Toward an <i>Ab Initio</i> Theory of High-Temperature Superconductors: A Study of Multilayer Cuprates
Bibliographic record
Abstract
Significant progress toward a theory of high-temperature superconductivity in cuprates has been achieved via the study of effective one- and three-band Hubbard models. Nevertheless, material-specific predictions, while essential for constructing a comprehensive theory, remain challenging due to the complex relationship between real materials and the parameters of the effective models. By combining cluster dynamical mean-field theory and density functional theory in a charge-self-consistent manner, here we show that the goal of material-specific predictions for high-temperature superconductors from first principles is within reach. To demonstrate the capabilities of our approach, we take on the challenge of explaining the remarkable physics of multilayer cuprates by focusing on the two representative <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:msub> <a:mrow> <a:mi>Ca</a:mi> </a:mrow> <a:mrow> <a:mo stretchy="false">(</a:mo> <a:mn>1</a:mn> <a:mo>+</a:mo> <a:mi>n</a:mi> <a:mo stretchy="false">)</a:mo> </a:mrow> </a:msub> <a:mrow> <a:msub> <a:mrow> <a:mi>Cu</a:mi> </a:mrow> <a:mrow> <a:mi>n</a:mi> </a:mrow> </a:msub> </a:mrow> <a:mrow> <a:msub> <a:mrow> <a:mi mathvariant="normal">O</a:mi> </a:mrow> <a:mrow> <a:mn>2</a:mn> <a:mi>n</a:mi> </a:mrow> </a:msub> <a:mrow> <a:msub> <a:mrow> <a:mi>Cl</a:mi> </a:mrow> <a:mrow> <a:mn>2</a:mn> </a:mrow> </a:msub> </a:mrow> </a:mrow> </a:mrow> </a:math> and <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:mrow> <f:msub> <f:mrow> <f:mi>HgBa</f:mi> </f:mrow> <f:mrow> <f:mn>2</f:mn> </f:mrow> </f:msub> </f:mrow> <f:mrow> <f:msub> <f:mrow> <f:mi>Ca</f:mi> </f:mrow> <f:mrow> <f:mo stretchy="false">(</f:mo> <f:mi>n</f:mi> <f:mo>−</f:mo> <f:mn>1</f:mn> <f:mo stretchy="false">)</f:mo> </f:mrow> </f:msub> <f:mrow> <f:msub> <f:mrow> <f:mi>Cu</f:mi> </f:mrow> <f:mrow> <f:mi>n</f:mi> </f:mrow> </f:msub> </f:mrow> <f:mrow> <f:msub> <f:mrow> <f:mi mathvariant="normal">O</f:mi> </f:mrow> <f:mrow> <f:mo stretchy="false">(</f:mo> <f:mn>2</f:mn> <f:mi>n</f:mi> <f:mo>+</f:mo> <f:mn>2</f:mn> <f:mo stretchy="false">)</f:mo> </f:mrow> </f:msub> </f:mrow> </f:mrow> </f:math> families. We shed light on the microscopic origin of many salient features of multilayer cuprates, in particular, the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>n</m:mi> </m:math> dependence of their superconducting properties. The growth of <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:msub> <o:mi>T</o:mi> <o:mi>c</o:mi> </o:msub> </o:math> from the single-layer to the trilayer compounds is here explained by the reduction of the charge transfer gap and, consequently, the growth of superexchange <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mi>J</q:mi> </q:math> as <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mi>n</s:mi> </s:math> increases. The origin of both is traced to the appearance of low-energy conduction bands reminiscent of standing wave modes confined within the stack of <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mrow> <u:msub> <u:mrow> <u:mi>CuO</u:mi> </u:mrow> <u:mrow> <u:mn>2</u:mn> </u:mrow> </u:msub> </u:mrow> </u:math> planes. We interpret the ultimate drop of <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:msub> <w:mi>T</w:mi> <w:mi>c</w:mi> </w:msub> </w:math> for <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:mi>n</y:mi> <y:mo>≥</y:mo> <y:mn>4</y:mn> </y:math> as a consequence of the inhomogeneous doping between the <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:mrow> <ab:msub> <ab:mrow> <ab:mi>CuO</ab:mi> </ab:mrow> <ab:mrow> <ab:mn>2</ab:mn> </ab:mrow> </ab:msub> </ab:mrow> </ab:math> planes, which prevents the emergence of superconductivity in the inner planes due to their insufficient effective hole doping, as we also highlight the existence of a minimal doping (4%) required for superconductivity to appear in one of the planes. We explain material-specific properties such as the larger propensity of <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:mrow> <cb:msub> <cb:mrow> <cb:mi>HgBa</cb:mi> </cb:mrow> <cb:mrow> <cb:mn>2</cb:mn> </cb:mrow> </cb:msub> </cb:mrow> <cb:mrow> <cb:msub> <cb:mrow> <cb:mi>Ca</cb:mi> </cb:mrow> <cb:mrow> <cb:mo stretchy="false">(</cb:mo> <cb:mi>n</cb:mi> <cb:mo>−</cb:mo> <cb:mn>1</cb:mn> <cb:mo stretchy="false">)</cb:mo> </cb:mrow> </cb:msub> <cb:mrow> <cb:msub> <cb:mrow> <cb:mi>Cu</cb:mi> </cb:mrow> <cb:mrow> <cb:mi>n</cb:mi> </cb:mrow> </cb:msub> </cb:mrow> <cb:mrow> <cb:msub> <cb:mrow> <cb:mi mathvariant="normal">O</cb:mi> </cb:mrow> <cb:mrow> <cb:mo stretchy="false">(</cb:mo> <cb:mn>2</cb:mn> <cb:mi>n</cb:mi>
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".