Damien P. George

Standard model on a domain-wall brane?

We propose a 4+1-dimensional action that is a candidate for realizing a standard-model-like effective theory for fields dynamically localized to a domain-wall brane. Our construction is in part based on the conjecture that the Dvali-Shifman mechanism for dynamically localizing gauge bosons to a domain wall works correctly in 4+1-d. Assuming this to be so, we require the gauge symmetry to be SU(5) in the bulk, spontaneously breaking to SU(3) x SU(2) x U(1) inside the domain wall, thus dynamically localizing the standard-model gauge bosons provided that the SU(5) theory in the bulk exhibits confinement. The wall is created jointly by a real singlet-Higgs field {eta} configured as a kink, and an SU(5) adjoint-Higgs field {chi} that takes nonzero values inside the wall. Chiral 3+1-dimensional quarks and leptons are confined and split along the bulk direction via their Yukawa couplings to {eta} and {chi}. The Higgs doublet and its color triplet SU(5) partner are similarly localized and split. The splittings can suppress colored-Higgs-induced proton decay and, because of the different localization profiles, the usual SU(5) mass relation m{sub e}=m{sub d} does not arise. Localized gravity is generated via the Randall-Sundrum alternative to compactification.

Fermions, scalars, and Randall-Sundrum gravity on domain-wall branes

We analyze the general features of localization of fermions and scalars in smoothed field-theoretical versions of the type 2 Randall-Sundrum braneworld model. A scalar field domain wall forms the brane, inducing warped gravity, and we study the mass spectra of the matter fields in the dimensionally reduced theory. We demonstrate explicitly that both scalar and fermion fields exhibit a continuum of properly normalizable modes starting at zero mass. If discrete bound modes are present in the gravity-free case, these become resonances in the continuum, while off-resonant modes are highly suppressed on the brane. We describe briefly how another scalar field can be used to break a symmetry on the domain wall while leaving it unbroken far from the wall, as has already been done in the flat space case. Finally we present numerical calculations for a toy model which demonstrates the decoupling of continuum modes at low energies, so the theory becomes four dimensional.

Kink modes and effective four dimensional fermion and Higgs brane models

In the construction of a classical smoothed out brane world model in five dimensions, one uses a dynamically generated domain wall (a kink) to localize an effective four dimensional theory. At the level of the Euler-Lagrange equations the kink sets up a potential well, a mechanism which has been employed extensively to obtain localized, four dimensional, massless chiral fermions. We present the generalization of this kink trapping mechanism for both scalar and fermionic fields, and retain all degrees of freedom that were present in the higher dimensional theory. We show that a kink background induces a symmetric modified Poeschl-Teller potential well, and give explicit analytic forms for all the bound modes and a restricted set of the continuum modes. We demonstrate that it is possible to confine an effective four dimensional scalar field with a quartic potential of arbitrary shape. This can be used to place the standard model electroweak Higgs field on the brane, and also generate nested kink solutions. We also consider the limits of the parameters in the theory which give thin kinks and localized and delocalized scalar and fermionic fields.

Stability of scalar fields in warped extra dimensions

This work sets up a general theoretical framework to study stability of models with a warped extra dimension where N scalar fields couple minimally to gravity. Our analysis encompasses Randall-Sundrum models with branes and bulk scalars, and general domain-wall models. We derive the Schrödinger equation governing the spin-0 spectrum of perturbations of such a system. This result is specialized to potentials generated using fake supergravity, and we show that models without branes are free of tachyonic modes. Turning to the existence of zero modes, we prove a criterion which relates the number of normalizable zero modes to the parities of the scalar fields. Constructions with definite parity and only odd scalars are shown to be free of zero modes and are hence perturbatively stable. We give two explicit examples of domain-wall models with a soft wall, one which admits a zero mode and one which does not. The latter is an example of a model that stabilizes a compact extra dimension using only bulk scalars and does not require dynamical branes.

Technology computer-aided design modelling of single-atom doping for fabrication of buried nanostructures

Future quantum devices may exploit arrays of dopants positioned with nanoscale precision in an intrinsic semiconductor matrix. One proposal for the fabrication of such an array is by the implantation of single low-energy dopant ions into prefabricated cells within the device, the arrival of each dopant being detected electrically. With the aid of technology computer-aided design (TCAD) modelling, we outline an electrical registration process which makes use of appropriately biased electrodes incorporated within the device to detect the space charge induced within the near-intrinsic substrate by a single-ion implant. A series of simulations aimed at optimizing the charge detection efficiency in such detectors are described, and found to be in good agreement with experimental measurements conducted to characterize fabricated test structures via high-energy He-ion implantation. We demonstrate this fabrication strategy to offer the potential of creating scalable arrangements of dopants for extended nanoscale device applications. Our interest in this scheme is the development of the Kane solid-state quantum computer (Kane B E 1998 Nature 393 133), which exploits as qubits31P atoms embedded with nanoscale precision in an array, within a pure28Si MOS architecture.

SU(5) grand unification on a domain-wall brane from an E{sub 6}-invariant action

An SU(5) grand unification scheme for effective 3+1-dimensional fields dynamically localized on a domain-wall brane is constructed. This is achieved through the confluence of the clash-of-symmetries mechanism for symmetry breaking through domain-wall formation, and the Dvali-Shifman gauge-boson localization idea. It requires an E{sub 6} gauge-invariant action, yielding a domain-wall solution that has E{sub 6} broken to differently embedded SO(10) x U(1) subgroups in the two bulk regions on opposite sides of the wall. On the wall itself, the unbroken symmetry is the intersection of the two bulk subgroups, and contains SU(5). A 4+1-dimensional fermion family in the 27 of E{sub 6} gives rise to localized left-handed zero modes in the 5*+10+1+1 representation of SU(5). The remaining ten fermion components of the 27 are delocalized exotic states, not appearing in the effective 3+1-dimensional theory on the domain-wall brane. The scheme is compatible with the type-2 Randall-Sundrum mechanism for graviton localization; the single extra dimension is infinite.

Neutrino mass and μ → e + γ from a mini-seesaw

The recently proposed “mini-seesaw mechanism” combines naturally suppressed Dirac and Majorana masses to achieve light Standard Model neutrinos via a low-scale seesaw. A key feature of this approach is the presence of multiple light (order GeV) sterile-neutrinos that mix with the Standard Model. In this work we study the bounds on these light sterile-neutrinos from processes like μ → e + γ, invisible Z-decays, and neutrino-less double beta-decay. We show that viable parameter space exists and that, interestingly, key observables can lie just below current experimental sensitivities. In particular, a motivated region of parameter space predicts a μ → e + γ branching fraction within the range to be probed by MEG.

IBIC characterisation of novel detectors for single atom doping of quantum computer devices

Abstract Single ion implantation and online detection is highly desirable for the emerging application, in which single 31P ions need to be inserted in prefabricated silicon cells to construct solid-state quantum bits (qubits). In order to fabricate qubit arrays, we have developed novel detectors that employ detector electrodes adjacent to the prefabricated cells that can detect single keV ion strikes appropriate for the fabrication of shallow phosphorus arrays. The method utilises a high purity silicon substrate with very high resistivity, a thin SiO2 surface layer, nanometer masks for the lateral positioning single phosphorus implantation, biased electrodes applied to the surface of the silicon and sensitive electronics that can detect the charge transient from single keV ion strikes. A TCAD (Technology Computer Aided Design) software package was applied in the optimisation of the device design and simulation of the detector performance. Here we show the characterisation of these detectors using ion beam induced charge (IBIC) with a focused 2 MeV He ions in a nuclear microprobe. The IBIC imaging method in a nuclear microprobe allowed us to measure the dead-layer thickness of the detector structure (required to be very thin for successful detection of keV ions), and the spatial distribution of the charge collection efficiency around the entire region of the detector. We show that our detectors have near 100% charge collection efficiency for MeV ions, extremely thin dead-layer thickness (about 7 nm) and a wide active region extending laterally from the electrodes (10–20 μm) where qubit arrays can be constructed. We demonstrate that the device can be successfully applied in the detection of keV ionisation energy from single events of keV X-rays and keV 31P ions.

Symmetry breaking, subgroup embeddings and the Weyl group

We present a systematic approach to writing adjoint Higgs vacuum expectation values (vevs), which break a symmetry G to differently embedded isomorphic copies of a subgroup belonging to the chain G ⊃ H1 ⊃ ··· ⊃ Hl, as linear combinations of each other. Given an adjoint Higgs vacuum expectation value h breaking G → H, a full complement of vevs breaking G to different embeddings of the subgroup H can be generated through the Weyl group orbit of h. An explicit formula for recovering each vev is given. We focus on the case when H stabilizes the highest weight of the lowest dimensional fundamental representation, where the formula is exceedingly simple. We also discuss cases when the Higgs field is not in the adjoint representation and apply these techniques to current research problems, especially in domain-wall brane model building.

Dynamics of the infinitely-thin kink

Abstract We consider the dynamics of the domain-wall kink soliton, in particular we study the zero mode of translation. In the infinitely-thin kink limit, we show that the zero mode is almost completely frozen out, the only remnant being a dynamically constrained four-dimensional mode of a single but arbitrary frequency. In relation to this result, we show that the usual mode expansion for dealing with zero modes – implicit collective coordinates – is not in fact a completely general expansion, and that one must use instead a traditional generalised Fourier analysis.