Measurement setup for the simultaneous determination of diffusivity and Seebeck coefficient in a multi-anvil apparatus Rev. Sci. Instrum. 83, 093903 (2012) Relationship between structure, magnetism, and thermoelectricity in CePd3Mx alloys J. Appl. Phys. 112, 063709 (2012) The microstructure network and thermoelectric properties of bulk (Bi,Sb)2Te3 Appl.The effective medium theory of thermal conductivity of two-phase composites studied by Nan et al. has been extended to investigate concentrated nanocomposites. Due to the presence of inter-particle phonon scattering processes in concentrated nanocomposites, the effective lattice thermal conductivity k eff varies more rapidly with the volume fraction of second-phase inclusions in the composite. Applying the new k eff expressions to monolithic material systems, the results are found to capture the experimental trend of monolithic nanostructured materials. In particular, it is noted that the dimensionless figure of merit, ZT, is nearly doubled by only reducing the lattice thermal conductivity. Two-phase nanocomposites have also been evaluated, demonstrating that these latter systems are very suited for high thermoelectric performance. Present study leads to several strategies for obtaining ZT $ 2 or higher in nanocomposites.

We present here a theory of fractional electricity and magnetism which is capable of describing phenomenon as disparate as the non-locality of the Pippard kernel in superconductivity and anomalous dimensions for conserved currents in holographic dilatonic models. While it is a standard result in field theory that the scaling dimension of conserved currents and their associated gauge fields are determined strictly by dimensional analysis and hence cannot change under any amount of renormalization, it is also the case that the standard conservation laws for currents, dJ = 0, remain unchanged in form if any differential operator that commutes with the total exterior derivative, [d,Ŷ ] = 0, multiplies the current. Such an operator, effectively changing the dimension of the current, increases the allowable gauge transformations in electromagnetism and is at the heart of Nöther's second theorem. However, this observation has not been exploited to generate new electromagnetisms. Here we develop a consistent theory of electromagnetism that exploits this hidden redundancy in which the standard gauge symmetry in electromagnetism is modified by the rotationally invariant operator, the fractional Laplacian. We show that the resultant theories all allow for anomalous (nontraditional) scaling dimensions of the gauge field and the associated current. Using the Caffarelli/Silvestre(Caffarelli and Silvestre, 2007) theorem, its extension(Nave and Phillips, 2019) to p-forms and the membrane paradigm, we show that either the boundary (UV) or horizon (IR) theory of holographic dilatonic models are both described by such fractional electromagnetic theories. We also show that the non-local Pippard kernel introduced to solve the problem of the Meissner effect in elemental superconductors can also be formulated as a special case of fractional electromagnetism. Because the holographic dilatonic models produce boundary theories that are equivalent to those arising from a bulk theory with a massive gauge field along the radial direction, the common thread linking both of these problems is the breaking of U (1) symmetry down to Z 2 . We show that the standard charge quantization rules fail when the gauge field acquires an anomalous dimension. The breakdown of charge quantization is discussed extensively in terms of the experimentally measurable modified Aharonov-Bohm effect in the strange metal phase of the cuprate superconductors.

We calculate the optical conductivity using several models for unparticle or scale-invariant matter. Within a Gaussian action for unparticles that is gauged with Wilson lines, we find that the conductivity computed from the Kubo formalism with vertex corrections yields no non-trivial deviation from the free-theory result. This result obtains because at the Gaussian level, unparticles are just a superposition of particle fields and hence any transport property must be consistent with free theory. Beyond the Gaussian approach, we adopt the continuous mass formulation of unparticles and calculate the Drude conductivity directly. We show that unparticles in this context can be tailored to yield an algebraic conductivity that scales as ω −2/3 with the associated phase angle between the imaginary and real parts of arctan σ 2 σ 1 = 60 • as is seen in the cuprates. Given the recent results [1][2][3] that gravitational crystals lack a power-law optical conductivity, this constitutes the first consistent account of the ω −2/3 conductivity and the phase angle seen in optimally doped cuprates. Our results indicate that at each frequency in the scaling regime, excitations on all energy scales contribute. Hence, incoherence is at the heart of the power-law in the optical conductivity in strongly correlated systems such as the cuprates.

Motivated by the overwhelming evidence some type of quantum criticality underlies the power-law for the optical conductivity and T −linear resistivity in the cuprates, we demonstrate here how a scale-invariant or unparticle sector can lead to a unifying description of the observed scaling forms. We adopt the continuous mass formalism or multi band (flavor) formalism of the unparticle sector by letting various microscopic parameters be mass-dependent. In particular, we show that an effective mass that varies with the flavor index as well as a running band edge and lifetime capture the AC and DC transport phenomenology of the cuprates. A key consequence of the running mass is that the effective dynamical exponent can differ from the underlying bare critical exponent, thereby providing a mechanism for realizing the fractional values of the dynamical exponent required in a previous analysis [1]. We also predict that regardless of the bare dynamical exponent, z, a non-zero anomalous dimension for the current is required. Physically, the anomalous dimension arises because the charge depends on the flavor, mass or energy. The equivalent phenomenon in a d + 1 gravitational construction is the running of the charge along the radial direction. The nature of the superconducting instability in the presence of scale invariant stuff shows that the transition temperature is not necessarily a monotonic function of the pairing interaction.