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, $\mu$, for a T=0 gapped system is removed by using the unique value $\mu(T\rightarrow 0)$, 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.Comment: Published version with supplemental material rebutting the recent criticism that our theorem fails if the ground-state degeneracy is lifte

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.Comment: 12 pages, 7 figures. V2: Final version as published in Phys. Rev. Lett, with detailed clarifications in the Appendi

Time Reversal Polarization and a Z\u3csub\u3e2\u3c/sub\u3e Adiabatic Spin Pump

We introduce and analyze a class of one-dimensional insulating Hamiltonians that, when adiabatically varied in an appropriate closed cycle, define a “Z2 pump.” For an isolated system, a single closed cycle of the pump changes the expectation value of the spin at each end even when spin-orbit interactions violate the conservation of spin. A second cycle, however, returns the system to its original state. When coupled to leads, we show that the Z2 pump functions as a spin pump in a sense that we define, and transmits a finite, though nonquantized, spin in each cycle. We show that the Z2 pump is characterized by a Z2 topological invariant that is analogous to the Chern invariant that characterizes a topological charge pump. The Z2 pump is closely related to the quantum spin Hall effect, which is characterized by a related Z2 invariant. This work presents an alternative formulation that clarifies both the physical and mathematical meaning of that invariant. A crucial role is played by time reversal symmetry, and we introduce the concept of the time reversal polarization, which characterizes time reversal invariant Hamiltonians and signals the presence or absence of Kramers degenerate end states. For noninteracting electrons, we derive a formula for the time reversal polarization that is analogous to Berry’s phase formulation of the charge polarization. For interacting electrons, we show that Abelian bosonization provides a simple formulation of the time reversal polarization. We discuss implications for the quantum spin Hall effect, and argue in particular that the Z2 classification of the quantum spin Hall effect is valid in the presence of electron electron interactions

\u3cem\u3eColloquium\u3c/em\u3e: Topological Insulators

Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator but have protected conducted states on their edge or surface. These states are possible due to the combination of spin-orbit interactions and time-reversal symmetry. The two-dimensional (2D) topological insulator is a quantum spin Hall insulator, which is a close cousin of the integer quantum Hall state. A three-dimensional (3D) topological insulator supports novel spin-polarized 2D Dirac fermions on its surface. In this Colloquium the theoretical foundation for topological insulators and superconductors is reviewed and recent experiments are described in which the signatures of topological insulators have been observed. Transport experiments on HgTe/CdTe quantum wells are described that demonstrate the existence of the edge states predicted for teh quantum spin hall insulator. Experiments on Bi1-xSbx, Bi\u3c2Se3, Bi2Te3 and Sb2Te3 are then discussed that establish these materials as 3D topological insulators and directly probe the topology of their surface states. Exotic states are described that can occur at the surface of a 3D topological insulator due to an induced energy gap. A magnetic gap leads to a novel quantum Hall state that gives rise to a topological magnetoelectric effect. A superconducting energy gap leads to a state that supports Majorana fermions and may provide a new venue for realizing proposals for topological quantum computation. Prospects for observing these exotic states are also discussed, as well as other potential device applications of topological insulators

Majorana Fermoins and Non-Abelian Statistics in Three Dimensions

We show that three dimensional superconductors, described within a Bogoliubov–de Gennes framework, can have zero energy bound states associated with pointlike topological defects. The Majorana fermions associated with these modes have non-Abelian exchange statistics, despite the fact that the braid group is trivial in three dimensions. This can occur because the defects are associated with an orientation that can undergo topologically nontrivial rotations. A feature of three dimensional systems is that there are ‘‘braidless’’ operations in which it is possible to manipulate the ground state associated with a set of defects without moving or measuring them. To illustrate these effects, we analyze specific architectures involving topological insulators and superconductors

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.Comment: 4 pages, 3 eps figure

Surface State Magnetization and Chiral Edge States on Topological Insulators

We study the interaction between a ferromagnetically ordered medium and the surface states of a topological insulator with a general surface termination that were identified recently [F. Zhang et al.Phys. Rev. B 86 081303(R) (2012)]. This interaction is strongly crystal face dependent and can generate chiral states along edges between crystal facets even for a uniform magnetization. While magnetization parallel to quintuple layers shifts the momentum of the Dirac point, perpendicular magnetization lifts the Kramers degeneracy at any Dirac points except on the side face, where the spectrum remains gapless and the Hall conductivity switches sign. Chiral states can be found at any edge that reverses the projection of the surface normal to the stacking direction of quintuple layers. Magnetization also weakly hybridizes noncleavage surfaces

Topological Insulators in Three Dimensions

We study three-dimensional generalizations of the quantum spin Hall (QSH) effect. Unlike two dimensions, where a single Z2 topological invariant governs the effect, in three dimensions there are 4 invariants distinguishing 16 phases with two general classes: weak (WTI) and strong (STI) topological insulators. The WTI are like layered 2D QSH states, but are destroyed by disorder. The STI are robust and lead to novel ‘‘topological metal’’ surface states. We introduce a tight binding model which realizes the WTI and STI phases, and we discuss its relevance to real materials, including bismuth