There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

Weyl and Dirac semimetals are three-dimensional phases of matter with gapless electronic excitations that are protected by topology and symmetry. As three-dimensional analogs of graphene, they have generated much recent interest. Deep connections exist with particle physics models of relativistic chiral fermions, and, despite their gaplessness, to solid-state topological and Chern insulators. Their characteristic electronic properties lead to protected surface states and novel responses to applied electric and magnetic fields. The theoretical foundations of these phases, their proposed realizations in solid-state systems, and recent experiments on candidate materials as well as their relation to other states of matter are reviewed.

Weyl and Dirac semimetals in three-dimensional solids

日本物理学会誌及びJournal of the Physical Society of Japanの月刊について

IN two previous notes1, Prof. Max Born and I have shown that one can obtain a theory of superconductivity by taking account of the fact that the interaction of the electrons with the ionic lattice is appreciable only near the boundaries of Brillouin zones, and particularly strong near the corners of these. This leads to the criterion that the metal should be superconductive if a set of corners of a Brillouin zone is lying very near the Fermi surface, considered as a sphere, which limits the region in the momentum space completely filled with electrons.

On the theory of superconductivity

We delineate quantum magnetism in the strongly spin-orbit coupled, distorted honeycomb-lattice antiferromagnet BiYbGeO$_{5}$. Our magnetization and heat capacity measurements reveal that its low-temperature behavior is well described by an effective $J_{\rm eff}=1/2$ Kramers doublet of Yb$^{3+}$. The ground state is nonmagnetic with a tiny spin gap. Temperature-dependent magnetic susceptibility, magnetization isotherm, and heat capacity could be modeled well assuming isolated spin dimers with anisotropic exchange interactions $J_{\rm Z} \simeq 2.6$~K and $J_{\rm XY} \simeq 1.3$~K. Heat capacity measurements backed by muon spin relaxation suggest the absence of magnetic long-range order down to at least 80\,mK both in zero field and in applied fields. This sets BiYbGeO$_5$ apart from Yb$_2$Si$_2$O$_7$ with its unusual regime of magnon Bose-Einstein condensation and suggests negligible interdimer couplings, despite only a weak structural deformation of the honeycomb lattice.

Quantum disordered ground state in the spin-orbit coupled Jeff = 1/2 distorted honeycomb magnet BiYbGeO5

The paper studies the effect of charge carrier doping on quantum criticality in the heavy-fermion metal YbRh2Si2. It focuses in particular on the critical temperature crossover-scale, which previously has been assigned as signature of the disintegration of heavy quasiparticles at the quantum critical point. The data are incompatible with the presumed Kondo breakdown and instead point at a Zeeman driven magnetic polarization underlying critical temperature.

Tuning low-energy scales in YbRh 2 Si 2 by non-isoelectronic substitution and pressure

Crystal structure and thermodynamic properties of Na 2 SrCo(PO 4 ) 2 , the chemical sibling of the triangular quantum spin-liquid candidate Na 2 BaCo(PO 4 ) 2 , are reported. From single crystal x-ray diﬀraction and high-resolution synchrotron x-ray powder diﬀraction, the compound was found to crystallize in the monoclinic space group P 2 1 /a at room temperature, in contrast to the trigonal Na 2 BaCo(PO 4 ) 2 . Above 650 K, the symmetry of Na 2 SrCo(PO 4 ) 2 changes to C 2 /m , while around 1025 K a further transformation toward trigonal symmetry is observed. The monoclinic symmetry leads to a small deformation of the CoO 6 octahedra beyond the trigonal distortion ubiquitous in this structure type, and results in the stronger g -tensor anisotropy ( g z /g xy = 1 . 6) as well as the increased XXZ anisotropy ( J z /J xy = 2 . 1) compared to the Ba compound ( g z /g xy = 1 . 1, J z /J xy = 1 . 5), while the average coupling strength, J av /k B = (2 J xy + J z ) / 3 k B (cid:39) 1 . 3 K, remains unchanged. The N´eel temperature increases from 140 mK (Ba) to 600 mK (Sr), and an uncompensated in-plane moment of 0 . 066(4) µ B / f.u. appears. We show that the ordering temperature of a triangular antiferromagnet is capably controlled by its structural distortions.

Deformation of the triangular spin-$\frac{1}{2}$ lattice in Na$_2$SrCo(PO$_4$)$_2$

The temperature and magnetic field dependence of the specific heat cp(T,H) in the superconducting mixed state as well as the upper critical field Hc2(T) have been measured for polycrystalline Y_xLu_{1-x}Ni_2B_2C and Y(Ni_{1-y}Pt_y)_2B_2C samples. The linear-in-T electronic specific heat contribution gamma(H)T exhibits significant deviations from the usual linear-in-H law for all x and y the transition metal site (T) resulting in a disorder dependent negative curvature of gamma(H). The deviations from that linear behaviour of our unsubstituted samples are the largest reported so far for any superconductor. The H_c2(T) data point to the quasi-clean limit for (Y,Lu)-substitutions and to a transition to the quasi-dirty limit for (Ni,Pt)-substitutions. The gamma(H) dependence is discussed in the unitary d-wave as well as in the quasi-clean s-wave limits. From a consideration of gamma(H) data only, d-wave pairing cannot be ruled out.

Specific heat and disorder in the mixed state of non-magnetic borocarbides

The transport properties of the semimetallic quasi-one-dimensional S=1/2 antiferromagnet Yb4As3 have been studied by performing low-temperature (T≥0.02 K) and high magneticfield (B≤60 T) measurements of the electrical resistivity ρ(T, B). For T ≿ 2 K a ‘heavy-fermion’-like behavior Δρ(T)=AT2 with huge and nearly field-independent coefficient A ≈ 3 µΩ cm/K2 is observed, whereas at lower temperatures ρ(T) deviates from this behavior and slightly increases to the lowest T. In B>0 and T ≾ 6 K the resistivity shows an anomalous magnetic-history dependence together with an unusual relaxation behavior. In the isothermal resistivity Shubnikov-de Haas (SdH) oscillations, arising from a low-density system of mobile As-4p holes, with a frequency of 25 T have been recorded. From the T- and B-dependence of the SdH oscillations an effective carrier mass of (0.275±0.005)m0 and a charge-carrier mean-free path of 215 A are determined. Furthermore, in B≥15 T, the system is near the quantum limit and spin-splitting effects are observed.

Philipp Gegenwart

Papers

Quantum disordered ground state in the spin-orbit coupled Jeff = 1/2 distorted honeycomb magnet BiYbGeO5

Tuning low-energy scales in YbRh 2 Si 2 by non-isoelectronic substitution and pressure

Deformation of the triangular spin-$\frac{1}{2}$ lattice in Na$_2$SrCo(PO$_4$)$_2$

Specific heat and disorder in the mixed state of non-magnetic borocarbides

Magnetotransport of the low-carrier density one-dimensional S=1/2 antiferromagnet Yb4As3