arXiv subjects

Robert E. Throckmorton

Publications and source records attributed to Robert E. Throckmorton.

23 records · Page 2Linked to original sources

arXiv2015

Many-body effects and ultraviolet renormalization in three-dimensional Dirac materials

We develop a theory for electron-electron interaction-induced many-body effects in three dimensional (3D) Weyl or Dirac semimetals, including interaction corrections to the polarizability, electron self-energy, and vertex function, up to second order in the effective fine structure constant of the Dirac material. These results are used to derive the higher-order ultraviolet renormalization of the Fermi velocity, effective coupling, and quasiparticle residue, revealing that the corrections to the renormalization group (RG) flows of both the velocity and coupling counteract the leading-order tendencies of velocity enhancement and coupling suppression at low energies. This in turn leads to the emergence of a critical coupling above which the interaction strength grows with decreasing energy scale. In addition, we identify a range of coupling strengths below the critical point in which the Fermi velocity varies non-monotonically as the low-energy, non-interacting fixed point is approached. Furthermore, we find that while the higher-order correction to the flow of the coupling is generally small compared to the leading order, the corresponding correction to the velocity flow carries an additional factor of the Dirac cone flavor number (the multiplicity of electron species, e.g. ground-state valley degeneracy arising from the band structure) relative to the leading-order result. Thus, for materials with a larger multiplicity, the regime of velocity non-monotonicity is reached for modest values of the coupling strength.

cond-mat.mes-hall↗

arXiv2014

Quantum multicriticality of bilayer graphene in the presence of a tunable energy gap

We develop a theory for quantum phases and quantum multicriticality in bilayer graphene in the presence of an explicit energy gap in the non-interacting spectrum by extending previous renormalization group (RG) analyses of electron-electron interactions in gapless bilayer graphene at finite temperature to include the effect of an electric field applied perpendicular to the sample. We determine the possible outcomes of the resulting RG equations, represented by "fixed rays" along which ratios of the coupling constants remain constant and map out the leading instabilities of the system for an interaction of the form of a Coulomb interaction that is screened by two parallel conducting plates placed equidistant from the electron. We find that some of the fixed rays on the "target plane" found in the zero-field case are no longer valid fixed rays, but that all four of the isolated rays are still valid. We also find five additional fixed rays that are not present in the zero-field case. We then construct maps of the leading instability (or instabilities) of the system for the screened Coulomb-like interaction as a function of the overall interaction strength and interaction range for four values of the applied electric field. We find that the pattern of leading instabilities is the same as that found in the zero-field case, namely that the system is unstable to a layer antiferromagnetic state for short-ranged interactions, to a nematic state for long-ranged interactions, and to both for intermediate-ranged interactions. However, if the interaction becomes too long-ranged or too weak, then the system will exhibit no instabilities. The ranges at which the nematic instability first appears, the antiferromagnetic instability disappears, and the nematic instability disappears all decrease with increasing applied electric field.

cond-mat.str-el↗

arXiv2012

Electronic multicriticality in bilayer graphene

We map out the possible ordered states in bilayer graphene at the neutrality point by extending the previous renormalization group treatment of many-body instabilities to finite temperature, trigonal warping and externally applied perpendicular electric field. We were able to analytically determine all outcomes of the RG flow equations for the 9 four-fermion coupling constants. While the full phase diagram exhibits a rich structure, we confirm that when forward scattering dominates, the only ordering tendency with divergent susceptibility at finite temperature is the nematic. At finite temperature this result is stable with respect to small back and layer imbalance scattering; further increasing their strength leads to the layer antiferromagnet. We also determine conditions for other ordered states to appear and compare our results to the special cases of attractive and repulsive Hubbard models where exact results are available.

cond-mat.str-el↗

arXiv2012

Fermions on bilayer graphene: symmetry breaking for B=0 and nu=0

We extend previous analyses of fermions on a honeycomb bilayer lattice via weak-coupling renormalization group (RG) methods with extremely short-range and extremely long-range interactions to the case of finite-range interactions. In particular, we consider different types of interactions including screened Coulomb interactions, much like those produced by a point charge placed either above a single infinite conducting plate or exactly halfway between two parallel infinite conducting plates. Our considerations are motivated by the fact that, in some recent experiments on bilayer graphene there is a single gate while in others there are two gates, which can function as the conducting planes and which, we argue, can lead to distinct broken symmetry phases. We map out the phases that the system enters as a function of the range of the interaction. We discover that the system enters an antiferromagnetic phase for short ranges of the interaction and a nematic phase at long ranges, in agreement with previous work. While the antiferromagnetic phase results in a gap in the spectrum, the nematic phase is gapless, splitting the quadratic degeneracy points into two Dirac cones each. We also consider the effects of an applied magnetic field on the system in the antiferromagnetic phase via variational mean field theory. At low fields, we find that the antiferromagnetic order parameter, Delta(B)-Delta(0) \sim B^2. At higher fields, when omega_c > 2*Delta_0, we find that Delta(B)=omega_c/[ln(omega_c/Delta(0))+C], where C=0.67 and omega_c=eB/m^*c. We also determine the energy gap for creating electron-hole excitations in the system, and, at high fields, we find it to be a*omega_c+2*Delta(B), where a is a non-universal, interaction-dependent, constant.

cond-mat.str-el↗

arXiv2010

Relaxation of Nuclear Magnetic Moments and Site-Selective NMR in d-Wave Superconductors

A new mechanism for relaxing the nuclear magnetic moments, in which a pair of spin-polarized BCS quasiparticles is emitted or absorbed, and which dominates at low temperature, is identified in type-II d-wave superconductors in an external magnetic field above Hc1. The results of the theory are compared with the NMR experiments on YBCO in high magnetic fields and found to agree without invoking antiferromagnetic order in the vortex core.

cond-mat.supr-con↗