Partha Goswami

Dielectric properties of graphene on transition metal dichalcogenide substrate

The tunability of the dielectric properties induced by the substrate driven interactions (SDI) and the exchange field (M) due to the ferro-magnetic impurities in graphene monolayer on transition metal dichalcogenide (TMDC) (viz., XY2 , X = Mo, W; Y = S, Se) around K and K prime points is reported here. The cavalcade of interactions involve sub-lattice-resolved, strongly enhanced intrinsic spin-orbit couplings(SOC), the extrinsic Rashba spin-orbit coupling (RSOC), and the orbital gap related to the transfer of the electronic charge from graphene to XY2. The RSOC allows for external tuning of the band gap in graphene and connects the nearest neighbors with spin-flip. We obtain the usual gapped bands with an effective, RSOC-dependent Zeeman field due to the interplay of SDI. Using these bands we obtain the closed analytical expression of the dielectric function in the finite doping case. The zero of the dielectric function corresponds to the collective mode. Upon including the full dispersion of graphene on TMDC, we find that there is in fact only one collective mode and it corresponds to charge plasmons. The dispersion of the latter yields the q^2/3 behavior and not the well known q^1/2 behavior. We also find that the plasmon frequency could be changed by the tuning of the chemical potential.

Exponentiation problem in the construction of an effective low-momentum Hamiltonian for bosons

The problem of exponentiation of connected-graph contributionsC, when one carries out only a partial trace of the density matrix of an assembly of bosons in order to construct an effective, low-momentum Hamiltonian, is examined. It is found that besides accounting for the exponentiation of connected graphs, disconnected graphs contribute certain termsD to connected-graph contributions. TheD-terms diminish as the number of iterations increases in the Singh’s renormalization-group theory for the present system. Therefore, these terms play no role in determining critical behaviour of the system.

Fermions on the low-buckled honey-comb structured lattice plane and classical Casimir–Polder force

We start with the well-known expression for the vacuum polarization and suitably modify it for 2+1-dimensional spin–orbit coupled (SOC) fermions on the low-buckled honey-comb structured lattice plane described by the low-energy Liu–Yao–Feng–Ezawa (LYFE) model Hamiltonian involving the Dirac matrices in the chiral representation obeying the Clifford algebra. The silicene and germanene fit this description suitably. They have the Dirac cones similar to those of graphene and SOC is much stronger. The system could be normal or ferromagnetic in nature. The silicene turns into the latter type if there is exchange field arising due to the proximity coupling to a ferromagnet (FM) such as depositing Fe atoms to the silicene surface. For the silicene, we find that the many-body effects considerably change the bare Coulomb potential by way of the dependence of the Coulomb propagator on the real-spin, iso-spin and the potential due to an electric field applied perpendicular to the silicene plane. The computation aspect of the Casimir–Polder force (CPF) needs to be investigated in this paper. An important quantity in this process is the dielectric response function (DRF) of the material. The plasmon branch was obtained by finding the zeros of DRF in the long-wavelength limit. This leads to the plasmon frequencies. We find that the collective charge excitations at zero doping, i.e., intrinsic plasmons, in this system, are absent in the Dirac limit. The valley-spin-split intrinsic plasmons, however, come into being in the case of the massive Dirac particles with characteristic frequency close to 10 THz. Our scheme to calculate the Casimir–Polder interaction (CPI) of a micro-particle with a sheet involves replacing the dielectric constant of the sample in the CPI expression obtained on the basis of the Lifshitz theory by the static DRF obtained using the expressions for the polarization function we started with. Though the approach replaces a macroscopic constant by a microscopic quantity, it has the distinct advantage of the many-body effect inclusion seamlessly. We find the result that for the nontrivial susceptibility and polarizability values of the sheet and micro-particle, respectively, there is crossover between attractive and repulsive behavior. The transition depends only on these response functions apart from the ratio of the film thickness and the micro-particle separation (D/d) and temperature. Furthermore, there is a longitudinal electric field induced topological insulator (TI) to spin-valley-polarized metal (SVPM) transition in silicene, which is also referred to as the topological phase transition (TPT). The low-energy SVP carriers at TPT possess gapless (massless) and gapped (massive) energy spectra close to the two nodal points in the Brillouin zone with maximum spin-polarization. We find that the magnitude of the CPF at a given ratio of the film thickness and the separation between the micro-particle and the film are greater at TPT than at the TI and trivial insulator phases.

ON d+id DENSITY WAVE AND SUPERCONDUCTING ORDERINGS IN HOLE-DOPED CUPRATES

The d+id-density wave (chiral DDW) order, at the anti-ferromagnetic wave vector Q = (π, π), is assumed to represent the pseudo-gap (PG) state of a hole-doped cuprate superconductor. The pairing interaction U(k, k′) required for d+id ordering comprises of (Ux2-y2(k, k′), Uxy(k, k′)), where and with U1 > U2. The d-wave superconductivity (DSC), driven by an assumed attractive interaction of the form where V1 is a model parameter, is discussed within the mean-field framework together with the d+id ordering. The single-particle excitation spectrum in the CDDW + DSC state is characterized by the Bogoluibov quasi-particle bands — a characteristic feature of SC state. The coupled gap equations are solved self-consistently together with the equation to determine the chemical potential (μ). With the pinning of the van Hove-singularities close to μ, one is able to calculate the thermodynamic and transport properties of the under-doped cuprates in a consistent manner. The electron specific heat displays non-Fermi liquid feature in the CDDW state. The CDDW and DSC are found to represent two competing orders as the former brings about a depletion of the spectral weight (and Raman response function density) available for pairing in the anti-nodal region of momentum space. It is also shown that the depletion of the spectral weight below Tc at energies larger than the gap amplitude occurs. This is an indication of the strong-coupling superconductivity in cuprates. The calculation of the ratio of the quasi-particle thermal conductivity αxx and temperature in the superconducting phase is found to be constant in the limit of near-zero quasi-particle scattering rate.

Spectral weight below Tc at energies larger than the gap amplitude in hole-doped cuprates

An important hallmark of the strong coupling superconductivity(SC) is the depletion of the spectral weight below Tc at energies larger than the gap amplitude. We show this explicitly within the BCS framework for a twodimensional fermion system on a square lattice starting with a mean-field Hamiltonian involving the singlet id-density wave (DDW) order, assumed to correspond to the pseudo-gap (PG) state, favored by the electronic repulsion and the coexisting d-wave superconductivity (DSC) driven by an assumed attractive interaction.

Investigation of a CDDW Hamiltonian to Explore Possibility of Magneto-Quantum Oscillations in Electronic Specific Heat of Hole-Doped Cuprates

We investigate a chiral d-density wave (CDDW) mean field model Hamiltonian in the momentum space suitable for the hole-doped cuprates, such as YBCO, in the pseudogap phase to obtain the Fermi surface (FS) topologies, including the anisotropy parameter(𝜀) and the elastic scattering by disorder potential (|𝑣0|). For 𝜀=0, with the chemical potential 𝜇=−0.27 eV for 10% doping level and |𝑣0|≥|𝑡| (where |𝑡|=0.25 eV is the first neighbor hopping), at zero/non-zero magnetic field (𝐵), the FS on the first Brillouin zone is found to correspond to electron pockets around antinodal regions and barely visible patches around nodal regions. For 𝜀≠0, we find Pomeranchuk distortion of FS. We next relate our findings regarding FS to the magneto-quantum oscillations in the electronic specific heat. Since the nodal quasiparticle energy values for 𝐵=0 are found to be greater than 𝜇 for |𝑣0|≥|𝑡|, the origin of the oscillations for nonzero 𝐵 corresponds to the Fermi pockets around antinodal regions. The oscillations are shown to take place in the weak disorder regime (|𝑣0|=0.25eV) only.

Thermal and quantum fluctuations induced additional gap in single-particle spectrum of d–p model

The possibility of thermal and quantum fluctuations induced attractive interaction leading to a pairing gap Δtq in the single-particle spectrum of d–p model in the limit of a large N of fermion flavor is investigated analytically. This is an anomalous pairing gap in addition to the one with d-wave symmetry originating from partially screened, inter-site coulomb interaction. The motivation was to search for a hierarchy of multiple many-body interaction scales in high-Tc superconductor as suggested by recent experimental findings. The pairing gap anisotropy stems from more than one source, namely, nearest neighbor hoppings and the p–d hybridization, but not the coupling of the effective interaction. The temperature at which Δtq vanishes may be driven to zero by using a tuning parameter to have access to quantum criticality (QC) only when N⪢1. For the physical case N=2, the usual coherent quasi-particle feature surfaces in the spectral weight everywhere in the momentum below the pairing gap Δtq. Thus it appears that the reduction in spin degeneracy has the effect of masking quantum criticality.

Microscopic approach to critical behavior in /sup 3/He-/sup 4/He mixtures. II. Thermodynamics of the effective Hamiltonian

The thermodynamics of a weakly interacting fermion-boson mixture has been worked out on the basis of the effective Hamiltonian derived in an earlier paper. Tricritical-point behavior is discussed in terms of the fields (T,..mu../sub 3/,..mu../sub 4/). For the degenerate phase of the mixture, the theory reproduces the classical Landau expansion near a tricritical point. For the nondegenerate phase, the theory differs materially from the Landau theory; it predicts tricritical exponents in agreement with those calculated by applying renormalization-group theory to phenomenological models, and a slope for the upper line larger than that of the lambda line in the x-T plane.