arXiv subjects

P. Goddard

Publications and source records attributed to P. Goddard.

6 recordsLinked to original sources

arXiv2020

Linear-in temperature resistivity from an isotropic Planckian scattering rate

A variety of "strange metals" exhibit resistivity that decreases linearly with temperature as $T\rightarrow 0$, in contrast with conventional metals where resistivity decreases as $T^2$. This $T$-linear resistivity has been attributed to charge carriers scattering at a rate given by $\hbar/\tau=\alpha k_{\rm B} T$, where $\alpha$ is a constant of order unity. This simple relationship between the scattering rate and temperature is observed across a wide variety of materials, suggesting a fundamental upper limit on scattering---the "Planckian limit"---but little is known about the underlying origins of this limit. Here we report a measurement of the angle-dependent magnetoresistance (ADMR) of Nd-LSCO---a hole-doped cuprate that displays $T$-linear resistivity down to the lowest measured temperatures. The ADMR unveils a well-defined Fermi surface that agrees quantitatively with angle-resolved photoemission spectroscopy (ARPES) measurements and reveals a $T$-linear scattering rate that saturates the Planckian limit, namely $\alpha = 1.2 \pm 0.4$. Remarkably, we find that this Planckian scattering rate is isotropic, i.e. it is independent of direction, in contrast with expectations from "hot-spot" models. Our findings suggest that $T$-linear resistivity in strange metals emerges from a momentum-independent inelastic scattering rate that reaches the Planckian limit.

cond-mat.str-el↗

arXiv2015

Mixed-symmetry octupole and hexadecapole excitations in the N=52 isotones

Background: Excitations with mixed proton-neutron symmetry have been previously observed in the $N=52$ isotones. Besides the well established quadrupole mixed-symmetry states (MSS), octupole and hexadecapole MSS have been recently proposed for the nuclei $^{92}$Zr and $^{94}$Mo. Purpose: The heaviest stable $N=52$ isotone $^{96}$Ru was investigated to study the evolution of octupole and hexadecapole MSS with increasing proton number. Methods: Two inelastic proton-scattering experiments on $^{96}$Ru were performed to extract branching ratios, multipole mixing ratios, and level lifetimes. From the combined data, absolute transition strengths were calculated. Results: Strong $M1$ transitions between the lowest-lying $3^-$ and $4^+$ states were observed, providing evidence for a one-phonon mixed-symmetry character of the $3^{(-)}_2$ and $4^+_2$ states. Conclusions: $sdg$-IBM-2 calculations were performed for $^{96}$Ru. The results are in excellent agreement with the experimental data, pointing out a one-phonon hexadecapole mixed-symmetry character of the $4^+_2$ state. The $\big< 3^-_1||M1||3^{(-)}_2\big>$ matrix element is found to scale with the $<2^+_{\mathrm{s}}||M1||2^+_{\mathrm{ms}}>$ matrix element.

nucl-ex↗

arXiv2011

Investigation of octupole vibrational states in 150Nd via inelastic proton scattering (p,p'g)

Octupole vibrational states were studied in the nucleus $^{150}\mathrm{Nd}$ via inelastic proton scattering with $\unit[10.9]{MeV}$ protons which are an excellent probe to excite natural parity states. For the first time in $^{150}\mathrm{Nd}$, both the scattered protons and the $γ$ rays were detected in coincidence giving the possibility to measure branching ratios in detail. Using the coincidence technique, the $B(E1)$ ratios of the decaying transitions for 10 octupole vibrational states and other negative-parity states to the yrast band were determined and compared to the Alaga rule. The positive and negative-parity states revealed by this experiment are compared with Interacting Boson Approximation (IBA) calculations performed in the (spdf) boson space. The calculations are found to be in good agreement with the experimental data, both for positive and negative-parity states.

nucl-ex↗

arXiv2004

Absence of field-induced charge-density wave states in (Per)$_2$Pt(mnt)$_2$

Graf {\it et al.} [Phys. Rev. Lett. {\bf 93} 076406 (2004)] recently attributed features in the magnetic-field-dependent longitudinal resistance of (Per)$_2$Pt(mnt)$_2$ to a cascade of field-induced charge-density waves (FICDWs). Here we show that a quantitative magnetotransport analysis reveals orbital quantization to be absent, disproving the presence of FICDWs. Our data show that the conduction is instead dominated by the sliding CDW collective mode at low temperatures.

cond-mat.str-el↗

arXiv1994

Conformal Field Theories, Representations and Lattice Constructions

An account is given of the structure and representations of chiral bosonic meromorphic conformal field theories (CFT's), and, in particular, the conditions under which such a CFT may be extended by a representation to form a new theory. This general approach is illustrated by considering the untwisted and $Z_2$-twisted theories, $H(Λ)$ and $\tilde H(Λ)$ respectively, which may be constructed from a suitable even Euclidean lattice $Λ$. Similarly, one may construct lattices $Λ_C$ and $\tildeΛ_C$ by analogous constructions from a doubly-even binary code $C$. In the case when $C$ is self-dual, the corresponding lattices are also. Similarly, $H(Λ)$ and $\tilde H(Λ)$ are self-dual if and only if $Λ$ is. We show that $H(Λ_C)$ has a natural ``triality'' structure, which induces an isomorphism $H(\tildeΛ_C)\equiv\tilde H(Λ_C)$ and also a triality structure on $\tilde H(\tildeΛ_C)$. For $C$ the Golay code, $\tildeΛ_C$ is the Leech lattice, and the triality on $\tilde H(\tildeΛ_C)$ is the symmetry which extends the natural action of (an extension of) Conway's group on this theory to the Monster, so setting triality and Frenkel, Lepowsky and Meurman's construction of the natural Monster module in a more general context. The results also serve to shed some light on the classification of self-dual CFT's. We find that of the 48 theories $H(Λ)$ and $\tilde H(Λ)$ with central charge 24 that there are 39 distinct ones, and further that all 9 coincidences are accounted for by the isomorphism detailed above, induced by the existence of a doubly-even self-dual binary code.

hep-th↗

arXiv1994

Quantisation of the SU(N) WZW Model at Level $k$

The quantisation of the Wess-Zumino-Witten model on a circle is discussed in the case of $SU(N)$ at level $k$. The quantum commutation of the chiral vertex operators is described by an exchange relation with a braiding matrix, $Q$. Using quantum consistency conditions, the braiding matrix is found explicitly in the fundamental representation. This matrix is shown to be related to the Racah matrix for $U_t(SL(N))$. From calculating the four-point functions with the Knizhnik-Zamolodchikov equations, the deformation parameter $t$ is shown to be $t=\exp({iπ/(k+N)})$ when the level $k\ge 2$. For $k=1$, there are two possible types of braiding, $t=\exp({iπ/(1+N)})$ or $t=\exp(iπ)$. In the latter case, the chiral vertex operators are constructed explicitly by extending the free field realisation a la Frenkel-Kac and Segal. This construction gives an explicit description of how to chirally factorise the $SU(N)_{k=1}$ WZW model.

hep-th↗