A remark on zeta functions of finite graphs via quantum walks

From the viewpoint of quantum walks, the Ihara zeta function of a finite graph can be said to be closely related to its evolution matrix. In this note we introduce another kind of zeta function of a graph, which is closely related to, as to say, the square of the evolution matrix of a quantum walk. Then we give to such a function two types of determinant expressions and derive from it some geometric properties of a finite graph. As an application, we illustrate the distribution of poles of this function comparing with those of the usual Ihara zeta function.Comment: 14 pages, 1 figur

Universal scaling for the spin-electricity conversion on surface states of topological insulators

We have investigated spin-electricity conversion on surface states of bulk-insulating topological insulator (TI) materials using a spin pumping technique. The sample structure is Ni-Fe|Cu|TI trilayers, in which magnetic proximity effects on the TI surfaces are negligibly small owing to the inserted Cu layer. Voltage signals produced by the spin-electricity conversion are clearly observed, and enhanced with decreasing temperature in line with the dominated surface transport at lower temperatures. The efficiency of the spin-electricity conversion is greater for TI samples with higher resistivity of bulk states and longer mean free path of surface states, consistent with the surface spin-electricity conversion

Additional Evidence for the Surface Origin of the Peculiar Angular-Dependent Magnetoresistance Oscillations Discovered in a Topological Insulator Bi_{1-x}Sb_{x}

We present detailed data on the unusual angular-dependent magnetoresistance oscillation phenomenon recently discovered in a topological insulator Bi_{0.91}Sb_{0.09}. Direct comparison of the data taken before and after etching the sample surface gives compelling evidence that this phenomenon is essentially originating from a surface state. The symmetry of the oscillations suggests that it probably comes from the (111) plane, and obviously a new mechanism, such as a coupling between the surface and the bulk states, is responsible for this intriguing phenomenon in topological insulators.Comment: 5 pages, 4 figures, Proceedings manuscript for the 19th International Conference on the Application of High Magnetic Fields in Semiconductor Physics and Nanotechnology (HMF-19

Superconductor derived from a topological insulator heterostructure

Topological superconductors (TSCs) are of significant current interest because they offer promising platforms for finding Majorana fermions. Here we report on a superconductor synthesized by intercalating Cu into a naturally formed topological insulator (TI) heterostructure consisting of Bi₂Se₃ TI units separated by nontopological PbSe units. Interestingly, in this TI-based superconductor, the specific-heat behavior suggests the occurrence of unconventional superconductivity with gap nodes. The existence of gap nodes in a strongly spin-orbit coupled superconductor would give rise to spin-split Andreev bound states that are the hallmark of topological superconductivity. Hence, this superconductor emerges as an intriguing candidate TSC

Electrical Resistivity Anisotropy from Self-Organized One-Dimensionality in High-Temperature Superconductors

We investigate the manifestation of the stripes in the in-plane resistivity anisotropy in untwinned single crystals of La_{2-x}Sr_{x}CuO_{4} (x = 0.02 - 0.04) and YBa_{2}Cu_{3}O_{y} (y = 6.35 - 7.0). It is found that both systems show strongly temperature-dependent in-plane anisotropy in the lightly hole-doped region and that the anisotropy in YBa_{2}Cu_{3}O_{y} grows with decreasing y below about 6.60 despite the decreasing orthorhombicity, which gives most direct evidence that electrons self-organize into a macroscopically anisotropic state. The transport is found to be easier along the direction of the spin stripes already reported, demonstrating that the stripes are intrinsically conducting in cuprates.Comment: 5 pages, 4 figures (including one color figure), final version accepted for publication in Phys. Rev. Let

The mechanism of hole carrier generation and the nature of pseudogap- and 60K-phases in YBCO

In the framework of the model assuming the formation of NUC on the pairs of Cu ions in CuO$_{2}$ plane the mechanism of hole carrier generation is considered and the interpretation of pseudogap and 60 K-phases in $YBa_{2}Cu_{3}O_{6+\delta}$. is offered. The calculated dependences of hole concentration in $YBa_{2}Cu_{3}O_{6+\delta}$ on doping $\delta$ and temperature are found to be in a perfect quantitative agreement with experimental data. As follows from the model the pseudogap has superconducting nature and arises at temperature $T^{*}>T_{c\infty}>T_{c}$ in small clusters uniting a number of NUC's due to large fluctuations of NUC occupation. Here $T_{c\infty}$ and $T_{c}$ are the superconducting transition temperatures of infinite and finite clusters of NUC's, correspondingly. The calculated $T^{*}(\delta)$ and $T_{n}(\delta)$ dependences are in accordance with experiment. The area between $T^{*}(\delta)$ and $T_{n}(\delta)$ corresponds to the area of fluctuations where small clusters fluctuate between superconducting and normal states owing to fluctuations of NUC occupation. The results may serve as important arguments in favor of the proposed model of HTSC.Comment: 12 pages, 7 figure