diff --git a/Timeline-of-Superconductivity-from-1900-to-2015.pdf b/Timeline-of-Superconductivity-from-1900-to-2015.pdf new file mode 100755 index 0000000..1786db9 Binary files /dev/null and b/Timeline-of-Superconductivity-from-1900-to-2015.pdf differ diff --git a/Timeline-of-Superconductivity-from-1900-to-2015.svg b/Timeline-of-Superconductivity-from-1900-to-2015.svg new file mode 100755 index 0000000..315c460 --- /dev/null +++ b/Timeline-of-Superconductivity-from-1900-to-2015.svg @@ -0,0 +1,3850 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + Room T + + + + + 2020 + 250 + 300 + CSH @ 270 GPa + + + x + + + LaH @ 170 GPa + 10 + + + + + + + + + + + + + + + + NdNiO + + + diff --git a/cuprate-phase.pdf b/cuprate-phase.pdf new file mode 100755 index 0000000..b9e4d60 Binary files /dev/null and b/cuprate-phase.pdf differ diff --git a/cylinder-vortex-state.tif b/cylinder-vortex-state.tif new file mode 100755 index 0000000..9c6b429 Binary files /dev/null and b/cylinder-vortex-state.tif differ diff --git a/references.bib b/references.bib index 170eda7..e119eca 100644 --- a/references.bib +++ b/references.bib @@ -71,3 +71,40 @@ Electrical conductivity or specific conductance is the reciprocal of electrical year = {2003}, pages = {29--67}, } + +@article{dai-synthesis-1995, + title = {Synthesis and neutron powder diffraction study of the superconductor {HgBa2Ca2Cu3O8} + δ by {Tl} substitution}, + volume = {243}, + issn = {0921-4534}, + url = {https://www.sciencedirect.com/science/article/pii/0921453494024618}, + doi = {10.1016/0921-4534(94)02461-8}, + abstract = {Substitution of Tl for Hg was performed in the Hg based 1223 phase HgBa2Ca2Cu3O8 + δ (Tc = 135 K), resulting in an increase of the superconducting transition temperature to 138 K for samples with a nominal composition of Hg0.8Tl0.2Ba2Ca2Cu3O8 + δ. The crystal structure of this solid solution has been investigated by neutron powder diffraction techniques at room temperature and at 10 K. The compound has the same crystal as Hg-1223 with the space group symmetry P4/mmm and lattice parameters a = 3.8489(1), c = 15.816(1) Å. Rietveld analysis results indicate that Hg is partially replaced by Tl, and the oxygen content, δ, is 0.33. The lattice-parameter changes resulting from the Tl substitution are too small to account for the Tc change by mimicking the effect of pressure. No phase transition occurs down to 10 K.}, + language = {en}, + number = {3}, + urldate = {2022-03-07}, + journal = {Physica C: Superconductivity}, + author = {Dai, P. and Chakoumakos, B. C. and Sun, G. F. and Wong, K. W. and Xin, Y. and Lu, D. F.}, + month = mar, + year = {1995}, + pages = {201--206}, +} + +@article{chubukov, +author = {Chubukov, Andrey and Pines, David and Schmalian, Jörg}, +year = {2002}, +month = {02}, +pages = {51}, +title = {A Spin Fluctuation Model for D-wave Superconductivity} +} + +@misc{ray-2016, title={Master's thesis: Structural investigation of La(2-x)Sr(x)CuO(4+y) - Following staging as a function of temperature}, url={https://figshare.com/articles/thesis/Structural_investigation_of_La_2_x_Sr_x_CuO_4_y_Following_staging_as_a_function_of_temperature/2075680/2}, DOI={10.6084/m9.figshare.2075680.v2}, abstractNote={A thesis submitted to the Niels Bohr Institute at the Faculty of Science at the University of Copenhagen, Denmark, in partial fulfilment of the requirements for the degree of Master of Science in physics. Submission date was November 19, 2015, and the defence was held on November 30, 2015, where the degree was also awarded. + +The cuprate La2-xSrxCuO4+y – a high-temperature superconductor – was discovered almost three decades ago. However the mechanisms behind the superconductivity in the material for different doping values x and y are still not fully understood. A small part of this large puzzle is added to the pile with this thesis, where results on the structure for several different samples are presented. + +The emphasis in this thesis is on a specific superstructure thought to be connected to the ordering of interstitial oxygen, known from the isostructural compound La2NiO4+y as staging. Four single crystal samples with different co-doping values are investigated by the use of both X-rays and neutrons. + +Staging is observed for all four samples at low temperatures with X-ray measurements. The sample with strontium doping x = 0.00 shows several coexisting staging levels with staging numbers between 2 and 8, with the highest contribution from a staging level between 4 and 5. The co-doped samples show increasing staging number with increasing x. It is found that the staging belongs to a structural phase assumed in space group Fmmm, while the unstaged fraction of the samples are in the Bmab space group. These two structural phases are found to have significantly different lengths of the long crystal axis for the two low x samples, in the order of a fraction of a percent, while the two higher x samples had a difference of only a small fraction of a permille. + +The temperature dependent phase transitions for both the Bmab structure and the staging reflections are investigated between 5 and 300 K. The critical exponents for the Bmab reflections are found to be significantly lower than results from similar materials in literature, although with transition temperatures consistent with literature for comparable sample compositions. It is found that the critical exponents for the staging reflections increase for increasing doping while the transition temperatures decrease, both consistent with results on the isostructural La2NiO4+y. + +Results from previous neutron measurements are found to be consistent with the X-ray measurements in this work, and measured reciprocal space maps from this work show a large variety of other superstructure reflections which will be interesting to investigate in the future.}, publisher={figshare}, author={Ray, Pia Jensen}, year={2016}, month={Feb} } diff --git a/superconductivity_assignment2_kvkempen.pdf b/superconductivity_assignment2_kvkempen.pdf index 1891b43..a8ae8f9 100644 Binary files a/superconductivity_assignment2_kvkempen.pdf and b/superconductivity_assignment2_kvkempen.pdf differ diff --git a/superconductivity_assignment2_kvkempen.tex b/superconductivity_assignment2_kvkempen.tex index 5df7dc5..8fe3455 100755 --- a/superconductivity_assignment2_kvkempen.tex +++ b/superconductivity_assignment2_kvkempen.tex @@ -31,6 +31,7 @@ \usepackage{amsmath} \usepackage{todonotes} \setuptodonotes{inline} +\usepackage{mhchem} \newcommand{\pfrac}[2]{\frac{\partial #1}{\partial #2}} @@ -218,6 +219,8 @@ If you apply an external magnetic field, this thus means that a superconductor w This generated current is called a supercurrent. Superconductivity is, however, a phase of the material. Superconductors only have these properties below a certain temperature, its critical temperature $T_c$, and can only expel a maximum external magnetic field, its critical magnetic field $B_c(T)$, which is a function of the temperature. +The zero resistance property follows from the perfect diagmagnetism. +It is impossible for the material to let these supercurrents flow indefinitely with resistance, as heat would be generated. The class of superconductors we have a model for, is the class of conventional superconductors. In this class, there are two types, called type-I and type-II superconductors. @@ -234,7 +237,51 @@ This passing through is done by creating normally conducting channels throughout This fixed amount is a multiple of the flux quantum $\Phi_0$. The material generates current around these channels in accordance to the Maxwell-Amp\`ere law, conforming to the let through magnetic field inside the vortex and cancelling the field on the outside the vortex. +There are lots of applications for both the perfect diagmagnetism and the zero resistivity. +There is even a Wiki about them: \url{https://en.wikipedia.org/wiki/Technological\_applications\_of\_superconductivity}. +What is most notable about these applications, is that maintaining a temperature below the critical temperature is the biggest challenge. +A real breakthrough for superconductivity would be the discovery of room-temperature superconductors at atmospheric pressure, or materials close to that. +Currently, the highest $T_c$ material we know is carbonaceous sulfur hydride (\ce{CH8S}) with $T_c = \SI{15}{\degreeCelsius}$ but at a pressure of a whopping $\SI{267}{\giga\pascal}$. +At atmospheric pressure, the highest $T_c$ material known is a cuprate \cite{dai-synthesis-1995} \ce{HgBa2Ca2Cu3O_{8+\delta}} at $T_c = \SI{135}{\kelvin}$. +The quest for this breakthrough is intensely researched, although most is experimental. +The clue is that most of the high $T_c$ materials that are being discovered, are unconventional superconductors. +As there is no theory for them (yet), the search is mostly educational guessing. +By trying to find patterns in the previously high $T_c$ materials, similar materials are studied to see if they also exhibit superconductivity. +One of the patterns is that superconductivity in cuprates is high $T_c$. +We'll focus on these materials in the following. +Currently, most hopeful candidates are cuprates. +These materials are made of layers of copper oxides (\ce{CuO2}) alternated with layers of other metal oxides. +The copper oxide layers are the superconductive layers, and the other metal oxides are used as charge reservoirs, doping electrons (or holes) into the copper oxide layers. +Due to the geometry of these materials, there is anisotropy in the resistivity of the material. +Parallel to the layers, superconductivity takes place in the copper oxide layers. +Perpendicular to the layers, this is not the case. + +The behaviour of the material can be tuned by tuning the doping, thus the other metal oxides as mentioned before. +A typical phase diagram as function of the doping can be seen in figure \ref{fig:cuprate-phase}. +The material can be steered from being antiferrimagnetic to superconductive by increasing doping. + +\begin{figure} + \centering + \includegraphics{cuprate-phase.pdf} + \caption{For high $T_c$ superconducting cuprates, a typical phase diagram as function of doping looks like this.\cite{chubukov} } + \label{fig:cuprate-phase} +\end{figure} + +As can be seen, there is an optimal doping fraction for achieving highest $T_c$. +Aiming for this doping yields the desired material. + +Now the question is what direction to search for. +The timeline in figure \ref{fig:timeline} might give a direction for the most promising types of cuprates to look into. +It could be, however, that other types have higher $T_c$. +A lot of creativity is therefore needed to find them. + +\begin{figure} + \centering + \includegraphics[width=\textwidth]{Timeline-of-Superconductivity-from-1900-to-2015.pdf} + \caption{The last century, a lot of research has been done in the direction of cuprate superconductivity. Pia Jensen Ray made this overview for his master thesis.\cite{ray-2016} The different paths are different types of cuprates. Please see his thesis for the meaning of the labels. On the right side, an idea of the temperature is givin by comparing it to common cooling agents.} + \label{fig:timeline} +\end{figure} --- @@ -243,10 +290,6 @@ The start was a good recap of the breakthroughs relevant to conventional superco but in pages 61--63, the theory is worked through a little quickly. I might reread it some times. - - -\todo{The essay so far is just a draft. Choosing a topic was hard. As we are to aim at bachelor students not knowing sc, I thought a proper introduction was appropriate.} - \section{Currents inside type-II superconducting cylinder} For $B_{c1} < B_E < B_{c2}$, the cylinder of type-II superconductor material is in the mixed state. In the mixed or vortex state, superconductors let through a number of finite flux quanta $\Phi_0$.