arXiv subjects

Richard A. Klemm

Publications and source records attributed to Richard A. Klemm.

At least 19 recordsLinked to original sources

arXiv2026

Magnetic resonance in quantum computing and in accurate measurements of the nuclear moments of atoms and molecules

Modern experimental techniques can generate magnetic fields of the form H(t) = H0 z-hat + H1 [x-hat cos(ωt) + y-hat sin(ωt)], at frequencies within an order of magnitude of the nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR) frequencies, ωn0 and ωe0, respectively, when acting on atoms or molecules. We derive simple closed-form expressions for the exact nuclear- and electronic-spin wave functions that enable controlled transitions between entangled states, allowing an atom or molecule to function as a quantum computer. These solutions also enable precise NMR or EPR measurements of nuclear moments in atoms and molecules. We present examples relevant to measurements of the nuclear moments of 14N, 7Li, and 133Cs. Because existing hyperfine measurements of the lowest three nuclear moments of 133Cs are mutually inconsistent, the proposed NMR/EPR experiments provide a route to measuring all seven of its nuclear moments with high precision.

physics.atom-ph↗

arXiv2026

Wave functions for the regular pentagonal two-dimensional quantum box and thin microstrip antenna

The general wave functions for the two-dimensional regular pentagonal quantum box and thin microstrip antenna are derived. As for the square, equilateral triangular, and circular disk-shaped boxes and antennas, there are two quantum nunbers $n$ and $m$. In those cases, $n\ge1 $ and $m\ge 0$ are both unlimited non-negative integers of any value. For the regular pentagon, only $n\ge1 $ is an unlimited positive quantum number, but $m_{\rm min}\le m\le 5$, where $m_{\rm min}=0$ for the pentagonal microstrip antenna with Neumann boundary conditions and $m_{\rm min}=1$ for the pentagonal quantum box with Dirichlet boundary conditions. Color-coded pictures of the wave functions for the regular pentagonal quantum box and microstrip antenna are presented for all allowed $m$ values and for $1\le n\le 2$ and for the microstrip antenna for all allowed $m$ values and $n=3$.

cond-mat.supr-con↗

arXiv2025

Terahertz source-on-a-chip with decade-long stability using layered superconductor elliptical microcavities

Coherent, continuous-wave, and electrically tunable chip-scale terahertz (THz) sources are critical for emerging applications in sensing, imaging, spectroscopy, communication, space and quantum technologies. Here, we demonstrate a robust source-on-a-chip THz emitter based on a layered high-temperature superconductor, engineered with an elliptical microcavity and capable of sustained coherent emission over an unprecedented operational lifetime exceeding 11 years. This compact THz source operates up to 60 K, with Tc= 90 K, delivering stable radiation in the 0.7-0.8 THz range, with on-chip electrical tunability from 100 GHz to 1 THz. Coherence arises from the phase-locked oscillation of intrinsic Josephson junction arrays, resonantly coupled to transverse electromagnetic modes within the cavity, analogous to a laser cavity, yielding collective macroscopic oscillations. THz emission remains detectable across a 0.5 m free-space open-air link at room temperature. We analyse the cavity-mode structure and extract THz photon generation rates up to 503 photons fs-1 in cryogenic conditions and 50-260 photons ps-1 over-the-air. These results establish long-term coherent THz emission from superconductors and chart a viable path toward scalable, tunable, solid-state coherent THz laser-on-a-chip platforms, especially for future classical and quantum systems.

quant-ph↗

arXiv2025

Model for the commensurate charge-density waves in under-hole-doped cuprate superconductors

A simple model of the commensurate charge-density wave (CCDW) portion of the underdoped pseudogap regions of monolayer Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6-x}$ (Bi2201), bilayer Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ (Bi2212), and trilayer Bi$_2$Sr$_2$Ca$_2$Cu$_3$O$_{10+δ}$ (Bi2223) cuprate superconductors is presented and studied. Above the superconducting transition temperature $T_c$ but below the pseudogap transition temperature $T_p > T_c$, the CCDW forms on the oxygen sites in the CuO$_2$ layers with excess charges of $\pmδe$, where $e$ is the electronic charge, forming on alternating oxygen sites. This model is equivalent to $N$-layer versions of the two-dimensional Ising model for spins on a square lattice with repulsive interactions $J' , J>0$ between near-neighbor inter- and intralayer sites, respectively. For strong coupling, we show analytically for sections of $L\times M\times N$ sites that the partition function in the $J'\rightarrow\pm \infty$ limits reduces to that for an effective single layer with $L\times M$ sites and $J$ replaced by $NJ$. The CCDW is therefore strongly enhanced and stabilized by multilayer structures, likely accounting for the enhanced THz emission observed from the intrinsic Josephson junctions in underdoped Bi2212 mesas and for the many experiments on Bi2212 and related compounds purporting to provide evidence for a superconducting order parameter with $d_{x^2-y^2}$-wave symmetry.

cond-mat.supr-con↗

arXiv2024

An advance in the arithmetic of the Lie groups as an alternative to the forms of the Campbell-Baker-Hausdorff-Dynkin theorem

The exponential of an operator or matrix is widely used in quantum theory, but it sometimes can be a challenge to evaluate. For non-commutative operators ${\bf X}$ and ${\bf Y}$, according to the Campbell-Baker-Hausdorff-Dynkin theorem, ${\rm e}^{{\bf X}+{\bf Y}}$ is not equivalent to ${\rm e}^{\bf X}{\rm e}^{\bf Y}$, but is instead given by the well-known infinite series formula. For a Lie algebra of a basis of three operators $\{{\bf X,Y,Z}\}$, such that $[{\bf X}, {\bf Y}] = κ{\bf Z}$ for scalar $κ$ and cyclic permutations, here it is proven that ${\rm e}^{a{\bf X}+b{\bf Y}}$ is equivalent to ${\rm e}^{p{\bf Z}}{\rm e}^{q{\bf X}}{\rm e}^{-p{\bf Z}}$ for scalar $p$ and $q$. Extensions for ${\rm e}^{a{\bf X}+b{\bf Y}+c{\bf Z}}$ are also provided. This method is useful for the dynamics of atomic and molecular nuclear and electronic spins in constant and oscillatory transverse magnetic and electric fields.

quant-ph↗

arXiv2022

Quantum spin Hall effect in two-dimensional metals without spin-orbit coupling

The quantum spin Hall effect has been observed in topological insulators using spin-orbit coupling as the probe, but it has not yet been observed in a metal. An experiment is proposed to measure the quantum spin Hall effect of an electron or hole in a two-dimensional (2D) metal by using the previously unexplored but relativistically generated 2D quantum spin Hall Hamiltonian, but without using spin-orbit coupling. A long cylindrical solenoid lies normally through the inner radius of a 2D metallic Corbino disk. The current $I_S$ surrounding the solenoid produces an azimuthal magnetic vector potential but no magnetic field in the disk. In addition, a radial electric field is generated across the disk by imposing either (a) a potential difference $Δv$ or (b) a radial charge current ${\bm I}$ across its inner and outer radii. Combined changes in $I_S$ and in either $Δv$ or ${\bm I}$ generate spontaneously quantized azimuthal charge and spin currents. The experiment is designed to measure these quantized azimuthal charge and spin currents in the disk consistently. The quantum Hamiltonians for experiments (a) and (b) are both solved exactly. A method to control the Joule heating is presented, which could potentially allow the quantum spin Hall measurements to be made at room temperature. Extensions of this design to an array of thermally-managed solenoids, each surrounded by thermally-managed stacks of 2D metallic Corbino disks, could function as a quantum computer that could potentially operate at room temperature.

cond-mat.mes-hall↗

arXiv2022

Angular dependence of the upper critical induction of clean $s$- and $d_{x^2-y^2}$-wave superconductors with self-consistent ellipsoidal effective mass and Zeeman anisotropies

We employ the Schr{ö}dinger-Dirac method generalized to an ellipsoidal effective mass anisotropy in order to treat the spin and orbital effective mass anisotropies self consistently, which is important when Pauli-limiting effects on the upper critical field characteristic of singlet superconductivity are present. By employing the Klemm-Clem transformations to map the equations of motion into isotropic form, we then calculate the upper critical magnetic induction $B_{c2}(θ, ϕ, T)$ at arbitrary directions and temperatures $T$ for isotropic $s$-wave and for anisotropic $d_{x^2-y^2}$-wave superconducting order parameters. As for anisotropic $s$-wave superconductors, the reduced upper critical field $b_{c2}$ is largest in the direction of the lowest effective mass, and is proportional to the universal orientation factor $α(θ,ϕ)$. However, for $d_{x^2-y^2}$-wave pairing, ${\bm B}_{c2}(π/2,ϕ,T)$ exhibits either a four-fold pattern with $C_4$ symmetry just below the transition temperature $T_c$ that rotates by $π/4$ as $T$ is lowered, or a two-fold pattern with $C_2$ symmetry, depending upon the planar effective mass anisotropy. This provides a new method to distinguish these pairing symmetries in clean unconventional superconductors.

cond-mat.supr-con↗

arXiv2022

Nuclear Magnetic Resonance for Arbitrary Spin Values in the Rotating Wave Approximation

In order to probe the transitions of a nuclear spin $s$ from one of its substate quantum numbers $m$ to another substate $m'$, the experimenter applies a magnetic field ${\bm B}_0$ in some particular direction, such along $\hat{\bm z}$, and then applies an weaker field ${\bm B}_1(t)$ that is oscillatory in time with the angular frequency $ω$, and is normally perpendicular to ${\bm B}_0$, such as ${\bm B}_1(t)=B_1\hat{\bm x}\cos(ωt)$. In the rotating wave approximation, ${\bm B}_1(t)=B_1[\hat{\bm x}\cos(ωt)+\hat{\bm y}\sin(ωt)]$. Although this problem is solved for spin $\frac{1}{2}$ in every quantum mechanics textbook, for the general spin $s$ case, its general solution has been published only for the overall probability of a transition between the states, but the time dependence of the probability of finding the nucleus in each of the substates has not previously been published. Here we present an elementary method to solve this problem exactly, and present figures for the time dependencies of the various substates states for a variety of initial substate probabilities for a variety of $s$ values. We found a new result: unlike the $s=\frac{1}{2}$ case, for which if the initial probability of finding the particle in one of the substates was 1, and the time dependence of the probabilities of each of the substates oscillates between 0 and 1, for higher spin values, the time dependencies of the probabilities finding the particle in each of its substates, which periodic, is considerably more complicated.

quant-ph↗

arXiv2021

Wave functions for high-symmetry, thin microstrip antennas and two-dimensional quantum boxes

For a spinless quantum particle in a one-dimensional box or an electromagnetic wave in a one-dimensional cavity, the respective Dirichlet and Neumann boundary conditions both lead to non-degenerate wave functions. However, in two spatial dimensions, the symmetry of the box or microstrip antenna is an important feature that has often been overlooked in the literature. In the high-symmetry cases of a disk, square, or equilateral triangle, the wave functions for each of those two boundary conditions are grouped into two distinct classes, which are one- and two-dimensional representations of the respective point groups, $C_{\infty v}$, $C_{4v}$, and $C_{3v}$. Here we present visualizations of representative wave functions for both boundary conditions and both one- and two-dimensional representations of those point groups. For the one-dimensional representations, color contour plots of the wave functions are presented. For the two-dimensional representations, the infinite degeneracies are presented as common nodal points and/or lines, the patterns of which are invariant under all operations of the respective point group. The wave functions with the Neumann boundary conditions have important consequences for the coherent terahertz emission from the intrinsic Josephson junctions in the high-temperature superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$: the enhancement of the output power from electromagnetic cavity resonances is only strong for wave functions that are not degenerate.

cond-mat.supr-con↗

arXiv2019

The Zeeman, Spin-Orbit, and Quantum Spin-Hall Interactions in Anisotropic and Low-Dimensional Conductors

When an electron or hole is in a conduction band of a crystal, it can be very different from 2, depending upon the crystalline anisotropy and the direction of the applied magnetic induction ${\bf B}$. In fact, it can even be 0! To demonstrate this quantitatively, the Dirac equation is extended for a relativistic electron or hole in an orthorhombically-anisotropic conduction band with effective masses $m_j$ for $j=1,2,3$ with geometric mean $m_g=(m_1m_2m_3)^{1/3}$. The appropriate Foldy-Wouthuysen transformations are extended to evaluate the non-relativistic Hamiltonian to $O({\rm m}c^2)^{-4}$, where ${\rm m}c^2$ is the particle's Einstein rest energy. For ${\bf B}||\hat{\bf e}_μ$, the Zeeman $g_μ$ factor is $2{\rm m}\sqrt{m_μ}/m_g^{3/2} + O({\rm m}c^2)^{-2}$. While propagating in a two-dimensional (2D) conduction band with $m_3\gg m_1,m_2$, $g_{||}<<2$, consistent with recent measurements of the temperature $T$ dependence of the parallel upper critical induction $B_{c2,||}(T)$ in superconducting monolayer NbSe$_2$ and in twisted bilayer graphene. While a particle is in its conduction band of an atomically thin one-dimensional metallic chain along $\hat{\bf e}_μ$, $g<<2$ for all ${\bf B}={\bf\nabla}\times{\bf A}$ directions and vanishingly small for ${\bf B}||\hat{\bf e}_μ$. The quantum spin Hall Hamiltonian for 2D metals with $m_1=m_2=m_{||}$ is $K[{\bf E}\times({\bf p}-q{\bf A})]_{\perp}σ_{\perp}+O({\rm m}c^2)^{-4}$, where ${\bf E}$ and ${\bf p}-q{\bf A}$ are the planar electric field and gauge-invariant momentum, $q=\mp|e|$ is the particle's charge, $σ_{\perp}$ is the Pauli matrix normal to the layer, $K=\pmμ_B/(2m_{||}c^2)$, and $μ_B$ is the Bohr magneton.

cond-mat.mes-hall↗

arXiv2019

Quantum Spin Hall Effect in Electric and Magnetic Fields without Spin-Orbit Coupling

From the Dirac equation of an electron in an anisotropic conduction band, the anisotropy of its motion dramatically affects its interaction with applied electric and magnetic fields. The quantum spin Hall effect (QSHE) is observable in two-dimensional metals without spin-orbit coupling. The dimensionality of the Zeeman interaction plays an important role in the QSHE, and profoundly modifies many interpretations of measurements of the Knight shift and of the upper critical field in highly anisotropic superconductors.

cond-mat.supr-con↗

arXiv2019

A relativistic electron in an anisotropic conduction band

The Dirac equation is extended for a relativistic electron in an orthorhombically-anisotropic conduction band. Its covariance is established with general proper and improper Lorentz transformations. In the non-relativistic limit, the kinetic and Zeeman energy terms of the Hamiltonian are both determined by the same three effective masses, and the quantum spin Hall effect is derived. This has important consequences for magnetic measurements of many classes of clean anisotropic semiconductors, metals, and superconductors. The Zeeman energy is vanishingly small for magnetic fields parallel to clean monolayers and in all directions in quasi-one-dimensional materials.

cond-mat.str-el↗

arXiv2018

Towards a Microscopic Theory of the Knight Shift in an Anisotropic, Multiband Type-II Superconductor

A method is proposed to extend the zero-temperature Hall-Klemm microscopic theory of the Knight shift $K$ in an anisotropic and correlated, multi-band metal to calculate $K(T)$ at finite temperatures $T$ both above and into its superconducting state. The transverse part of the magnetic induction ${\bf B}(t)={\bf B}_0+{\bf B}_1(t)$ causes adiabatic changes suitable for treatment with the Keldysh contour formalism and analytic continuation onto the real axis. We propose that the Keldysh-modified version of the Gor'kov method can be used to evaluate $K(T)$ at high ${\bf B}_0$ both in the normal state, and by quantizing the conduction electrons or holes with Landau orbits arising from ${\bf B}_0$, also in the entire superconducting regime for an anisotropic, multiband Type-II BCS superconductor. Although the details have not yet been calculated in detail, it appears that this approach could lead to the simple result $K_S(T)\approx a({\bf B}_0)-b({\bf B}_0)|Δ({\bf B}_0,T)|^2$, where $2|Δ({\bf B}_0,T)|$ is the effective superconducting gap. More generally, this approach can lead to analytic expressions for $K_S(T)$ for anisotropic, multiband Type-II superconductors of various orbital symmetries that could aid in the interpretation of experimental data on unconventional superconductors.

cond-mat.supr-con↗

arXiv2015

Pristine and intercalated transition metal dichalcogenide superconductors

Transition metal dichalcogenides (TMDs) are quasi-two-dimensional layered compounds exhibiting strongly competing charge-density wave (CDW) and superconducting (SC) order parameters (OPs). The weak van der Waals interlayer bonding between hexagonal layers of octahedral or trigonal prismatic TMD building blocks allows for many polytypes. The non-superconducting $1T$ polytypes can have one or more CDWs. The $2H$ polytypes have two or more Fermi surfaces and saddle bands, allowing for dual orderings, which can be coexisting CDW and SC orderings, two SC gaps as in MgB$_2$, or two CDW gaps. The CDW transitions $T_{\rm CDW}$s usually greatly exceed the low superconducting $T_{\rm c}$s, their orbital OPs are generally highly anisotropic and can even contain nodes, are remarkably similar to the the high-$T_{\rm c}$ cuprate pseudogaps, and the SC OPs can be greatly affected by their presence. In 2$H$-NbSe$_2$, the CDW renders its general $s$-wave SC OP orbital symmetry to be highly anisotropic and strongly reduces its Josephson coupling strength ($I_{\rm c}R_{\rm n}$) with Pb. Pressure and intercalation generally suppress the CDWs, enhancing $T_{\rm c}$. The misfit intercalation compound (LaSe)$_{1.14}$(NbSe$_2$) and many intercalated $2H$-TMDs, such as TaS$_2$(pyridine)$_{1/2}$, have completely incoherent $c$-axis transport, dimensional-crossover effects, and behave as stacks of intrinsic Josephson junctions. Except for the anomalously large violation of the Pauli limit of the upper critical field of (LaSe)$_{1.14}$(NbSe$_2$), these properties are very similar to those of the cuprate Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ and of the organic layered superconductor, $κ$-(ET)$_2$Cu[N(CN)$_2$]Br. Intercalates of TMDs with water and metallic ions are very similar to Na$_x$CoO$_2\cdot y$H$_2$O.

cond-mat.supr-con↗

arXiv2014

Double ellipsoidal Fermi surface model of the normal state of ferromagnetic superconductors

We model the normal state of ferromagnetic superconductors with two general ellipsoidal Fermi surfaces (FSs), one for each spin projection $σ=\{\uparrow,\downarrow\}$, each with its ferromagnetically split chemical potential $μ_σ$ and its three distinct single particle effective masses, $\{m_{iσ}\}$, the geometric mean of which is $m_σ$. We study this model in the presence of an arbitrarily oriented magnetic induction, ${\bf B}=μ_{0}{\bf H}+{\bf M_{0}}$, where ${\bf M_{0}}$ includes the Ising-like spontaneous ferromagnetic order, which for URhGe is in the $c$-axis direction above the superconducting transition temperature $T_c$. We assume the low-$T$ total particle density $Σ_σ n_σ({\bf B})$ to be independent of ${\bf B}$, and obtain a self-consistent asymptotic expansion for $\sum_σΠ^{3/2}_σ({\bf B})$ in even powers of ${\bf B}$, where $Π_σ({\bf B})=m_σ({\bf B})μ_σ({\bf B})$. We assume that the $μ_σ({\bf B})$ are linear in ${\bf B}$ for both spins due to the Zeeman interaction and that the remaining even ${\bf B}$ dependence in the $Π_σ({\bf B})$ arises only from $m_{\downarrow}({\bf B})$. Our analogous expression for the Sommerfeld constant $γ({\bf B})$ leads to good fits to the $γ({\bf H})$ data of Aoki and Flouquet [J. Phys. Soc. Jpn. \textbf{81}, 011003 (2012)] obtained for the ferromagnetic superconductor URhGe in the ferromagnetic, non-superconducting phase, with the applied magnetic field ${\bf H}$ along each of the three crystallographic directions. We discuss this model in terms of the reentrant superconducting properties of URhGe and UCoGe. This model can be generalized to an arbitrary number of ellipsoidal FSs.

cond-mat.supr-con↗

arXiv2014

Is the anisotropy of the upper critical field of Sr$_2$RuO$_4$ consistent with a helical $p$-wave state?

We calculate the angular and temperature $T$ dependencies of the upper critical field $H_{c2}(θ,ϕ,T)$ for the $C_{4v}$ point group helical $p$-wave states, assuming a single uniaxial ellipsoidal Fermi surface, Pauli limiting, and strong spin-orbit coupling that locks the spin-triplet $\vec{\bf d}$-vectors onto the layers. Good fits to the Sr$_2$RuO$_4$ $H_{c2,a}(θ,T)$ data of Kittaka {\it et al.} [Phys. Rev. B {\bf 80}, 174514 (2009)] are obtained. Helical states with $\vec{\bf d}(\vec{\bf k})=k_x\vec{\bf x}-k_y\vec{\bf y}$ and $k_y\vec{\bf x}+k_x\vec{\bf y}$ (or $k_x\vec{\bf x}+k_y\vec{\bf y}$ and $k_y\vec{\bf x}-k_x\vec{\bf y}$) produce $H_{c2}(90^{\circ},ϕ,T)$ that greatly exceed (or do not exhibit) the four-fold azimuthal anisotropy magnitudes observed in Sr$_2$RuO$_4$ by Kittaka {\it et al.} and by Mao {\it et al.} [Phys. Rev. Lett. {\bf 84}, 991 (2000)], respectively.

cond-mat.supr-con↗

arXiv2014

First-order chiral to non-chiral transition in the angular dependence of the upper critical induction of the Scharnberg-Klemm $p$-wave pair state

We calculate the temperature $T$ and angular $(θ,ϕ)$ dependence of the upper critical induction $B_{c2}(θ,ϕ,T)$ for parallel-spin superconductors with an axially symmetric $p$-wave pairing interaction pinned to the lattice and a dominant ellipsoidal Fermi surface (FS). For all FS anisotropies, the chiral Scharnberg-Klemm state $B_{c2}(θ,ϕ,T)$ exceeds that of the chiral Anderson-Brinkman-Morel state, and exhibits a kink at $θ=θ^{*}(T,ϕ)$, indicative of a first-order transition from its chiral, nodal-direction behavior to its non-chiral, antinodal-direction behavior. Applicability to Sr$_2$RuO$_4$, UCoGe, and topological superconductors such as Cu$_x$Bi$_2$Se$_3$ is discussed.

cond-mat.supr-con↗

arXiv2013

Local SiC photoluminescence evidence of non-mutualistic hot spot formation and sub-THz coherent emission from a rectangular Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ mesa

From the photoluminescence of SiC microcrystals uniformly covering a rectangular mesa of the high transition temperature $T_c$ superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$, the local surface temperature $T({\bm r})$ was directly measured during simultaneous sub-THz emission from the $N\sim10^3$ intrinsic Josephson junctions (IJJs) in the mesa. At high bias currents $I$ and low bath temperatures $T_{\rm bath}\lesssim~35$ K, the center of a large elliptical hot spot with $T({\bm r})> T_c$ jumps dramatically with little current-voltage characteristic changes. The hot spot doesn't alter the ubiquitous primary and secondary emission conditions: the ac Josephson relation and the electromagnetic cavity resonance excitation, respectively. Since the intense sub-THz emission was observed for high $T_{\rm bath}\gtrsim~50$ K in the low $I$ bias regime where hot spots are absent, hot spots can not provide the primary mechanisms for increasing the output power, the tunability, or for promoting the synchronization of the $N$ IJJs for the sub-THz emission, but can at best coexist non-mutualistically with the emission. No $T({\bm r})$ standing waves were observed.

cond-mat.supr-con↗