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D. F. Agterberg

Publications and source records attributed to D. F. Agterberg.

At least 37 records · Page 2Linked to original sources
arXiv2016

Superconductivity and spin-orbit coupling in non-centrosymmetric materials: a review

In non-centrosymmetric superconductors, where the crystal structure lacks a centre of inversion, parity is no longer a good quantum number and an electronic antisymmetric spin-orbit coupling (ASOC) is allowed to exist by symmetry. If this ASOC is sufficiently large, it has profound consequences on the superconducting state. For example, it generally leads to a superconducting pairing state which is a mixture of spin-singlet and spin-triplet components. The possibility of such novel pairing states, as well as the potential for observing a variety of unusual behaviours, led to intensive theoretical and experimental investigations. Here we review the experimental and theoretical results for superconducting systems lacking inversion symmetry. Firstly we give a conceptual overview of the key theoretical results. We then review the experimental properties of both strongly and weakly correlated bulk materials, as well as two dimensional systems. Here the focus is on evaluating the effect of ASOC on the superconducting properties and the extent to which there is evidence for singlet-triplet mixing. This is followed by a more detailed overview of theoretical aspects of non-centrosymmetric superconductivity. This includes the effects of the ASOC on the pairing symmetry and the superconducting magnetic response, magneto-electric effects, superconducting finite momentum pairing states, and the potential of non-centrosymmetric superconductors to display topological superconductivity.

cond-mat.supr-con↗
arXiv2016

Pairing of j=3/2 fermions in half-Heusler superconductors

We theoretically consider the superconductivity of the topological half-Heusler semimetals YPtBi and LuPtBi. We show that pairing occurs between j=3/2 fermion states, which leads to qualitative differences from the conventional theory of pairing between j=1/2 states. In particular, this permits Cooper pairs with quintet or septet total angular momentum, in addition to the usual singlet and triplet states. Purely on-site interactions can generate s-wave quintet time-reversal symmetry-breaking states with topologically nontrivial point or line nodes. These local s-wave quintet pairs reveal themselves as d-wave states in momentum space. Furthermore, due to the broken inversion symmetry in these materials, the s-wave singlet state can mix with a p-wave septet state, again with topologically-stable line nodes. Our analysis lays the foundation for understanding the unconventional superconductivity of the half-Heuslers.

cond-mat.supr-con↗
arXiv2012

Kondo effect in the presence of spin-orbit coupling

We study the T=0 Kondo physics of a spin-1/2 impurity in a non-centrosymmetric metal with spin-orbit interaction. Within a simple variational approach we compute ground state properties of the system for an {\it arbitrary} form of spin-orbit coupling consistent with the crystal symmetry. This coupling produces an unscreened impurity magnetic moment and can lead to a significant change of the Kondo energy. We discuss implications of this finding both for dilute impurities and for heavy-fermion materials without inversion symmetry.

cond-mat.str-el↗
arXiv2012

Role of spin-orbit coupling on the electronic structure and properties of SrPtAs

The effect of spin-orbit coupling on the electronic structure of the layered iron-free pnictide superconductor, SrPtAs, has been studied using the full potential linearized augmented plane wave method. The anisotropy in Fermi velocity, conductivity and plasma frequency stemming from the layered structure are found to be enhanced by spin-orbit coupling. The relationship between spin-orbit interaction and the lack of two-dimensional inversion in the PtAs layers is analyzed within a tight-binding Hamiltonian based on the first-principles calculations. Finally, the band structure suggests that electron doping could increase $T_c$.

cond-mat.supr-con↗
arXiv2011

Hexagonal pnictide SrPtAs: superconductivity with locally broken inversion symmetry

Unlike other pnictides, SrPtAs has a hexagonal structure, containing layers with As-Pt atoms that form a honeycomb lattice. These layers lack inversion symmetry which allows for a spin-orbit coupling that we show has a dramatic effect on superconductivity in this material. In particular, for conventional s-wave superconductivity in SrPtAs, both the spin susceptibility and the paramagnetic limiting field are enhanced significantly with respect to that usually expected for s-wave superconductors. SrPtAs provides a prime example of a superconductor with locally broken inversion symmetry.

cond-mat.supr-con↗
arXiv2011

Magnetoelectric effects, helical phases, and FFLO phases in superconductors without inversion symmetry

This chapter emphasizes new magnetic properties that arise when inversion symmetry is broken in a superconductor. There are two aspects that will be covered in detail. The first topic encompasses physics related to superconducting magnetoelectric effects that arise from broken inversion symmetry. Broken inversion symmetry allow for Lifshitz invariants in the free energy which can be viewed as a coupling between the magnetic induction and the supercurrent. There are similarities between these invariants and the better known Dzyaloshinskii-Moyira interaction in magnetic systems. These Lifshitz invariants give rise to anomalous magnetic properties as well as new phases in the presence of magnetic fields. Here, we will describe the consequences of these Lifshitz invariants, provide estimates for the relative magnitudes of the novel effects, and discuss the important role that crystal symmetry plays in understanding this physics. Finally, we provide a discussion of the fate of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phases in broken inversion superconductors. In particular, we show how broken inversion symmetry can have a profound effect on the stability, existence, and properties of FFLO phases.

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arXiv2011

Competing s-wave and d-wave order in A15 superconductors

Competing pairing channels have been proposed in superfluid $^3$He, in the high temperature cuprate superconductors, and pnictide superconductors. While strong experimental support exists for this in superfluid $^3$He, the case for superconductors is weaker. Here, we show that $A15$ superconductors provide a compelling example for competing superconducting order. We present microscopic arguments that $A15$ superconductors have a competing d-wave order in addition to usual s-wave superconductivity and show that this d-wave order provides a unifying explanation for a series of diverse experimental results. These include: the emergence of a sharp mode in the superconducting state seen by Raman spectroscopy; the observed shrinking of the vortex core at anomalously low fields; and the large anisotropy measured in the upper critical field. We further show that multiple superconducting gaps can appear when these $A15$ superconductors are strained.

cond-mat.supr-con↗
arXiv2011

Role of d-wave pairing in $A15$ superconductors

We argue that the recent Raman spectroscopy observation of a sharp mode in s-wave superconducting V$_3$Si is due to a competing d-wave pairing state. We present microscopic arguments for the origin of this d-wave order. We further argue that the d-wave order explains the observed shrinking of the vortex core structure at anomalously low magnetic fields and the large anisotropy observed in the upper critical field.

cond-mat.supr-con↗
arXiv2011

Conventional and charge six superfluids from melting hexagonal Fulde-Ferrell-Larkin-Ovchinnikov phases in two dimensions

We consider defect mediated melting of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) and pair density wave (PDW) phases in two dimensions. Examining mean-field ground states in which the spatial oscillations of the FFLO/PDW superfluid order parameter exhibit hexagonal lattice symmetry, we find that thermal melting leads to a variety of novel phases. We find that a spatially homogeneous charge six superfluid can arise from melting a hexagonal vortex-anitvortex lattice FFLO/PDW phase. The charge six superfluid has an order parameter corresponding to a bound state of six fermions. We further find that a hexagonal vortex-free FFLO/PDW phase can melt to yield a conventional (charge two) homogeneous superfluid. A key role is played by topological defects that combine fractional vortices of the superfluid order and fractional dislocations of the lattice order.

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arXiv2010

Generic nodeless Larkin Ovchinnikov states due to singlet-triplet mixing

Larkin-Ovchinnikov (LO) states typically have a singlet-gap that vanishes along real-space lines. These real-space nodes lead to Andreev midgap states which can serve as a signature of LO pairing. We show that at these nodes, an odd-parity, spin-triplet component is always induced, leading to a nodeless LO phase. We find the two-dimensional weak coupling, clean limit s-wave phase diagram when this spin-triplet part is included. The triplet component is large and increases the stability of the FFLO phase. We also show that the spin-triplet contribution pushes the midgap states away from zero energy. Finally, we show how our results can be explained phenomenologically though Lifshitz invariants. These invariants provide a simple approach to understand the role of unconventional pairing states, spin-orbit coupling, and inhomogeneous mixed singlet-triplet states that are not due to a FFLO instability. We discuss our results in the context of organic superconductors.

cond-mat.supr-con↗
arXiv2009

Order parameter and vortices in the superconducting Q-phase of CeCoIn5

Recently, it has been reported that the low-temperature high-magnetic field phase in CeCoIn5 (Q-phase), has spin-density wave (SDW) order that only exists within this phase. This indicates that the SDW order is the result of the development of pair density wave (PDW) order in the superconducting phase that coexists with d-wave superconductivity. Here we develop a phenomenological theory for these coexisting orders. This provides selection rules for the PDW order and further shows that the detailed structure of this order is highly constrained. We then apply our theory to the the vortex phase. This reveals vortex phases in which the d-wave vortex cores exhibit charge density wave (CDW) order and further reveals that the SDW order provides a unique probe of the vortex phase.

cond-mat.str-el↗
arXiv2009

Dislocations and vortices in pair density wave superconductors

With the ground breaking work of the Fulde, Ferell, Larkin, and Ovchinnikov (FFLO), it was realized that superconducting order can also break translational invariance; leading to a phase in which the Cooper pairs develop a coherent periodic spatially oscillating structure. Such pair density wave (PDW) superconductivity has become relevant in a diverse range of systems, including cuprates, organic superconductors, heavy fermion superconductors, cold atoms, and high density quark matter. Here we show that, in addition to charge density wave (CDW) order, there are PDW ground states that induce spin density wave (SDW) order when there is no applied magnetic field. Furthermore, we show that PDW phases support topological defects that combine dislocations in the induced CDW/SDW order with a fractional vortex in the usual superconducting order. These defects provide a mechanism for fluctuation driven non-superconducting CDW/SDW phases and conventional vortices with CDW/SDW order in the core.

cond-mat.str-el↗
arXiv2007

Spatial line nodes and fractional vortex pairs in the Fulde-Ferrell-Larkin-Ovchinnikov phase

A Zeeman magnetic field can induce a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase in spin-singlet superconductors. Here we argue that there is a non-trivial solution for the FFLO vortex phase that exists near the upper critical field in which the wavefunction has only spatial line nodes that form intricate and unusual three-dimensional structures. These structures include a crisscrossing lattice of two sets of non-parallel line nodes. We show that these solutions arise from the decay of conventional Abrikosov vortices into pairs of fractional vortices. We propose that neutron scattering studies can observe these fractional vortex pairs through the observation of a lattice of 1/2 flux quanta vortices. We also consider related phases in non-centrosymmetric (NC) superconductors.

cond-mat.str-el↗
arXiv2007

Theory of vortices in hybridized ballistic/diffusive-band superconductors

We study the electronic structure in the vicinity of a vortex in a two-band superconductor in which the quasiparticle motion is ballistic in one band and diffusive in the other. This study is based on a model appropriate for such a case, that we have introduced recently [Phys. Rev. B 73, 220501(R) (2006)]. We argue that in the two-band superconductor MgB_2 such a case is realised. Motivated by the experimental findings on MgB_2, we assume that superconductivity in the diffusive band is ``weak'', i.e., mostly induced. We examine intriguing features of the order parameter, the current density, and the vortex core spectrum in the ``strong'' ballistic band under the influence of hybridization with the ``weak'' diffusive band. Although the order parameter in the diffusive band is induced, the characteristic length scales in the two bands differ due to Coulomb interactions. The current density in the vortex core is dominated by the contribution from the ballistic band, while outside the core the contribution from the diffusive band can be substantial, or even dominating. The current density in the diffusive band has strong temperature dependence, exhibiting the Kramer-Pesch effect when hybridization is strong. A particularly interesting feature of our model is the possibility of additional bound states near the gap edge in the ballistic band, that are prominent in the vortex centre spectra. This contrasts with the single band case, where there is no gap-edge bound state in the vortex centre. We find the above-mentioned unique features for parameter values relevant for MgB_2.

cond-mat.supr-con↗
arXiv2006

Stability of magnetic-field induced helical phase in Rashba superconductors

Due to the lack of both parity and time reversal symmetries, the Rashba superconductors CePt_3Si, CeRhSi_3, and CeIrSi_3, in the presence of a magnetic field, are unstable to helical (single plane-wave) order. We develop a microscopic theory for such superconductors and examine the stability of this helical phase. We show that the helical phase typically occupies most of the magnetic field-temperature phase diagram. However, we also find that this phase is sometimes unstable to a multiple-q phase, in which both the magnitude and the phase of the order parameter are spatially varying. We find the position of this helical to multiple-q phase transition. We further examine the density of states and identify features unique to the helical phase.

cond-mat.supr-con↗
arXiv2006

Microscopic theories for cubic and tetrahedral superconductors: application to PrOs_4Sb_{12}

We examine weak-coupling theory for unconventional superconducting states of cubic or tetrahedral symmetry for arbitrary order parameters and Fermi surfaces and identify the stable states in zero applied field. We further examine the possibility of having multiple superconducting transitions arising from the weak breaking of a higher symmetry group to cubic or tetrahedral symmetry. Specifically, we consider two higher symmetry groups. The first is a weak crystal field theory in which the spin-singlet Cooper pairs have an approximate spherical symmetry. The second is a weak spin orbit coupling theory for which spin-triplet Cooper pairs have a cubic orbital symmetry and an approximate spherical spin rotational symmetry. In hexagonal UPt_3, these theories easily give rise to multiple transitions. However, we find that for cubic materials, there is only one case in which two superconducting transitions occur within weak coupling theory. This sequence of transitions does not agree with the observed properties of PrOs_4Sb_{12}. Consequently, we find that to explain two transitions in PrOs_4Sb_{12} using approximate higher symmetry groups requires a strong coupling theory. In view of this, we finally consider a weak coupling theory for which two singlet representations have accidentally nearly degenerate transition temperatures (not due to any approximate symmetries). We provide an example of such a theory that agrees with the observed properties of PrOs_4Sb_{12}.

cond-mat.supr-con↗
arXiv2006

S-wave/spin-triplet order in superconductors without inversion symmetry: Li$_2$Pd$_3$B and Li$_2$Pt$_3$B

We investigate the order parameter of noncentrosymmetric superconductors Li$_2$Pd$_3$B and Li$_2$Pt$_3$B via the behavior of the penetration depth $λ(T)$. The low-temperature penetration depth shows BCS-like behavior in Li$_2$Pd$_3$B, while in Li$_2$Pt$_3$B it follows a linear temperature dependence. We propose that broken inversion symmetry and the accompanying antisymmetric spin-orbit coupling, which admix spin-singlet and spin-triplet pairing, are responsible for this behavior. The triplet contribution is weak in Li$_2$Pd$_3$B, leading to a wholly open but anisotropic gap. The significantly larger spin-orbit coupling in Li$_2$Pt$_3$B allows the spin-triplet component to be larger in Li$_2$Pt$_3$B, producing line nodes in the energy gap as evidenced by the linear temperature dependence of $λ(T)$. The experimental data are in quantitative agreement with theory.

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