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Register a new userChiral anomaly and anomalous finite-size conductivity in graphene
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Graphene is a monolayer of carbon atoms packed into a hexagon lattice to host two pairs of massless two-dimensional Dirac fermions in the absence of or with negligible spin-orbit coupling. It is known that the existence of non-zero electric polarization in reduced momentum space which is associated with a hidden chiral symmetry will lead to the zero-energy flat band of zigzag nanoribbon. The Adler-Bell-Jackiw chiral anomaly or non-conservation of chiral charges at different valleys can be realized in a confined ribbon of finite width. In the laterally diffusive regime, the finite-size correction to conductivity is always positive and goes inversely with the square of the lateral dimension W, which is different from the finite-size correction inversely with W from boundary modes. This anomalous finite-size conductivity reveals the signature of the chiral anomaly in graphene, and is measurable experimentally.
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We investigated the thermal conductivity K of graphene ribbons and graphite slabs as the function of their lateral dimensions. Our theoretical model considered the anharmonic three-phonon processes to the second-order and included the angle-dependent phonon scattering from the ribbon edges. It was found that the long mean free path of the long-wavelength acoustic phonons in graphene can lead to an unusual non-monotonic dependence of the thermal conductivity on the length L of a ribbon. The effect is pronounced for the ribbons with the smooth edges (specularity parameter p>0.5). Our results also suggest that - contrary to what was previously thought - the bulk-like 3D phonons in graphite can make a rather substantial contribution to its in-plane thermal conductivity. The Umklapp-limited thermal conductivity of graphite slabs scales, for L below ~ 10 micrometers, as log(L) while for larger L, the thermal conductivity approaches a finite value following the dependence K_0 - AtimesL^-1/2, where K_0 and A are parameters independent of the length. Our theoretical results clarify the scaling of the phonon thermal conductivity with the lateral sizes in graphene and graphite. The revealed anomalous dependence K(L) for the micrometer-size graphene ribbons can account for some of the discrepancy in reported experimental data for graphene.
We theoretically study the finite-size effects in the dynamical response of a quantum anomalous Hall insulator in the disk geometry. Semi-analytic and numerical results are obtained for the wavefunctions and energies of the disk within a continuum Dirac Hamiltonian description subject to a topological infinite mass boundary condition. Using the Kubo formula, we obtain the frequency-dependent longitudinal and Hall conductivities and find that optical transitions between edge states contribute dominantly to the real part of the dynamic Hall conductivity for frequency values both within and beyond the bulk band gap. We also find that the topological infinite mass boundary condition changes the low-frequency Hall conductivity to $ e^2/h $ in a finite-size system from the well-known value $ e^2/2h $ in an extended system. The magneto-optical Faraday rotation is then studied as a function of frequency for the setup of a quantum anomalous Hall insulator mounted on a dielectric substrate, showing both finite-size effects of the disk and Fabry-Perot resonances due to the substrate. Our work demonstrates the important role played by the boundary condition in the topological properties of finite-size systems through its effects on the electronic wavefunctions.
As the three-dimensional analogs of graphene, Weyl semimetals display signatures of chiral anomaly which arises from charge pumping between the lowest chiral Landau levels of the Weyl nodes in the presence of parallel electric and magnetic fields. In this work, we study the pseudo chiral anomaly and its transport signatures in graphene ribbon with zigzag edges. Here pseudo refers to the case where the inverse of width of zigzag graphene ribbon plays the same role as magnetic field in three-dimensional Weyl semimetals. The valley chiral bands in zigzag graphene ribbons can be introduced by edge potentials, giving rise to the nonconservation of chiral current, i.e., pseudo chiral anomaly, in the presence of a longitudinal electric field. Further numerical results reveal that pseudo magnetoconductivity of zigzag graphene ribbons is positive and has a nearly quadratic dependence on the pseudofield, which is regarded as the transport signature of pseudo chiral anomaly.
We study theoretically the minimal conductivity of monolayer graphene in the presence of Rashba spin-orbit coupling. The Rashba spin-orbit interaction causes the low-energy bands to undergo trigonal-warping deformation and for energies smaller than the Lifshitz energy, the Fermi circle breaks up into parts, forming four separate Dirac cones. We calculate the minimal conductivity for an ideal strip of length $L$ and width $W$ within the Landauer--Buttiker formalism in a continuum and in a tight binding model. We show that the minimal conductivity depends on the relative orientation of the sample and the probing electrodes due to the interference of states related to different Dirac cones. We also explore the effects of finite system size and find that the minimal conductivity can be lowered compared to that of an infinitely wide sample.
We theoretically consider the effect of plasmon collective modes on the frequency-dependent conductivity of graphene in the presence of the random static potential of charged impurities. We develop an equation of motion approach suitable for the relativistic Dirac electrons in graphene that allows analytical high-frequency asymptotic solution in the presence of both disorder and interaction. We show that the presence of the acoustic plasmon pole (i.e. the plasmon frequency vanishing at long wavelengths as the square-root of wavevector) in the inverse dynamical dielectric function of graphene gives rise to a strong variation with frequency of the screening effect of the relativistic electron gas in graphene on the potential of charged impurities. The resulting frequency-dependent impurity scattering rate gives rise to a broad peak in the frequency-dependent graphene optical conductivity with the amplitude and the position of the peak being sensitive to the detailed characteristics of disorder and interaction in the system. This sample (i.e. disorder, elecron density and interaction strength) dependent redistribution of the spectral weight in the frequency-dependent graphene conductivity may have already been experimentally observed in optical measurements.
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