arXiv subjects

Charles L. Kane

Publications and source records attributed to Charles L. Kane.

24 records · Page 2Linked to original sources

arXiv2013

Absence of Luttinger's Theorem due to Zeros in the Single-Particle Green Function

We show exactly with an SU(N) interacting model that even if the ambiguity associated with the placement of the chemical potential, $μ$, for a T=0 gapped system is removed by using the unique value $μ(T\rightarrow 0)$, Luttinger's sum rule is violated even if the ground-state degeneracy is lifted by an infinitesimal hopping. The failure stems from the non-existence of the Luttinger-Ward functional for a system in which the self-energy diverges. Since it is the existence of the Luttinger-Ward functional that is the basis for Luttinger's theorem which relates the charge density to sign changes of the single-particle Green function, no such theorem exists. Experimental data on the cuprates are presented which show a systematic deviation from the Luttinger count, implying a breakdown of the electron quasiparticle picture in strongly correlated electron matter.

cond-mat.str-el↗

arXiv2011

Theoretical investigation of the evolution of the topological phase of Bi$_{2}$Se$_{3}$ under mechanical strain

The topological insulating phase results from inversion of the band gap due to spin-orbit coupling at an odd number of time-reversal symmetric points. In Bi$_2$Se$_3$, this inversion occurs at the $Γ$ point. For bulk Bi$_2$Se$_3$, we have analyzed the effect of arbitrary strain on the $Γ$ point band gap using Density Functional Theory. By computing the band structure both with and without spin-orbit interactions, we consider the effects of strain on the gap via Coulombic interaction and spin-orbit interaction separately. While compressive strain acts to decrease the Coulombic gap, it also increases the strength of the spin-orbit interaction, increasing the inverted gap. Comparison with Bi$_2$Te$_3$ supports the conclusion that effects on both Coulombic and spin-orbit interactions are critical to understanding the behavior of topological insulators under strain, and we propose that the topological insulating phase can be effectively manipulated by inducing strain through chemical substitution.

cond-mat.mtrl-sci↗

arXiv2011

A new experimental approach for the exploration of topological quantum phenomena : Topological Insulators and Superconductors

The three-dimensional topological insulator (originally called "topological insulators") is the first example in nature of a topologically ordered electronic phase existing in three dimensions that cannot be reduced to multiple copies of quantum-Hall-like states. Their topological order can be realized at room temperatures without magnetic fields and they can be turned into magnets and exotic superconductors leading to world-wide interest and activity in topological insulators. One of the major challenges in going from quantum Hall-like 2D states to 3D topological insulators is to develop new experimental approaches/methods to precisely probe this novel form of topological-order since the standard tools and settings that work for IQH-state also work for QSH states. The method to probe 2D topological-order is exclusively with charge transport, which either measures quantized transverse conductance plateaus in IQH systems or longitudinal conductance in quantum spin Hall (QSH) systems. In a 3D topological insulator, the boundary itself supports a two dimensional electron gas (2DEG) and transport is not (Z$_2$) topologically quantized. In this paper, we review the birth of momentum- and spin-resolved spectroscopy as a new experimental approach and as a directly boundary sensitive method to study and prove topological-order in three-dimensions via the direct measurements of the topological invariants {$ν_o$} that are associated with the Z$_2$ topology of the spin-orbit band structure and opposite parity band inversions, which led to the experimental discovery of the first 3D topological insulators. We also discuss how spectroscopic methods are leading to the identification of spin-orbit superconductors that may work as Majorana platforms and can be used to identify topological superconductors - yet another class of new state of matter.

cond-mat.mes-hall↗

arXiv2011

Interface Between Topological and Superconducting Qubits

We propose and analyze an interface between a topological qubit and a superconducting flux qubit. In our scheme, the interaction between Majorana fermions in a topological insulator is coherently controlled by a superconducting phase that depends on the quantum state of the flux qubit. A controlled phase gate, achieved by pulsing this interaction on and off, can transfer quantum information between the topological qubit and the superconducting qubit.

cond-mat.mes-hall↗

arXiv2000

Electronic Structure of Carbon Nanotube Ropes

We present a tight binding theory to analyze the motion of electrons between carbon nanotubes bundled into a carbon nanotube rope. The theory is developed starting from a description of the propagating Bloch waves on ideal tubes, and the effects of intertube motion are treated perturbatively in this basis. Expressions for the interwall tunneling amplitudes between states on neighboring tubes are derived which show the dependence on chiral angles and intratube crystal momenta. We find that conservation of crystal momentum along the tube direction suppresses interwall coherence in a carbon nanorope containing tubes with random chiralities. Numerical calculations are presented which indicate that electronic states in a rope are localized in the transverse direction with a coherence length corresponding to a tube diameter.

cond-mat.mes-hall↗

arXiv1999

High-Field Electrical Transport in Single-Wall Carbon Nanotubes

Using low-resistance electrical contacts, we have measured the intrinsic high-field transport properties of metallic single-wall carbon nanotubes. Individual nanotubes appear to be able to carry currents with a density exceeding 10^9 A/cm^2. As the bias voltage is increased, the conductance drops dramatically due to scattering of electrons. We show that the current-voltage characteristics can be explained by considering optical or zone-boundary phonon emission as the dominant scattering mechanism at high field.

cond-mat.mes-hall↗