Torus actions of complexity one in non-general position

Let the compact torus $T^{n-1}$ act on a smooth compact manifold $X^{2n}$ effectively with nonempty finite set of fixed points. We pose the question: what can be said about the orbit space $X^{2n}/T^{n-1}$ if the action is cohomologically equivariantly formal (which essentially means that $H^{odd}(X^{2n};\mathbb{Z})=0$). It happens that homology of the orbit space can be arbitrary in degrees $3$ and higher. For any finite simplicial complex $L$ we construct an equivariantly formal manifold $X^{2n}$ such that $X^{2n}/T^{n-1}$ is homotopy equivalent to $\Sigma^3L$. The constructed manifold $X^{2n}$ is the total space of the projective line bundle over the permutohedral variety hence the action on $X^{2n}$ is Hamiltonian and cohomologically equivariantly formal. We introduce the notion of the action in $j$-general position and prove that, for any simplicial complex $M$, there exists an equivariantly formal action of complexity one in $j$-general position such that its orbit space is homotopy equivalent to $\Sigma^{j+2}M$.Comment: 14 page

Fingerprints of angulon instabilities in the spectra of matrix-isolated molecules

The formation of vortices is usually considered to be the main mechanism of angular momentum disposal in superfluids. Recently, it was predicted that a superfluid can acquire angular momentum via an alternative, microscopic route -- namely, through interaction with rotating impurities, forming so-called `angulon quasiparticles' [Phys. Rev. Lett. 114, 203001 (2015)]. The angulon instabilities correspond to transfer of a small number of angular momentum quanta from the impurity to the superfluid, as opposed to vortex instabilities, where angular momentum is quantized in units of $\hbar$ per atom. Furthermore, since conventional impurities (such as molecules) represent three-dimensional (3D) rotors, the angular momentum transferred is intrinsically 3D as well, as opposed to a merely planar rotation which is inherent to vortices. Herein we show that the angulon theory can explain the anomalous broadening of the spectroscopic lines observed for CH$_3$ and NH$_3$ molecules in superfluid helium nanodroplets, thereby providing a fingerprint of the emerging angulon instabilities in experiment.Comment: 7 pages + supplemen

Large non-adiabatic hole polarons and matrix element effects in the angle-resolved photoemission spectroscopy of dielectric cuprates

It has been made an extention of the conventional theory based on the assumption of the well isolated Zhang-Rice singlet to be a first electron-removal state in dielectric copper oxide. One assumes the photohole has been localised on either small (pseudo)Jahn-Teller polaron or large non-adiabatic polaron enclosed one or four to five $CuO_4$ centers, respectively, with active one-center valent $(^{1}A_{1g}-{}^{1,3}E_{u})$ manifold. In the framework of the cluster model we have performed a model microscopic calculation of the ${\bf k}$-dependence of the matrix element effects and photon polarization effects for the angle-resolved photoemission in dielectric cuprate like $Sr_{2}CuO_{2}Cl_{2}$. We show that effects like the ''remnant Fermi surface'' detected in ARPES experiment for $Ca_{2}CuO_{2}Cl_{2}$ may be, in fact, a reflection of the matrix element effects, not a reflection of the original band-structure Fermi surface, or the strong antiferromagnetic correlations. The measured dispersion-like features in the low-energy part of the ARPES spectra may be a manifestation of the complex momentum-dependent spectral line-shape of the large PJT polaron response, not the dispersion of the well-isolated Zhang-Rice singlet in antiferromagnetic matrix.Comment: 16 pages, TeX, 9 eps figures adde

Surface Conductivity of Si(100) and Ge(100) Surfaces Determined from Four-Point Transport Measurements Using an Analytical N-Layer Conductance Model

An analytical N-layer model for charge transport close to a surface is derived from the solution of Poisson's equation and used to describe distance-dependent electrical four-point measurements on the microscale. As the N-layer model comprises a surface channel, multiple intermediate layers and a semi-infinite bulk, it can be applied to semiconductors in combination with a calculation of the near-surface band-bending to model very precisely the measured four-point resistance on the surface of a specific sample and to extract a value for the surface conductivity. For describing four-point measurements on sample geometries with mixed 2D-3D conduction channels often a very simple parallel-circuit model has so far been used in the literature, but the application of this model is limited, as there are already significant deviations, when it is compared to the lowest possible case of the N-layer model, i.e. the 3-layer model. Furthermore, the N-layer model is applied to published distance-dependent four-point resistance measurements obtained with a multi-tip scanning tunneling microscope (STM) on Germanium(100) and Silicon(100) with different bulk doping concentrations resulting in the determination of values for the surface conductivities of these materials.Comment: 11 pages, 6 color figure

Four-point probe measurements using current probes with voltage feedback to measure electric potentials

We present a four-point probe resistance measurement technique which uses four equivalent current measuring units, resulting in minimal hardware requirements and corresponding sources of noise. Local sample potentials are measured by a software feedback loop which adjusts the corresponding tip voltage such that no current flows to the sample. The resulting tip voltage is then equivalent to the sample potential at the tip position. We implement this measurement method into a multi-tip scanning tunneling microscope setup such that potentials can also be measured in tunneling contact, allowing in principle truly non-invasive four-probe measurements. The resulting measurement capabilities are demonstrated for BiSbTe$_3$ and Si$(111)-(7\times7)$ samples

Surface and Step Conductivities on Si(111) Surfaces

Four-point measurements using a multi-tip scanning tunneling microscope (STM) are carried out in order to determine surface and step conductivities on Si(111) surfaces. In a first step, distance-dependent four-point measurements in the linear configuration are used in combination with an analytical three-layer model for charge transport to disentangle the 2D surface conductivity from non-surface contributions. A termination of the Si(111) surface with either Bi or H results in the two limiting cases of a pure 2D or 3D conductance, respectively. In order to further disentangle the surface conductivity of the step-free surface from the contribution due to atomic steps, a square four-probe configuration is applied as function of the rotation angle. In total this combined approach leads to an atomic step conductivity of $\sigma_\mathrm{step} = (29 \pm 9)$ $\mathrm{\Omega}^{-1} \mathrm{m}^{-1}$ and to a step-free surface conductivity of $\sigma_\mathrm{surf} = (9 \pm 2) \cdot 10^{-6}\,\mathrm{\Omega}^{-1}/\square$ for the Si(111)-(7$\times$7) surface.Comment: Main paper: 5 pages, 4 figures, Supplemental material: 6 pages, 3 figures. The Supplemental Material contains details on the sample preparation and measurement procedure, additional experimental results for Si(111) samples with different doping levels, and the description of the three-layer conductance mode