Fourier Response of a Memristor: Generation of High Harmonics with Increasing Weights

We investigate the Fourier transform of the current through a memristor when the applied-voltage frequency is smaller than the characteristic memristor frequency, and the memristor shows hysteresis in the current-voltage plane. We find that when the hysteresis curve is "smooth", the current Fourier transform has weights at odd and even harmonics that decay rapidly and monotonically with the order of the harmonic; when the hysteresis curve is "sharp", the Fourier transform of the current is significantly broader, with non-monotonic weights at high harmonics. We present a simple model which shows that this qualitative change in the Fourier spectrum is solely driven by the saturation of memristance during a voltage cycle, and not independently by various system parameters such as applied or memristor frequencies, and the non-linear dopant drift.Comment: 5 pages, 3 figure

The robust \mP\mT-symmetric chain and properties of its Hermitian counterpart

We study the properties of a parity- and time-reversal- (PT) symmetric tight-binding chain of size N with position-dependent hopping amplitude. In contrast to the fragile PT-symmetric phase of a chain with constant hopping and imaginary impurity potentials, we show that, under very general conditions, our model is {\it always} in the PT-symmetric phase. We numerically obtain the energy spectrum and the density of states of such a chain, and show that they are widely tunable. By studying the size-dependence of inverse participation ratios, we show that although the chain is not translationally invariant, most of its eigenstates are extended. Our results indicate that tight-binding models with non-Hermitian PT-symmetric hopping have a robust PT-symmetric phase and rich dynamics which may be explored in coupled waveguides.Comment: 10 pages, 3 figures; significant text and references revisio

Origin of maximal symmetry breaking in even PT-symmetric lattices

By investigating a parity and time-reversal (PT) symmetric, $N$-site lattice with impurities $\pm i\gamma$ and hopping amplitudes $t_0 (t_b)$ for regions outside (between) the impurity locations, we probe the origin of maximal PT-symmetry breaking that occurs when the impurities are nearest neighbors. Through a simple and exact derivation, we prove that the critical impurity strength is equal to the hopping amplitude between the impurities, $\gamma_c=t_b$, and the simultaneous emergence of $N$ complex eigenvalues is a robust feature of any PT-symmetric hopping profile. Our results show that the threshold strength $\gamma_c$ can be widely tuned by a small change in the global profile of the lattice, and thus have experimental implications.Comment: 3 pages, 1 figur

Memristor: modulating resistance via electron-ion interactions

poster abstractMemristor – a resistor with memory – is a long-postulated but recently discovered new circuit element that complements the three well-known circuit elements, namely a resistor, a capacitor, and an inductor. It was experimentally realized in a titanium oxide thin film doped with oxygen vacancies. The resistance of a memristor, and memristive system in general, depends on the electrical charge that has flown through it and not just on the voltage applied to it. We use a nonlinear, asymmetric drift model to describe the motion of dopant ions that, in turn, determines the effective resistance of the memristor. This interplay between ionic and electronic transport provides a natural mechanism for memory and switching behavior. We obtain the electrical properties of basic memristive circuits, and show that they exhibit non-exponential current and charge decay, negative differential conductance, and frequency-dependent hysteresis in the current-voltage characteristics. We then present a Lagrangian approach to describe the dynamics of memristive systems and its implications to quantum effects in memristors and other memory elements such as mem-capacitors and mem-inductors

Wigner crystal and bubble phases in graphene in the quantum Hall regime

Graphene, a single free-standing sheet of graphite with honeycomb lattice structure, is a semimetal with carriers that have linear dispersion. A consequence of this dispersion is the absence of Wigner crystallization in graphene, since the kinetic and potential energies both scale identically with the density of carriers. We study the ground state of graphene in the presence of a strong magnetic field focusing on states with broken translational symmetry. Our mean-field calculations show that at integer fillings a uniform state is preferred, whereas at non-integer filling factors Wigner crystal states (with broken translational symmetry) have lower energy. We obtain the phase diagram of the system. We find that it is qualitatively similar to that of quantum Hall systems in semiconductor heterostructures. Our analysis predicts that non-uniform states, including Wigner crystal state, will occur in graphene in the presence of a magnetic field and will lead to anisotropic transport in high Landau levels.Comment: New references added; 9 pages, 9 figures, (paper with high-resolution images is available at http://www.physics.iupui.edu/yogesh/graphene.pdf