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The Design Of Primary Holding Magnet For The Lanl Neutron Electric Dipole Moment Experiment, Piya Amara Palamure Jan 2023

The Design Of Primary Holding Magnet For The Lanl Neutron Electric Dipole Moment Experiment, Piya Amara Palamure

Theses and Dissertations--Physics and Astronomy

The measurement of the permanent electric dipole moment of the neutron (nEDM) plays a significant role in searching for sources of beyond standard model CP violating physics. The goal of the Los Alamos National Laboratory (LANL) nEDM experiment is to push the upper limit of the nEDM to < 3 × 10−27 e·cm (68 % CL). A highly uniform magnetic field is key to achieving this sensitivity for the nEDM measurement by reducing the systematic uncertainties associated with the magnetic field non-uniformity. The B0 coil was designed to achieve a field uniformity of < 0.3 nT·m−1 at a nominal holding field of 1 µT. This document will outline a novel technique employed in the construction of the B0 coil using printed circuit boards (PCBs) and will present preliminary field maps obtained with the B0 coil housed in a magnetically shielded room (MSR) at LANL.

As Ultra Cold Neutrons (UCNs) move from the source to the measurement cells, the UCNs experience a large magnetic field gradient in the region between the layers of the MSR. This large gradient would otherwise cause depolarization of the UCNs. To mitigate this, a double cos θ coil will serve as the …


Design Of The Highly Uniform Magnetic Field And Spin-Transport Magnetic Field Coils For The Los Alamos National Lab Neutron Electric Dipole Moment Experiment, Jared Brewington Jan 2023

Design Of The Highly Uniform Magnetic Field And Spin-Transport Magnetic Field Coils For The Los Alamos National Lab Neutron Electric Dipole Moment Experiment, Jared Brewington

Theses and Dissertations--Physics and Astronomy

Charge-Parity (CP) violation is one of Sakharov's three conditions which serve as guidelines for the generation of a matter-antimatter asymmetry in the early universe. The Standard Model (SM) of particle physics contains sources of CP violation which can be used to predict the baryon asymmetry. The observed baryon asymmetry is not predicted from SM calculations, meaning there must be additional sources of CP violation beyond the Standard Model (BSM) to generate the asymmetry. Permanent electric dipole moments (EDMs), which are inherently parity- and time reversal- violating, present a promising avenue for the discovery of new sources of CP violation to …


Beam Dynamics Simulations And Systematic Studies For The Muon G-2 Experiment At Fermilab, Abel M. Lorente Campos Jan 2023

Beam Dynamics Simulations And Systematic Studies For The Muon G-2 Experiment At Fermilab, Abel M. Lorente Campos

Theses and Dissertations--Physics and Astronomy

The first results of the positive muon anomalous magnetic moment from the Muon g-2 Experiment at Fermilab differs from the Standard Model prediction by 3.3 standard deviations, with an experimental uncertainty of 0.46 ppm. Combining this result with the previous measurement from the Brookhaven National Laboratory, it sets the difference between experiment and theory at 4.2 standard deviations. The goal of the Muon g-2 Experiment at Fermilab is to increase this discrepancy to 5 standard deviations, which would require unprecedented precision in the measurements of 0.14 ppm. Of significant importance to achieving this precision, beam and spin dynamics simulations are …


Measurements Of The Binding Energies Of Ions On Plastic Surfaces In Liquid Nitrogen, Ashok Timsina Jan 2023

Measurements Of The Binding Energies Of Ions On Plastic Surfaces In Liquid Nitrogen, Ashok Timsina

Theses and Dissertations--Physics and Astronomy

To improve the present limit of the neutron electric dipole moment (nEDM) from 1.8*10-26 e. cm to ~ 3*10-28 e. cm, the nEDM@SNS experiment plans to increase neutron density by storing ultracold neutrons in superfluid helium-4. In this experiment, the central part of the apparatus consists of two deuterated tetraphenyl butadiene (dTPB) coated poly(methyl methacrylate) (PMMA) cells, which are sandwiched between grounded and high-voltage electrodes. To achieve such precision, the externally applied electric field has to be stable at the 1% level over a time period of about 1000 s. Several sources of ambient ionizing radiation generate charged …


Aspects Of Topology In Moiré Graphene, Ahmed Khalifa Jan 2023

Aspects Of Topology In Moiré Graphene, Ahmed Khalifa

Theses and Dissertations--Physics and Astronomy

Moiré materials, such as twisted bilayer graphene, have provided a rich platform for fundamental physics and potential technological applications. Superconductivity,
correlated insulators, and Chern insulators are examples of phenomena that have been found experimentally in moiré systems. The interplay of strong electron-electron interactions and topology lies at the heart of the mechanism driving these phenomena. In this work, we study the topological aspects of moiré graphene materials, such as the valley Chern and Chern insulating phases. To study the topological response of these phases, we construct models to describe the edge states which are the telltale signs of nontrivial topology. …


Symbolic Computation Of Squared Amplitudes In High Energy Physics With Machine Learning, Abdulhakim Alnuqaydan Jan 2023

Symbolic Computation Of Squared Amplitudes In High Energy Physics With Machine Learning, Abdulhakim Alnuqaydan

Theses and Dissertations--Physics and Astronomy

The calculation of particle interaction squared amplitudes is a key step in the calculation of cross sections in high-energy physics. These complex calculations are currently performed using domain-specific symbolic algebra tools, where the computational time escalates rapidly with an increase in the number of loops and final state particles. This dissertation introduces an innovative approach: employing a transformer-based sequence-to-sequence model capable of accurately predicting squared amplitudes of Standard Model processes up to one-loop order when trained on symbolic sequence pairs. The primary objective of this work is to significantly reduce the computational time and, more importantly, develop a model that …


Elastic And Inelastic Compton Scattering From Deuterium At 61 Mev, Danula Godagama Jan 2022

Elastic And Inelastic Compton Scattering From Deuterium At 61 Mev, Danula Godagama

Theses and Dissertations--Physics and Astronomy

A Compton scattering experiment using deuteron as target nuclei was carried out at the HIγS free electron laser facility at Durham, NC, with the goal of extracting the electromagnetic scalar polarizabilities of the neutron, αn and βn. A beam of 61~MeV gamma photons with a narrow energy spread was incident on a liquid deuterium target. The scattered gamma rays were detected at three scattering angles, 55o, 115o and 150o. Backward-scattered gamma rays were detected using two large-volume NaI spectrometers with energy resolution (σE/E) better than 2%. The combined effect of …


Studies Of Time Variations Of The Magnetic Field In The Nedm@Sns Experiment, Mojtaba Behzadipour Jan 2022

Studies Of Time Variations Of The Magnetic Field In The Nedm@Sns Experiment, Mojtaba Behzadipour

Theses and Dissertations--Physics and Astronomy

It is thought that equal quantities of matter and antimatter were generated at the moment of the Big Bang. However, observations of the Universe show that there is a significant excess of matter over antimatter. The matter-antimatter asymmetry in the Universe (baryon to photon ratio) is observed to be of the order of 10-10 [1]. Baryogenesis is a possible explanation for the matter-antimatter asymmetry of the universe. In 1967, Sakharov proposed three criteria necessary for Baryogenesis. The three conditions are: 1) baryon number violation, 2) C and CP violation and 3) departure from thermal equilibrium. However, the Standard Model's …


Angular Distribution Of Electron-Helium Scattering In The Presence Of A 1.17 Ev Laser Field, Brian N. Kim Jan 2022

Angular Distribution Of Electron-Helium Scattering In The Presence Of A 1.17 Ev Laser Field, Brian N. Kim

Theses and Dissertations--Physics and Astronomy

We have measured relative differential cross sections for 350 eV electrons scattered by a helium target in the presence of 1.17 eV photons from an Nd:YAG laser. We report an angular distribution of free-free electrons that were scattered elastically at angles between 15o and 80o and of free-free electrons that underwent the process of electron-impact excitation of helium to its unresolved (1s2s)1S and (1s2p)1P excited states at angles between 1o and 80o. Our experiments test the momentum transfer dependence and the relationship between elastic and inelastic scattering in the Kroll-Watson approximation. …


An Energy-Integrated Analysis For Measuring The Anomalous Precession Frequency For The Muon G − 2 Experiment At Fermilab, Laura Kelton Jan 2022

An Energy-Integrated Analysis For Measuring The Anomalous Precession Frequency For The Muon G − 2 Experiment At Fermilab, Laura Kelton

Theses and Dissertations--Physics and Astronomy

In the search for physics beyond the Standard Model, the Muon g − 2 Experiment at Fermilab (E989) will make the most precise measurement of the anomalous magnetic moment of the muon, aμ. Improvements in precision come from both increased statistics and new techniques to significantly reduce previous systematic uncertainties. The muon aμ is determined by extracting both the anomalous spin precession frequency, ωa, and the average magnetic field sampled by the muons, B. Traditionally an energy threshold analysis method which requires reconstruction of decay positrons from the muon decay, μ+ → e+ …


Cryogenic Magnetic Field Monitoring System In The Sns Neutron Edm Experiment, Umit Hasan Coskun Jan 2022

Cryogenic Magnetic Field Monitoring System In The Sns Neutron Edm Experiment, Umit Hasan Coskun

Theses and Dissertations--Physics and Astronomy

A permanent neutron electric dipole moment (nEDM), dn, would violate charge-conjugation and parity (CP) symmetry. The neutron electric dipole moment currently has a global limit of dn < 1.8 x 10-26 e cm (90% CL). This limit is intended to be improved by two orders of magnitude by the nEDM experiment at the Spallation Neutron Source (SNS nEDM), dn ~ 10-28 e cm. The magnetic field non-uniformities within the experimental region must be precisely monitored and managed in order to suppress systematic effects in the experiment caused by magnetic field gradients. The estimation of magnetic field components within …


Extraction Of Deep Inelastic Cross Sections Using A 10.4 Gev Electron Beam And A Polarized Helium-3 Target, Murchhana Roy Jan 2022

Extraction Of Deep Inelastic Cross Sections Using A 10.4 Gev Electron Beam And A Polarized Helium-3 Target, Murchhana Roy

Theses and Dissertations--Physics and Astronomy

Experiment E12-06-121 at Jefferson Lab aims to do a precision measurement of the neutron spin structure function g2 using inclusive inelastic scattering of electrons over a large kinematic range of x and Q2. The third moment of the linear combination of the spin structure functions g1 and g2, d2, is one of the cleanest higher twist observables and contains information on quark-gluon correlations. It is connected to the "color polarizability" or "color Lorentz force" of the nucleon. The experimental data taking was successfully conducted in Hall C using a longitudinally polarized electron …


Thermalization And Quantum Information In Conformal Field Theory, Ashish Kakkar Jan 2022

Thermalization And Quantum Information In Conformal Field Theory, Ashish Kakkar

Theses and Dissertations--Physics and Astronomy

The consequences of the constraints of conformal symmetry are far-reaching within
theoretical physics. In this dissertation we address a series of questions in conformal
field theory: 1) We calculate the spectrum of qKdV charges in a large central charge
expansion. 2) We determine the corrections to bulk information geometry from 1/N
contributions to holographic correlators. 3) We study the higher genus partitions
functions of CFTs associated with classical and quantum error-correcting codes.


High Performance Data Acquisition And Analysis Routines For The Nab Experiment, David Mathews Jan 2022

High Performance Data Acquisition And Analysis Routines For The Nab Experiment, David Mathews

Theses and Dissertations--Physics and Astronomy

Probes of the Standard Model of particle physics are pushing further and further into the so-called “precision frontier”. In order to reach the precision goals of these experiments, a combination of elegant experimental design and robust data acquisition and analysis is required. Two experiments that embody this philosophy are the Nab and Calcium-45 experiments. These experiments are probing the understanding of the weak interaction by examining the beta decay of the free neutron and Calcium-45 respectively. They both aim to measure correlation parameters in the neutron beta decay alphabet, a and b. The parameter a, the electron-neutrino correlation coefficient, is …


Enhancements To Uniformity Of Magnetic Fields At The Sns Nedm Experiment, Ahmad Saftah Jan 2022

Enhancements To Uniformity Of Magnetic Fields At The Sns Nedm Experiment, Ahmad Saftah

Theses and Dissertations--Physics and Astronomy

The nEDM experiment at the Spallation Neutron Source (SNS) aims to increase
experimental sensitivity to hadronic CP violation by nearly two orders of magnitude.To do that the nEDMSNS experiment requires an extremely uniform magnetic field to maintain 3He polarization during transit to the measurement cell. The Magnetic Shield Enclosure (MSE) coil provides the required field. However, the superconducting shield distorts the MSE field.

This thesis discusses a magnetic cloak for the nEDM@SNS experiment that can restore the MSE field uniformity and cos theta coils designed to test the magnetic cloak in the first part. The second part of this …


Understanding The Degradation Mechanism In Methyl Ammonium Lead Halide Perovskite And Black Phosphorene Via Electrical Transport Study, Huda Saleh Aljeailan Jan 2022

Understanding The Degradation Mechanism In Methyl Ammonium Lead Halide Perovskite And Black Phosphorene Via Electrical Transport Study, Huda Saleh Aljeailan

Theses and Dissertations--Physics and Astronomy

This work seeks to understand the degradation mechanism of technically important material systems such as black phosphorene (BP), arsenic phosphorene (AsP) and Methyl ammonium lead iodide (CH3NH3PbI3) perovskite. Degradation studies were conducted by studying the in-situ electrical transport properties (resistance and thermoelectric power (TEP)) of these materials in vacuum (under annealed condition) and after exposure to the ambient air.

BP and both exhibited p-type semiconducting (positive TEP) behavior under annealed conditions and the changes in their transport properties upon exposure to ambient air can be explained as due to the charge transfer between the …


Neutron Spectroscopy Of The Parity-Violating 0.734 Ev Neutron Resonance In Lanthanum-139 In Preparation For The Noptrex Time Reversal Violation Experiment, Danielle Schaper Jan 2022

Neutron Spectroscopy Of The Parity-Violating 0.734 Ev Neutron Resonance In Lanthanum-139 In Preparation For The Noptrex Time Reversal Violation Experiment, Danielle Schaper

Theses and Dissertations--Physics and Astronomy

One of the most outstanding questions in physics is the matter-antimatter asymmetry of the Universe, resulting from excess baryogenesis processes during the early moments of the formation of the Universe. At present, the types of processes needed to explain this matter excess, so-called `CP-violating processes' are known to exist within the present framework of the Standard Model of particle physics. However, decades of research has shown that our understanding of the origin of these processes is incomplete, as we do not presently know of enough sources of CP-violating processes to account for the large baryon asymmetry that we observe. The …


Magnetization Dynamics In A Modified Square Artificial Spin Ice, Amrit Kaphle Jan 2022

Magnetization Dynamics In A Modified Square Artificial Spin Ice, Amrit Kaphle

Theses and Dissertations--Physics and Astronomy

Artificial spin ices are magnetic metamaterials consisting of nanomagnet arrays in a 2-D lattice. Typically, these nanomagnet arrays are binary macrospins that can only be in an up or down state similar to the Ising spins. They have been intensively used to study magnetic frustration and ordering phenomena in a controlled environment. The hexagonal artificial spin ice and square artificial spin ice are among the most heavily studied systems. In this dissertation, we designed a modified square artificial spin ice system by an ordered substitution of a double-segment for a nanomagnet array in the unit cell of square artificial spin …


Data Acquisition, Analysis And Simulations For The Fermilab Muon G−2 Experiment, Fang Han Jan 2022

Data Acquisition, Analysis And Simulations For The Fermilab Muon G−2 Experiment, Fang Han

Theses and Dissertations--Physics and Astronomy

The goal of the new Muon g-2 E989 experiment at Fermi National Accelerator Laboratory (FNAL) is a precise measurement of the muon anomalous magnetic moment, aμ ≡ (g-2)/2. The previous BNL experiment measured the anomaly aμ(BNL) with an uncertainty of 0.54 parts per million (ppm). The discrepancy between the current standard model calculation of the aμ(SM) and the previous measurement aμ(BNL) is over 3σ. The FNAL Muon g-2 experiment aims at increasing the precision to 140 parts per billion (ppb) to resolve the discrepancy between the theoretical …


Energy Integrated Ratio Analysis Of The Anomalous Precession Frequency In The Fermilab Muon G-2 Experiment, Ritwika Chakraborty Jan 2022

Energy Integrated Ratio Analysis Of The Anomalous Precession Frequency In The Fermilab Muon G-2 Experiment, Ritwika Chakraborty

Theses and Dissertations--Physics and Astronomy

The muon’s anomalous magnetic moment, aμ, provides a unique way for probing physics beyond the standard model experimentally as it gathers contributions from all the known and unknown forces and particles in nature. The theoretical prediction of aμ has been in greater than 3 σ tension with the experimental measurement since the results of the Muon g-2 Experiment at the Brookhaven National Laboratory (E-821) were published in the early 2000s with a precision of 540 ppb. To settle this tension, the new Fermilab Muon g - 2 Experiment (E-989) is currently taking data with the aim of …


Predicting Material Properties: Applications Of Multi-Scale Multiphysics Numerical Modeling To Transport Problems In Biochemical Systems And Chemical Process Engineering, Tom Pace Jan 2021

Predicting Material Properties: Applications Of Multi-Scale Multiphysics Numerical Modeling To Transport Problems In Biochemical Systems And Chemical Process Engineering, Tom Pace

Theses and Dissertations--Physics and Astronomy

Material properties are used in a wide variety of theoretical models of material behavior. Descriptive properties quantify the nature, structure, or composition of the material. Behavioral properties quantify the response of the material to an imposed condition. The central question of this work concerns the prediction of behavioral properties from previously determined descriptive properties through hierarchical multi-scale, multiphysics models implemented as numerical simulations. Applications covered focus on mass transport models, including sequential enzyme-catalyzed reactions in systems biology, and an industrial chemical process in a common reaction medium.


Topics In Quantum Quench And Entanglement, Sinong Liu Jan 2021

Topics In Quantum Quench And Entanglement, Sinong Liu

Theses and Dissertations--Physics and Astronomy

The dissertation includes two parts.

In Part I, we study non-equilibrium phenomena in various models associated with global quantum quench. It is known that local quantities, when subjected to global quantum quench across or approaching critical points, exhibit a variety of universal scaling behaviors at various quench rates. To investigate if similar scaling holds for non-local quantities, we consider the scaling behavior of circuit complexity under quantum quench across the critical massless point in Majorana fermion field theory of the one-dimensional integrable transverse field Ising model and find it obeys such scaling. To investigate if similar scaling holds for non-relativistic …


Strongly Correlated Phases In Quantum Hall Systems, Amartya Saha Jan 2021

Strongly Correlated Phases In Quantum Hall Systems, Amartya Saha

Theses and Dissertations--Physics and Astronomy

Quantum Hall systems have a one-body energy spectrum consisting of dispersion-less Landau levels. Electron-electron interactions thus dominate in partially filled Landau levels, which exhibit a myriad of strongly correlated phases such as quantum hall ferromagnets and fractional quantum Hall phases. We study two examples of these phenomena.

In the first project, we explore the ground state of a system with an interface between two semi-infinite regions with fillings ν= 4 and ν= 3 respectively. The width of the interface can be controlled by varying the background potential, which provides an additional tuning parameter. For a certain range of …


Optical Metasurfaces, Fatih Balli Jan 2021

Optical Metasurfaces, Fatih Balli

Theses and Dissertations--Physics and Astronomy

Traditional optical elements, such as refractive lenses, mirrors, phase plates and polarizers have been used for various purposes such as imaging systems, lithographic printing, astronomical observations and display technology. Despite their long-term achievements, they can be bulky and not suitable for miniaturization. On the other hand, recent nanotechnology advances allowed us to manufacture micro and nanoscale devices with ultra-compact sizes. Metasurfaces, 2D engineered artificial interfaces, have emerged as candidates to replace traditional refractive lenses with ultra-thin miniaturized optical elements. They possess sub-wavelength unit cell structures with a specific geometry and material selection. Each unit cell can uniquely tailor the phase, …


Analyzing The Effect Of Second-Class Currents On Neutron Beta Decay Observables And The Effect Of Thomas Rotation On The Relativistic Transformations Of Electromagnetic Fields, Lakshya Malhotra Jan 2021

Analyzing The Effect Of Second-Class Currents On Neutron Beta Decay Observables And The Effect Of Thomas Rotation On The Relativistic Transformations Of Electromagnetic Fields, Lakshya Malhotra

Theses and Dissertations--Physics and Astronomy

The next generation of neutron beta decay measurements will attempt to analyze various beta decay observables of up to O(10-4) precision. At this level of experimental precision, the effects of second-class currents will contribute theoretical uncertainties to the interpretation of these measurements. Therefore, it is important to investigate the effects of these second-class currents on decay parameters, such as the Fierz interference term b which is linear in beyond standard model couplings. A maximum likelihood statistical framework and Rfit techniques are employed to study these second-class currents effects. Inputs to the Rfit technique are obtained through …


Effective Field Theory Applications: From Dark Matter To Neutrino Nucleon Scattering, Qing Chen Jan 2021

Effective Field Theory Applications: From Dark Matter To Neutrino Nucleon Scattering, Qing Chen

Theses and Dissertations--Physics and Astronomy

Weakly-interacting-massive-particles (WIMPs) are a large class of viable dark matter candidates. We compute cross sections for electroweak-doublet WIMPs scattering on atomic nuclei, at leading and subleading order using heavy WIMP effective field theory. Neutrino-nucleon charged current elastic scattering is an important process in the detectors of long baseline accelerator neutrino oscillation experiments. We compute QED radiative corrections to this process employing soft-collinear effective field theory.


Magnetization Dynamics In Kagome Artificial Spin Ice Considering The Effect Of Vertex And Geometrical Lattice Distortion, Ali Frotanpour Jan 2021

Magnetization Dynamics In Kagome Artificial Spin Ice Considering The Effect Of Vertex And Geometrical Lattice Distortion, Ali Frotanpour

Theses and Dissertations--Physics and Astronomy

Artificial spin ices (ASI) have been shown to exhibit dynamic magnetic responses that are dramatically different from plane magnetic thin films. A number of magnetic ASI have been fabricated and measured in recent years. However, some important effects including influence of vertex and geometrical distortion on their dynamic response have not been addressed. This dissertation adopts Ferromagnetic Resonance (FMR) spectroscopy to study magnetization dynamics in fabricated artificial spin ices with a contentiously distorted Honeycomb geometry with the specific goal of exploring how the vertex and lattice distortion affect the dynamic magnetic response. Samples were patterned using electron beam lithography techniques. …


Large N Fields And Holography, Animik Ghosh Jan 2020

Large N Fields And Holography, Animik Ghosh

Theses and Dissertations--Physics and Astronomy

We study (nearly) AdS/CFT holography within the context of the Sachdev-Ye- Kitaev (SYK) model. We present a systematic procedure to extract the dynamics of the low energy Schwarzian mode in SYK type models with a single energy scale J and emergent reparametrization symmetry in the infrared within the framework of perturbation theory. We develop a systematic approach using Feynman diagrams in bilocal theory to obtain a formal expression for the enhanced and O(1) corrections to the bilocal propagator and apply this general technique to large q SYK. We show that the Schwarzian theory describes a sector of a general class …


Transverse And Longitudinal Thermal Diffusivity Measurements Of Polymer And Small Molecule Organic Semiconductors With Different Techniques, Maryam Shahi Jan 2020

Transverse And Longitudinal Thermal Diffusivity Measurements Of Polymer And Small Molecule Organic Semiconductors With Different Techniques, Maryam Shahi

Theses and Dissertations--Physics and Astronomy

The main thrust of this research was to develop new probes to measure thermal conductivities (κ) of small-molecule crystals, as well as polymer blends of organic semiconductors, both to screen these for possible applications, e.g. as thermoelectric power generators, and to gain an understanding of thermal transport in them. Emphasis has been on the crystals of “TIPS pentacene” [TIPS = 6,13 bis(triisopropylsilylethynyl), and free-standing films of PEDOT:PSS [poly(3,4-ethylenedioxythiophene) polystyrene sulfonate] for different electrochemical and thermoelectric applications. Separate techniques were used for in-plane and transverse thermal conductivities in which 𝜅𝜅 is determined indirectly from measurements of the thermal diffusivity (D ≡ …


Graphene In A Uniform Magnetic Field, Ankur Das Jan 2020

Graphene In A Uniform Magnetic Field, Ankur Das

Theses and Dissertations--Physics and Astronomy

We study monolayer graphene in a uniform magnetic field in the absence and presence of interactions. In the non-interacting limit, for p/q flux quanta per unit cell (p, q are coprime integer), the central two bands have 2q Dirac points in the Brillouin zone (BZ) in the nearest-neighbor model. These touchings and their locations are guaranteed by chiral symmetry and the lattice symmetries of the honeycomb structure. If we add a staggered potential and a next-nearest-neighbor hopping we find that their competition leads to a topological phase transition. We also study the stability of the Dirac touchings to one-body perturbations …