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Register a new userQuantum multifractality in thermal conduction across random interfaces
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Self-affine morphology of random interfaces governs their functionalities across tribological, geological, (opto-)electrical and biological applications. However, the knowledge of how energy carriers or generally classical/quantum waves interact with structural irregularity is still incomplete. In this work, we study vibrational energy transport through random interfaces exhibiting different correlation functions on the two-dimensional hexagonal lattice. We show that random interfaces at the atomic scale are Cantor composites populated on geometrical fractals, thus multifractals, and calculate their quantized conductance using atomistic approaches. We obtain a universal scaling law, which contains self-similarity for mass perturbation, and exponential scaling of structural irregularity quantified by fractal dimension. The multifractal nature and Cantor-composite picture may also be extendable to charge and photon transport across random interfaces.
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Statistical properties of critical wave functions at the spin quantum Hall transition are studied both numerically and analytically (via mapping onto the classical percolation). It is shown that the index $eta$ characterizing the decay of wave function correlations is equal to 1/4, at variance with the $r^{-1/2}$ decay of the diffusion propagator. The multifractality spectra of eigenfunctions and of two-point conductances are found to be close-to-parabolic, $Delta_qsimeq q(1-q)/8$ and $X_qsimeq q(3-q)/4$.
We present an ultra-high-precision numerical study of the spectrum of multifractal exponents $Delta_q$ characterizing anomalous scaling of wave function moments $<|psi|^{2q}>$ at the quantum Hall transition. The result reads $Delta_q = 2q(1-q)[b_0 + b_1(q-1/2)^2 + ...]$, with $b_0 = 0.1291pm 0.0002$ and $b_1 = 0.0029pm 0.0003$. The central finding is that the spectrum is not exactly parabolic, $b_1 e 0$. This rules out a class of theories of Wess-Zumino-Witten type proposed recently as possible conformal field theories of the quantum Hall critical point.
The statistical properties of wave functions at the critical point of the spin quantum Hall transition are studied. The main emphasis is put onto determination of the spectrum of multifractal exponents $Delta_q$ governing the scaling of moments $<|psi|^{2q}>sim L^{-qd-Delta_q}$ with the system size $L$ and the spatial decay of wave function correlations. Two- and three-point correlation functions are calculated analytically by means of mapping onto the classical percolation, yielding the values $Delta_2=-1/4$ and $Delta_3=-3/4$. The multifractality spectrum obtained from numerical simulations is given with a good accuracy by the parabolic approximation $Delta_qsimeq q(1-q)/8$ but shows detectable deviations. We also study statistics of the two-point conductance $g$, in particular, the spectrum of exponents $X_q$ characterizing the scaling of the moments $<g^q >$. Relations between the spectra of critical exponents of wave functions ($Delta_q$), conductances ($X_q$), and Green functions at the localization transition with a critical density of states are discussed.
The needs for efficient heat removal and superior thermal conduction in nano/micro devices have triggered tremendous studies in low-dimensional materials with high thermal conductivity. Hexagonal boron nitride (h-BN) is believed to be one of the candidates for thermal management and heat dissipation due to its novel physical properties, i.e. thermal conductor and electrical insulator. Here we reported interfacial thermal resistance between few-layer h-BN and its silicon oxide substrate using differential 3 omega method. The measured interfacial thermal resistance is around ~1.6*10-8 m2K/W for monolayer h-BN and ~3.4*10-8 m2K/W for 12.8nm-thick h-BN in metal/h-BN/SiO2 interfaces. Our results suggest that the voids and gaps between substrate and thick h-BN flakes limit the interfacial thermal conduction. This work provides a deeper understanding of utilizing h-BN flake as lateral heat spreader in electronic and optoelectronic nano/micro devices with further miniaturization and integration.
We point out that the effective channel for the interfacial thermal conductance, the inverse of Kapitza resistance, of metal-insulator/semiconductor interfaces is governed by the electron-phonon interaction mediated by the surface states allowed in a thin region near the interface. Our detailed calculations demonstrate that the interfacial thermal conductance across Pb/Pt/Al/Au-diamond interfaces are only slightly different among these metals, and reproduce well the experimental results of the interfacial thermal conductance across metal-diamond interfaces observed by Stoner et al. [Phys. Rev. Lett. 68, 1563 (1992)] and most recently by Hohensee et al. [Nature Commun. 6, 6578 (2015)].
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