Characterization of helical Luttinger liquids in microwave stepped-impedance edge resonators

Exact Green's functions and Bosonization of a Luttinger liquid coupled to impedances

The exact Green's functions of a finite-size Luttinger Liquid (LL) connected to impedances are computed at zero and finite temperature. Bosonization for a LL with Impedance boundary conditions (IBC) is proven to hold. The LL with open boundary conditions (for both Neumann and Dirichlet cases) is explicitly recovered as a special limit when one has infinite impedances. Additionally when the impedances are equal to the characteristic impedance of the Luttinger liquid then the finite Luttinger liquid is shown to be effectively equivalent to an infinite Luttinger liquid.

Probing the intrinsic shot noise of a Luttinger liquid through impedance matching

We argue that a simple way to bypass reflections at the boundaries of a finite Luttinger liquid (LL) connected to electrodes is to match load and drain impedances to the characteristic impedance of the LL viewed as a mesoscopic transmission line. For an impedance matched LL, this implies that the AC and DC shot noise properties of a finite LL are identical to those of an infinite LL. Even for an impedance mismatched LL, we show by a careful analysis of reflections that the intrinsic infinite LL properties can still be extracted yielding possibly irrational charges for the LL elementary excitat…

Interface resistances and AC transport in a Luttinger liquid

We consider a Luttinger liquid (LL) connected to two reservoirs when the two sample-reservoir interface resistances $R_{S}$ and $R_{D}$ are arbitrary (not necessarily quantized at half-the-quantum of resistance). We compute exactly the dynamical impedance of a Luttinger liquid and generalize earlier expressions for its dynamical conductance in the following situations. (i) We first consider a gated Luttinger liquid. It is shown that the Luttinger liquid parameters $u$ and $K$ and the interface resistances $R_{S}$ and $% R_{D}$ can be experimentally determined by measuring both the dynamical co…

室温下Bi4Br4中的阶梯量子自旋霍尔态的直接可视化

Direct Visualization of Room-temperature Stair-stepped Quantum Spin Hall States in Bi4Br4

本研究通过微波阻抗显微镜直接可视化Bi4Br4中室温下的阶梯量子自旋霍尔态，并展示了其稳定的拓扑特性及可扩展的堆叠结构。

A technique to directly excite Luttinger liquid collective modes in carbon nanotubes at GHz frequencies

We present a technique to directly excite Luttinger liquid collective modes in carbon nanotubes at GHz frequencies. By modeling the nanotube as a nano-transmission line with distributed kinetic and magnetic inductance as well as distributed quantum and electrostatic capacitance, we calculate the complex, frequency dependent impedance for a variety of measurement geometries. Exciting voltage waves on the nano-transmission line is equivalent to directly exciting the yet-to-be observed one dimensional plasmons, the low energy excitation of a Luttinger liquid. Our technique has already been applie…

Tunneling into 1D and quasi-1D conductors and Luttinger-liquid behavior

The paper addresses the problem whether and how it is possible to detect the Luttinger-liquid behavior from the $IV$ curves for tunneling to 1D or quasi-1D conductors. The power-law non-ohmic $IV$ curve, which is usually considered as a manifestation of the Luttinger-liquid behavior, can be also deduced from the theory of the Coulomb blockaded junction between 3D conductors affected by the environment effect. In both approaches the power-law exponents are determined by the ratio of the impedance of an effective electric circuit to the quantum resistance. Though two approaches predict different…