Phase diagram of two interacting helical states

We consider two coupled time-reversal-invariant helical edge modes of the same helicity, such as would occur on two stacked quantum spin Hall insulators. In the presence of interaction, the low-energy physics is described by two collective modes, one corresponding to the total current flowing around the edge and the other one describing relative fluctuations between the two edges.We find that quite generically, the relative mode becomes gapped at low temperatures, but only when tunneling between the two helical modes is nonzero. There are two distinct possibilities for the gapped state depending on the relative size of different interactions. If the intraedge interaction is stronger than the interedge interaction, the state is characterized as a spin-nematic phase. However, in the opposite limit, when the interaction between the helical edge modes is strong compared to the interaction within each mode, a spin-density wave forms, with emergent topological properties. First, the gap protects the conducting phase against localization by weak nonmagnetic impurities; second, the protected phase hosts localized zero modes on the ends of the edge that may be created by sufficiently strong nonmagnetic impurities

Shot Noise at High Temperatures

We consider the possibility of measuring non-equilibrium properties of the current correlation functions at high temperatures (and small bias). Through the example of the third cumulant of the current (${\cal{S}}_3$) we demonstrate that odd order correlation functions represent non-equilibrium physics even at small external bias and high temperatures. We calculate ${\cal{S}}_3=y(eV/T) e^2 I$ for a quasi-one-dimensional diffusive constriction. We calculate the scaling function $y$ in two regimes: when the scattering processes are purely elastic and when the inelastic electron-electron scattering is strong. In both cases we find that $y$ interpolates between two constants. In the low (high) temperature limit $y$ is strongly (weakly) enhanced (suppressed) by the electron-electron scattering.Comment: 11 pages 4 fig. submitted to Phys. Rev.

Pumping current of a Luttinger liquid with finite length

We study transport properties in a Tomonaga-Luttinger liquid in the presence of two time-dependent point like weak impurities, taking into account finite-length effects. By employing analytical methods and performing a perturbation theory, we compute the backscattering pumping current (I_bs) in different regimes which can be established in relation to the oscillatory frequency of the impurities and to the frequency related to the length and the renormalized velocity (by the electron-electron interactions) of the charge density modes. We investigate the role played by the spatial position of the impurity potentials. We also show how the previous infinite length results for I_bs are modified by the finite size of the system.Comment: 9 pages, 7 figure

Electron-electron scattering effects on the Full Counting Statistics of Mesoscopic Conductors

In the hot electron regime, electron-electron scattering strongly modifies not only the shot noise but also the full counting statistics. We employ a method based on a stochastic path integral to calculate the counting statistics of two systems in which noise in the hot electron regime has been experimentally measured. We give an analytical expression for the counting statistics of a chaotic cavity and find that heating due to electron-electron scattering renders the distribution of transmitted charge symmetric in the shot noise limit. We also discuss the frequency dispersion of the third order correlation function and present numerical calculations for the statistics of diffusive wires in the hot electron regime

Partitioning Graphs to Speed Up Dijkstra's Algorithm

In this paper, we consider Dijkstra's algorithm for the point-to-point shortest path problem in large and sparse graphs with a given layout. Lauther presented a method that uses a partitioning of the graph to perform a preprocessing which allows to speed-up Dijkstra's algorithm considerably. We present an experimental study that evaluates which partitioning methods are suited for this approach. In particular, we examine partitioning algorithms from computational geometry and compare their impact on the speed-up of the shortest-path algorithm. Using a suited partitioning algorithm speed-up factors of 500 and more were achieved. Furthermore, we present an extension of this speed-up technique to multiple levels of partitionings. With this multi-level variant, the same speed-up factors can be achieved with smaller space requirements. It can therefore be seen as a compression of the precomputed data that conserves the correctness of the computed shortest paths

Current Fluctuations and Electron-Electron Interactions in Coherent Conductors

We analyze current fluctuations in mesoscopic coherent conductors in the presence of electron-electron interactions. In a wide range of parameters we obtain explicit universal dependencies of the current noise on temperature, voltage and frequency. We demonstrate that Coulomb interaction decreases the Nyquist noise. In this case the interaction correction to the noise spectrum is governed by the combination $\sum_nT_n(T_n-1)$, where $T_n$ is the transmission of the $n$-th conducting mode. The effect of electron-electron interactions on the shot noise is more complicated. At sufficiently large voltages we recover two different interaction corrections entering with opposite signs. The net result is proportional to $\sum_nT_n(T_n-1)(1-2T_n)$, i.e. Coulomb interaction decreases the shot noise at low transmissions and increases it at high transmissions.Comment: 16 pages, 2 figure