Orbital Symmetry and Orbital Excitations in High- T c Superconductors

We discuss a few possibilities of high-<inline-formula> <math display="inline"> <semantics> <msub> <mi>T</mi> <mi>c</mi> </msub> </semantics> </math> </inline-formula> superconductivity with more than one orbital symmetry contributing to the pairing. First, we show that the high energies of orbital excitations in various cuprates suggest a simplified model with a single orbital of <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo>&#8722;</mo> <msup> <mi>y</mi> <mn>2</mn> </msup> </mrow> </semantics> </math> </inline-formula> symmetry doped by holes. Next, several routes towards involving both <inline-formula> <math display="inline"> <semantics> <msub> <mi>e</mi> <mi>g</mi> </msub> </semantics> </math> </inline-formula> orbital symmetries for doped holes are discussed: (i) some give superconductivity in a CuO<inline-formula> <math display="inline"> <semantics> <msub> <mrow></mrow> <mn>2</mn> </msub> </semantics> </math> </inline-formula> monolayer on Bi2212 superconductors, Sr<inline-formula> <math display="inline"> <semantics> <msub> <mrow></mrow> <mn>2</mn> </msub> </semantics> </math> </inline-formula>CuO<inline-formula> <math display="inline"> <semantics> <msub> <mrow></mrow> <mrow> <mn>4</mn> <mo>&#8722;</mo> <mi>&#948;</mi> </mrow> </msub> </semantics> </math> </inline-formula>, Ba<inline-formula> <math display="inline"> <semantics> <msub> <mrow></mrow> <mn>2</mn> </msub> </semantics> </math> </inline-formula>CuO<inline-formula> <math display="inline"> <semantics> <msub> <mrow></mrow> <mrow> <mn>4</mn> <mo>&#8722;</mo> <mi>&#948;</mi> </mrow> </msub> </semantics> </math> </inline-formula>, while (ii) others as nickelate heterostructures or Eu<inline-formula> <math display="inline"> <semantics> <msub> <mrow></mrow> <mrow> <mn>2</mn> <mo>&#8722;</mo> <mi>x</mi> </mrow> </msub> </semantics> </math> </inline-formula>Sr<inline-formula> <math display="inline"> <semantics> <msub> <mrow></mrow> <mi>x</mi> </msub> </semantics> </math> </inline-formula>NiO<inline-formula> <math display="inline"> <semantics> <msub> <mrow></mrow> <mn>4</mn> </msub> </semantics> </math> </inline-formula>, could in principle realize it as well. At low electron filling of Ru ions, spin-orbital entangled states of <inline-formula> <math display="inline"> <semantics> <msub> <mi>t</mi> <mrow> <mn>2</mn> <mi>g</mi> </mrow> </msub> </semantics> </math> </inline-formula> symmetry contribute in Sr<inline-formula> <math display="inline"> <semantics> <msub> <mrow></mrow> <mn>2</mn> </msub> </semantics> </math> </inline-formula>RuO<inline-formula> <math display="inline"> <semantics> <msub> <mrow></mrow> <mn>4</mn> </msub> </semantics> </math> </inline-formula>. Finally, electrons with both <inline-formula> <math display="inline"> <semantics> <msub> <mi>t</mi> <mrow> <mn>2</mn> <mi>g</mi> </mrow> </msub> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <msub> <mi>e</mi> <mi>g</mi> </msub> </semantics> </math> </inline-formula> orbital symmetries contribute to the superconducting properties and nematicity of Fe-based superconductors, pnictides or FeSe. Some of them provide examples of orbital-selective Cooper pairing.

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