Superconductivity at Warwick

Superconductivity @ Warwick

A Brief History of Superconductivity

The Discovery of Superconductivity

The phenomenon of superconductivityLink opens in a new window was first observed in mercury by Kamerlingh Onnes in Leiden in 1911 [1].

In the superconducting state the dc electrical resistivity of a superconducting material is zero below the critical temperature, T_c, of the material.

Heike Kamerlingh OnnesLink opens in a new window who was the first to liquefy helium in 1908 and then discovered superconductivity in 1911.

Nobel Prize in Physics: 1913

Heike Kamerlingh Onnes, was awarded the 1913 Nobel Prize in Physics Link opens in a new window"for his investigations on the properties of matter at low temperatures which led, inter alia, to the production of liquid helium".

A magnet floating over a high temperature superconductor

A magnet floating above a disc of ceramic superconductor due to a combination of flux pinning and flux expulsion..

Meissner-Ochsenfeld Effect

The magnetic properties exhibited by superconductors are just as dramatic. If a type I superconductor is placed in a magnetic field below a critical value H_c, then cooled through its superconducting transition temperature, T_c, the magnetic flux originally present in the sample is ejected from the specimen. This is called the Meissner (OchsenfeldLink opens in a new window) effect [2].

Mixed State and the Flux-Line-Lattice

If a type IILink opens in a new window superconductor is cooled below T_c in a magnetic field less than its lower critical field, (H<H_c1), it will also enter the Meissner state.

For fields above the lower critical field H_c1, but below an upper critical field H_c2, (H_c1 < H < H_c2), type II superconductors enter a mixed state in which the material is threaded by an array of lines of magnetic flux forming an Abrikosov or flux line lattice (FLL) [3].

Nobel Prize in Physics: 2003

A. Abrikosov, V.L. Ginzburg, A.J. Leggett were awarded the 2003 Nobel Prize in PhysicsLink opens in a new window "for pioneering contributions to the theory of superconductors and superfluids".

Leo Esaki, Ivar Gaiever and Brian David Josephson

A. A. Abrikosov V. L. Ginzburg and A. J. Leggett.

Hexagonal arrangement of magnetic flux lines in pure Nb imaged using neutrons.

John Bardeen, Leon Cooper, and J. Robert Schrieffer, 1972 Nobel laureates for their BCS theory of superconductivity.

BCS Theory

The superconducting state results from an ordering of the conduction electrons into Cooper pairs via an electron-phonon exchange coupling. The nature and origin of this ordering was explained by Bardeen, Cooper, and Schrieffer (BCS). All elemental and most alloy superconductors are s-wave BCS superconductors [4].

Nobel Prize in Physics: 1972

John Bardeen, Leon Neil Cooper and John Robert Schrieffer were awarded the 1972 Nobel Prize in Physics Link opens in a new window"for their jointly developed theory of superconductivity, usually called the BCS-theory".

Applications of Superconductors

Superconducting wire is used to make magnets for many applications including NMR/MRI, particle physics, controlled fusion, as well as any materials research that requires magnetic fields. We have several superconducting magnets in the group that can generate fields of up to 17 T.

Under suitable conditions, remarkable macroscopic quantum mechanical effects associated with the tunnelling of the superconducting electron pairs are observed. These include the ac and dc Josephson effects [5]. SQUIDs (superconducting quantum interference device) are now used in applications.

A Quantum Design thin film SQUID sensor.

We have two SQUID magnetometers that we use for research.

High-temperature Superconductors

K. Alex Muller and J. Georg Bednorz from IBM Zurich discovered ceramic high temperature superconductors.

Nobel Prize in Physics: 1987

K. Alex Muller and J. Georg Bednorz were awarded the 1987 Nobel Prize in Physics Link opens in a new window"for their important break-through in the discovery of superconductivity in ceramic materials".

YBa₂Cu₃O_7-_d, a cuprate superconductor with a T_cof 92 K.

Note the Cu-O octahedra and chains are shown in red, with the Y (blue) and Ba (yellow) ions acting as spacers.

Superconducting transition temperature versus time for different classes of superconducting materials, highlighting the high-T_c revolution.

Nobel Prize in Physics: 1973

The Nobel Prize in Physics 1973Link opens in a new window was divided, one half jointly to Leo Esaki and Ivar Giaever "for their experimental discoveries regarding tunneling phenomena in semiconductors and superconductors, respectively" and the other half to Brian David Josephson "for his theoretical predictions of the properties of a supercurrent through a tunnel barrier, in particular those phenomena which are generally known as the Josephson effects"

Leo Esaki, Ivar Gaiever and Brian David Josephson.

The discovery by Bednorz and Müller of high temperature superconductivity in the cuprates [6] along with the observation of superconductivity in heavy fermion materials [7], the doped carbon fullerenes and some organic materials [8], and then later the iron based superconductors [9], has led to a resurgence of interest in superconductivity [10-11].

SNS data for the heavy fermion superconductor UPt3

SANS data showing the change in the morphology of the flux line lattice in the heavy fermion superconductor UPt₃ [7].

There are many organic and fullerene superconductors including Cs₃C₆₀ with T_cs of up to nearly 40 K [8].

Phase diagram of Fe based superconductors

The iron-based superconductors were first discovered in 2008 and display transition temperatures up to 55 K [9].

Experimental evidence for exotic p and d wave superconductivity was been presented [12]. A number of materials that show a coexistence of magnetism and superconductivity have also been discovered [13]. These materials allowed us to investigate the interplay between two phenomena that are usually mutually exclusive. A whole range of subtle and fascinating new behaviours have been observed in the mixed state of superconductors including flux creep, thermally activated flux flow, flux pancakes, FLL melting, reversible and irreversible behaviour, the peak effect and the generalised Fulde-Ferrel-Larkin-Ovchinnokov state to name but a few!

100 Years of Superconductivity

Physics World: 100 Years of SuperconductivityLink opens in a new window - Published in 2011- an issue of Physics World celebrating the 100^thanniversary of the discovery of superconductivity.

The Physics of Superconductors

Read more about the physics of superconductors at

www.superconductors.orgLink opens in a new window.

References

[1] H. Kamerlingh Onnes, Leiden Comm. 120b 122b, 124c, (1911).

[2] W. Meissner and R. Ochsenfeld, Naturwissenschaften 21, 787 (1933).

[3] A. A. Abrikosov, Sov. Phys JETP 5, 1174 (1957).

[4] J. Bardeen, L. N. Cooper and J. R. Schrieffer, Phys. Rev. 106, 162 (1957);108, 1175 (1957).

[5] B. D. Josephson Phys. Lett. 1, 251 (1962).

[6] G. Bednorz and K. A. Müller, Z. Phys. B 64, 189 (1986); E. Dagotto, Correlated electrons in high-temperature superconductors, Rev. Mod. Phys. 66, 763 (1994).

[7] G. R. Stewart Rev. Mod. Phys. 56, 755 (1984) and references therein. For more details of the data shown in the figure see, A. Huxley, P. Rodiere, D. M. Paul, N. van Dijk, R. Cubitt and J. Flouquet, Realignment of the flux-line lattice by a change of symmetry of superconductivity in UPt₃, Nature 406, 160 (2000).

[8] A. F. Hebard, M. J. Rosseinsky, R. C. Haddon, D. W. Murphy, S. H. Glarum, T. T. M. Palstra, A. P. Ramirez, and A. R. Kortan, Superconductivity at 18-K in potassium-doped C-60, Nature 350, 600 (1991); Y. Ihara, et al., NMR Study of the Mott transitions to superconductivity in the two Cs₃C₆₀ phases. Phys. Rev. Lett. 104, 256402 (2010).

[9] Y. Kamihara, T. Watanabe, M. Hirano, H. Hosono, Iron-based layered superconductor LaO_1-xF_xFeAs (x = 0.05 - 0.12) with T_c = 26 K, JACS 130, 3296 (2008); D. C. Johnston, The puzzle of high temperature superconductivity in layered iron pnictides and chalcogenides, Adv. Phys. 59, 803 (2010) and references therein; G. R. Stewart, Superconductivity in iron compounds, Rev. Mod. Phys. 83, 1589-1652(2011) and references therein.

[10] Good introductory textbooks on superconductivity for undergraduates: M. Cyrot and D. Pavuna, Introduction to superconductivity and high-Tc materials(World Scientific, River Edge, N.J, 1992); J.R. Waldram, Superconductivity of metals and cuprates (Institute of Physics Publishing, Bristol, 1996); G. Burns, High-temperature superconductivity: an introduction (Academic Press, London,1992); C. P. Poole, H. A. Farach and R. J. Creswick, Superconductivity (Academic Press, San Diego, London, 1995).

Graduate level textbooks: D. R. Tilley and J. Tilley, Superfluidity and Superconductivity, (IOP Publishing, Bristol, 1996), 3rd ed.; Michael Tinkham, Introduction to superconductivity, (London McGraw-Hill, New York, 1975).

[11] There are many websites with useful information on superconductors including www.superconductors.org and a site at Oak Ridge NationalLink opens in a new window in the USA.

[12] P. G. Kealey, T. M. Riseman, E. M. Forgan, L. M. Galvin, A. P. Mackenzie, S. L. Lee, D. M. Paul, R. Cubitt, D. F. Agterberg, R. Heeb, Z. Q. Mao and Y. Maeno, Reconstruction from small-angle neutron scattering measurements of the real space, magnetic field distribution in the mixed state of Sr₂RuO₄, Phys. Rev. Lett. 84, 6094 (2000).

[13] R. Nagarajan et al. Phys. Rev. Lett.72, 274 (1994); R. J. Cava et al. Nature (London) 367, 252 (1994).

Superconductivity at Warwick

Superconductivity at Warwick - the First 25 Years (1985 - 2010)

Since the Group was established in 1985, we have made a number of important contributions to the understanding of the physics of superconducting materials. Other groups here at Warwick including Theory and the NMR have also worked on superconducting materials.

We began working on high temperature superconductors shortly after their discovery in 1986. We studied the unusual vibrational and structural behaviour of the compound La_1.85Ba_0.15CuO₄ [1] and investigated the nature of the magnetic ordering in the rare earth-Ba₂Cu₃O₇ series of compounds [2].

Imaging the FLL in a Superconductor using Small Angle Neutron Scattering

In 1990 we began using neutron scattering to study the mixed state of the high temperature superconductors. The neutrons are diffracted by the ordered periodic distribution of the magnetic flux within the sample with contrast being provided by the variation in the magnetic induction. These diffraction experiments must be performed on a small angle diffraction instrument, since the typical lattice spacing in the available range of magnetic field with the optimum neutron wavelength leads to scattering angles of < 0.5 degree. We examined the vortex lattice structure in YBa₂Cu₃O₇ [3] and were the first to directly observe the melting and decomposition of the magnetic-flux lattice in the high-T_c superconductor Bi_2.15Sr_1.95CaCu₂O_8+x [4].

First Observation of the FLL using Neutron Diffraction in a High-T_c Material

In an applied magnetic field, magnetic flux can enter the superconductor as quantized flux lines. In conventional type II superconductors, these lines form a lattice but in high-T_c superconductors flux lattice was appreciably influenced by thermal fluctuations and may 'melt' at temperatures well below T_c. Flux lines in high- Tc materials were first imaged by "decorating" the ends of the lines with magnetic particles, but such experiments are limited to very low fields and only show the behaviour at surfaces. In 1990 we reported the first observation of magnetic flux lines in the bulk of a crystal of YBa₂Cu₃O₇, using small-angle neutron diffraction.

Contour plot of flux-line lattice scattering: difference at 20 K between field-cooled and zero-field data. The experimental data at lower temperatures confirm the existence of a vortex lattice of singly quantized flux lines. The results at higher temperatures showed that neutron diffraction could be used to investigate the melting of the flux lattice [3].

First Direct Observation of FLL Melting in a High-T_c Material

The flux line lattice inside a single crystal of Bi_2.15Sr_1.95CaCu₂O_8+x (BSCCO) was observed using small-angle neutron diffraction. The diffracted intensity goes rapidly to zero at a magnetic field-dependent flux lattice melting temperature; this melting coincides with the appearance of finite resistance within the superconducting state. The flux lattice signal can also be made to disappear at low temperatures by applying a sufficiently high field, probably because of the decomposition of flux lines into two-dimensional 'pancake' vortices [4].

The first reported observation of FLL melting in BSCCO using SANS. Diffraction patterns from the flux lattice in BSCCO at an applied magnetic field of 47.5 mT at temperatures of (a) 1.5 K, (b) 56 K and (c) 62 K. We identify the melting temperature as 60 K at this field.

Single-crystal Growth Using an Image Furnace

In 1985 we began our highly successful programme Single Crystal Growth @ Warwick. Using the first infra-red image furnace installed in the UK we produced high quality samples of many types of superconductors. We also used more conventional flux and vapour transport growth methods to produce crystals.

Bi2Sr2CaCu2O8 single crystal extracted for a larger boule grown using an image furnace here at Warwick.

A single crystal of Bi₂Sr₂CaCu₂O₈ grown in the IR image furnace at Warwick [5].

Warwick installed the first IR furnace in the UK in 1992. We now have three IR image furnaces at Warwick.

R.p. Singh et al J. Crystal Growth 361 129 2012

Single crystal of Nb_0.18Re_0.82synthesized by the FZT using a four mirror optical furnace equipped with Xe arc lamps [6].

Magnetic Superconductors

In 1994 we began work on a new class of superconductors with the general chemical formula RNi₂B₂C (R = rare earth) [7]. The layered structure of these materials means that for some of this series there is a co-existence of long-range magnetic order with superconductivity at the same temperature. This is very rare and provided us with an exciting opportunity to study the interplay between these two phenomena.

The borocarbides have been shown to exhibit a rich variety of magnetic and superconducting properties. We grew single crystals of many different members of the RNi₂B₂C family of materials. We investigated the properties of these samples in both the normal and superconducting state, via transport, magnetometry and heat capacity measurements

We also used neutron scattering, magnetometry and local Hall probes to probe the complex behaviour of the normal and superconducting states of these materials [8-9].

Superconducting and magnetic H-T phase diagram of HoNi₂B₂C (see Ref. 9 for more details).

Flux line lattice imaged via SANS in TmNi2B2C

An image of the flux-line lattice in the magnetic superconductor TmNi₂B₂C.

The Flux-Line Lattice in Magnetic Superconductors

Our studies of the flux-line lattice (FLL) in various superconductors were a marked success and created considerable international interest. We refined our neutron scattering techniques and greatly enhanced the resolution with which it is possible to make such measurements. This allowed us to perform a series of very high resolution experiments in magnetic superconductors examining the role of "non-local" effects in determining the distortion of the FLL and permitted a completely new slant on the problem of the coexistence of magnetism and superconductivity to be developed.

These measurements were complemented by the "global" magnetisation and resistivity studies undertaken in our laboratories. Data were also collected through a collaboration with a group in Cambridge, using a miniature Hall detector array to study the "local" magnetisation across single crystal samples. Our studies on HoNi₂B₂C demonstrated the power of this technique for understanding the role of the magnetic modulations on pinning the flux distributions.

Small Angle Neutron Scattering on Materials Related to MgB₂

The ternary silicide superconductor CaAlSi has the same AlB₂-type layered structure as MgB₂. The flux-line lattice in CaAlSi was studied by small-angle neutron scattering. A well-defined hexagonal flux-line lattice is seen just above H_c1 in an applied field of only 54 Oe. A 30 degree reorientation of this vortex lattice has been observed in a very low field of 200 Oe. This reorientation transition appears to be first-order and could be explained by nonlocal effects [10].

SANS diffraction patterns of CaAlSi taken at 2 K in applied magnetic fields of 97, 185, 250, and 294 Oe, respectively. (e) Schematic diagram of the FLL patterns in real-space (upper panel) and the corresponding diffraction patterns (lower panel).

References

[1] H. A. Mook, D. M. Paul, B. C. Sales, L. A. Boatner, and L. Cussen, Magnetic-ordering in GdBa₂Cu₃O_6.14, Physical Review B 38, 12008 (1988); D. M. Paul, H. A. Mook, A. W. Hewat, B. C. Sales, L. A. Boatner, J. O. Ramey, and L. Cussen, Magnetic-Ordering in the High-Temperature Superconductor ErBa₂Cu₃O_7-_d, Phys. Rev. B 39, 4291 (1989).

[2] G. Balakrishnan, N. R. Bernhoeft, Z. A. Bowden, D. M. Paul and A. D. Taylor, Vibrational anomalies in the superconducting compound La_1.85Ba_0.15CuO₄, Nature 327, 45 (1987); D. M. Paul, G. Balakrishnan, N. R. Bernhoeft, W. I. F. David and W. T. A. Harrison, Anomalous structural behavior of the superconducting compound La_1.85Ba_0.15CuO₄, Phys. Rev. Lett. 58, 1976 (1987).

[3] E. M. Forgan, D. M. Paul, H. A. Mook, P. A. Timmins, H. Keller, S. Sutton, and J. S. Abell, Observation by neutron-diffraction of the magnetic-flux lattice in single-crystal YBa₂Cu₃O_7-_d, Nature 343, 735 (1990); M. Yethiraj, H. A. Mook, G. D. Wignall, R. Cubitt, E. M. Forgan, D. M. Paul, and T. Armstrong, Small-angle neutron-scattering study of flux line lattices in twinned YBa₂Cu₃O₇, Phys. Rev. Lett. 70, 857 (1993); M. Yethiraj, H. A. Mook, G. D. Wignall, R. Cubitt, E. M. Forgan, S. L. Lee, D. M. Paul and T. Armstrong, Anisotropic vortex lattice in YBa₂Cu₃O₇, Phys. Rev. Lett. 71, 3019 (1993).

[4] R. Cubitt, E. M. Forgan, G. Yang, S. L. Lee, D. M. Paul, H. A. Mook, M. Yethiraj, P. H. Kes, T. W. Li, A. A. Menovsky, Z. Tarnawski and K. Mortensen, Direct observation of magnetic-flux lattice melting and decomposition in the high-T_c superconductor Bi_2.15Sr_1.95CaCu₂O_8+x, Nature 365, 407 (1993).

[5] G. Balakrishnan, D. M. Paul, M. R. Lees and A. T. Boothroyd, Physica C, Single-crystal growth of Bi₂Sr₂CaCu₂O₈ using an infrared image furnace, 206, 148 (1993); G. Balakrishnan, D. M. Paul and M. R. Lees, Superconducting properties of doped and off-stoichiometric Bi₂Sr₂CaCu₂O₈ single-crystals, Physica B 194, 2197 (1994).

[6] R. P. Singh, M. Smidman, M. R. Lees, D. M. Paul and G. Balakrishnan, Crystal growth of the non-centrosymmetric superconductor Nb_0.18Re_0.82, J. Cryst. Growth 361, 129 (2012).

[7] R. Nagarajan et al., Phys. Rev. Lett. 72, 274 (1994); R. J. Cava et al., Nature (London) 367, 252 (1994).

[8] L. J. Chang, C. V. Tomy, D. M. Paul and C. Ritter, Magnetic structure of TmNi₂B₂C, Phys. Rev. B 54, 9031(1996); C. V. Tomy et al., Anisotropic magnetic properties of TbNi₂B₂C single crystals, Phys. Rev. B 53, 307(1996); C. V. Tomy, M. R. Lees, L. Afalfiz, G. Balakrishnan and D. M. Paul, Superconductivity and magnetism in DyNi₂B₂C single-crystals, Phys. Rev. B, 52, 9186 (1995).

[9] C. D. Dewhurst, R. A. Doyle, E. Zeldov and D. M. Paul, Interaction between magnetic order and the vortex lattice in HoNi₂B₂C, Phys. Rev. Lett. 82, 827 (1999).

[10] P. K. Biswas, M. R. Lees, G. Balakrishnan, D. Q. Liao, D. S. Keeble, J. L. Gavilano, N. Egetenmeyer, C. D. Dewhurst, and D. M. Paul, First-order reorientation rransition of the flux-line lattice in CaAlSi, Phys. Rev. Lett. 108, 077001 (2012).

Recent Research at Warwick

Superconductivity at Warwick - 2010 to the Present Day

We continue to study the physics of superconductors. Our work uses both polycrystalline and single crystal samples, many of which we prepare ourselves. We have investigated the role that structure and spin-orbit coupling play in determining the properties of superconductors. We have also continued our studies of high-temperature superconductors, focusing particularly on the fermiology of these materials.

Unconventional and Exotic Superconductors

In conventional superconductors, the superconductivity arises from an electron-phonon coupling of electrons to form Cooper pairs, with a single, s-wave, isotropic gap. In unconventional materials, the Cooper pairs may be coupled by other interactions, the pair wave function may be an odd-parity spin-triplet, or there may be multiple superconducting bands.

Unconventional superconductivity can be found in number of different classes of materials. As well as the cuprate [1], pnictide [2] and heavy fermion superconductors [3], there are materials with noncentrosymmetric crystal structures [4], with strong spin-orbit coupling, e.g., those containing 4d and 5d metals, and systems with unusual crystallographic geometries, e.g., kagome lattice superconductors [5].

Unconventional superconductors can exhibit a variety of physical effects including exotic superconducting gap structures (lines or nodes in the superconducting gap), upper critical fields exceeding the Pauli limit, time reversal symmetry breaking, and topological effects.

Noncentrosymmetric Superconductors

We have worked on a number of superconductors with a noncentrosymmetric (NCS) structure. In a noncentrosymmetric structure, i.e. a system without inversion symmetry, parity is no longer a meaningful label. The lack of inversion symmetry induces an antisymmetric spin-orbit coupling (SOC) which can lift the degeneracy of the conduction band electrons and may cause the superconducting pair wavefunction to contain a mixture of singlet and triplet spin states.

The breakdown of the usual classification of superconductors into even-parity, (pseudo) spin-singlet and odd-parity, spin-triplet states means that a variety of physical effects that may previously have been forbidden are now allowed. Examples include exotic superconducting gap structures (lines or nodes in the superconducting gap), magnetoelectric effects such as a helical phase and upper critical fields exceeding the Pauli limiting field, time reversal symmetry breaking, and even topological effects and unusual surface states [4].

Noncentrosymmetric crystal structure of CePt₃Si. Studies of this NCS superconductor with antiferromagnetic order [6] led to a rapid growth in the research on NCS superconductors [4].

Time Reversal Symmetry Breaking in Re₆Zr

Singh Physical Review Letters 112 107002 (2014).

Zero-field μSR time spectra for Re₆Zr collected at 0.3 (closed symbols) and 8.0 K (open symbols), below and above T_c, with least squares fits to the data made using a Gaussian Kubo-Toyabe function with an exponential decay. A LF-μSR spectrum in an applied field of 10 mT at 0.3 K is also shown.

We have used muon spectroscopy to reveal that time-reversal symmetry breaking occurs in the NCS superconductor Re₆Zr [7]. We have also made detailed studies of the normal and superconducting state of Re₆Zr [8].

_{[7] R. P. Singh et al., Phys. Rev. Lett. 112, 107002 (2014).}_{[8] D. A. Mayoh et al., Phys. Rev. B 96, 064521 (2017).}

Centrosymmetric and Noncentrosymmetric Structures in Re₃W

We discovered that Re₃W can be reversibly switched between a centrosymmetric (CS) and noncentrosymmetric (NCS) structure [9-10].

It is possible to alternate between the different phases by annealing or re-melting the sample.

Magnetic susceptibility versus temperature for CS and NCS Re3W

Temperature dependence of the magnetic susceptibility for the NCS cubic and the CS hexagonal Re₃W measured in a magnetic field of 20 Oe. The superconducting properties of Re₃W depend strongly on the structure. T_c, H_c1, H_c2, change between the two structures [9-10].

_{[9] P. K. Biswas et al., Phys. Rev. B 84, 184529 (2011).}_{[10] P. K. Biswas et al., Phys. Rev. B 85, 134505 (2012).}

Unconventional Superconductivity in La₇M₃ (M = Ir, Pd, Ni)

We have used muon spectroscopy, as well as a range of in-house characterization methods to study the normal and superconducting-state properties of the La₇M₃ (M = Ir, Pd, Ni) family of noncentrosymmtric superconductors.

Barker et al. Physical Review Letterrs115 267001 (2015)

Muon spectroscopy was used to provide evidence of time reversal symmetry breaking in La₇Ir₃.

Despite the clear signature of TRSB in this and other members of the La₇M₃ family of materials [11-12], they all appear to be a rather conventional s-wave superconductors.

_{[11] J.A.T. Barker et al., Phys. Rev. Lett. 115, 267001 (2015);}_{[12] D.A. Mayoh et al., Phys. Rev. B103, 024507 (2021).}

Chiral Superconductors LaPt₃P and Nb/TaRh₂B₂

P. K. Biswas et al. Nature Communications 12 504 (2021)

We showed that the weakly correlated pnictide LaPt₃P has a chiral d-wave singlet superconducting ground state [13].

_{[13] P. K. Biswas et al., Nature Commun. 12, 2504 (2021).}

D. A. M. Mayoh et al. Journal of Physics Condensed Matter 31 465601 (2019)

NbRh₂B₂ and TaRh₂B₂ have chiral structures. The H_c2(0) = 18(1) T of NbRh₂B₂ exceeds the Pauli limit [14]. TaRh₂B₂ shows evidence of multigap superconductivity [15].

_{[14] D. A. Mayoh et al., J. Phys. Condens. Matter 31, 465601 (2019). [15] D. A. Mayoh et al., Phys. Rev. B 98, 014502 (2018).}

Evidence for Superconductivity with Broken Time-Reversal Symmetry in Locally Noncentrosymmetric SrPtAs

P. K. Biswas. et al., Physical Review B 87, 180503 (2013) - Figure 3.jpg

Upper panel: Temperature-dependent part of the electronic relaxation rate Λ(T) for two different samples of SrPtAs measured at two different μSR facilities.

The lower lower panel shows the temperature dependence of Λ in a weak LF of 9 mT.

_{[16] P. K. Biswas et al., Phys. Rev. B 87, 180503 (2013).}

Muon-spin-rotation/relaxation (μSR) measurements were use to show that the superconducting state of locally non-centrosymmetric SrPtAs breaks time-reversal symmetry. A dominantly d + id (chiral d-wave) order parameter is most consistent with our experimental data.

Type I and Type II behaviour in noncentrosymmetric LaPdSi₃ and LaPtSi₃

M. Smidman et al., Physical Review B 89, 094509 (2014) - Figure 3

Magnetization and heat capacity measurements showed LaPdSi₃ (T_c = 2.65(5) K) is a weakly coupled, fully gapped, type I superconductor.

M. Smidman et al., Physical Review B 89, 094509 (2014) - Figure 9

In contrast, LaPtSi₃ (T_c = 1.52(6) K) is a fully gapped type II superconductor with a GL parameter of 2.49(4).

_{[17] M. Smidman et al., Phys. Rev. B 89, 094509 (2014).}

Quantum Muon Diffusion and the Preservation of TRS in Type-I Rhenium

D. G. C. Jonas et al., Physical Review B 105 L020503 (2022) Figure 2.

Zero-field muon-spin relaxation spectra for type-I rhenium above and below T_c.

D. G. C. Jonas et al., Physical Review B 105 L020503 (2022) Figure 3.

Muon hopping rate as a function of temperature, ν(T).

Rhenium exhibiting type-II superconductivity has been previously reported to break time-reversal symmetry in the superconducting state. We have investigated a sample of type-I rhenium. Zero-field muon-spin relaxation measurements indicate that time-reversal symmetry is preserved in the superconducting state. Muon diffusion is observed, which is due to quantum mechanical tunnelling between interstitial sites.

_{[19] D. C. J. Jonas et al., Phys. Rev. B 105, L020503 (2022).}

Scroll here to read about some of our work on superconductors with a noncentrosymmetric structure

High Temperature Superconductors - Continued

We have continued our studies of cuprate superconductors, investigating the transport properties in "strange metals". These are materials that exhibit resistivity that decreases linearly with temperature as the temperature decreases to zero.

We have also used angle-dependent magnetoresistive (ADMR) studies in high magnetic fields to study the nature of the pseudogap phase and the Fermi surface in cuprates.

(a) Temperature doping phase diagram of Nd-LSCO. (b) In plane resistivity. (c) ADMR geometry. (d) The 3D Fermi surface of Nd-LSCO.

_{[20] G. Grissonnanche et al. Nature 595, 668 (2021).}

Linear-in temperature resistivity from an isotropic Planckian scattering rate

A variety of ‘strange metals’ exhibit resistivity that decreases linearly with temperature as the temperature decreases to zero, in contrast to conventional metals where resistivity decreases quadratically with temperature. This linear-in-temperature resistivity has been attributed to charge carriers scattering at a rate given by ħ/τ = αk_BT, where α is a constant of order unity, ħ is the Planck constant and k_B is the Boltzmann constant. This simple relationship between the scattering rate and temperature is observed across a wide variety of materials, suggesting a fundamental upper limit on scattering—the "Planckian limit" - but little is known about the underlying origins of this limit. In this study we reported a measurement of the ADMR of La_1.6−xNd_0.4Sr_xCuO₄ - a hole-doped cuprate that shows linear-in-temperature resistivity down to the lowest measured temperatures. The ADMR shows a well defined Fermi surface that agrees quantitatively with angle-resolved photoemission spectroscopy (ARPES) measurements and reveals a linear-in-temperature scattering rate that saturates at the Planckian limit, namely α = 1.2 ± 0.4. Remarkably, we found that this Planckian scattering rate is isotropic, that is, it is independent of direction, in contrast to expectations from ‘hotspot’ models. Our findings suggested that linear-in-temperature resistivity in strange metals emerges from a momentum independent inelastic scattering rate that reaches the Planckian limit.

Fermi surface transformation at the pseudogap critical point of a cuprate superconductor

We used angle-dependent magneto-resistance (ADMR) to measure the Fermi surface of the La_1.6–xNd_0.4Sr_xCuO₄ (Nd-LSCO) cuprate. Outside the pseudogap phase, we fitted the ADMR data and extract a Fermi surface geometry that is in excellent agreement with ARPES data. Within the pseudogap phase, the ADMR is qualitatively different, revealing a transformation of the Fermi surface.

Fang et al Nature Physics18.558 (2022) Fig. 1 ab

ADMR above and below the pseudogap critical doping p* in Nd-LSCO. Temperature–doping phase diagram of the hole-doped cuprate Nd-LSCO in zero magnetic field. The pseudogap phase is highlighted in red (onset temperature T* is taken from the resistivity and ARPES measurements). Also shown is the geometry of the ADMR measurements.

Fang et al Nature Physics18.558 (2022) Fig. 1 cd

Angle-dependent c-axis resistivity ρ_zz(θ) of Nd-LSCO for p = 0.21 (<p*) and p = 0.24 (>p*). The data were taken at T = 25 K and B = 45 T as a function of θ for ϕ= 0°, 15°, 30° and 45°, and normalized by the θ = 0 value, ρ_zz(0).

_{[21] Y. Fang et al. Nature Physics 18, 558 (2022).}

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