# On the Remarkable Superconductivity of FeSe and Its Close Cousins

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## Abstract

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**Contents**

1 | Introduction | 2 |

2 | Overview | 4 |

2.1 Iron Pnictides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 4 | |

2.2 How FeSe Is Different from Pnictides.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 5 | |

2.3 Theoretical Approaches to Pairing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 7 | |

3 | Bulk FeSe | 9 |

3.1 Electronic Structure of FeSe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 9 | |

3.2 Magnetic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 14 | |

3.2.1 Long Range Order. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 14 | |

3.2.2 Spin Fluctuations in Normal State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 15 | |

3.3 Superconducting Gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 17 | |

3.3.1 Thermodynamic Probe of Quasiparticle Excitations. . . . . . . . . . . . . . . . . . . . . . . . . . . | 17 | |

3.3.2 STM/ARPES Measurements of Gap Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 19 | |

3.3.3 Orbital Selective Pairing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 20 | |

3.3.4 BCS-BEC Crossover Scenario. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 24 | |

3.3.5 Spin Fluctuations in Superconducting State .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 25 | |

4 | Effects of Physical and Chemical Pressure | 26 |

4.1 FeSe under Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 26 | |

4.2 FeSe under Chemical Pressure: S Substituion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 27 | |

4.3 Diminishing Correlations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 28 | |

4.4 Abrupt Change in Gap Symmetry in Tetragonal Phase. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 28 | |

4.5 Bogoliubov Fermi Surface Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 29 | |

5 | FeSe/STO Monolayer + Dosing of FeSe Surfaces | 30 |

5.1 Single Layer Films of FeSe on SrTiO_{3} . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 30 | |

5.1.1 Electronic Structure and Electron Doping. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 30 | |

5.1.2 Structure of the Interface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 31 | |

5.1.3 Transition Temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 31 | |

5.2 Dosing of FeSe Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 32 | |

5.3 Replica Bands and Phonons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 32 | |

5.4 Pairing State in Monolayers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 34 | |

5.4.1 e-Pocket only Pairing: d- and Bonding–Antibonding s-Wave. . . . . . . . . . . . . . . . . . . | 34 | |

5.4.2 SOC Driven Pair States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 34 | |

5.4.3 Incipient Band s± Pairing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 35 | |

5.5 Impurity Experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 36 | |

6 | FeSe Intercalates | 36 |

6.1 Alkali-Intercalated FeSe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 36 | |

6.2 Organic Intercalates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 37 | |

6.3 LiOH Intercalates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 37 | |

7 | Topological Phases of Matter in Iron-Based Superconductors | 39 |

7.1 Basic Properties of Fe${}_{1+y}$Te${}_{1-x}$Se${}_{x}$ .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 39 | |

7.2 Theoretical Proposals for Topological Bands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 41 | |

7.3 Experimental Evidence for Topological Bands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 43 | |

7.4 Topological Superconductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 44 | |

7.5 Experimental Evidence for Majorana Zero Modes: Defect States. . . . . . . . . . . . . . . . . . . . . . . | 46 | |

7.6 Experimental Evidence for Majorana Zero Modes: Vortex States. . . . . . . . . . . . . . . . . . . . . . . | 47 | |

7.7 One-Dimensional Dispersive Majorana Modes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 50 | |

7.8 Higher-Order Topological States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 50 | |

8 | Conclusions | 51 |

References | 52 |

## 1. Introduction

## 2. Overview

#### 2.1. Iron Pnictides

#### 2.2. How FeSe Is Different from Pnictides

#### 2.3. Theoretical Approaches to Pairing

## 3. Bulk FeSe

#### 3.1. Electronic Structure of FeSe

#### 3.2. Magnetic Properties

#### 3.2.1. Long Range Order

#### 3.2.2. Spin Fluctuations in Normal State

#### 3.3. Superconducting Gap

#### 3.3.1. Thermodynamic Probe of Quasiparticle Excitations

#### 3.3.2. STM/ARPES Measurements of Gap Structure

#### 3.3.3. Orbital Selective Pairing

#### 3.3.4. BCS-BEC Crossover Scenario

#### 3.3.5. Spin Fluctuations in Superconducting State

## 4. Effects of Physical and Chemical Pressure

#### 4.1. FeSe under Pressure

#### 4.2. FeSe under Chemical Pressure: S Substituion

#### 4.3. Diminishing Correlations

#### 4.4. Abrupt Change in Gap Symmetry in Tetragonal Phase

#### 4.5. Bogoliubov Fermi Surface Scenario

**k**$\left)\right||{\Delta}_{2}($

**k**$\left)\right|-{\delta}^{2}$, such that the change from trivial to topologically nontrivial, accompanied by the creation of the Bogoliubov Fermi surface, occurs when the Pfaffian changes sign from positive to negative. Although $\delta $ is expected to be small, the topological transition can be achieved due to the nodal (or near-nodal) structure of the intraband gaps.

## 5. FeSe/STO Monolayer + Dosing of FeSe Surfaces

#### 5.1. Single Layer Films of FeSe on SrTiO${}_{3}$

#### 5.1.1. Electronic Structure and Electron Doping

#### 5.1.2. Structure of the Interface

#### 5.1.3. Transition Temperature

#### 5.2. Dosing of FeSe Surface

#### 5.3. Replica Bands and Phonons

#### 5.4. Pairing State in Monolayers

#### 5.4.1. e-Pocket only Pairing: d- and Bonding–Antibonding s-Wave

#### 5.4.2. SOC Driven Pair States

#### 5.4.3. Incipient Band ${s}_{\pm}$ Pairing

#### 5.5. Impurity Experiments

## 6. FeSe Intercalates

#### 6.1. Alkali-Intercalated FeSe

#### 6.2. Organic Intercalates

#### 6.3. LiOH Intercalates

## 7. Topological Phases of Matter in Iron-Based Superconductors

#### 7.1. Basic Properties of Fe${}_{1+y}$Te${}_{1-x}$Se${}_{x}$

#### 7.2. Theoretical Proposals for Topological Bands

#### 7.3. Experimental Evidence for Topological Bands

#### 7.4. Topological Superconductivity

#### 7.5. Experimental Evidence for Majorana Zero Modes: Defect States

#### 7.6. Experimental Evidence for Majorana Zero Modes: Vortex States

#### 7.7. One-Dimensional Dispersive Majorana Modes

#### 7.8. Higher-Order Topological States

## 8. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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