He also started
work with Bob Schrieffer on the theory of charge-density wave conduction within a Lee-Rice domain, and persuaded an
experimental group at Exxon to study the physics of charge-density wave conduction in NbSe
_{3} and
o-TaS
_{3},
for which Klemm synthesized the crystals exhibiting the lowest threshold electric field for conduction available at the
time.
During most of his career, Klemm has worked on the theory of anisotropic superconductors, working with John Clem at
ISU on the anisotropic Ginzburg-Landau model for the lower critical field at an arbitrary field direction, and made many
theoretical studies of the high temperature superconductors YBCO and Bi2212. In particular, he was impressed by the
extremely careful work of Qiang Li at
Brookhaven National Laboratory, who made c-axis twist junctions of Bi2212. Klemm convinced Li to use this technique to undertake the best experimental test of the orbital symmetry of the superconducting order parameter,
by studying the c-axis critical current at many different twist junction angles, in the vicinity of the transition, where
heating issues are not a problem. The results proved definitively that the order parameter in that material with nominal C
_{2v}^{13} point group symmetry was at least 20% s-wave for all temperatures up to T
_{c}. This
experiment proved that all theories based upon repulsive interactions or magnetic interactions were false, in contradiction to the prevailing opinion. Since then, the experiment has been reproduced using artificial cross whiskers and naturally-formed cross-whisker junctions by
groups in Tsukuba, Japan and in Moscow, Russia. In addition, very recent experiments in a variety of laboratories have determined that the electron-phonon interaction does indeed play a crucial role in the pairing interaction, and it appears that the phonon responsible for the superconductivity
is the half-breathing mode, which occurs at the position in the first Brillouin zone where the saddle bands of extended van Hove singularities are prominent.
Most recently, Klemm has been collaborating with Prof. Kazuo Kadowaki at the University of Tsukuba, Japan. They are working on the angular dependence of the coherent terahertz radiation
emitted from mesas of Bi2212, which act as stacks of Josephson junctions. In particular, they have been interested in determining the primary microscopic source of the
coherent radiation. There are presently two basic models of this source. The most popular model is to treat the
mesa as a cavity that amplifies the ac Josephson frequencies formed when a dc voltage is applied across the stack of junctions. The other model is to treat the mesa as an electric dipole antenna, in which the ac Josephson supercurrent is itself the radiation source.
In the existing rectangular mesa geometries, the cavity modes for wave formation across the mesa width are harmonic, as in the natural harmonic frequency spectrum of a violin string, and can be made to match the harmonic frequency spectrum of the ac Josephson current, which occurs from the non-linearities in all Josephson junctions, making a clear distinction between these two mechanisms difficult. However, Klemm then proposed to study cylindrical mesa geometries, for which the anharmonic cavity modes
are analogous to the frequency spectrum of a drum, so that only one of the ac Josephson supercurrent frequencies could be amplified in the cavity model. Experiments to test this idea are currently underway. In addition, Klemm and Kadowaki, along with Tokyo Instruments, filed an international idea patent on July 17, 2008, in which they claimed that the removal of the superconducting substrate
might lead to an enhancement of the output power by three orders of magnitude, potentially up to 5 mW, sufficient for many device applications. After consulting with friends and family on a name for the device, they denoted this device the Josephson STAR-emitter, where STAR is an acronym for stimulated terahertz amplified radiation. Klemm thanks Stephanie Sirgo Johnston for suggesting this name.
Schematic views of c-axis twist junctions designed to test for a d
_{x}2
_{-y}2-wave order parameter
Schematic view of the lead attachments to a bicrystal containing a c-axis twist junction. [Q. Li et al., Phys. Rev. Lett.
83, 4160 (1999).]
High resolution transmission electron microscope picture [Y. Zhu et al., Phys. Rev. B
57, 8601 (1998)] of three cross-sections of a 36.45
^{o} Bi2212 c-axis twist junction.
Off-axis electron holography picture [M. A. Schofield et al., Phys. Rev. B
67, 224512 (2003)] of four Bi2212 c-axis twist junctions.
C-axis critical currents measured across intrinsic and the 50
^{o} twist junction. [Q. Li et al., Phys. Rev. Lett.
83, 4160 (1999).]
C-axis critical current densities across the intrinsic and twist junctions of four samples at temperatures just below T
_{c}.[Q. Li et al., Phys. Rev. Lett.
83, 4160 (1999).]
Ratios of the c-axis critical current densities across the twist junctions to those across the intrinsic single crystal junctions at 0.9T
_{c}, as a function of the twist angle.[Q. Li et al., Phys. Rev. Lett.
83, 4160 (1999).]
Sketches of the simplest forms of the four possible pairing symmetries in a tetragonal crystal. The red and green portions have opposite signs.
Sketch of the equivalent sites with the allowed symmetries in a tetragonal crystal with C
_{4v} point group symmetry. Table: Group symmetry operations and the associated order parameter symmetries. [R. Klemm et al., Phys. Rev. B
61, 5913 (2000)]
Sketch of the orthorhombic distortion appropriate for Bi2212 with approximate C
_{2v}^{13} point group symmetry. Table: Associated mixed order parameter symmetries for intrinsically perfect Bi2212. [R. Klemm et al., Phys. Rev. B
61, 5913 (2000)]
Top: Photomicrographs of naturally-formed c-axis cross whiskers. Bottom: Relative abundance of naturally-formed cross whiskers as a function of cross angle.
[Yu. Latyshev et al., Phys. Rev. B
70, 094517 (2004)].
Log-log plot of the resistance versus junction area for the naturally-formed cross-whisker junctions studied. Inset: Resistance versus temperature across one cross-whisker junctions. [Yu. Latyshev et al., Phys. Rev. B
70, 094517 (2004)].
Compilation of the log
_{10}[J
_{c}^{J}(A/cm
^{2})] data of the Li et al. c-axis twist junctions (solid diamonds), the Takano et al. [Y. Takano et al., Phys. Rev. B
65, 140513 (2002)] artificial cross-whisker data (open circles), and the Latyshev et al. [Yu. Latyshev et al., Phys. Rev. B
70, 094517 (2004)] naturally-formed cross-whisker data at low T (stars, solid squares and circles). From R. A. Klemm, Phil. Mag.
85, 801 (2005).
Most recently, Klemm has taken on a new area of interest in nanomagnetism. In particular, he began by studying the synamics of small classical spins coupled via
the Heisenberg interaction. More recently, he has studied equal-spin dimers, taking account of the quantum effects
arising from the Heisenberg interaction. Then, he expanded that work to include the single-ion and symmetric exchange anisotropies, in collaboration with Dmitri Efremov. Most recently, they have finished a long series of calculations
extending that work to equal spin tetramers, such as Ni
_{4}, which have been of great interest to experimentalists in the field. They treated the
single-ion and exchange anisotropies in first-order perturbation theory, and added the effects of biquadratic and three-center quartic interactions, which can play an important role in antiferromagnetic tetramers. They also showed how to extract some of the
microscopic, single-spin interactions from the second excited state manifold using electron paramagnetic resonance.
Most recently, they have been working on the Dzyaloshinskii-Moriya interactions, which can be important in
single molecule magnets with sufficiently low symmetry, and they showed that this interaction can lead to
new multiferroic effects, in which the magnetic interactions can generate an electric polarization.
Spin-spin time correlation function for the N-spin equivalent neighbor model [R. Klemm and M. Ameduri, Phys. Rev. B
66, 012403 (2002).]
Comparison the the predictions for the level-crossing inductions of a spin-5/2 dimer [D. V. Efremov and R. A. Klemm, Phys. Rev. B
74, 064408 (2006)] with data on [Fe(salen)Cl]
_{2} [Y. Shapira et al., Phys. Rev.
59, 1046 (1999)].
Magnetization at T=0 of antiferromagnetic (AFM) spin 1/2 tetramers with the Heisenberg and Dzyaloshinskii-Moriya (DM) interactions for S
_{4} symmetry.
Electric polarization arising from the DM interactions in spin 1/2 AFM tetramers with S
_{4} symmetry and DM interactions
Electric polarization at 45
^{o} azimuthal angle as a function of axial angle for AFM spin 1/2 tetramers with S
_{4} and DM interactions.
Magnetization at T=0 of spin 1/2 tetramers with the Heisenberg and DM interactions for S
_{4} symmetry.
Electric polarization arising from the DM interactions in spin 1 AFM tetramers with S
_{4} symmetry and DM interactions
Electric polarization at 45
^{o} azimuthal angle as a function of axial angle for AFM spin 1 tetramers with S
_{4} and DM interactions.