Abstract: We provide and analyze a periodic Anderson model for studying magnetism and superconductivity in $\mathrm{U}{\mathrm{Te}}_{2}$, a recently discovered candidate for a topological spin-triplet superconductor. The 24-band tight-binding model reproduces the band structure obtained from a $\mathrm{D}\mathrm{F}\mathrm{T}+U$ calculation consistent with an angle-resolved photoemission spectroscopy. The Coulomb interaction of $f$-electrons enhances Ising ferromagnetic fluctuation along the $a$-axis and stabilizes spin-triplet superconductivity of either ${B}_{3u}$ or ${A}_{u}$ symmetry. When effects of pressure are taken into account in hopping integrals, the magnetic fluctuation changes to an antiferromagnetic one, and accordingly spin-singlet superconductivity of ${A}_{g}$ symmetry is stabilized. Based on the results, we propose pressure-temperature and magnetic field-temperature phase diagrams revealing multiple superconducting phases as well as an antiferromagnetic phase. In particular, a mixed-parity superconducting state with spontaneous inversion symmetry breaking is predicted.

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10 results found

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28,684 Citations

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Abstract: We show that a Weyl superconductor can absorb light via a novel surface-to-bulk mechanism, which we dub the topological anomalous skin effect. This occurs even in the absence of disorder for a single-band superconductor, and is facilitated by the topological splitting of the Hilbert space into bulk and chiral surface Majorana states. In the clean limit, the effect manifests as a characteristic absorption peak due to surface-bulk transitions. We also consider the effects of bulk disorder, using the Keldysh response theory. For weak disorder, the bulk response is reminiscent of the Mattis-Bardeen result for $s$-wave superconductors, with strongly suppressed spectral weight below twice the pairing energy, despite the presence of gapless Weyl points. For stronger disorder, the bulk response becomes more Drude-like and the $p$-wave features disappear. We show that the surface-bulk signal survives when combined with the bulk in the presence of weak disorder. The topological anomalous skin effect can therefore serve as a fingerprint for Weyl superconductivity. We also compute the Meissner response in the slab geometry, incorporating the effect of the surface states.

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Topics: Superconductivity (52%)

10 Citations

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Abstract: We performed AC calorimetry and magnetoresistance measurements under pressure for H || a-axis (easy-magnetization axis) in the novel heavy-fermion superconductor UTe2. Thanks to the thermodynamic information, multiple superconducting phases have been revealed under pressure and magnetic field. The (H,T) phase diagram of superconductivity under pressure displays an abrupt increase of the upper critical field (Hc2) at low temperature and in the high field region, and a strong convex curvature of Hc2 at high temperature. This behavior of Hc2 and the multiple superconducting phases require a state for the superconducting order parameter more complex than a spin-triplet equal spin pairing. Above the superconducting critical pressure, Pc, we find strong indications that the possible magnetic order is closer to antiferromagnetism than to ferromagnetism.

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Topics: Critical field (71%), Superconductivity (57%), Magnetoresistance (54%) ... read more

7 Citations

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Abstract: Materials with multiple superconducting phases are rare. Here, we report the discovery of two-phase unconventional superconductivity in CeRh2As2 Using thermodynamic probes, we establish that the superconducting critical field of its high-field phase is as high as 14 tesla, even though the transition temperature is only 0.26 kelvin. Furthermore, a transition between two different superconducting phases is observed in a c axis magnetic field. Local inversion-symmetry breaking at the cerium sites enables Rashba spin-orbit coupling alternating between the cerium sublayers. The staggered Rashba coupling introduces a layer degree of freedom to which the field-induced transition and high critical field seen in experiment are likely related.

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Topics: Critical field (68%), Superconductivity (56%), Transition temperature (51%) ... read more

6 Citations

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Abstract: Superconductivity has its universal origin in the formation of bound (Cooper) pairs of electrons that can move through the lattice without resistance below the superconducting transition temperature Tc[1]. While electron Cooper pairs in most superconductors form anti-parallel spin-singlets with total spin S=0 [2,3], they can also form parallel spin-triplet Cooper pairs with S=1 and an odd parity wavefunction[4-6], analogous to the equal spin pairing state in the superfluid 3He[7]. Spin-triplet pairing is important because it can host topological states and Majorana fermions relevant for fault tolerant quantum computation[8-11]. However, spin-triplet pairing is rare and has not been unambiguously identified in any solid state systems. Since spin-triplet pairing is usually mediated by ferromagnetic (FM) spin fluctuations[4-6], uranium based heavy-fermion materials near a FM instability are considered ideal candidates for realizing spin-triplet superconductivity[12-14]. Indeed, UTe2, which has a Tc=1.6K [15,16], has been identified as a strong candidate for chiral spin-triplet topological superconductor near a FM instability[15-22], although the system also exhibits antiferromagnetic (AF) spin fluctuations[23,24]. Here we use inelastic neutron scattering (INS) to show that superconductivity in UTe2 is coupled with a sharp magnetic excitation at the Brillouin zone (BZ) boundary near AF order, analogous to the resonance seen in high-Tc copper oxide[25-27], iron-based[28,29], and heavy-fermion superconductors[30-32]. We find that the resonance in UTe2 occurs below Tc at an energy Er=7.9kBTc (kB is Boltzmann's constant) and at the expense of low-energy spin fluctuations. Since the resonance has only been found in spin-singlet superconductors near an AF instability[25-32], its discovery in UTe2 suggests that AF spin fluctuations can also induce spin-triplet pairing for superconductivity[33].

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Topics: Cooper pair (57%), Pairing (55%), Superconductivity (54%) ... read more

3 Citations

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71 results found

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28,684 Citations

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Abstract: Topological insulators are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors. They are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time-reversal symmetry. These topological materials have been theoretically predicted and experimentally observed in a variety of systems, including HgTe quantum wells, BiSb alloys, and Bi2Te3 and Bi2Se3 crystals. Theoretical models, materials properties, and experimental results on two-dimensional and three-dimensional topological insulators are reviewed, and both the topological band theory and the topological field theory are discussed. Topological superconductors have a full pairing gap in the bulk and gapless surface states consisting of Majorana fermions. The theory of topological superconductors is reviewed, in close analogy to the theory of topological insulators.

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Topics: Topological order (73%), Symmetry protected topological order (71%), Topological insulator (70%) ... read more

9,145 Citations

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Abstract: This paper reviews the theory of anisotropic superfluid phases and its application to the new A and B phases of liquid $^{3}\mathrm{He}$. It is tutorial in nature and advanced formal techniques are avoided; even the formalism of second quantization is not required. After an initial discussion of the Fermi-liquid theory of Landau and its application to the normal phase of liquid $^{3}\mathrm{He}$, the idea of instability against formation of Cooper pairs is introduced. The effective interaction in liquid $^{3}\mathrm{He}$ is considered, with emphasis on the spin-dependent interaction arising from virtual spin polarization of the medium ("spin fluctuation exchange"). Next, a self-contained discussion of the "weak-coupling" BCS theory as applied to anisotropic superfluids is given, with special attention to the "Ginzburg-Landau" region close to the transition temperature. Formulas are derived for the specific heat, spin susceptibility, normal density tensor, and static spin-dependent correlation properties of superfluids with both singlet and triplet pairing: In the triplet case the ideas of "spin superfluid velocity" and "spin superfluid density" are also introduced. After a preliminary comparison of the weak-coupling theory with experiment, it is shown that feedback effects due to the modification, by formation of Cooper pairs, of the effective interaction connected with spin fluctuation exchange can produce results which are qualitatively different from those of the weak-coupling theory. An attempt is made to reformulate recent graph-theoretical treatments of this phenomenon in a more elementary language, and considerations based on possible invariant forms of the free energy are also introduced. The properties of the so-called Anderson-Brinkman-Morel and Balian-Werthamer states, which are commonly identified with $^{3}\mathrm{He}$-A and B, respectively, are studied in detail. Next, the effects which tend to orient the Cooper pair wave function in a given experimental situation are discussed; in this context the form of the free energy terms arising from spatial variation of the wave function is explored. A semiphenomenological theory of the nuclear magnetic resonance properties is developed and applied in particular to the case of unsaturated cw resonance; the analogy with the Josephson effect is emphasized. The question of relaxation and linewidths is also briefly discussed. A partial account is given of the theory of finite-wavelength collective oscillations, with particular reference to first, second, and fourth sound and spin waves. The splitting of the A-normal transition in a magnetic field is considered, with special attention to the possibility it offers of testing theories of the "spin fluctuation" type. Finally, a brief assessment is made of the extent to which the current experimental data support the conventional identification of $^{3}\mathrm{He}$-A and B and the spin fluctuation theory, and some outstanding problems and possibilities are outlined. Subjects not discussed include "first-principles" theories of the effective interaction in $^{3}\mathrm{He}$ collective excitations in the "collisionless" regime, and the problem of ultrasonic absorption, "orbit waves," and the theory of the kinetic coefficients.

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Topics: Spin polarization (56%), Spin wave (56%), Quasiparticle (54%) ... read more

1,395 Citations

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Abstract: This article is a review of recent developments in the phenomenological description of unconventional superconductivity. Starting with the BCS theory of superconductivity with anisotropic Cooper pairing, the authors explain the group-theoretical derivation of the generalized Ginzburg-Landau theory for unconventional superconductivity. This is used to classify the possible superconducting states in a system with given crystal symmetry, including strong-coupling effects and spin-orbit interaction. On the basis of the BCS theory the unusual low-temperature properties and the (resonant) impurity scattering effects are discussed for superconductors with anisotropic pairing. Using the Ginzburg-Landau theory, the authors study several bulk properties of such superconductors: spontaneous lattice distortion, upper critical magnetic field, splitting of a phase transition due to uniaxial stress. Two possible mechanisms for ultrasound absorption are discussed: collective modes and damping by domain-wall motion. The boundary conditions for the Ginzburg-Landau theory are derived from a correlation function formulation and by group-theoretical methods. They are applied to a study of the Josephson and proximity effects if unconventional superconductors are involved there. The magnetic properties of superconductors that break time-reversal symmetry are analyzed. Examples of current and magnetic-field distributions close to inhomogeneities of the superconducting order parameter are given and their physical origin is discussed. Vortices in a superconductor with a multicomponent order parameter can exhibit various topological structures. As examples the authors show fractional vortices on domain walls and nonaxial vortices in the bulk. Furthermore, the problem of the possible coexistence of a superconducting and a magnetically ordered phase in an unconventional superconductor is analyzed. The combination of two order parameters that are almost degenerate in their critical temperature is considered with respect to the phase-transition behavior and effects on the lower and upper critical fields. Because heavy-fermion superconductors---which are possible realizations of unconventional superconductivity---have been the main motivation for the phenomenological studies presented here, the authors compare the theoretical results with the experimental facts and data. In particular, they emphasize the intriguing features of the compound U${\mathrm{Pt}}_{3}$ and consider in detail the alloy ${\mathrm{U}}_{1\ensuremath{-}x}{\mathrm{Th}}_{x}{\mathrm{Be}}_{13}$.

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Topics: Fractional vortices (65%), Unconventional superconductor (61%), Proximity effect (superconductivity) (59%) ... read more

1,379 Citations

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Abstract: This review elaborates pedagogically on the fundamental concept, basic theory, expected properties, and materials realizations of topological superconductors. The relation between topological superconductivity and Majorana fermions are explained, and the difference between dispersive Majorana fermions and a localized Majorana zero mode is emphasized. A variety of routes to topological superconductivity are explained with an emphasis on the roles of spin-orbit coupling. Present experimental situations and possible signatures of topological superconductivity are summarized with an emphasis on intrinsic topological superconductors.

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Topics: Symmetry protected topological order (64%), Topological order (63%), MAJORANA (54%)

773 Citations