From 32aa00582b896ab56f8a0158e413b63ea0eeed31 Mon Sep 17 00:00:00 2001 From: Julian van Doorn Date: Mon, 26 Jun 2023 17:36:40 +0200 Subject: [PATCH] Minor patches. --- chapters/appendices/derivations.tex | 2 +- chapters/introduction/main.tex | 4 +- chapters/samples/main.tex | 3 + chapters/theory/main.tex | 6 +- preamble.tex | 2 +- sources.bib | 178 ++++++++++++++++++++-------- 6 files changed, 140 insertions(+), 55 deletions(-) diff --git a/chapters/appendices/derivations.tex b/chapters/appendices/derivations.tex index 3af2a72..5e04312 100644 --- a/chapters/appendices/derivations.tex +++ b/chapters/appendices/derivations.tex @@ -25,7 +25,7 @@ \section{Phase-flux relation} \end{align} Substituting $\vec{v}$ with a more useable expression in terms of the current density $\vec{J}$ and $\lambda$ using Equation~\ref{eqn:london-penetration-depth}. \begin{align} - \vec{J} = -2e|\psi|^2\vec{v} = -\frac{m_e}{\lambda^2e\mu_0}\vec{v} \Rightarrow \vec{v} = -\frac{\lambda^2e\mu_0}{m_e}\vec{J} + \vec{J} = -2e|\Psi|^2\vec{v} = -\frac{m_e}{\lambda^2e\mu_0}\vec{v} \Rightarrow \vec{v} = -\frac{\lambda^2e\mu_0}{m_e}\vec{J} \end{align} Combining the two equations gives us a useable expression for $\vec{A}$ in the loop: \begin{align} diff --git a/chapters/introduction/main.tex b/chapters/introduction/main.tex index 28e131d..6cb7d57 100644 --- a/chapters/introduction/main.tex +++ b/chapters/introduction/main.tex @@ -1,9 +1,9 @@ % !TEX root = ../../thesis.tex \chapter{Introduction} -Josephson junctions have a wide variety of applications. Notable applications are qubits\cite{placeNewMaterialPlatform2021,pechenezhskiySuperconductingQuasichargeQubit2020}, dissipationless electronics through Josephson diodes\cite{zhangReconfigurableMagneticfieldfreeSuperconducting2023a,ciacciaGateTunableJosephson2023} and microscopic imaging techniques\cite{clarkeSQUIDHandbook2004,rogSQUIDontipMagneticMicroscopy2022,pranceSensitivityDCSQUID2023}. The behaviour of a Josephson junctions is governed by their current-phase relation (CPR). Probing the CPR can lead to new insights and applications. By measuring the CPR it is possible to if the junction's behaviour is ballistic or diffusive\cite{endresCurrentPhaseRelation2023,kayyalhaHighlySkewedCurrent2020}. Additionally, it has proven the existence of $0$-$\pi$ and $\varphi_0$ junctions\cite{frolovMeasurementCurrentPhaseRelation2004,muraniBallisticEdgeStates2017} as well as non-$2\pi$ periodic CPRs\cite{endresCurrentPhaseRelation2023}. +Josephson junctions have a wide variety of applications. Notable applications are qubits\cite{placeNewMaterialPlatform2021,pechenezhskiySuperconductingQuasichargeQubit2020}, dissipationless electronics through Josephson diodes\cite{zhangReconfigurableMagneticfieldfreeSuperconducting2023a,ciacciaGateTunableJosephson2023} and microscopic imaging techniques\cite{clarkeSQUIDHandbook2004,rogSQUIDontipMagneticMicroscopy2022,pranceSensitivityDCSQUID2023}. The behaviour of a Josephson junctions is governed by their current-phase relation (CPR). Probing the CPR can lead to new insights and applications. By measuring the CPR it is possible to if the junction's behaviour is ballistic or diffusive\cite{endresCurrentPhaseRelation2023,kayyalhaHighlySkewedCurrent2020}. Additionally, it has proven the existence of $0$-$\pi$ and $\varphi_0$ junctions\cite{frolovMeasurementCurrentPhaseRelation2004,muraniBallisticEdgeStates2017,strambiniJosephsonPhaseBattery2020,szombatiJosephsonPh0junctionNanowire2016} as well as non-$2\pi$ periodic CPRs\cite{endresCurrentPhaseRelation2023}. In our group there is an interest in the CPR of rings of \ce{Sr2RuO4}. Recent work by Lahabi \textit{et al.} provides evidence for the existence of chiral domain walls in homogenous rings of \ce{Sr2RuO4}\cite{lahabiSpintripletSupercurrentsOdd2018} that act as Josephson junctions. As such \ce{Sr2RuO4} rings show dc-SQUID like behaviour without the presence of constrictions, grain boundaries or an interface with a different material. More definitive proof for chiral domain walls could be found by measuring the Josephson energy\cite{lahabiSpintripletSupercurrentsOdd2018,sigristRoleDomainWalls1999}. The most elegant way to determine the Josephson energy is to measure the CPR. -This thesis utilizes a method based on the work of Frolov \textit{et al.}. The reader is referred to \cite{frolovMeasurementCurrentPhaseRelation2004,frolovCurrentphaseRelationsJosephson2005} for their work. We explore a method to measure the current-phase relation of a single Josephson junction which, if successful, can be extended in later studies to measure the current-phase relation of \ce{Sr2RuO4} rings. +This thesis utilizes a method based on the work of Frolov \textit{et al.}. The reader is referred to~\cite{frolovMeasurementCurrentPhaseRelation2004,frolovCurrentphaseRelationsJosephson2005} for their work. We explore a method to measure the current-phase relation of a single Josephson junction which, if successful, can be extended in later studies to measure the current-phase relation of \ce{Sr2RuO4} rings. The next chapter will lay a theoretical foundation for our method. Chapter~\ref{chapter:method} delves deeper into the method and presents numerical calculations to guide our expectations. Then our results are presented on a per sample. Finally a conclusion is drawn and we sketch an outlook for future research. \ No newline at end of file diff --git a/chapters/samples/main.tex b/chapters/samples/main.tex index 8a5cb1b..4bed632 100644 --- a/chapters/samples/main.tex +++ b/chapters/samples/main.tex @@ -5,11 +5,14 @@ \chapter{Samples} \section{Sample CP1.2H} \input{chapters/samples/CP1.2H/main} +\newpage \section{Sample CP2.6B} \input{chapters/samples/CP2.6B/main} +\newpage \section{Sample CP3.5A} \input{chapters/samples/CP3.5A/main} +\newpage \section{Sample CP2.6B revisited} \input{chapters/samples/CP2.6B_revisited/main} \ No newline at end of file diff --git a/chapters/theory/main.tex b/chapters/theory/main.tex index bc40a98..c6201b8 100644 --- a/chapters/theory/main.tex +++ b/chapters/theory/main.tex @@ -12,7 +12,7 @@ \section{Superconductors} \end{equation} Both $\left|\Psi\right|$ and $\varphi$ are functions of position. The behaviour of this wave function is described by the Ginzburg-Landau theory. In this theory, $|\Psi|^2$ is a measure for the density of Cooper pairs (units of \unit{\per\cubic\meter}). The super current density (\unit{\ampere\per\square\meter}) is given by\footnote{See \citetitle{tinkhamIntroductionSuperconductivity} equation 4.14a.}: \begin{equation} - \vec{J_s} = e^* |\psi|^2 \vec{v_s} = \frac{e^*}{m^*} |\psi|^2 \left(\hbar \nabla \varphi-\frac{e^*}{c} \vec{A}\right) \stackrel{\text{SI}}{=} \frac{e}{m_e} |\psi|^2 \left(\hbar \nabla \varphi + 2e \vec{A}\right) + \vec{J_s} = e^* |\Psi|^2 \vec{v_s} = \frac{e^*}{m^*} |\Psi|^2 \left(\hbar \nabla \varphi-\frac{e^*}{c} \vec{A}\right) \stackrel{\text{SI}}{=} \frac{e}{m_e} |\Psi|^2 \left(\hbar \nabla \varphi + 2e \vec{A}\right) \label{eqn:super-current} \end{equation} @@ -32,7 +32,7 @@ \subsection{Characteristic length scales} The second length scale is the penetration depth $\lambda$. It is a measure for the `stiffness' of the phase. A small $\lambda$ means $\varphi$ can change easily. This means larger super currents are possible. The currents can screen magnetic fields which penetrate roughly on the same length scale. The penetration depth in Ginzburg-Landau theory at \qty{0}{\kelvin} is given by\footnote{See \citetitle{tinkhamIntroductionSuperconductivity} equation 4.8.}: \begin{align} - \lambda(0) &= \sqrt{\frac{m^*c^2}{4\pi|\psi|^2e^{*2}}} \stackrel{\text{SI}}{=} \sqrt{\frac{m_e}{2|\psi|^2e^2\mu_0}} + \lambda(0) &= \sqrt{\frac{m^*c^2}{4\pi|\Psi|^2e^{*2}}} \stackrel{\text{SI}}{=} \sqrt{\frac{m_e}{2|\Psi|^2e^2\mu_0}} \label{eqn:london-penetration-depth} \end{align} The penetration depth too is dependent on temperature and decreases for higher temperatures. For more information on length scales the reader is referred to \citetitle{tinkhamIntroductionSuperconductivity} by \citeauthor{tinkhamIntroductionSuperconductivity}. @@ -102,7 +102,7 @@ \section{dc-SQUID magnetometers} \label{fig:schematic-dc-SQUID} \end{figure} -This behaviour gives rise to the `dc-SQUID interference pattern' (SQI). Such a pattern is shown in Figure~\ref{example-SQI}. Most importantly, this pattern is exactly $\Phi_0$ periodic independent of any device geometries. As such it is very easy to calibrate. Two parameters are important for the sensitivity and hysteresis\cite{clarkeSQUIDHandbook2004}: +This behaviour gives rise to the `dc-SQUID interference pattern' (SQI). Such a pattern is shown in Figure~\ref{fig:example-SQI}. Most importantly, this pattern is exactly $\Phi_0$ periodic independent of any device geometries. As such it is very easy to calibrate. Two parameters are important for the sensitivity and hysteresis\cite{clarkeSQUIDHandbook2004}: \begin{equation} \beta_c = \frac{2\pi}{\Phi_0}I_cR^2C \tag{Stewart-McCumber parameter} diff --git a/preamble.tex b/preamble.tex index 6b46f5d..a74a973 100644 --- a/preamble.tex +++ b/preamble.tex @@ -8,7 +8,7 @@ % Use siunitx to write out units and quantities, use special formatting for the units. \usepackage{siunitx} -\sisetup{separate-uncertainty = true, multi-part-units = single, inter-unit-product = \ensuremath { { } \cdot { } }, range-units = single, list-units = single} +\sisetup{separate-uncertainty = true, multi-part-units = single, inter-unit-product = \ensuremath { { } \cdot { } }, range-units = single, list-units = single, exponent-product=\cdot} \DeclareSIUnit\fluxquantum{\text{\ensuremath{\Phi_0}}} % Setup bibliography (instead of relying on the way lion-msc does it using natbib). diff --git a/sources.bib b/sources.bib index cce9d85..7ae310d 100644 --- a/sources.bib +++ b/sources.bib @@ -2,8 +2,7 @@ @article{bardeenTheorySuperconductivity1957 title = {Theory of {{Superconductivity}}}, author = {Bardeen, J. and Cooper, L. N. and Schrieffer, J. R.}, date = {1957-12-01}, - journaltitle = {Physical Review}, - shortjournal = {Phys. Rev.}, + journaltitle = {Phys. Rev.}, volume = {108}, number = {5}, pages = {1175--1204}, @@ -21,7 +20,6 @@ @article{bishop-vanhornSuperScreenOpensourcePackage2022 author = {Bishop-Van Horn, Logan and Moler, Kathryn A.}, date = {2022-11-01}, journaltitle = {Computer Physics Communications}, - shortjournal = {Computer Physics Communications}, volume = {280}, pages = {108464}, issn = {0010-4655}, @@ -57,8 +55,7 @@ @article{cirilloSuperconductingProximityEffect2005 title = {Superconducting Proximity Effect and Interface Transparency in {{Nb}} ∕ {{PdNi}} Bilayers}, author = {Cirillo, C. and Prischepa, S. L. and Salvato, M. and Attanasio, C. and Hesselberth, M. and Aarts, J.}, date = {2005-10-14}, - journaltitle = {Physical Review B}, - shortjournal = {Phys. Rev. B}, + journaltitle = {Phys. Rev. B}, volume = {72}, number = {14}, pages = {144511}, @@ -82,6 +79,22 @@ @mvbook{clarkeSQUIDHandbook2004 file = {/Users/julian/Zotero/storage/GI6IHPGN/Clarke and Braginski - 2004 - The SQUID Handbook.pdf} } +@article{dellaroccaMeasurementCurrentPhaseRelation2007, + title = {Measurement of the {{Current-Phase Relation}} of {{Superconducting Atomic Contacts}}}, + author = {Della Rocca, M. L. and Chauvin, M. and Huard, B. and Pothier, H. and Esteve, D. and Urbina, C.}, + date = {2007-09-20}, + journaltitle = {Phys. Rev. Lett.}, + volume = {99}, + number = {12}, + pages = {127005}, + issn = {0031-9007, 1079-7114}, + doi = {10.1103/PhysRevLett.99.127005}, + url = {https://link.aps.org/doi/10.1103/PhysRevLett.99.127005}, + urldate = {2023-06-21}, + langid = {english}, + file = {/Users/julian/Zotero/storage/B5PFLRYY/Della Rocca et al. - 2007 - Measurement of the Current-Phase Relation of Super.pdf} +} + @online{eewebCoilInductanceCalculator, title = {Coil {{Inductance Calculator}}}, author = {EEWeb}, @@ -97,8 +110,7 @@ @article{endresCurrentPhaseRelation2023 title = {Current–{{Phase Relation}} of a {{WTe}} {\textsubscript{2}} {{Josephson Junction}}}, author = {Endres, Martin and Kononov, Artem and Arachchige, Hasitha Suriya and Yan, Jiaqiang and Mandrus, David and Watanabe, Kenji and Taniguchi, Takashi and Schönenberger, Christian}, date = {2023-05-24}, - journaltitle = {Nano Letters}, - shortjournal = {Nano Lett.}, + journaltitle = {Nano Lett.}, volume = {23}, number = {10}, pages = {4654--4659}, @@ -172,8 +184,7 @@ @article{golubovCurrentphaseRelationJosephson2004a title = {The Current-Phase Relation in {{Josephson}} Junctions}, author = {Golubov, A. A. and Kupriyanov, M. Yu. and Il'ichev, E.}, date = {2004-04-26}, - journaltitle = {Reviews of Modern Physics}, - shortjournal = {Rev. Mod. Phys.}, + journaltitle = {Rev. Mod. Phys.}, volume = {76}, number = {2}, pages = {411--469}, @@ -189,8 +200,7 @@ @article{gumannMicroscopicTheorySuperconductorconstrictionsuperconductor2007 title = {Microscopic Theory of Superconductor-Constriction-Superconductor {{Josephson}} Junctions in a Magnetic Field}, author = {Gumann, A. and Dahm, T. and Schopohl, N.}, date = {2007-08-24}, - journaltitle = {Physical Review B}, - shortjournal = {Phys. Rev. B}, + journaltitle = {Phys. Rev. B}, volume = {76}, number = {6}, pages = {064529}, @@ -207,8 +217,7 @@ @article{hartCurrentphaseRelationsInAs2019 shorttitle = {Current-Phase Relations of {{InAs}} Nanowire {{Josephson}} Junctions}, author = {Hart, Sean and Cui, Zheng and Menard, Gerbold and Deng, Mingtang and Antipov, Andrey and Lutchyn, Roman M. and Krogstrup, Peter and Marcus, Charles M. and Moler, Kathryn A.}, date = {2019-08-26}, - journaltitle = {Physical Review B}, - shortjournal = {Phys. Rev. B}, + journaltitle = {Phys. Rev. B}, volume = {100}, number = {6}, eprint = {1902.07804}, @@ -228,8 +237,7 @@ @article{jackelDirectMeasurementCurrentphase1974a title = {Direct Measurement of Current-Phase Relations in Superconducting Weak Links}, author = {Jackel, L. D. and Buhrman, R. A. and Webb, W. W.}, date = {1974-10-01}, - journaltitle = {Physical Review B}, - shortjournal = {Phys. Rev. B}, + journaltitle = {Phys. Rev. B}, volume = {10}, number = {7}, pages = {2782--2785}, @@ -261,8 +269,7 @@ @article{kayyalhaHighlySkewedCurrent2020 title = {Highly Skewed Current–Phase Relation in Superconductor–Topological Insulator–Superconductor {{Josephson}} Junctions}, author = {Kayyalha, Morteza and Kazakov, Aleksandr and Miotkowski, Ireneusz and Khlebnikov, Sergei and Rokhinson, Leonid P. and Chen, Yong P.}, date = {2020-01-30}, - journaltitle = {npj Quantum Materials}, - shortjournal = {npj Quantum Mater.}, + journaltitle = {npj Quantum Mater.}, volume = {5}, number = {1}, pages = {1--7}, @@ -304,8 +311,7 @@ @article{likharevSuperconductingWeakLinks1979 title = {Superconducting Weak Links}, author = {Likharev, K. K.}, date = {1979-01-01}, - journaltitle = {Reviews of Modern Physics}, - shortjournal = {Rev. Mod. Phys.}, + journaltitle = {Rev. Mod. Phys.}, volume = {51}, number = {1}, pages = {101--159}, @@ -322,7 +328,6 @@ @article{linYBaCuNano2020 author = {Lin, Jianxin and Müller, Benedikt and Linek, Julian and Karrer, Max and Wenzel, Malte and Martínez-Pérez, Maria José and Kleiner, Reinhold and Koelle, Dieter}, date = {2020}, journaltitle = {Nanoscale}, - shortjournal = {Nanoscale}, volume = {12}, number = {9}, pages = {5658--5668}, @@ -339,8 +344,7 @@ @article{martin-roderoMicroscopicTheoryJosephson1994 title = {Microscopic Theory of {{Josephson}} Mesoscopic Constrictions}, author = {Martín-Rodero, A. and García-Vidal, F. J. and Levy Yeyati, A.}, date = {1994-01-24}, - journaltitle = {Physical Review Letters}, - shortjournal = {Phys. Rev. Lett.}, + journaltitle = {Phys. Rev. Lett.}, volume = {72}, number = {4}, pages = {554--557}, @@ -356,8 +360,7 @@ @article{maxfieldSuperconductingPenetrationDepth1965 title = {Superconducting {{Penetration Depth}} of {{Niobium}}}, author = {Maxfield, B. W. and McLean, W. L.}, date = {1965-08-30}, - journaltitle = {Physical Review}, - shortjournal = {Phys. Rev.}, + journaltitle = {Phys. Rev.}, volume = {139}, pages = {A1515-A1522}, publisher = {{American Physical Society}}, @@ -373,8 +376,7 @@ @article{muraniBallisticEdgeStates2017 title = {Ballistic Edge States in {{Bismuth}} Nanowires Revealed by {{SQUID}} Interferometry}, author = {Murani, Anil and Kasumov, Alik and Sengupta, Shamashis and Kasumov, Yu A. and Volkov, V. T. and Khodos, I. I. and Brisset, F. and Delagrange, Raphaëlle and Chepelianskii, Alexei and Deblock, Richard and Bouchiat, Hélène and Guéron, Sophie}, date = {2017-07-05}, - journaltitle = {Nature Communications}, - shortjournal = {Nat Commun}, + journaltitle = {Nat Commun}, volume = {8}, number = {1}, pages = {15941}, @@ -414,8 +416,7 @@ @article{PhysRevLett.90.167001 title = {Phase Sensitive Experiments in Ferromagnetic-Based Josephson Junctions}, author = {Guichard, W. and Aprili, M. and Bourgeois, O. and Kontos, T. and Lesueur, J. and Gandit, P.}, date = {2003-04}, - journaltitle = {Physical Review Letters}, - shortjournal = {Phys. Rev. Lett.}, + journaltitle = {Phys. Rev. Lett.}, volume = {90}, number = {16}, pages = {167001}, @@ -430,8 +431,7 @@ @article{PhysRevLett.92.217001 title = {Spontaneous Supercurrent Induced by Ferromagnetic {{π}} Junctions}, author = {Bauer, A. and Bentner, J. and Aprili, M. and Della Rocca, M. L. and Reinwald, M. and Wegscheider, W. and Strunk, C.}, date = {2004-05}, - journaltitle = {Physical Review Letters}, - shortjournal = {Phys. Rev. Lett.}, + journaltitle = {Phys. Rev. Lett.}, volume = {92}, number = {21}, pages = {217001}, @@ -447,8 +447,7 @@ @article{placeNewMaterialPlatform2021 author = {Place, Alexander P. M. and Rodgers, Lila V. H. and Mundada, Pranav and Smitham, Basil M. and Fitzpatrick, Mattias and Leng, Zhaoqi and Premkumar, Anjali and Bryon, Jacob and Vrajitoarea, Andrei and Sussman, Sara and Cheng, Guangming and Madhavan, Trisha and Babla, Harshvardhan K. and Le, Xuan Hoang and Gang, Youqi and Jäck, Berthold and Gyenis, András and Yao, Nan and Cava, Robert J. and de Leon, Nathalie P. and Houck, Andrew A.}, options = {useprefix=true}, date = {2021-03-19}, - journaltitle = {Nature Communications}, - shortjournal = {Nat Commun}, + journaltitle = {Nat Commun}, volume = {12}, number = {1}, pages = {1779}, @@ -468,8 +467,7 @@ @article{poddMicroSQUIDsControllableAsymmetry2007 title = {Micro-{{SQUIDs}} with Controllable Asymmetry via Hot-Phonon Controlled Junctions}, author = {Podd, G. J. and Hutchinson, G. D. and Williams, D. A. and Hasko, D. G.}, date = {2007-04-02}, - journaltitle = {Physical Review B}, - shortjournal = {Phys. Rev. B}, + journaltitle = {Phys. Rev. B}, volume = {75}, number = {13}, pages = {134501}, @@ -481,6 +479,22 @@ @article{poddMicroSQUIDsControllableAsymmetry2007 file = {/Users/julian/Zotero/storage/7XY82I6I/Podd et al. - 2007 - Micro-SQUIDs with controllable asymmetry via hot-p.pdf;/Users/julian/Zotero/storage/K786AILE/PhysRevB.75.html} } +@article{pranceSensitivityDCSQUID2023, + title = {Sensitivity of a {{DC SQUID}} with a Non-Sinusoidal Current-Phase Relation in Its Junctions}, + author = {Prance, J. R. and Thompson, M. D.}, + date = {2023-05-30}, + journaltitle = {Applied Physics Letters}, + volume = {122}, + number = {22}, + pages = {222601}, + issn = {0003-6951}, + doi = {10.1063/5.0151607}, + url = {https://doi.org/10.1063/5.0151607}, + urldate = {2023-06-13}, + abstract = {In ballistic superconductor–normal metal–superconductor Josephson junctions, such as those made from graphene or high mobility semiconductors, the current-phase relation may not have the common, sinusoidal form but can be skewed to have a peak supercurrent at a phase difference greater than π / 2. Here, we use a numerical simulation that includes thermal noise to investigate the sensitivity of a DC superconducting quantum interference device (SQUID) with such junctions. The simulation uses a resistively and capacitively shunted junction model where the current-phase relation of each junction can be defined as an arbitrary function. The modulation, transfer function, noise, and sensitivity of a SQUID are calculated for different types of current-phase relation. For the examples considered here, we find that the flux sensitivity of the SQUID is always degraded by forward skewing of the current-phase relation, even in cases where the transfer function of the SQUID has been improved.}, + file = {/Users/julian/Zotero/storage/2QTHFNLE/Prance and Thompson - 2023 - Sensitivity of a DC SQUID with a non-sinusoidal cu.pdf;/Users/julian/Zotero/storage/MS2SK8CX/Sensitivity-of-a-DC-SQUID-with-a-non-sinusoidal.html} +} + @article{prigozhin3DSimulationSuperconducting2018, title = {{{3D}} Simulation of Superconducting Magnetic Shields and Lenses Using the Fast {{Fourier}} Transform}, author = {Prigozhin, Leonid and Sokolovsky, Vladimir}, @@ -504,7 +518,6 @@ @article{rhoderickCurrentDistributionThin1962 author = {Rhoderick, E.H. and Wilson, E.M.}, date = {1962-06}, journaltitle = {Nature}, - shortjournal = {Nature}, volume = {194}, number = {4834}, pages = {1167--1167}, @@ -564,8 +577,7 @@ @article{sharonCurrentinducedSQUIDBehavior2016 title = {Current-Induced {{SQUID}} Behavior of Superconducting {{Nb}} Nano-Rings}, author = {Sharon, Omri J. and Shaulov, Avner and Berger, Jorge and Sharoni, Amos and Yeshurun, Yosef}, date = {2016-06-20}, - journaltitle = {Scientific Reports}, - shortjournal = {Sci Rep}, + journaltitle = {Sci Rep}, volume = {6}, number = {1}, pages = {28320}, @@ -585,8 +597,7 @@ @article{shellyExistenceShapiroSteps2020 title = {Existence of {{Shapiro Steps}} in the {{Dissipative Regime}} in {{Superconducting Weak Links}}}, author = {Shelly, Connor D. and See, Patrick and Rungger, Ivan and Williams, Jonathan M.}, date = {2020-02-26}, - journaltitle = {Physical Review Applied}, - shortjournal = {Phys. Rev. Appl.}, + journaltitle = {Phys. Rev. Appl.}, volume = {13}, number = {2}, pages = {024070}, @@ -603,7 +614,6 @@ @article{sigristRoleDomainWalls1999 author = {Sigrist, Manfred and Agterberg, Daniel F.}, date = {1999-11-01}, journaltitle = {Progress of Theoretical Physics}, - shortjournal = {Progress of Theoretical Physics}, volume = {102}, number = {5}, pages = {965--981}, @@ -619,8 +629,7 @@ @article{singhColossalProximityEffect2015 title = {Colossal {{Proximity Effect}} in a {{Superconducting Triplet Spin Valve Based}} on the {{Half-Metallic Ferromagnet CrO}} 2}, author = {Singh, A. and Voltan, S. and Lahabi, K. and Aarts, J.}, date = {2015-05-26}, - journaltitle = {Physical Review X}, - shortjournal = {Phys. Rev. X}, + journaltitle = {Phys. Rev. X}, volume = {5}, number = {2}, pages = {021019}, @@ -632,12 +641,27 @@ @article{singhColossalProximityEffect2015 file = {/Users/julian/Zotero/storage/ADC62GHU/Singh et al. - 2015 - Colossal Proximity Effect in a Superconducting Tri.pdf} } +@article{soutoJosephsonDiodeEffect2022, + title = {Josephson {{Diode Effect}} in {{Supercurrent Interferometers}}}, + author = {Souto, Rubén Seoane and Leijnse, Martin and Schrade, Constantin}, + date = {2022-12-22}, + journaltitle = {Phys. Rev. Lett.}, + volume = {129}, + number = {26}, + pages = {267702}, + issn = {0031-9007, 1079-7114}, + doi = {10.1103/PhysRevLett.129.267702}, + url = {https://link.aps.org/doi/10.1103/PhysRevLett.129.267702}, + urldate = {2023-06-21}, + langid = {english}, + file = {/Users/julian/Zotero/storage/27XK57NC/Souto et al. - 2022 - Josephson Diode Effect in Supercurrent Interferome.pdf} +} + @article{spantonCurrentPhaseRelations2017, title = {Current–Phase Relations of Few-Mode {{InAs}} Nanowire {{Josephson}} Junctions}, author = {Spanton, Eric M. and Deng, Mingtang and Vaitiekėnas, Saulius and Krogstrup, Peter and Nygård, Jesper and Marcus, Charles M. and Moler, Kathryn A.}, date = {2017-12}, - journaltitle = {Nature Physics}, - shortjournal = {Nature Phys}, + journaltitle = {Nature Phys}, volume = {13}, number = {12}, pages = {1177--1181}, @@ -657,8 +681,7 @@ @article{stoutimoreSecondharmonicCurrentphaseRelation2018 title = {Second-Harmonic Current-Phase Relation in {{Josephson}} Junctions with Ferromagnetic Barriers}, author = {Stoutimore, M. J. A. and Rossolenko, A. N. and Bolginov, V. V. and Oboznov, V. A. and Rusanov, A. Y. and Baranov, D. S. and Pugach, N. and Frolov, S. M. and Ryazanov, V. V. and Van Harlingen, D. J.}, date = {2018-10-26}, - journaltitle = {Physical Review Letters}, - shortjournal = {Phys. Rev. Lett.}, + journaltitle = {Phys. Rev. Lett.}, volume = {121}, number = {17}, eprint = {1805.12546}, @@ -674,6 +697,46 @@ @article{stoutimoreSecondharmonicCurrentphaseRelation2018 file = {/Users/julian/Zotero/storage/J8AYW528/Stoutimore et al. - 2018 - Second-harmonic current-phase relation in Josephso.pdf;/Users/julian/Zotero/storage/85A66VLV/1805.html} } +@article{strambiniJosephsonPhaseBattery2020, + title = {A {{Josephson}} Phase Battery}, + author = {Strambini, Elia and Iorio, Andrea and Durante, Ofelia and Citro, Roberta and Sanz-Fernández, Cristina and Guarcello, Claudio and Tokatly, Ilya V. and Braggio, Alessandro and Rocci, Mirko and Ligato, Nadia and Zannier, Valentina and Sorba, Lucia and Bergeret, F. Sebastián and Giazotto, Francesco}, + date = {2020-08}, + journaltitle = {Nat. Nanotechnol.}, + volume = {15}, + number = {8}, + pages = {656--660}, + publisher = {{Nature Publishing Group}}, + issn = {1748-3395}, + doi = {10.1038/s41565-020-0712-7}, + url = {https://www.nature.com/articles/s41565-020-0712-7}, + urldate = {2023-06-26}, + abstract = {A classical battery converts chemical energy into a persistent voltage bias that can power electronic circuits. Similarly, a phase battery is a quantum device that provides a persistent phase bias to the wave function of a quantum circuit. It represents a key element for quantum technologies based on phase coherence. Here we demonstrate a phase battery in a hybrid superconducting circuit. It consists of an n-doped InAs nanowire with unpaired-spin surface states, that is proximitized by Al superconducting leads. We find that the ferromagnetic polarization of the unpaired-spin states is efficiently converted into a persistent phase bias φ0 across the wire, leading to the anomalous Josephson effect1,2. We apply an external in-plane magnetic field and, thereby, achieve continuous tuning of φ0. Hence, we can charge and discharge the quantum phase battery. The observed symmetries of the anomalous Josephson effect in the vectorial magnetic field are in agreement with our theoretical model. Our results demonstrate how the combined action of spin–orbit coupling and exchange interaction induces a strong coupling between charge, spin and superconducting phase, able to break the phase rigidity of the system.}, + issue = {8}, + langid = {english}, + keywords = {Electronic devices,Magnetic devices,Superconducting devices}, + file = {/Users/julian/Zotero/storage/W45FTK74/Strambini et al. - 2020 - A Josephson phase battery.pdf} +} + +@article{szombatiJosephsonPh0junctionNanowire2016, + title = {Josephson Φ0-Junction in Nanowire Quantum Dots}, + author = {Szombati, D. B. and Nadj-Perge, S. and Car, D. and Plissard, S. R. and Bakkers, E. P. a. M. and Kouwenhoven, L. P.}, + date = {2016-06}, + journaltitle = {Nature Phys}, + volume = {12}, + number = {6}, + pages = {568--572}, + publisher = {{Nature Publishing Group}}, + issn = {1745-2481}, + doi = {10.1038/nphys3742}, + url = {https://www.nature.com/articles/nphys3742}, + urldate = {2023-06-22}, + abstract = {A so-called Josephson ϕ0-junction based on a nanowire quantum dot is reported. By means of electrostatic gating, it is possible to controllably introduce a phase offset taking any value between 0 and π in the ground state of the junction.}, + issue = {6}, + langid = {english}, + keywords = {Superconducting devices,Superconducting properties and materials}, + file = {/Users/julian/Zotero/storage/EB2WHAM6/Szombati et al. - 2016 - Josephson ϕ0-junction in nanowire quantum dots.pdf} +} + @book{tinkhamIntroductionSuperconductivity, title = {Introduction to {{Superconductivity}}}, author = {Tinkham, Michael}, @@ -685,6 +748,26 @@ @book{tinkhamIntroductionSuperconductivity file = {/Users/julian/Zotero/storage/BRPWIQNH/Tinkham - Introduction to Superconductivity.pdf} } +@article{tkachovHelicalAndreevBound2013, + title = {Helical {{Andreev}} Bound States and Superconducting {{Klein}} Tunneling in Topological Insulator {{Josephson}} Junctions}, + author = {Tkachov, G. and Hankiewicz, E. M.}, + date = {2013-08-02}, + journaltitle = {Phys. Rev. B}, + volume = {88}, + number = {7}, + eprint = {1304.1893}, + eprinttype = {arxiv}, + eprintclass = {cond-mat}, + pages = {075401}, + issn = {1098-0121, 1550-235X}, + doi = {10.1103/PhysRevB.88.075401}, + url = {http://arxiv.org/abs/1304.1893}, + urldate = {2023-06-22}, + abstract = {Currently, much effort is being put into detecting unconventional p-wave superconductivity in Josephson junctions based on topological insulators (TIs). For that purpose we propose to use superconducting Klein tunneling, i.e. the reflectionless passage of Cooper pairs through a potential barrier in a gated ballistic junction. This phenomenon occurs due to the fact that the supercurrent is carried by helical Andreev bound states (ABSs) characterized by spin-momentum locking similar to the normal-state carriers. We derive the spectrum of the helical ABSs and the corresponding Josephson current for a junction made on the surface of a three-dimensional TI. The superconducting Klein tunneling is predicted to yield a non-sinusoidal current-phase relation and an anomalous critical current \$I\_c\$ that does not vanish with increasing barrier strength. We also analyze the dependence of the I\_cR\_n product (where R\_n is the normal-state junction resistance) on the microscopic parameters of the superconductor/TI interface, which leads to lower I\_cR\_n values than expected from previous models of the proximity-effect Josephson junctions.}, + keywords = {Condensed Matter - Mesoscale and Nanoscale Physics}, + file = {/Users/julian/Zotero/storage/KF962RNN/Tkachov and Hankiewicz - 2013 - Helical Andreev bound states and superconducting K.pdf;/Users/julian/Zotero/storage/PZAUAMBD/1304.html} +} + @online{TN2513PSQUIDPracticum, title = {{{TN2513-P SQUID Practicum Manual}}}, url = {https://nsweb.tn.tudelft.nl/~gsteele/SQUID_practicum/TN2513-P%20SQUID%20Practicum%20Manual.html}, @@ -707,8 +790,7 @@ @article{yasuiSpontaneousEmergenceJosephson2020 title = {Spontaneous Emergence of {{Josephson}} Junctions in Homogeneous Rings of Single-Crystal {{Sr2RuO4}}}, author = {Yasui, Yuuki and Lahabi, Kaveh and Becerra, Victor Fernández and Fermin, Remko and Anwar, Muhammad Shahbaz and Yonezawa, Shingo and Terashima, Takahito and Milošević, Milorad V. and Aarts, Jan and Maeno, Yoshiteru}, date = {2020-04-09}, - journaltitle = {npj Quantum Materials}, - shortjournal = {npj Quantum Mater.}, + journaltitle = {npj Quantum Mater.}, volume = {5}, number = {1}, pages = {1--8},