kinetic energy. Using a sum rule, I derive an exact expression for the lowest possible KE (E_{bound}) for any state without doubly occupied sites. KE of relevant slave-boson and Schwinger-boson mean-field states -- which exhibit complete spin-charge separation -- are found to be much larger than E_{bound}. Examination of n(k) shows that the large increse in KE is due to excessive depletion of electrons from the bottom of the band (Schwinger boson) and of holes from the top (slave boson). To see whether the excess KE is simply due to poor treatment of the constraints, I solve the constraint problem analytically for the Schwinger boson case in the J = 0 limit. This restores gauge invariance, incorrectly violated in MF theories. The result is a generalized Hartree-Fock state of the Hubbard model, but one that includes spin waves. Even after constraints are imposed correctly, the KE remains much larger than E_{bound}. These results support the notion, advanced earlier [PRB 61, 8663 (2000)] that spin-charge separation in the MF state costs excessive KE, and makes the state unstable toward recombination processes which lead to superconductivity in d = 2 and a Fermi liquid state in higher dimensions.

cond-mat.str-el↗

arXiv2001

On Possible Coexistence of Superconductivity and Charge Density Wave in Hole Doped C$_{60}$

We study metallic behavior and superconductivity in C$_{60}$ materials in terms of a tight binding model characterized by an intramolecular, nonretarded attraction. It was shown previously that, at intermediate coupling, the model possesees a state in which s-wave superconductivity coexists with a charge density wave, the latter stabilized by intersite repulsion. The CDW causes $T_c$ to decrease near half filling. We examine the conditions under which such a state may exist in C$_{60}$. The key issue is the role of metallic screening which is treated in a parameter-free fashion. We show that screening is strong enough to stabilize a conventional (i.e., without a CDW) state in electron-doped C$_{60}$ and A$_3$C$_{60}$. But in hole-doped C$_{60}$, for which $T_c$ peaks away from half filling, a CDW-superconductor can not be ruled out. We discuss some normal state anomalies for such a state.

cond-mat↗

arXiv1999

Spin-Charge Binding Mechanism for Superconductivity in Cuprates

A spin-charge recombination route to superconductivity, proposed earlier (1992)], is examined using the Schwinger boson representation of the t-J model. The representation is known to work well at half-filling. It was shown in the earlier paper that, away from half filling, spin-charge recombination into electrons occurs directly through the hopping term as the system tries to recover the kinetic energy lost in forming the "spins" (magnetic moments). Recombination is strong enough in 2-D to (1) destroys long-range magnetic order and (2) restores the large Fermi surface. But the normal state remains incoherent, characterize by a Fermi liquid of holons and bosonic spinons which are paired into singlets. The singlets evolve out of half-filling and are responsible for the spin-gap behavior. They induce a pairing of holons and bind with the latter (to recover additional kinetic energy). In this paper we show that $d_{x^2-y^2}$ symmetry of the order parameter and the shape of the T_c vs doping curve, observed in cuprate superconductors, emerge naturally as a consequence of the symmetry of the spinon pairs. The latter symmetry (p-wave), however, is already determined at half-filling. Thus the nature of the superconducting state is intimately connected with that of quantum spin fluctuations in the insulator!

cond-mat↗

arXiv1997

Metal-Insulator Transition in Disordered and Interacting Systems

This paper is being withdrawn.

cond-mat↗

arXiv1997

Spin Gap and Superconductivity in the Interlayer Pair Tunneling Model

A simple interlayer pair tunneling is solved exactly. We find that in the normal state spin-1/2 particle and hole excitations are gapped. But the state is an unusual metal, characterized by novel fermionic spin zero and charge +2e and -2e excitations that exist about their own Fermi surfaces. The model is consistent with a number of properties of the underdoped cuprates. At finite temperature the Fermi surface appears partially gapped, and at high temperatures the spin gap disappears completely. Superconductivity is induced by an additional intralyer interaction which opens a gap in the charge-fermion spectrum. The symmetry of this charge gap (and hence that of the order parameter) is igenerally different from the symmetry of one-electron or - hole gap. The former can be a d wave, while the latter is more complex.

cond-mat↗

arXiv1995

Fermi Liquid - Non-Fermi Liquid Transition in the Double Exchange Model

Motivated by recent discovery of colossal magnetoresistance in La$_(1-x)$Ca$x$MnO$_3$ and other manganites, we have studied the double exchange model. We argue that the forced alignment of conduction-electron spin with the core spins that causes ferromagnetism also projects out a large part of the Hilbert space needed for coherent propagation of electrons carrying spin and charge. As a result, the electron becomes a composite object and its Green's function exhibits a two-fluid character: a coherent Fermi-liquid component associated with the ferromagnetically ordered core spins, and a non-Fermi liquid component associated with the disordered spins. With increasing temperature, there is continuous transfer of spectral weight from the Fermi liquid to the non-Fermi liquid component, until the former disappears above $T_c$. In an applied field spectral weight is transferred from the non-Fermi liquid to the component. Implications for the manganites are discussed.

cond-mat↗

arXiv1995

Confinement in the Three-dimensional Anisotropic $t$-$J$ Model

The normal-state resistivity of the cuprate superconductors is metallic in the $ab$ plane but is characteristic of an insulator along the $c$ direction, leading to the possibility of the remarkable phenomenon of confinement. By continuity, such a behavior is not expected to occur in a Fermi liquid. We consider the anisotropic $t$-$J$ model with the c-axis parameters $t_c$ and $J_c$ different from their in-plane counterparts, $t$ and $J$. Within the slave-fermion mean-field approximation it is shown that the spiral state exhibits charge-confinement in the intermediate $δ$ regime for a range of values of $t_c/t$. In the confined state the hopping amplitude $ = 0$ along the c direction so that c-axis resitivity is infinite at $T = 0$.

cond-mat↗