These lectures present the Fermi-liquid theory of superconductivity, which is applicable to a broad range of systems that are candidates for non-s wave pairing, {\it e.g.} the heavy fermions, organic metals and the CuO superconductors. Ginzburg-Landau (GL) theory provides an important link between experimental properties of non-s wave superconductors and the more general Fermi-liquid theory. The multiple superconducting phases of UPt$_3$ provide an ideal example of the role that is played by the GL theory for non-s wave superconductors. The difference between non-s wave superconductivity and conventional anisotropic superconductivity is illustrated here by the unique effects that impurities are predicted to have on the properties of non-s wave superconductors.
The Mott transition is one of the fundamental issues in condensed matter physics, especially in the system with antiferromagnetic long-range order. However the Mott transition in quantum spin liquid (QSL) systems without long-range order is rare. Here we report the observation of the pressure-induced insulator to metal transition followed by the emergence of superconductivity in the QSL candidate NaYbSe2 with triangular lattice of 4f Yb$_3^+$ ions. Detail analysis of transport properties at metallic state shows an evolution from non-Fermi liquid to Fermi liquid behavior when approaching the vi…
Fractionalized Fermi liquids (FL$^\ast$) have been introduced as non-Fermi-liquid metallic phases, characterized by coexisting electron-like charge carriers and local moments which itself form a fractionalized spin liquid. Here we investigate a Kondo lattice model on the honeycomb lattice with compass interactions among the local moments, a concrete model hosting FL$^\ast$ phases based on Kitaev's $\mathbb{Z}_2$ spin liquid. We characterize the FL$^\ast$ phases via perturbation theory, and we employ a Majorana-fermion mean-field theory to map out the full phase diagram. Most remarkably we find…
Superconducting LaOFeAs family of even electron metallic systems have striking resemblance to odd electron cuprates. We suggest that this resemblance is caused by presence of two coupled 2D resonating valence bond systems in LaOFeAs . Bond charge repulsion and Hund coupling fuse the 2 species of valence bonds into closed strings with a Haldane gap, resulting in a quantum string liquid. A pair of doped holes (electrons) creates an open string and remain at the ends as holon(doublon). Charge -2e spin singlet strings condense to produce high Tc superconductivity. Higher Tc's are likely in our str…
We report neutron scattering measurements, which reveal spin-liquid polymorphism in a '11' iron chalcogenide superconductor, a poorly-metallic magnetic FeTe tuned towards superconductivity by substitution of a small amount of Tellurium with iso-electronic Sulphur. We observe liquid-like magnetic dynamics, which is described by a competition of two phases with different local structure, whose relative abundance depends on temperature. One is the ferromagnetic (FM) plaquette phase observed in the non-superconducting FeTe, which preserves the C$_4$ symmetry of the underlying square lattice and is…
Recently, Matsukawa et al. have discovered a new superconductor Pr_2Ba_4Cu_7O_15-delta in which metallic CuO double chains are responsible for the superconductivity. To investigate the superconductivity, we employ the d-p double chain model where the tight-binding parameters are determined so as to fit the LDA band structure. On the basis of the Tomonaga-Luttinger liquid theory, we obtain the phase diagram including the superconducting phase in the weak coupling limit. We also calculate the Luttinger liquid parameter K_rho as a function of the electron density $n$ by using the Hartree-Fock app…
Exotic superconductivity in the doped Kitaev quantum spin liquid
Institute for Solid State Physics, University of Tokyo（东京大学固体物理研究所）；Department of Applied Science, Graduate School of Sciences and Technology for Innovation, Yamaguchi University（山口大学理工学综合研究科应用科学系）
We study an exactly-solvable model which shows a zero-temperature transition from a non-Fermi liquid to a Fermi liquid as a function of particle density. The quantum critical point separating these two states is not associated with the usual ordering transition of a bosonic degree of freedom. We analyze the properties of this critical point in terms of an effective density of states, and we use this concept to generalize this transition to a class of related quantum critical points. We study the superconducting instability of the low-density (non-Fermi liquid) regime and we show that it has an…
An unconventional superconducting phase is explored developing out of a non Fermi-liquid phase of the two-channel Anderson lattice model. It is characterized by a composite order parameter comprising of a local spin or orbital degree of freedom bound to triplet Cooper pairs with an isotropic and a nearest neighbour form factor. The superconducting transition temperature peaks in the moderate intermediate valence regime and vanishes at integral valence. The gap function is non analytic and odd in frequency, and a pseudo-gap develops in the conduction electron density of states which vanishes as…
In the d-electron system YFe$_2$Ge$_2$, an unusually high and temperature dependent Sommerfeld ratio of the specific heat capacity $C/T \sim 100~\mathrm{mJ/(molK^2)}$ and an anomalous power law temperature dependence of the electrical resistivity $ρ\simeq ρ_0 + AT^{3/2}$ signal Fermi liquid breakdown, probably connected to a close-by quantum critical point. Full resistive transitions, accompanied by DC diamagnetic screening fractions of up to 80\% suggest that pure samples of YFe$_2$Ge$_2$ superconduct below $1.8~\mathrm{K}$.
The quantum spin liquid candidate NaYbSe$_2$ was recently reported to exhibit a Mott transition under pressure. Superconductivity was observed in the high-pressure metallic phase, raising the question concerning its relation with the low-pressure quantum spin liquid ground state. Here we combine the density functional theory and the dynamical mean-field theory to explore the underlying mechanism of the insulator-to-metal transition and superconductivity and establish an overall picture of its electronic phases under pressure. Our results suggest that NaYbSe$_2$ is a charge-transfer insulator a…
Low-temperature thermodynamic properties of strongly interacting Fermi liquids with fermion condensate are investigated. We demonstrate that the spin susceptibility of these systems exhibits the Curie-Weiss law, and the entropy contains a temperature-independent term. The excessive entropy is released at the superconducting transition, enhancing the specific heat jump Delta C and rendering it proportional to the effective Curie constant. The theoretical results are favorably compared with the experimental data on the heavy fermion metal CeCoIn5, as well as He-3 films.
We describe a new kind of quantum critical point in the context of quantum anti-ferromagnetism in 2d that can be understood as a quantum critical spin liquid. Based on the comparison of exponents with previous numerical work, we argue it describes a transition from an anti-ferromagnetic Néel ordered state to a VBS-like state. We argue further that the symplectic fermions capture the proper degrees of freedom in the zero temperature phase that is the parent to the superconducting phase in the cuprates. We then show that our model reproduces some features found recently in experiments and also i…
Nuclear quadrupole resonance measurements were performed on the heavy fermion superconductor Ce2PdIn8. Above the Kondo coherence temperature T_coh \simeq 30K, the spin-lattice relaxation rate 1/T_1 is temperature independent, whereas at lower temperatures, down to the onset of superconductivity at T_c = 0.64K, it is nearly proportional to T^{1/2}. Below T_c, 1/T_1 shows no coherence peak and decreases as T^3 down to 75mK. All these findings indicate that Ce2PdIn8 is close to the antiferromagnetic quantum critical point, and the superconducting state has an unconventional character with line no…
It has long been proposed that doping a chiral spin liquid (CSL) or fractional quantum Hall state can give rise to topological superconductivity. Despite of intensive effort, definitive evidences still remain lacking. We address this problem by studying the $t$-$J$ model supplemented by time-reversal symmetry breaking chiral interaction $J_χ$ on the triangular lattice using density-matrix renormalization group with a finite concentration $δ$ of doped holes. It has been established that the undoped, i.e., $δ$=0, system has a CSL ground state in the parameter region $0.32\le J_χ/J \le 0.56$. Upo…
I study an Extended Periodic Anderson Model (EPAM) with non-local hybridisation, $V_{fc}$, and a coulomb interaction, $U_{fc}$, between localised $f$ electrons and wide band conduction ($c$) electrons. Within DMFT, a quantum phase transition (QPT) driven by soft $f$-valence fluctuations, accompanied by a discontinuous jump in the Fermi volume, is found as $V_{fc}$ is tuned across a critical value. Near the associated QCP, an unconventional superconductive instability, driven by these extended, singular valence fluctuations, naturally emerges. {\it All} these phenomena are representative of obs…
We observe superconductivity below a critical temperature TC = 1.8 K in single-crystal Ir3Te8, which also exhibits normal-state diamagnetism and a linear temperature dependence of electrical resistivity for a wide temperature interval, 20 K < T < 700 K. Single-crystal Ir3Te8 also undergoes a structural phase transition at TS = 350 K from a cubic (above TS) to a rhombohedral lattice below TS. Our first-principles electronic structure calculations reveal two bands crossing the Fermi level; despite the three-dimensional lattice, one band is quasi-two-dimensional, and is responsible for the observ…
We clarify the new concept of gravitationally dressed Fermi liquids we have proposed to describe the normal state of high Tc superconductors. In this note we distinguish between weakly gravitationally dressed Fermi liquids which fall in the class of the canonical Fermi liquid theory (with quasiparticle excitations), and strongly gravitationally dressed Fermi liquids (with quasiunparticle excitations) which represent the high dimensional generalization of Luttinger liquids, with specific features. Such weakly or strongly gravitationally dressed Fermi liquids lead naturally to the previously pro…
Superconductivity in FeTe0.8S0.2 is successfully induced by an electrochemical reaction using an ionic liquid solution. A clear correlation between the Fe concentration in the solution and the manifestation of superconductivity was confirmed, suggesting that superconductivity was induced by the deintercalation of excess iron.
The Schwinger-boson theory of the frustrated square lattice antiferromagnet yields a stable, gapped $\mathbb{Z}_2$ spin liquid ground state with time-reversal symmetry, incommensurate spin correlations and long-range Ising-nematic order. We obtain an equivalent description of this state using fermionic spinons (the fermionic spinons can be considered to be bound states of the bosonic spinons and the visons). Upon doping, the $\mathbb{Z}_2$ spin liquid can lead to a fractionalized Fermi liquid (FL*) with small Fermi pockets of electron-like quasiparticles, while preserving the $\mathbb{Z}_2$ to…
A series of LiFe$_{1-x}$Co$_{x}$As compounds with different Co concentrations have been studied by transport, optical spectroscopy, angle-resolved photoemission spectroscopy and nuclear magnetic resonance. We observed a Fermi liquid to non-Fermi liquid to Fermi liquid (FL-NFL-FL) crossover alongside a monotonic suppression of the superconductivity with increasing Co content. In parallel to the FL-NFL-FL crossover, we found that both the low-energy spin fluctuations and Fermi surface nesting are enhanced and then diminished, strongly suggesting that the NFL behavior in LiFe$_{1-x}$Co$_{x}$As is…
We propose an exactly solvable model for $j_{\text{eff}}=\frac32$ local moments on the honeycomb lattice. Our construction is guided by a symmetry analysis and by the requirement of an exact solution in terms of a Majorana fermion representation for multipole operators. The main interaction in the model can be interpreted as a bond-dependent quadrupole-quadrupole interaction. When time reversal symmetry is explicitly broken, we obtain a gapped spin liquid with a single chiral Majorana edge mode. We also investigate another solvable model in which the time-reversal-invariant spin liquid is coup…
The interplay between magnetism and superconductivity in the newly discovered heavy-fermion superconductor CePt$_3$Si has been investigated using the zero-field $μ$SR technique. The $μ$SR data indicate that the whole muon ensemble senses spontaneous internal fields in the magnetic phase, demonstrating that magnetism occurs in the whole sample volume. This points to a microscopic coexistence between magnetism and heavy-fermion superconductivity.
We investigate models of electrons in the Sachdev-Ye-Kitaev class with random and all-to-all electron hopping, electron spin exchange, and Cooper-pair hopping. An attractive on-site interaction between electrons leads to superconductivity at low temperatures. Depending on the relative strengths of the hopping and spin exchange, the normal state at the critical temperature is either a Fermi-liquid or a non-Fermi liquid. We present a large-$M$ (where spin symmetry is enlarged to SU$(M)$) study of the normal state to superconductor phase transition. We describe the transition temperature, the sup…
We study the five-orbital Hubbard-Holstein model for iron pnictides with small electron-phonon interaction due to Fe-ion Einstein oscillators. Using the fluctuation-exchange (FLEX) approximation, orbital fluctuations evolve inversely proportional to the temperature, and therefore the resistivity shows linear or convex T-dependence for wide range of temperatures. We also analyze the Eliashberg gap equation, and show that s-wave superconducting state without sign reversal (s_{++}-wave state) emerges when the orbital fluctuations dominate the spin fluctuations. When both fluctuations are comparab…
We revisit the interplay between superconductivity and quantum criticality when thermal effects from virtual static bosons are included. These contributions, which arise from an effective theory compactified on the thermal circle, strongly affect field-theoretic predictions even at small temperatures. We argue that they are ubiquitous in a wide variety of models of non-Fermi liquid behavior, and generically produce a parametric suppression of superconducting instabilities. We apply these ideas to non-Fermi liquids in $d=2$ space dimensions, obtained by coupling a Fermi surface to a Landau-damp…
We study the five-orbital Hubbard model including the charge quadrupole interaction for iron pnictides. Using the fluctuation-exchange (FLEX) approximation, orbital fluctuations evolve inversely proportional to the temperature, and therefore the resistivity shows linear or convex T-dependence for wide range of temperatures. We also analyze the Eliashberg gap equation, and show that s-wave superconducting state without sign reversal (s++ -wave state) emerges when the orbital fluctuations dominate over the spin fluctuations. When both fluctuations are comparable, their competition gives rise to …
We investigate the behavior of weak ferromagnetic metals close to the ferromagnetic critical point. We show that in the limit of small magnetic moment the low temperature metallic phase is rigorously described by a local ferromagnetic Fermi liquid that has a momentum-independent self-energy. Whereas, non-Fermi liquid features develop at higher temperatures. Furthermore, we find that an instability towards s-wave superconductivity is possible when the exchange splitting is comparable to the superconducting gap.
A detailed analysis is given of the T^2 term in the resistivity observed in electron-doped SrTiO3. Novel bandstructure data are presented, which provide values for the bare mass, density of states, and plasma frequency of the quasiparticles as a function of doping. It is shown that these values are renormalized by approximately a factor 2 due to electron-phonon interaction. It is argued that the quasiparticles are in the anti-adiabatic limit with respect to electron-phonon interaction. The condition of anti-adiabatic coupling renders the interaction mediated through phonons effectively non-ret…
Ca(Fe$_{1-x}$Rh$_x$)$_2$As$_2$ undergoes successive phase transitions with increasing Rh doping in the $T$ $=$ 0 limit. The antiferromagnetic-metal phase with orthorhombic structure at 0.00 $\le$ $x$ $\le$ 0.020 is driven to a superconducting phase with uncollapsed-tetragonal (ucT) structure at 0.020 $\le$ $x$ $\le$ 0.024; a non-superconducting collapsed-tetragonal (cT) phase takes over at $x$ $\geq$ 0.024. The breakdown of Fermi-liquid transport is observed in the ucT phase above $T_{\rm c}$. In the adjacent cT phase, Fermi-liquid transport is restored along with a disappearance of supercondu…
The electronic structure of the high-Tc cuprates is studied in terms of "large-U" and "small-U" orbitals. A striped structure and three types of quasiparticles are obtained, polaron-like "stripons" carrying charge, "svivons" carrying spin, and "quasielectrons" carrying both. The anomalous properties are explained, and specifically the behavior of the resistivity, Hall constant, and thermoelectric power. High-temperature superconductivity results from transitions between pair states of quasielectrons and stripons.
It is shown that the main features of the phase diagram for high Tc superconductivity can be calculated as a function of doping in a simple, essentially unique non-Landau/Fermi liquid with quartic interactions. The phase diagram depends on a single parameter 0<gamma<1 determined by the strength of the interaction at short distances. A new d-wave gap equation has solutions that fall under a superconducting dome, which terminates at the renormalization group fixed point. Optimal doping is estimated to occur just below 3/2 π^2. The overall scale for Tc is set by the recently measured universal no…
An NQR experiment revealed superconductivity of Pr$_2$Ba$_4$Cu$_7$O$_{15-δ}$ (Pr247) to be realized on CuO double chain layers and suggests possibility of novel one-dimensional(1D) superconductivity. To clarify the nature of the 1D superconductivity, we calculate the band dispersions of Pr247 by using the generalized gradient approximation(GGA). It indicates that Fermi surface of CuO double chains is well described to the electronic structure of a quasi-1D system. Assuming the zigzag Hubbard chain model to be an effective model of the system, we derive tight binding parameters of the model fro…
Beyond the conventional electron pairing mediated by phonons, high-temperature superconductivity in cuprates is believed to stem from quantum spin liquid (QSL). The unconventional superconductivity by doping a spin liquid/Mott insulator, is a long-sought goal but a principal challenge in condensed matter physics because of the lack of an ideal QSL platform. Here we report the pressure induced metallization and possible unconventional superconductivity in $NaYbSe_{2}$, which belongs to a large and ideal family of triangular lattice spin liquid we revealed recently and is evidenced to possess a …
We study a model of a two-dimensional repulsive Fermi gas with Rashba spin-orbit coupling $α_R$, and investigate the superconducting instability using renormalization group approach. We find that in general superconductivity is enhanced as the dimensionless ratio 1/2mα_R^2/E_F$ increases, resulting in unconventional superconducting states which break time reversal symmetry.
Whether the doped t-J model on the Kagome lattice supports exotic superconductivity has not been decisively answered. In this paper, we propose a new class of variational states for this model and perform large-scale variational Monte Carlo simulation on it. The proposed variational states are parameterized by the SU(2)-gauge-rotation angles, as the SU(2)-gauge structure hidden in the Gutzwiller-projected mean-field ansatz for the undoped model is broken upon doping. These variational doped states smoothly connect to the previously studied U(1) $π$-flux or $0$-flux states, and energy minimizat…
The possible ground states of the undoped and doped Kitaev-Heisenberg model on a triangular lattice are studied. For the undoped system, a combination of the numerical exact diagonalization calculation and the four-sublattice transformation analysis suggests one possible exotic phase and four magnetically ordered phases including a collinear stripe pattern and a noncollinear spiral pattern in the global phase diagram. The exotic phase near the antiferromagnetic (AF) Kitaev point is further investigated by using the Schwinger-fermion mean-field method, and we obtain an energetically favorable $…
Near a quantum-critical point in a metal strong fermion-fermion interaction mediated by a soft collective boson gives rise to incoherent, non-Fermi liquid behavior. It also often gives rise to superconductivity which masks the non-Fermi liquid behavior. We analyze the interplay between superconductivity and fermionic incoherence for a set of quantum-critical models with effective dynamical interaction between low-energy fermions. We argue that superconductivity always develops above a quantum-critical point, no matter how strong the fermionic self-energy is. We argue that superconductivity sho…
The interplay of magnetism and unconventional superconductivity (d singlet wave or p triplet wave) in strongly correlated electronic system (SCES) is discussed with recent examples found in heavy fermion compounds. A short presentation is given on the formation of the heavy quasiparticle with the two sources of a local and intersite enhancement for the effective mass. Two cases of the coexistence or repulsion of antiferromagnetism and superconductivity are given with CeIn3 and CeCoIn5. A spectacular example is the emergence of superconductivity in relatively strong itinerant ferromagnets UGe2 …
We explore superconductivity in strongly interacting electrons on a decorated honeycomb lattice (DHL). An easy-plane ferromagnetic interaction arises from spin-orbit coupling in the Mott insulating phase, which favors a triplet resonance valence bond spin liquid state. Hole doping leads to partial occupation of a flat band and to triplet superconductivity. The order parameter is highly sensitive to the doping level and the interaction parameters, with $p+ip$, $f$ and $p+f$ superconductivity found, as the flat band leads to instabilities in multiple channels. Typically, first order transitions …
The recent observation of superconductivity at the interfaces between KTaO3 and EuO (or LaAlO3) offers a new example of emergent phenomena at oxide interfaces. This superconductivity exhibits an unusual strong dependence on the crystalline orientation of KTaO3 and its superconducting transition temperature Tc is nearly one order of magnitude higher than that of the seminal LaAlO3/SrTiO3 interface. To understand its mechanism, it is crucial to address if the formation of oxide interfaces is indispensable for the presence of superconductivity. Here, by exploiting ionic liquid (IL) gating, we obt…
Divergencies appearing in perturbation expansions of interacting many-body systems can often be removed by expanding around a suitably chosen renormalized (instead of the non-interacting) Hamiltonian. We describe such a renormalized perturbation expansion for interacting Fermi systems, which treats Fermi surface shifts and superconductivity with an arbitrary gap function via additive counterterms. The expansion is formulated explicitly for the Hubbard model to second order in the interaction. Numerical soutions of the self-consistency condition determining the Fermi surface and the gap functio…
We analyze a mean-field model of electrons on a square lattice with two types of interaction: forward scattering favoring a d-wave Pomeranchuk instability and a BCS pairing interaction driving d-wave superconductivity. Tuning the interaction parameters a rich variety of phase diagrams is obtained. If the BCS interaction is not too strong, Fermi surface symmetry breaking is stabilized around van Hove filling, and coexists with superconductivity at low temperatures. For pure forward scattering Fermi surface symmetry breaking occurs typically via a first order transition at low temperatures. The …
We model the underdoped cuprates using fermions moving in a background with local antiferromagnetic order. The antiferromagnetic order fluctuates in orientation, but not in magnitude, so that there is no long-range antiferromagnetism, but a 'topological' order survives. The normal state is described as a fractionalized Fermi liquid (FL*), with electron-like quasiparticles coupled to the fractionalized excitations of the fluctuating antiferromagnet. The electronic quasiparticles reside near pocket Fermi surfaces enclosing total area x (the dopant density), centered away from the magnetic Brillo…
We review magnetic, superconducting and non-Fermi-liquid properties of the structurally layered heavy-fermion compounds Ce$_n$M$_m$In$_{3n+2m}$ (M=Co, Rh, Ir). These properties suggest d-wave superconductivity and proximity to an antiferromagetic quantum-critical point.
In quantum materials, electrons that have strong correlations tend to localize, leading to quantum spins as the building blocks for low-energy physics. When strongly correlated electrons coexist with more weakly-correlated conduction electrons, multiple channels of effective interactions develop and compete with each other. The competition creates quantum fluctuations having a large spectral weight, with the associated entropies reaching significant fractions of $R\ln 2$ per electron. Advancing a framework to understand how the fluctuating local moments influence unconventional superconductivi…
We address the problem of superconductivity for non-Fermi liquids using two commonly adopted, yet apparently distinct methods: 1) the renormalization group (RG) and 2) Eliashberg theory. The extent to which both methods yield consistent solutions for the low energy behavior of quantum metals has remained unclear. We show that the perturbative RG beta function for the 4-Fermi coupling can be explicitly derived from the linearized Eliashberg equations, under the assumption that quantum corrections are approximately local across energy scales. We apply our analysis to the test case of phonon medi…
We discuss a physical mechanism of a non-BCS nature which can stabilize a superconducting state in a {\it strongly repulsive} electronic system. By considering the two-dimensional Hubbard model with spatially modulated electron hoppings, we demonstrate how kinetic-energy frustration can lead to robust d-wave superconductivity at {\it arbitrarily} large on-site repulsion. This phenomenon should be observable in experiments using fermionic atoms, e.g. ${}^{40}K$, in specially prepared optical lattices.
Quantum spin liquids (QSLs), in which spins are highly entangled, have been considered a groundwork for generating exotic superconductivity.Despite numerous efforts, superconductivity emerging from QSLs has been unrealized in actual materials due to the difficulties in stabilizing QSL states with metallic conductivity.Recently, an organic compound, $κ$-(BEDT-TTF)$_4$Hg$_{2.89}$Br$_8$, with a nearly regular triangular lattice of molecular dimers was recognized as a candidate for doped QSLs. In this study, we report an unusual superconducting phase of $κ$-(BEDT-TTF)$_4$Hg$_{2.89}$Br$_8$: unexpec…
We revisit the issue of superconductivity at the quantum-critical point (QCP) between a 2D paramagnet and a spin-density-wave metal with ordering momentum (π,π). This problem is highly non-trivial because the system at criticality displays a non-Fermi liquid behavior and because the effective coupling constant λfor the pairing is generally of order one, even when the actual interaction is smaller than fermionic bandwidth. Previous study [M. A. Metlitski, S. Sachdev, Phys.Rev.B 82, 075128 (2010)] has found that the renormalizations of the pairing vertex are stronger than in BCS theory and hold …
The importance of introducing the SO(5) singlet into the new novel model of non-Fermi liquid proposed by LeClair and collaborators is pointed out. This SO(5) singlet order parameter leads to a phase transition between the normal metal and the pseudogap region in the phase diagram for the anti-ferromagnetic (AF) phase and the (d-wave) superconducting (SC) phase. A non-zero value for this order can increase substantially the critical temperature of the SC transition.
We introduce a simple but powerful zero temperature Stoner model to explain the unusual phase diagram of the ferromagnetic superconductor, UGe2. Triplet superconductivity is driven in the ferromagnetic phase by tuning the majority spin Fermi level through one of two peaks in the paramagnetic density of states (DOS). Each peak is associated with a metamagnetic jump in magnetisation. The twin peak DOS may be derived from a tight-binding, quasi-one-dimensional bandstructure, inspired by previous bandstructure calculations.
