arXiv subjects

N. Kumar

Publications and source records attributed to N. Kumar.

82 records · Page 5Linked to original sources

arXiv1998

Blocking of inter-subspace tunneling by intra subspace inelastic scattering

In recent years the notion of intrinsic decoherence and dephasing of a particle interacting with its environment is being investigated intensively. This has an important bearing on a plausible causal connection between incoherent c-axis resistivity and high-temperature superconductivity. In our work we study the tunnel supression and incoherent motion of a particle tunneling between two sites. The bosonic excitations of the environment are coupled to only one site inducing on-site spin flips. We show that this on-site spin flip scattering makes the tunnel motion incoherent. In the high-temperature limit incoherent rate or hopping rate has been calculated. We also briefly discuss the renormalization of the effective tunneling by environmental coupling at zero temperature following Wegner's renormalization group procedure.

cond-mat.supr-con↗

arXiv1998

Effect of Landauer's blowtorch on the equilibration rate in a bistable potential

Kinetic aspect of Landauer's blowtorch effect is investigated for a model double-well potential with localized heating. Using the supersymmetric approach, we derive an approximate analytical expression for the equilibration rate as function of the strength, width and the position of the hot zone, and the barrier height. We find that the presence of the hot zone enhances the equilibration rate, which is found to be an increasing function of the strength and width of the hot zone. Our calculations also reveal an intriguing result, namely, that placing the hot zone away from the top of the potential barrier enhances the rate more than when it is placed close to it. A physically plausible explanation for this is attempted. The above analytical results are borne out by detailed numerical solution of the associated Smoluchowski equation for the inhomogeneous medium.

cond-mat↗

arXiv1998

Geometric phase for a dimerized disordered continuum: Topological shot noise

Geometric phase shift associated with an electron propagating through a dimerized-disordered continuum is shown to be 0, or $\pm π$ (modulo 2$π$), according as the associated circuit traversed in the two-dimensional parameter space excludes, or encircles a certain singularity. This phase-shift is a topological invariant. Its discontinuous dependence on the electron energy and disorder implies a statistical spectral and conductance fluctuation in a corresponding mesoscopic system. Inasmuch as the fluctuation derives from the discreteness of the phase shift, it may aptly be called a topological shot-noise.

cond-mat↗

arXiv1998

C-axis resistivity and high Tc superconductivity

Recently we had proposed a mechanism for the normal-state C-axis resistivity of the high-T$_c$ layered cuprates that involved blocking of the single-particle tunneling between the weakly coupled planes by strong intra-planar electron-electron scattering. This gave a C-axis resistivity that tracks the ab-plane T-linear resistivity, as observed in the high-temperature limit. In this work this mechanism is examined further for its implication for the ground-state energy and superconductivity of the layered cuprates. It is now argued that, unlike the single-particle tunneling, the tunneling of a boson-like pair between the planes prepared in the BCS-type coherent trial state remains unblocked inasmuch as the latter is by construction an eigenstate of the pair annihilation operator. The resulting pair-delocalization along the C-axis offers energetically a comparative advantage to the paired-up trial state, and, thus stabilizes superconductivity. In this scheme the strongly correlated nature of the layered system enters only through the blocking effect, namely that a given electron is effectively repeatedly monitored (intra-planarly scattered) by the other electrons acting as an environment, on a time-scale shorter than the inter-planar tunneling time. Possible relationship to other inter-layer pairing mechanisms proposed by several workers in the field is also briefly discussed.

cond-mat.supr-con↗

arXiv1997

Normal state c-axis resistivity of high T_c cuprate superconductors

It is shown that a strong intraplanar incoherent scattering can effectively block the interplanar coherent tunneling between the weakly coupled planes of the highly anisotropic but clean (intrinsic) materials such as the optimally doped high-T_c layered cuprate superconductors. The calculated normal-state C-axis resistivity ρ_c(T) then follows the metal-like temperature dependence of the ab-plane resistivity ρ_{ab}(T) at high temperatures. At low enough temperatures, however, ρ_c(T) exhibits a non-metal like upturn even as ρ_{ab}(T) remains metallic. Moreover, in the metallic regime, ρ_c(T) is not limited by the maximum metallic resistivity of Mott-Ioffe-Regel. This correlation between the intrinsic ρ_c(T) and ρ_{ab}(T) is observed in the normal state of the high-T_c stoichiometric cuprates.

cond-mat.supr-con↗

arXiv1997

Hall angle in high-T_c cuprates: Anomalous temperature dependence and anisotropic scattering

The anisotropy of the scattering rates, 1/$τ_{tr} \propto T$ and 1/$τ_H \propto T^2$, implied effectively by the anomalous temperature dependence of the normal-state in-plane Hall angle, $\cot θ\propto T^2$, observed in the high-T$_c$ layered cuprates is reasoned out to be a natural consequence of the semiclassical Boltzmann transport equation with crossed electric (E) and magnetic (H) fields. It is argued that while the scattering rate 1/$τ_{tr}$ describes the longitudinal relaxation of the dipolar E-perturbations to the circular zero-field reference distribution function which is known to correspond to a non-Fermi liquid with 1/$τ_{tr} \propto T$, the scattering rate 1/$τ_H$ describes the transverse relaxation of the H-perturbations to the E-induced shifted reference distribution which is Fermi-liquid-like giving 1/$τ_H \propto T^2$. Incorporation of impurity scattering gives $\cot θ_H = aT^2 + b$ in agreement with the observed temperature dependence.

cond-mat.supr-con↗

arXiv1996

A note on magnetic-field induced level-density condensation in a two-dimensional electron gas with point scatterers

The density-of-states (DOS) for a magnetized (B) two-dimensional electron gas (2DEG) containing point scatterers of arbitrary strengths, concentration ($n_s$) and distribution is analyzed. It is shown from the first principles that for $n_s \leq B/Φ_o \equiv n_B$, the areal density of flux quanta $Φ_o \equiv hc/e$, the DOS retains the extensive degeneracy characteristic of the Landau levels, but reduced by a factor $(1 - {n_s}/{n_B})$. This elementary but exact result gives a level condensation for magnetic field $B > n_sΦ_o$, as first noted by Brézin {\em et al.}. Its implications for the Integral Quantum Hall Effect and for Random Matrix Theory are pointed out.

cond-mat↗

arXiv1996

Optimal barrier subdivision for Kramers' escape rate

We examine the effect of subdividing the potential barrier along the reaction coordinate on Kramers' escape rate for a model potential. Using the known supersymmetric potential approach, we show the existence of an optimal number of subdivisions that maximises the rate.

cond-mat↗

arXiv1996

Disorder and Integral Quantum Hall Effect

The quantum Hall conductance of a disordered two-dimensional gas of non-interacting electrons is re-examined for its integrity against disorder in the limit of no mixing between different Landau levels. The exact one-electron eigenstates of the disordered system are shown to be current carrying, with exactly the same Hall current as in the absence of disorder. There are no localized states. Accordingly, each extensively degenerate Landau level, now broadened out by the disorder, continues to contribute exactly one quantum of Hall conductance ($e^2/2π\hbar$). In the absence of any localized (non-current carrying) states, the Hall plateaus can now arise only through an actual gap in the density of states separating the broadened Landau levels. Implications for 2D localization are discussed.

cond-mat↗

arXiv1996

Statistics of Mesoscopic Fluctuations of Quantum Capacitance

The Thouless formula $G = (e^2/h)(E_c/Δ)$ for the two-probe dc conductance $G$ of a d-dimensional mesoscopic cube is re-analysed to relate its quantum capacitance $C_Q$ to the reciprocal of the level spacing $Δ$. To this end, the escape time-scale $τ$ occurring in the Thouless correlation energy $E_c = \hbar/τ$ is interpreted as the {\em time constant} $τ= RC_Q$ with $RG \equiv$ 1, giving at once $C_Q = (e^2/2πΔ)$. Thus, the statistics of the quantum capacitance is directly related to that of the level spacing, which is well known from the Random Matrix Theory for all the three universality classes of statistical ensembles. The basic questions of how intrinsic this quantum capacitance can arise purely quantum-resistively, and of its observability {\em vis-a-vis} the external geometric capacitance that combines with it in series, are discussed.

cond-mat↗