Directional ballistic transport in the two-dimensional metal PdCoO2

In an idealized infinite crystal, the material properties are constrained by the symmetries of its unit cell. Naturally, the point-group symmetry is broken by the sample shape of any finite crystal, yet this is commonly unobservable in macroscopic metals. To sense the shape-induced symmetry lowering in such metals, long-lived bulk states originating from anisotropic Fermi surfaces are needed. Here we show how strongly facetted Fermi surfaces and long quasiparticle mean free paths present in microstructures of PdCoO2 yield an in-plane resistivity anisotropy that is forbidden by symmetry on an infinite hexagonal lattice. Bar shaped transport devices narrower than the mean free path are carved from single crystals using focused ion beam (FIB) milling, such that the ballistic charge carriers at low temperatures frequently collide with both sidewalls defining a channel. Two symmetry-forbidden transport signatures appear: the in-plane resistivity anisotropy exceeds a factor of 2, and transverse voltages appear in zero magnetic field. We robustly identify the channel direction as the source of symmetry breaking via ballistic Monte- Carlo simulations and numerical solution of the Boltzmann equation

h/e oscillations in interlayer transport of delafossites

Funding: This project was funded by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant no. 715730, MiTopMat) and also was supported by the Max Planck Society. A.P.M. and R.M. acknowledge support from the Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter (EXC 2147). M.D.B., P.M., and V.S. acknowledge studentship funding from the EPSRC under grant no. EP/L015110/1. A.S. was supported by the Israel Science Foundation, the European Research Council (Project LEGOTOP), and the DFG through projectno.CRC-183. M.K. acknowledges support from the SIRIUS irradiation facility through project no. EMIR 2019 18-7099.Microstructures can be carefully designed to reveal the quantum phase of the wave-like nature of electrons in a metal. Here, we report phase-coherent oscillations of out-of-plane magnetoresistance in the layered delafossites PdCoO2 and PtCoO2 The oscillation period is equivalent to that determined by the magnetic flux quantum, h/e, threading an area defined by the atomic interlayer separation and the sample width, where h is Planck's constant and e is the charge of an electron. The phase of the electron wave function appears robust over length scales exceeding 10 micrometers and persisting up to temperatures of T > 50 kelvin. We show that the experimental signal stems from a periodic field modulation of the out-of-plane hopping. These results demonstrate extraordinary single-particle quantum coherence lengths in delafossites.PostprintPeer reviewe

Directional ballistic transport in the two-dimensional metal PdCoO2

This project was supported by the Max Planck Society and the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (MiTopMat, grant agreement no. 715730). M.D.B. and P.H.M. acknowledge EPSRC for PhD studentship support through grant number EP/L015110/1. Research in Dresden benefits from the environment of the Excellence Cluster ct.qmat. A.S. acknowledges support from an ARCS Foundation Fellowship, a Ford Foundation Predoctoral Fellowship and a National Science Foundation Graduate Research Fellowship. A.S. would thanks Z. Gomez and E. Huang for helpful discussions and T. Devereaux for letting us use his group cluster. Computational work was performed on the Sherlock cluster at Stanford University and on resources of the National Energy Research Scientific Computing Center, supported by the DOE under contract DE_AC02-05CH11231. T.S. acknowledges support from the Emergent Phenomena in Quantum Systems initiative of the Gordon and Betty Moore Foundation, and from the Natural Sciences and Engineering Research Council of Canada (NSERC), in particular the Discovery Grant (RGPIN-2020-05842), Accelerator Supplement (RGPAS-2020-00060) and Discovery Launch Supplement (DGECR-2020-00222). T.S. contributed to this work prior to joining AWS. D.G.-G.’s and A.W.B.’s involvement in calculations was supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division under contract DE-AC02-76SF00515. E.Z. and M.M. thank the International Max Planck Research School for Chemistry and Physics of Quantum Materials (IMPRS-CPQM) for financial support. G.B. and D.A.B. acknowledge support from the Natural Sciences and Engineering Research Council of Canada (NSERC Discovery Grant RGPIN-2018-04280) and from the Canada First Research Excellence Fund.In an idealized infinite crystal, the material properties are constrained by the symmetries of the unit cell. The point-group symmetry is broken by the sample shape of any finite crystal, but this is commonly unobservable in macroscopic metals. To sense the shape-induced symmetry lowering in such metals, long-lived bulk states originating from an anisotropic Fermi surface are needed. Here we show how a strongly facetted Fermi surface and the long quasiparticle mean free path present in microstructures of PdCoO2 yield an in-plane resistivity anisotropy that is forbidden by symmetry on an infinite hexagonal lattice. We fabricate bar-shaped transport devices narrower than the mean free path from single crystals using focused ion beam milling, such that the ballistic charge carriers at low temperatures frequently collide with both of the side walls that define the channel. Two symmetry-forbidden transport signatures appear: the in-plane resistivity anisotropy exceeds a factor of 2, and a transverse voltage appears in zero magnetic field. Using ballistic Monte Carlo simulations and a numerical solution of the Boltzmann equation, we identify the orientation of the narrow channel as the source of symmetry breaking.Publisher PDFPeer reviewe

Super-geometric electron focusing on the hexagonal Fermi surface of PdCoO2

The project was supported by the Max-Planck Society and has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 715730). M.D.B. acknowledges studentship funding from EPSRC under grant no. EP/I007002/1. A.L.S. acknowledges support from a Ford Foundation Predoctoral Fellowship and a National Science Foundation Graduate Research Fellowship. A.L.S. would like to thank Edwin Huang for helpful discussions and Tom Devereaux for letting us use his group cluster. Computational work was performed on the Sherlock cluster at Stanford University and on resources of the National Energy Research Scientific Computing Center, supported by DOE under contract DE_AC02-05CH11231. D.G.G.’s and A.W.B.’s work was supported by the U.S. Department of Energy, Office of Science, Basic EnergySciences, Materials Sciences and Engineering Division, under Contract No. DE-AC02-76SF00515.Geometric electron optics may be implemented in solids when electron transport is ballistic on the length scale of a device. Currently, this is realized mainly in 2D materials characterized by circular Fermi surfaces. Here we demonstrate that the nearly perfectly hexagonal Fermi surface of PdCoO2 gives rise to highly directional ballistic transport. We probe this directional ballistic regime in a single crystal of PdCoO2 by use of focused ion beam (FIB) micro-machining, defining crystalline ballistic circuits with features as small as 250 nm. The peculiar hexagonal Fermi surface naturally leads to enhanced electron self-focusing effects in a magnetic field compared to circular Fermi surfaces. This super-geometric focusing can be quantitatively predicted for arbitrary device geometry, based on the hexagonal cyclotron orbits appearing in this material. These results suggest a novel class of ballistic electronic devices exploiting the unique transport characteristics of strongly faceted Fermi surfaces.Publisher PDFPeer reviewe

Providing Information by Resource- Constrained Data Analysis

The Collaborative Research Center SFB 876 (Providing Information by Resource-Constrained Data Analysis) brings together the research fields of data analysis (Data Mining, Knowledge Discovery in Data Bases, Machine Learning, Statistics) and embedded systems and enhances their methods such that information from distributed, dynamic masses of data becomes available anytime and anywhere. The research center approaches these problems with new algorithms respecting the resource constraints in the different scenarios. This Technical Report presents the work of the members of the integrated graduate school

Spatial control of heavy-fermion superconductivity in CeIrIn5

M.D.B. acknowledges studentship funding from EPSRC under grant EP/I007002/1.Although crystals of strongly correlated metals exhibit a diverse set of electronic ground states, few approaches exist for spatially modulating their properties. In this study, we demonstrate disorder-free control, on the micrometer scale, over the superconducting state in samples of the heavy-fermion superconductor CeIrIn5. We pattern crystals by focused ion beam milling to tailor the boundary conditions for the elastic deformation upon thermal contraction during cooling. The resulting nonuniform strain fields induce complex patterns of superconductivity, owing to the strong dependence of the transition temperature on the strength and direction of strain. These results showcase a generic approach to manipulating electronic order on micrometer length scales in strongly correlated matter without compromising the cleanliness, stoichiometry, or mean free path.PostprintPeer reviewe

Measuring the Power Consumption of Smartphones

Smartphones are becoming a part of everyday life and as such, a better understanding of hardware and software power consumption is crucial to develop more efficient smartphones. In order to extend battery life, application developers and phone designers must become aware of the limitations of a phone’s CPU power, as well as the LCD display consumption and connectivity via WiFi, 3G, and GPS systems. We present power consumption measurements of an HTC Incredible S and compare these results to known analytical models. The evaluation shows that power consumption is considerably varying with different types of smartphones and that well known models underestimate the actual consumption. The results illustrate that touching the screen nearly doubles the power consumption , which is not captured by any analytical model. Moreover, we present in which way the transmitted packet size of WiFi and cellular communications affect the power consumption

Super-geometric electron focusing on the hexagonal Fermi surface of PdCoO₂

Geometric electron optics may be implemented in solids when electron transport is ballistic on the length scale of a device. Currently, this is realized mainly in 2D materials characterized by circular Fermi surfaces. Here we demonstrate that the nearly perfectly hexagonal Fermi surface of PdCoO2 gives rise to highly directional ballistic transport. We probe this directional ballistic regime in a single crystal of PdCoO2 by use of focused ion beam (FIB) micro-machining, defining crystalline ballistic circuits with features as small as 250 nm. The peculiar hexagonal Fermi surface naturally leads to enhanced electron self-focusing effects in a magnetic field compared to circular Fermi surfaces. This super-geometric focusing can be quantitatively predicted for arbitrary device geometry, based on the hexagonal cyclotron orbits appearing in this material. These results suggest a novel class of ballistic electronic devices exploiting the unique transport characteristics of strongly faceted Fermi surfaces.</p

<i>h/e</i> oscillations in interlayer transport of delafossites

Microstructures can be carefully designed to reveal the quantum phase of the wave-like nature of electrons in a metal. Here, we report phase-coherent oscillations of out-of-plane magnetoresistance in the layered delafossites PdCoO2 and PtCoO2 The oscillation period is equivalent to that determined by the magnetic flux quantum, h/e, threading an area defined by the atomic interlayer separation and the sample width, where h is Planck's constant and e is the charge of an electron. The phase of the electron wave function appears robust over length scales exceeding 10 micrometers and persisting up to temperatures of T &gt; 50 kelvin. We show that the experimental signal stems from a periodic field modulation of the out-of-plane hopping. These results demonstrate extraordinary single-particle quantum coherence lengths in delafossites.</p