scholarly journals Majorana zero modes induced by superconducting phase bias

2022 ◽  
Author(s):  
Omri Lesser ◽  
Yuval Oreg
Keyword(s):  
Time Reversal ◽  
Time Reversal Symmetry ◽  
Zero Modes ◽  
Topological Quantum ◽  
Potential Applications ◽  
Long Time ◽  
Phase Bias ◽  
The Subject ◽  
Topological Quantum Computation ◽  
Gap States

Abstract Majorana zero modes in condensed matter systems have been the subject of much interest in recent years. Their non-Abelian exchange statistics, making them a unique state of matter, and their potential applications in topological quantum computation, earned them attention from both theorists and experimentalists. It is generally understood that in order to form Majorana zero modes in quasi-one-dimensional topological insulators, time-reversal symmetry must be broken. The straightforward mechanisms for doing so—applying magnetic fields or coupling to ferromagnets—turned out to have many unwanted side effects, such as degradation of superconductivity and the formation of sub-gap states, which is part of the reason Majorana zero modes have been eluding direct experimental detection for a long time. Here we review several proposal that rely on controlling the phase of the superconducting order parameter, either as the sole mechanism for time-reversal-symmetry breaking, or as an additional handy knob used to reduce the applied magnetic field. These proposals hold practical promise to improve Majorana detection, and they shed light on the physics underlying the formation of the topological superconducting state.

scholarly journals Majorana zero modes in impurity-assisted vortex of LiFeAs superconductor

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Lingyuan Kong ◽  
Lu Cao ◽  
Shiyu Zhu ◽  
Michał Papaj ◽  
Guangyang Dai ◽  
...  
Keyword(s):  
Quantum Computation ◽  
Zero Mode ◽  
Scanning Tunneling ◽  
Homogeneous Material ◽  
Dirac Fermions ◽  
Tunneling Microscopy ◽  
Zero Modes ◽  
Topological Quantum ◽  
One Step ◽  
Topological Quantum Computation

AbstractThe iron-based superconductor is emerging as a promising platform for Majorana zero mode, which can be used to implement topological quantum computation. One of the most significant advances of this platform is the appearance of large vortex level spacing that strongly protects Majorana zero mode from other low-lying quasiparticles. Despite the advantages in the context of physics research, the inhomogeneity of various aspects hampers the practical construction of topological qubits in the compounds studied so far. Here we show that the stoichiometric superconductor LiFeAs is a good candidate to overcome this obstacle. By using scanning tunneling microscopy, we discover that the Majorana zero modes, which are absent on the natural clean surface, can appear in vortices influenced by native impurities. Our detailed analysis reveals a new mechanism for the emergence of those Majorana zero modes, i.e. native tuning of bulk Dirac fermions. The discovery of Majorana zero modes in this homogeneous material, with a promise of tunability, offers an ideal material platform for manipulating and braiding Majorana zero modes, pushing one step forward towards topological quantum computation.

scholarly journals DMRG study of strongly interacting $\mathbb{Z}_2$ flatbands: a toy model inspired by twisted bilayer graphene

2020 ◽  
Vol 3 (2) ◽  
Author(s):  
Paul Eugenio ◽  
Ceren Dag
Keyword(s):  
Magnetic Field ◽  
Time Reversal ◽  
Ground States ◽  
Bilayer Graphene ◽  
Chern Number ◽  
Strong Interactions ◽  
Time Reversal Symmetry ◽  
Density Matrix Renormalization ◽  
Topological Quantum ◽  
Twisted Bilayer Graphene

Strong interactions between electrons occupying bands of opposite (or like) topological quantum numbers (Chern=\pm1=±1), and with flat dispersion, are studied by using lowest Landau level (LLL) wavefunctions. More precisely, we determine the ground states for two scenarios at half-filling: (i) LLL’s with opposite sign of magnetic field, and therefore opposite Chern number; and (ii) LLL’s with the same magnetic field. In the first scenario – which we argue to be a toy model inspired by the chirally symmetric continuum model for twisted bilayer graphene – the opposite Chern LLL’s are Kramer pairs, and thus there exists time-reversal symmetry (\mathbb{Z}_2ℤ2). Turning on repulsive interactions drives the system to spontaneously break time-reversal symmetry – a quantum anomalous Hall state described by one particle per LLL orbital, either all positive Chern |{++\cdots+}\rangle|++⋯+⟩ or all negative |{--\cdots-}\rangle|−−⋯−⟩. If instead, interactions are taken between electrons of like-Chern number, the ground state is an SU(2)SU(2) ferromagnet, with total spin pointing along an arbitrary direction, as with the \nu=1ν=1 spin-\frac{1}{2}12 quantum Hall ferromagnet. The ground states and some of their excitations for both of these scenarios are argued analytically, and further complimented by density matrix renormalization group (DMRG) and exact diagonalization.

scholarly journals GEOMETRIC PHASES AND TOPOLOGICAL QUANTUM COMPUTATION

2003 ◽  
Vol 01 (01) ◽  
pp. 1-23 ◽  
Author(s):  
VLATKO VEDRAL
Keyword(s):  
Quantum Computation ◽  
Large Scale ◽  
Quantum Computer ◽  
Fault Tolerant ◽  
Geometric Phases ◽  
Quantum Phases ◽  
Topological Quantum ◽  
Universal Quantum ◽  
The Subject ◽  
Topological Quantum Computation

In the first part of this review we introduce the basics theory behind geometric phases and emphasize their importance in quantum theory. The subject is presented in a general way so as to illustrate its wide applicability, but we also introduce a number of examples that will help the reader understand the basic issues involved. In the second part we show how to perform a universal quantum computation using only geometric effects appearing in quantum phases. It is then finally discussed how this geometric way of performing quantum gates can lead to a stable, large scale, intrinsically fault-tolerant quantum computer.

scholarly journals Scalable designs for quasiparticle-poisoning-protected topological quantum computation with Majorana zero modes

2017 ◽  
Vol 95 (23) ◽  
Author(s):  
Torsten Karzig ◽  
Christina Knapp ◽  
Roman M. Lutchyn ◽  
Parsa Bonderson ◽  
Matthew B. Hastings ◽  
...  
Keyword(s):  
Quantum Computation ◽  
Zero Modes ◽  
Topological Quantum ◽  
Topological Quantum Computation

scholarly journals A Short Introduction to Topological Quantum Computation

2017 ◽  
Vol 3 (3) ◽  
Author(s):  
Ville Lahtinen ◽  
Jiannis Pachos
Keyword(s):  
Quantum Computation ◽  
Condensed Matter ◽  
Quantum Computers ◽  
Short Introduction ◽  
Entry Level ◽  
Zero Modes ◽  
Topological Quantum ◽  
Topological Quantum Computation ◽  
Superconducting Nanowire ◽  
Energy Physics

This review presents an entry-level introduction to topological quantum computation -- quantum computing with anyons. We introduce anyons at the system-independent level of anyon models and discuss the key concepts of protected fusion spaces and statistical quantum evolutions for encoding and processing quantum information. Both the encoding and the processing are inherently resilient against errors due to their topological nature, thus promising to overcome one of the main obstacles for the realisation of quantum computers. We outline the general steps of topological quantum computation, as well as discuss various challenges faced by it. We also review the literature on condensed matter systems where anyons can emerge. Finally, the appearance of anyons and employing them for quantum computation is demonstrated in the context of a simple microscopic model -- the topological superconducting nanowire -- that describes the low-energy physics of several experimentally relevant settings. This model supports localised Majorana zero modes that are the simplest and the experimentally most tractable types of anyons that are needed to perform topological quantum computation.

AN INDEX THEOREM FOR GRAPHENE

2007 ◽  
Vol 21 (30) ◽  
pp. 5113-5120 ◽  
Author(s):  
JIANNIS K. PACHOS ◽  
MICHAEL STONE
Keyword(s):  
Graphene Sheet ◽  
Good Description ◽  
Index Theorem ◽  
Continuous Limit ◽  
Zero Energy ◽  
Arbitrary Geometry ◽  
Numerical Studies ◽  
Topological Quantum ◽  
Potential Applications ◽  
Topological Quantum Computation

We consider a graphene sheet folded in an arbitrary geometry, compact or with nanotube-like open boundaries. In the continuous limit, the Hamiltonian takes the form of the Dirac operator, which provides a good description of the low energy spectrum of the lattice system. We derive an index theorem that relates the zero energy modes of the graphene sheet with the topology of the lattice. The result coincides with analytical and numerical studies for the known cases of fullerene molecules and carbon nanotubes, and it extends to more complicated molecules. Potential applications to topological quantum computation are discussed.

scholarly journals Giant spontaneous Hall effect in a nonmagnetic Weyl–Kondo semimetal

2021 ◽  
Vol 118 (8) ◽  
pp. e2013386118 ◽  
Author(s):  
Sami Dzsaber ◽  
Xinlin Yan ◽  
Mathieu Taupin ◽  
Gaku Eguchi ◽  
Andrey Prokofiev ◽  
...  
Keyword(s):  
Hall Effect ◽  
Time Reversal ◽  
Anomalous Hall Effect ◽  
Time Reversal Symmetry ◽  
Strong Electron ◽  
Band Theory ◽  
Fermion Systems ◽  
Topological Quantum ◽  
Interacting Systems ◽  
Nontrivial Topology

Nontrivial topology in condensed-matter systems enriches quantum states of matter to go beyond either the classification into metals and insulators in terms of conventional band theory or that of symmetry-broken phases by Landau’s order parameter framework. So far, focus has been on weakly interacting systems, and little is known about the limit of strong electron correlations. Heavy fermion systems are a highly versatile platform to explore this regime. Here we report the discovery of a giant spontaneous Hall effect in the Kondo semimetal Ce3Bi4Pd3 that is noncentrosymmetric but preserves time-reversal symmetry. We attribute this finding to Weyl nodes—singularities of the Berry curvature—that emerge in the immediate vicinity of the Fermi level due to the Kondo interaction. We stress that this phenomenon is distinct from the previously detected anomalous Hall effect in materials with broken time-reversal symmetry; instead, it manifests an extreme topological response that requires a beyond-perturbation-theory description of the previously proposed nonlinear Hall effect. The large magnitude of the effect in even tiny electric and zero magnetic fields as well as its robust bulk nature may aid the exploitation in topological quantum devices.

scholarly journals Visibility of noisy quantum dot-based measurements of Majorana qubits

2021 ◽  
Vol 10 (6) ◽  
Author(s):  
Aleksei Khindanov ◽  
Dmitry Pikulin ◽  
Torsten Karzig
Keyword(s):  
Quantum Dots ◽  
Quantum Dot ◽  
Differential Capacitance ◽  
High Fidelity ◽  
Current Interest ◽  
Noise Coupling ◽  
Zero Modes ◽  
Topological Quantum ◽  
Conservative Noise ◽  
Topological Quantum Computation

Measurement schemes of Majorana zero modes (MZMs) based on quantum dots (QDs) are of current interest as they provide a scalable platform for topological quantum computation. In a coupled qubit-QD setup we calculate the dependence of the charge of the QD and its differential capacitance on experimentally tunable parameters for both 2-MZM and 4-MZM measurements. We quantify the effect of noise on the measurement visibility by considering 1/f noise in detuning, tunneling amplitudes or phase. We find that on- or close-to-resonance measurements are generally preferable and predict, using conservative noise estimates, that noise coupling to the QDs is not a limitation to high-fidelity measurements of topological qubits.

scholarly journals Time-reversal symmetry, anomalies, and dualities in (2+1)$d$

2018 ◽  
Vol 5 (1) ◽  
Author(s):  
Clay Cordova ◽  
Po-Shen Hsin ◽  
Nathan Seiberg
Keyword(s):  
Time Reversal ◽  
Gauge Theories ◽  
Dirac Fermion ◽  
Global Symmetry ◽  
Time Reversal Symmetry ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Long Distance ◽  
Free Theory ◽  
Topological Quantum

We study continuum quantum field theories in 2+1 dimensions with time-reversal symmetry \cal T. The standard relation {\cal T}^2=(-1)^F is satisfied on all the “perturbative operators” i.e. polynomials in the fundamental fields and their derivatives. However, we find that it is often the case that acting on more complicated operators {\cal T}^2=(-1)^F {\cal M} with \cal M a non-trivial global symmetry. For example, acting on monopole operators, \cal M could be \pm1±1 depending on the magnetic charge. We study in detail U(1)U(1) gauge theories with fermions of various charges. Such a modification of the time-reversal algebra happens when the number of odd charge fermions is 2 ~{\rm mod }~4, e.g. in QED with two fermions. Our work also clarifies the dynamics of QED with fermions of higher charges. In particular, we argue that the long-distance behavior of QED with a single fermion of charge 22 is a free theory consisting of a Dirac fermion and a decoupled topological quantum field theory. The extension to an arbitrary even charge is straightforward. The generalization of these abelian theories to SO(N)SO(N) gauge theories with fermions in the vector or in two-index tensor representations leads to new results and new consistency conditions on previously suggested scenarios for the dynamics of these theories. Among these new results is a surprising non-abelian symmetry involving time-reversal.

Sign in / Sign up

Export Citation Format

Share Document