The Hubbard model on a Sierpinski gasket fractal is carefully examined within a Hartree-Fock mean field approach. We examine the influence of a magnetic flux threading the gasket on its ground state energy, persistent current and the Drude weight. Both an isotropic gasket and its anisotropic counterpart have been examined. The variance in the patterns of the calculated physical quantities are discussed for two situations, viz, at half-filling and when the `band' is less than half-filled. The phase reversal of the persistent currents and the change of the Drude weight as a function of the Hubbard interaction are found to exhibit interesting patterns that have so far remained unaddressed.
Magneto-transport of interacting electrons in a Sierpinski gasket fractal is studied within a mean field approach. We work out the three-terminal transport and study the interplay of the magnetic flux threading the planar gasket and the dephasing effect introduced by the third lead. For completeness we also provide results of the two-terminal transport in presence of electron-electron interaction. It is observed that dephasing definitely reduces the transport, while the magnetic field generates a continuum in the transmission spectrum signaling a band of extended eigenstates in this non-transl…
We numerically simulate the dynamics of aggregation of interacting atomic clusters deposited on a surface. We show that the shape of the structures resulting from their aggregation-limited random walk is affected by the presence of a binary interparticle Laplacian potential due to, for instance, the surface stress field. We characterize the morphologies we obtain by their Hausdorff fractal dimension as well as the so-called external fractal dimension, which appears more sensitive to the potential. We demonstrate the relevance of our model by comparing it to previously published experimental re…
We present an overview of the theoretical understanding of Hofstadter butterflies in monolayer and bilayer graphene. After a brief introduction on the past work in conventional semiconductor systems, we discuss the novel electronic properties of monolayer and bilayer graphene that helped to detect experimentally the fractal nature of the energy spectrum. We have discussed the theoretical background on the Moiré pattern in graphene. This pattern was crucial in determining the butterfly structure. We have also touched upon the role of electron-electron interaction in the butterfly pattern in gra…
The critical two-terminal conductance $g_c$ and the spatial fluctuations of critical eigenstates are investigated for a disordered two dimensional model of non-interacting electrons subject to spin-orbit scattering (Ando model). For square samples, we verify numerically the relation $σ_c=1/[2π(2-D(1))] e^2/h$ between critical conductivity $σ_c=g_c=(1.42\pm 0.005) e^2/h$ and the fractal information dimension of the electron wave function, $D(1)=1.889\pm 0.001$. Through a detailed numerical scaling analysis of the two-terminal conductance we also estimate the critical exponent $ν=2.80\pm 0.04$ t…
We suggest a new type of substrates for the Surface Enhanced Raman Scattering measurements with the geometry based on self-similar fractal space filling curves. As an example, we have studied theoretically the dielectric response properties of doped semiconductor nanostructures, where the conducting electrons are trapped in the effective potential having the geometry of the Hilbert curve. We have found that the system may exhibit the induced charge distribution specific for either two dimensional or one dimensional systems, depending on the frequency of the external applied field. We have demo…
In this work, we show that modulating the fractal dimension of nanoporous gold allows its effective dielectric response to be tailored over a wide spectral range of infrared wavelengths. In particular, the plasma edge and effective plasma frequency depend linearly on the fractal dimension, which can be controlled by varying the pore and ligament sizes. Importantly, the fractal porous metal exhibits superior plasmonic properties compared to its bulk counterpart. These properties, combined with a longer skin depth on the order of 100-200 nm, enables the penetration of optical energy deep into th…
Motivated by the experimental search for Bose condensation of quasiparticles in semiconductors, the response functions of a weakly interacting Bose gas, with isotropic but non-quadratic dispersion, are considered. Non-quadratic dispersion modifies the definition of particle current, and leads to modified sum rules for the current-current response function. The effect of these modifications on the Berezhinski-Kosterlitz-Thouless transition is discussed.
We investigate characteristic features of both non-interacting and interacting electrons in a Möbius strip, the simplest possible one-sided topological system, in presence of an Aharonov-Bohm flux $ϕ$. Using Hartree-Fock mean field theory we determine energy eigenvalues for the interacting model, while for the non-interacting system an analytical prescription is given. The interplay between longitudinal and vertical motions of electrons along with on-site Hubbard interaction yield several anomalous features of persistent current associated with energy-flux characteristics. The variation of cur…
Chiral surface states in topological insulators are robust against interactions, non-magnetic disorder and localization, yet topology does not yield protection in transport. This work presents a theory of interacting topological insulators in an external electric field, starting from the quantum Liouville equation for the many-body density matrix. Out of equilibrium, topological insulators acquire a current-induced spin polarization. Electron-electron interactions renormalize the non-equilibrium spin polarization and charge conductivity, and disorder in turn enhances this renormalization by a …
Anomalous thermoelectric Hall response of interacting 2D Dirac fermions
Department of Physics and Astronomy, University of Manchester（曼彻斯特大学物理与天文系）；Department of Physics, The Hong Kong University of Science and Technology（香港科技大学物理系）
Magnetic response of interacting electrons in a zigzag carbon nanotube threaded by a magnetic flux is investigated within a Hartree-Fock mean field approach. Following the description of energy spectra for both non-interacting and interacting cases we analyze the behavior of persistent current in individual branches of a nanotube. Our present investigation leads to a possibility of getting a filling-dependent metal-insulator transition in a zigzag carbon nanotube.
The transient response of a quantum dot with strong Coulomb interaction to a fast change in the gate potential, as well as the stationary ac-response to a slow harmonic variation of the gate potential are computed by means of a real-time diagrammatic expansion in the tunnel-coupling strength. We find that after a fast switching, the relaxation of charge and spin are governed by a single time constant each, which differ from each other due to Coulomb repulsion. We compare the response to a step potential with the $RC$ time extracted from the ac response.
A Sierpinski gasket fractal network model is studied in respect of its electronic spectrum and magneto-transport when each arm of the gasket is replaced by a diamond shaped Aharonov-Bohm interferometer, threaded by a uniform magnetic flux. Within the framework of a tight binding model for non-interacting, spinless electrons and a real space renormalization group method we unravel a class of extended and localized electronic states. In particular, we demonstrate the existence of extreme localization of electronic states at a special finite set of energy eigenvalues, and an infinite set of energ…
We develop a generic method in Liouville space to describe the dissipative dynamics of coherent interacting quantum dots with adiabatic time dependence beyond linear response. We show how the adiabatic response can be related to effective quantities known from real-time renormalization group methods for stationary quantities. We propose the study of a generalized $RC$-time as a characteristic time scale. We apply the method to the interacting resonant level model and calculate the nonlinear adiabatic charge response to time-dependent gate voltages, tunneling barriers and Coulomb interaction. T…
We evaluate the dynamic structure factor $S(q,ω)$ of interacting one-dimensional spinless fermions with a nonlinear dispersion relation. The combined effect of the nonlinear dispersion and of the interactions leads to new universal features of $S(q,ω)$. The sharp peak $S\propto qδ(ω-uq)$, characteristic for the Tomonaga-Luttinger model, broadens up; $S(q,ω)$ for a fixed $q$ becomes finite at arbitrarily large $ω$. The main spectral weight, however, is confined to a narrow frequency interval of the width $δω\sim q^2/m$. At the boundaries of this interval the structure factor exhibits power-law …
We compute electromagnetic, gravitational and mixed linear response functions of two- dimensional free fermions in external quantizing magnetic field at an integer filling factor. The results are presented in the form of the effective action and as an expansion of currents and stresses in wave-vectors and frequencies of the probing electromagnetic and metric fields. We identify the terms in linear response functions coming from geometric Chern-Simons, Wen-Zee, and gravitational Chern-Simons terms in effective action. We derive the expressions for Hall conductivity, Hall viscosity and find the …
In this work we explore magnetic response of interacting electrons in a spatially non-uniform disordered system, where impurities are introduced in one sector of the geometry keeping the other one free. The interaction among the electrons are taken in the well known Hubbard form which leads to several anomalous features in energy spectra and flux driven circular current, depending on the concentration of up and down spin electrons. For smaller systems with less number of electrons we present exact results which always give a clear picture to understand the basic mechanisms, while for large sys…
We develop a stochastic description of the topological properties in an interacting Chern insulator. We confirm the Mott transition's first-order nature in the interacting Haldane model on the honeycomb geometry, from a mean-field variational approach, supported by density matrix renormalization group results and Ginzburg-Landau arguments. From the Bloch sphere, we make predictions for circular dichroism of light related to the quantum Hall conductivity on the lattice and in the presence of interactions. This analysis shows that the topological number can be measured from the light response at…
