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A special issue of Condensed Matter (ISSN 2410-3896). This special issue belongs to the section "Superconductivity".

Deadline for manuscript submissions: closed (30 November 2019) | Viewed by 49901

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Special Issue Editors

Prof. Dr. Antonio Bianconi

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Guest Editor

Rome International Center for Materials Science Superstripes (RICMASS), Via dei Sabelli 119A, 00185 Roma, Italy
Interests: synchrotron radiation research; protein fluctuations; active sites of metalloproteins; origin of life; selected molecules in prebiotic world; quantum phenomena in complex matter; quantum confinement; superstripes in complex matter; lattice complexity in transition metal oxides; high Tc superconductors; valence fluctuation materials
Special Issues, Collections and Topics in MDPI journals

Prof. Dr. Andrea Perali

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Guest Editor

Scuola del Farmaco e Divisione di Fisica, Edificio di Fisica, Università di Camerino, Via Madonna delle Carceri 9, 62032 Camerino, Italy
Interests: high-Tc superconductivity (theory and phenomenology); multiband superconductivity; quantum size effects and shape resonances in superconductors; nanoscale superconductors; superconducting heterostructures; BCS-BEC crossover; pseudogap; superconducting fluctuations; ultracold fermions: superfluidity and BCS-BEC crossover; electron–hole superfluidity
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Room Temperature Superconductivity (RTS) has been realized in highly pressurized LaH_y, with y≈10, which is capable of exhibiting superconductivity at temperatures below 260 K (-13 °C) by a collaboration of the groups of Russell J. Hemley at George Washington University, of Viktor V. Struzhkin, at Geophysical Laboratory of Carnegie Institution and of Yue Meng at Argonne National Laboratory (arXiv:1808.07695), increasing the critical temperature found few days before by Eremets group at some lower temperatures (arXiv:1808.07039) in a similar system.

Superconductivity at winter-time temperatures near the temperature at which ice forms is an epochal scientific achievement. The highest T_c known previously was in highly pressurized hydrogen sulfide, H₃S, where the transition temperature is 203 K (−70 °C). The record for superconductivity at atmospheric pressure is held by cuprates, which superconduct at temperatures as high as 138 K (−135 °C) .

Since quantum phenomena are known to manifest at atomic or subatomic scales, or at very high energies, the majority of researchers have previously had doubts about whether room-temperature superconductivity was actually achievable. In fact, superconductivity is a manifestation of quantum coherence at a macroscopic level, which was considered by the majority of scientists to be possible only near zero temperature. This was supported by the well-established BCS theory formulated in 1957, which predicted that the dream of technologists, a room-temperature superconductor, could not exist; the maximum temperature for superconductivity according to BCS theory was just 30 K. However, BCS considers superconductivity based on cooper pairing mediated by phonons in a weak coupling regime appearing in a homogeneous 3D metal with high electron-density, with an isotropic Fermi surface and a phonon spectrum with much less energy than the Fermi surface’s energy.

The experimental realization of room temperature superconductivity has changed this perception, showing that quantum coherence on a large, macroscopic scale is possible nearly at room temperature, supporting the unpopular ideas of some scientists who proposed reaching RTS in systems that are beyond the standard BCS approximations.

Little (1964) proposed RTS driven by an electron-mediated mechanism in one-dimensional organic conductors. Ginsburg (1968) proposed RTS driven by an excitonic mechanism. Ashcroft (1968) proposed RTS in metallic hydrogen at very high pressure. Eagles (1969) proposed strong paring without superconductivity near the limit for BEC condensation at very low electron density. Müller (1986) proposed approaching RTS driven by very large electron-phonon coupling driven by the Jahn-Teller effect, and discovered high-temperature superconductors in doped perovskites. Bianconi (1993) proposed RTS driven by a Fano resonance between a BCS condensate and a BCS-BEC condensate in the appearing Fermi surface by tuning the chemical potential around the Lifshitz transition to produce the appearance of a new Fermi surface spot in quasi 2D or quasi 1D electronic matter. Perali et al (1996) have provided a theory for the numerical solution of Bogoliubov equations for multi gap systems that are able to predict RTS in superlattices of “1D” or “2D” structures.

The present experimental result supports the Neil Ashcroft theory developed in these last 50 years as for example in

Hemley, R. J. & Ashcroft, N. W. The revealing role of pressure in the condensed matter sciences. Physics Today 51, 26-32 (1998). doi:10.1063/1.882374.
Ashcroft, N. W. Symmetry and Higher Superconductivity in the Lower Elements, In Symmetry and Heterogeneity in High Temperature Superconductors, NATO Science Series II: Mathematics, Physics and Chemistry (Bianconi A. ed.) 214 (2006), pp. 3-20, (Springer Netherlands, 2006 doi:10.1007/1-4020-3989-1_1
Liu, H., Naumov, I. I., Hoffmann, R., Ashcroft, N. W. & Hemley, R. J. Potential high-Tc superconducting lanthanum and yttrium hydrides at high pressure. Proceedings of the National Academy of Sciences 114, 6990-6995 (2017). doi:10.1073/pnas.1704505114

The data accumulated in the successful search for RTS should be used as the key ingredients for other RTS in hydrides which is one of key topics of this Special Issue. Moreover today the researchers look for how to realize superconducting devices at atmospheric pressure operating at high temperatures for quantum computers. New atomic scale systems like “2D”, graphene-like, and “1D” structures, as thick as a single atom or molecule are synthesized opening new venues for room temperature superconductors.

Regards,

Prof. Antonio Bianconi
Prof. Andrea Perali
Guest Editors

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Keywords

sulfur hydrides
lanthanum hydrides
strong coupling superconductivity
Lifshitz transitions
superconducting dome
multi gap superconductivity
zero point motion
high energy phonon modes
pressure driven structural phase transitions
Van Hove singularities
soft lattices
incommensurate phases
nanoscale phase separation

Published Papers (13 papers)

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Research

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16 pages, 4314 KiB

Open AccessArticle

Multi-Band Superconductivity and the Steep Band/Flat Band Scenario

by Annette Bussmann-Holder, Hugo Keller, Arndt Simon and Antonio Bianconi

Condens. Matter 2019, 4(4), 91; https://doi.org/10.3390/condmat4040091 - 27 Nov 2019

Cited by 14 | Viewed by 3115

Abstract

The basic features of multi-band superconductivity and its implications are derived. In particular, it is shown that enhancements of the superconducting transition temperature take place due to interband interactions. In addition, isotope effects differ substantially from the typical BCS scheme as soon as polaronic coupling effects are present. Special cases of the model are polaronic coupling in one band as realized e.g., in cuprates, coexistence of a flat band and a steep band like in MgB₂, crossovers between extreme cases. The advantages of the multiband approach as compared to the single band BCS model are elucidated and its rather frequent realization in actual systems discussed. Full article

(This article belongs to the Special Issue From cuprates to Room Temperature Superconductors)

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17 pages, 2156 KiB

Open AccessArticle

Classifying Induced Superconductivity in Atomically Thin Dirac-Cone Materials

by Evgueni F. Talantsev

Condens. Matter 2019, 4(3), 83; https://doi.org/10.3390/condmat4030083 - 18 Sep 2019

Cited by 8 | Viewed by 4950

Abstract

Recently, Kayyalha et al. (Phys. Rev. Lett., 2019, 122, 047003) reported on the anomalous enhancement of the self-field critical currents (I_c(sf,T)) at low temperatures in Nb/BiSbTeSe₂-nanoribbon/Nb Josephson junctions. The enhancement was attributed to the low-energy Andreev-bound states arising from the winding of the electronic wave function around the circumference of the topological insulator BiSbTeSe₂ nanoribbon. It should be noted that identical enhancement in I_c(sf,T) and in the upper critical field (B_c2(T)) in approximately the same reduced temperatures, were reported by several research groups in atomically thin junctions based on a variety of Dirac-cone materials (DCM) earlier. The analysis shows that in all these S/DCM/S systems, the enhancement is due to a new superconducting band opening. Taking into account that several intrinsic superconductors also exhibit the effect of new superconducting band(s) opening when sample thickness becomes thinner than the out-of-plane coherence length (ξ_c(0)), we reaffirm our previous proposal that there is a new phenomenon of additional superconducting band(s) opening in atomically thin films. Full article

(This article belongs to the Special Issue From cuprates to Room Temperature Superconductors)

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22 pages, 641 KiB

Open AccessArticle

Mechanism of High-Temperature Superconductivity in Correlated-Electron Systems

by Takashi Yanagisawa

Condens. Matter 2019, 4(2), 57; https://doi.org/10.3390/condmat4020057 - 19 Jun 2019

Cited by 10 | Viewed by 5784

Abstract

It is very important to elucidate the mechanism of superconductivity for achieving room temperature superconductivity. In the first half of this paper, we give a brief review on mechanisms of superconductivity in many-electron systems. We believe that high-temperature superconductivity may occur in a system with interaction of large-energy scale. Empirically, this is true for superconductors that have been found so far. In the second half of this paper, we discuss cuprate high-temperature superconductors. We argue that superconductivity of high temperature cuprates is induced by the strong on-site Coulomb interaction, that is, the origin of high-temperature superconductivity is the strong electron correlation. We show the results on the ground state of electronic models for high temperature cuprates on the basis of the optimization variational Monte Carlo method. A high-temperature superconducting phase will exist in the strongly correlated region. Full article

(This article belongs to the Special Issue From cuprates to Room Temperature Superconductors)

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16 pages, 2232 KiB

Open AccessArticle

Evaluating Superconductors through Current Induced Depairing

by Milind N. Kunchur

Condens. Matter 2019, 4(2), 54; https://doi.org/10.3390/condmat4020054 - 17 Jun 2019

Cited by 4 | Viewed by 2862

Abstract

The phenomenon of superconductivity occurs in the phase space of three principal parameters: temperature T, magnetic field B, and current density j. The critical temperature

T_{c}

is one of the first parameters that is measured and in a certain way defines [...] Read more.

The phenomenon of superconductivity occurs in the phase space of three principal parameters: temperature T, magnetic field B, and current density j. The critical temperature

T_{c}

is one of the first parameters that is measured and in a certain way defines the superconductor. From the practical applications point of view, of equal importance is the upper critical magnetic field

B_{c 2}

and conventional critical current density

j_{c}

(above which the system begins to show resistance without entering the normal state). However, a seldom-measured parameter, the depairing current density

j_{d}

, holds the same fundamental importance as

T_{c}

and

B_{c 2}

, in that it defines a boundary between the superconducting and normal states. A study of

j_{d}

sheds unique light on other important characteristics of the superconducting state such as the superfluid density and the nature of the normal state below

T_{c}

, information that can play a key role in better understanding newly-discovered superconducting materials. From a measurement perspective, the extremely high values of

j_{d}

make it difficult to measure, which is the reason why it is seldom measured. Here, we will review the fundamentals of current-induced depairing and the fast-pulsed current technique that facilitates its measurement and discuss the results of its application to the topological-insulator/chalcogenide interfacial superconducting system. Full article

(This article belongs to the Special Issue From cuprates to Room Temperature Superconductors)

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8 pages, 627 KiB

Open AccessArticle

Scaling between Superfluid Density and T_c in Overdoped La_2−xSr_xCuO₄ Films

by Evandro V. L. de Mello

Condens. Matter 2019, 4(2), 52; https://doi.org/10.3390/condmat4020052 - 06 Jun 2019

Viewed by 2416

Abstract

We used an electronic phase separation approach to interpret the scaling between the low-temperature superfluid density average

ρ_{sc} (0)

and the superconducting critical temperature

T_{c}

on overdoped La

_{2 - x}

_{x}

CuO

_{4}

films. Guided by the [...] Read more.

We used an electronic phase separation approach to interpret the scaling between the low-temperature superfluid density average

ρ_{sc} (0)

and the superconducting critical temperature

T_{c}

on overdoped La

_{2 - x}

_{x}

CuO

_{4}

films. Guided by the observed nematic and incommensurate charge ordering (CO), we performed simulations with a free energy that reproduces charge domains with wavelength

λ_{C O}

and provides a scale to local superconducting interactions. Under these conditions a complex order parameter with amplitude

Δ_{d} (r_{i})

and phase

θ (r_{i})

may develop at a domain i. We assumed that these domains are coupled by Josephson energy

E_{J} (r_{i j})

, proportional to the local superfluid density

ρ_{sc} (r_{i j})

. Long-range order occured when the average

E_{J} (T_{c})

\sim k_{B} T_{c}

. The linear

ρ_{s c} (0)

vs.

T_{c}

relation was satisfied whenever CO was present, even with almost vanishing charge amplitudes. Full article

(This article belongs to the Special Issue From cuprates to Room Temperature Superconductors)

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17 pages, 5114 KiB

Open AccessArticle

Multiple Electronic Components and Lifshitz Transitions by Oxygen Wires Formation in Layered Cuprates and Nickelates

by Thomas Jarlborg and Antonio Bianconi

Condens. Matter 2019, 4(1), 15; https://doi.org/10.3390/condmat4010015 - 21 Jan 2019

Cited by 9 | Viewed by 2953

Abstract

There is growing compelling experimental evidence that a quantum complex matter scenario made of multiple electronic components and competing quantum phases is needed to grab the key physics of high critical temperature (T_c) superconductivity in layered cuprates. While it is known that defect self-organization controls T_c, the mechanism remains an open issue. Here we focus on the theoretical prediction of the multiband electronic structure and the formation of broken Fermi surfaces generated by the self-organization of oxygen interstitials O_i atomic wires in the spacer layers in HgBa₂CuO_4+δ, La₂CuO_4+δ and La₂NiO_4+δ, by means of self-consistent Linear Muffin-Tin Orbital (LMTO) calculations. The electronic structure of a first phase of ordered O_i atomic wires and of a second glassy phase made of disordered O_i impurities have been studied through supercell calculations. We show the common features of the influence of O_i wires in the electronic structure in three types of materials. The ordering of O_i into wires leads to a separation of the electronic states between the O_i ensemble and the rest of the bulk. The wire formation first produces quantum confined localized states near the wire, which coexist with, Second, delocalized states in the Fermi surface (FS) of doped cuprates. A new scenario emerges for high T_c superconductivity, where Kitaev wires with Majorana bound states are proximity-coupled to a 2D d-wave superconductor. Full article

(This article belongs to the Special Issue From cuprates to Room Temperature Superconductors)

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Review

Jump to: Research

23 pages, 5058 KiB

Open AccessReview

Probing Phase Separation and Local Lattice Distortions in Cuprates by Raman Spectroscopy

by Efthymios Liarokapis

Condens. Matter 2019, 4(4), 87; https://doi.org/10.3390/condmat4040087 - 01 Nov 2019

Cited by 4 | Viewed by 2732

Abstract

It is generally accepted that high temperature superconductors emerge when extra carriers are introduced in the parent state, which looks like a Mott insulator. Competition of the order parameters drives the system into a poorly defined pseudogap state before acquiring the normal Fermi liquid behavior with further doping. Within the low doping level, the system has the tendency for mesoscopic phase separation, which seems to be a general characteristic in all high Tc compounds, but also in the materials of colossal magnetoresistance or the relaxor ferroelectrics. In all these systems, metastable phases can be created by tuning physical variables, such as doping or pressure, and the competing order parameters can drive the compound to various states. Structural instabilities are expected at critical points and Raman spectroscopy is ideal for detecting them, since it is a very sensitive technique for detecting small lattice modifications and instabilities. In this article, phase separation and lattice distortions are examined on the most characteristic family of high temperature superconductors, the cuprates. The effect of doping or atomic substitutions on cuprates is examined concerning the induced phase separation and hydrostatic pressure for activating small local lattice distortions at the edge of lattice instability. Full article

(This article belongs to the Special Issue From cuprates to Room Temperature Superconductors)

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46 pages, 730 KiB

Open AccessReview

Dzyaloshinskii–Moriya Coupling in 3d Insulators

by Alexander Moskvin

Condens. Matter 2019, 4(4), 84; https://doi.org/10.3390/condmat4040084 - 12 Oct 2019

Cited by 22 | Viewed by 4331

Abstract

We present an overview of the microscopic theory of the Dzyaloshinskii–Moriya (DM) coupling in strongly correlated 3d compounds. Most attention in the paper centers around the derivation of the Dzyaloshinskii vector, its value, orientation, and sense (sign) under different types of the (super)exchange interaction and crystal field. We consider both the Moriya mechanism of the antisymmetric interaction and novel contributions, in particular, that of spin–orbital coupling on the intermediate ligand ions. We have predicted a novel magnetic phenomenon, weak ferrimagnetism in mixed weak ferromagnets with competing signs of Dzyaloshinskii vectors. We revisit a problem of the DM coupling for a single bond in cuprates specifying the local spin–orbital contributions to the Dzyaloshinskii vector focusing on the oxygen term. We predict a novel puzzling effect of the on-site staggered spin polarization to be a result of the on-site spin–orbital coupling and the cation-ligand spin density transfer. The intermediate ligand nuclear magnetic resonance (NMR) measurements are shown to be an effective tool to inspect the effects of the DM coupling in an external magnetic field. We predict the effect of a strong oxygen-weak antiferromagnetism in edge-shared CuO

_{2}

chains due to uncompensated oxygen Dzyaloshinskii vectors. We revisit the effects of symmetric spin anisotropy directly induced by the DM coupling. A critical analysis will be given of different approaches to exchange-relativistic coupling based on the cluster and the DFT (density functional theory) based calculations. Theoretical results are applied to different classes of 3d compounds from conventional weak ferromagnets (

α

-Fe

_{2}

_{3}

, FeBO

_{3}

, FeF

_{3}

, RFeO

_{3}

, RCrO

_{3}

, …) to unconventional systems such as weak ferrimagnets (e.g., RFe

_{1 - x}

_{x}

_{3}

), helimagnets (e.g., CsCuCl

_{3}

), and parent cuprates (La

_{2}

CuO

_{4}

, …). Full article

(This article belongs to the Special Issue From cuprates to Room Temperature Superconductors)

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14 pages, 2778 KiB

Open AccessReview

T_c and Other Cuprate Properties in Relation to Planar Charges as Measured by NMR

by Michael Jurkutat, Andreas Erb and Jürgen Haase

Condens. Matter 2019, 4(3), 67; https://doi.org/10.3390/condmat4030067 - 11 Jul 2019

Cited by 10 | Viewed by 3253

Abstract

Nuclear magnetic resonance (NMR) in cuprate research is a prominent bulk local probe of magnetic properties. NMR also, as was shown over the last years, actually provides a quantitative measure of local charges in the CuO

_{2}

plane. This has led to fundamental [...] Read more.

_{2}

plane. This has led to fundamental insights, e.g., that the maximum

T_{c}

is determined by the sharing of the parent planar hole between Cu and O. Using bonding orbital hole contents on planar Cu and O measured by NMR, instead of the total doping x, the thus defined two-dimensional cuprate phase diagram reveals significant differences between the various cuprate materials. Even more importantly, the reflected differences in material chemistry appear to set a number of electronic properties as we discuss here, for undoped, underdoped and optimally doped cuprates. These relations should advise attempts at a theoretical understanding of cuprate physics as well as inspire material chemists towards new high-

T_{c}

materials. Probing planar charges, NMR is also sensitive to charge variations or ordering phenomena in the CuO

_{2}

plane. Thereby, local charge order on planar O in optimally doped YBCO could recently be proven. Charge density variations seen by NMR in both planar bonding orbitals with amplitudes between 1% to 5% appear to be omnipresent in the doped CuO

_{2}

plane, i.e., not limited to underdoped cuprates and low temperatures. Full article

(This article belongs to the Special Issue From cuprates to Room Temperature Superconductors)

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14 pages, 329 KiB

Open AccessReview

The Ancient Romans’ Route to Charge Density Waves in Cuprates

by Sergio Caprara

Condens. Matter 2019, 4(2), 60; https://doi.org/10.3390/condmat4020060 - 25 Jun 2019

Cited by 11 | Viewed by 2737

Abstract

An account is given of the main steps that led the research group in Rome, to which the author belongs, to the formulation of the charge-density-wave scenario for high-

T_{c}

superconducting cuprates. The early finding of the generic tendency of strongly correlated [...] Read more.

An account is given of the main steps that led the research group in Rome, to which the author belongs, to the formulation of the charge-density-wave scenario for high-

T_{c}

superconducting cuprates. The early finding of the generic tendency of strongly correlated electron systems with short range interactions to undergo electron phase separation was subsequently contrasted with the homogenizing effect of the long-range Coulomb interaction. The two effects can find a compromise in the formation of incommensurate charge density waves. These charge density waves are inherently dynamical and are overdamped as a consequence of the possibility to decay in electron-hole pairs, yet tend to maintain a (quantum) critical character, which is mirrored in their marked momentum and frequency dependence and in their strong variation with temperature and doping. These dynamical incommensurate charge density waves act as mediators of pairing lading to high-

T_{c}

superconductivity, and provide the scattering mechanism that produces the observed violation of the Fermi-liquid paradigm in the metallic phase. Full article

(This article belongs to the Special Issue From cuprates to Room Temperature Superconductors)

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19 pages, 3341 KiB

Open AccessReview

Fermi-Bose Mixtures and BCS-BEC Crossover in High-T_c Superconductors

by Maxim Yu. Kagan and Antonio Bianconi

Condens. Matter 2019, 4(2), 51; https://doi.org/10.3390/condmat4020051 - 03 Jun 2019

Cited by 22 | Viewed by 4299

Abstract

In this review article we consider theoretically and give experimental support to the models of the Fermi-Bose mixtures and the BCS-BEC (Bardeen Cooper Schrieffer–Bose Einstein) crossover compared with the strong-coupling approach, which can serve as the cornerstones on the way from high-temperature to room-temperature superconductivity in pressurized metallic hydrides. We discuss some key theoretical ideas and mechanisms proposed for unconventional superconductors (cuprates, pnictides, chalcogenides, bismuthates, diborides, heavy-fermions, organics, bilayer graphene, twisted graphene, oxide hetero-structures), superfluids and balanced or imbalanced ultracold Fermi gases in magnetic traps. We build a bridge between unconventional superconductors and recently discovered pressurized hydrides superconductors H₃S and LaH₁₀ with the critical temperature close to room temperature. We discuss systems with a line of nodal Dirac points close to the Fermi surface and superconducting shape resonances, and hyperbolic superconducting networks which are very important for the development of novel topological superconductors, for the energetics, for the applications in nano-electronics and quantum computations. Full article

(This article belongs to the Special Issue From cuprates to Room Temperature Superconductors)

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19 pages, 417 KiB

Open AccessReview

Time Reversal Symmetry Breaking Superconductors: Sr₂RuO₄ and Beyond

by Karol Izydor Wysokiński

Condens. Matter 2019, 4(2), 47; https://doi.org/10.3390/condmat4020047 - 09 May 2019

Cited by 16 | Viewed by 4391

Abstract

Recent work done on the time reversal symmetry (TRS) breaking superconductors is reviewed in this paper. The special attention is paid to Sr

_{2}

RuO

_{4}

believed to be spin triplet chiral p-wave superconductor which break TRS and is expected to posses non-trivial [...] Read more.

Recent work done on the time reversal symmetry (TRS) breaking superconductors is reviewed in this paper. The special attention is paid to Sr

_{2}

RuO

_{4}

believed to be spin triplet chiral p-wave superconductor which break TRS and is expected to posses non-trivial topological properties. The family of TRS breaking superconductors is growing relatively fast, with many of its newly discovered members being non-centrosymmetric. However not only Sr

_{2}

RuO

_{4}

but also many other superconductors which possess center of inversion also break TRS. The TRS is often identified by means of the muon spin relaxation (

μ

SR) and the Kerr effect. Both methods effectively measure the appearance of the spontaneous bulk magnetic field below superconducting transition temperature. This compound provides an example of the material whose many band, multi-condensate modeling has enjoyed a number of successes, but the full understanding has not been achieved yet. We discuss in some details the properties of the material. Among them is the Kerr effect and by understanding has resulted in the discovery of the novel mechanism of the phenomenon. The mechanism is universal and thus applicable to all systems with multi-orbital character of states at the Fermi energy. Full article

(This article belongs to the Special Issue From cuprates to Room Temperature Superconductors)

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16 pages, 1078 KiB

Open AccessReview

Orbital Symmetry and Orbital Excitations in High-T_c Superconductors

by Andrzej M. Oleś, Krzysztof Wohlfeld and Giniyat Khaliullin

Condens. Matter 2019, 4(2), 46; https://doi.org/10.3390/condmat4020046 - 06 May 2019

Cited by 10 | Viewed by 4676

Abstract

We discuss a few possibilities of high-

T_{c}

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 [...] Read more.

We discuss a few possibilities of high-

T_{c}

x^{2} - y^{2}

symmetry doped by holes. Next, several routes towards involving both

e_{g}

orbital symmetries for doped holes are discussed: (i) some give superconductivity in a CuO

_{2}

monolayer on Bi2212 superconductors, Sr

_{2}

CuO

_{4 - δ}

, Ba

_{2}

CuO

_{4 - δ}

, while (ii) others as nickelate heterostructures or Eu

_{2 - x}

_{x}

NiO

_{4}

, could in principle realize it as well. At low electron filling of Ru ions, spin-orbital entangled states of

t_{2 g}

symmetry contribute in Sr

_{2}

RuO

_{4}

. Finally, electrons with both

t_{2 g}

and

e_{g}

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. Full article

(This article belongs to the Special Issue From cuprates to Room Temperature Superconductors)

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