# Rebecca Flint

## Prof. Rebecca Flint

### Contact Information

Assistant Professor
Department of Physics and Astronomy
Iowa State University
12 Physics Hall
Ames, IA 50011

Office: Zaffarano A523
Telephone: 515-294-7377
Email: lastname at iastate.edu

 I am a condensed matter theorist at Iowa State University, working on various problems in strongly correlated electronic systems. I tend to be interested in translating abstract theoretical ideas to real materials, and vice versa. I was an undergraduate in physics at Caltech, a graduate student in the condensed matter theory group at Rutgers University and most recently a Simons Postdoctoral Fellow in the condensed matter theory group at MIT. My curriculum vitae.

### Research Interests

 The search for fundamentally new states of matter is a major driving force in condensed matter, and the peculiar regime between local and itinerant physics is one of the most fruitful places to look. Here, strong electronic correlations realize exotic phases not simply related to free electrons or their Fermi surface instabilities. Instead, these phases are characterized by new broken symmetries or even topological order, and these materials can carry low energy collective modes that fractionalize the electron's charge and spin. For example, spin liquids are magnetic states that break no symmetries, and yet form a highly correlated topologically ordered state with neutral spin 1/2 excitations. There are now several good spin liquid candidates, but it is necessary to examine how realistic models affect the spin liquid physics. Currently, I am interested in the possible chiral spin liquid in Pr2Ir2O7 and in how to realize the J1-J2 honeycomb lattice spin liquid in real d-electron materials. Heavy fermion materials also realize a variety of exotic phases; these materials combine electrons from the two extremes: localized electrons, which form magnetic moments or spins, and itinerant electrons, which form a metallic band. At low temperatures, these two species become strongly entangled as the itinerant electrons screen the local moments, effectively melting the spins to form a heavy Fermi liquid. When there are two, competing screening channels instead of one, the two channels ultimately cooperate to melt the spins into an exotic symmetry-breaking phase composite pair superconductivity, which is a purely local mechanism for d-wave superconductivity relevant to the 115 materials, and hastatic order, a time-reversal symmetry breaking phase without any large moments that describes the hidden order in URu2Si2. I am currently working to extend these ideas to Pr based materials.

### Publications

• Discovery of an Unconventional Charge Density Wave at the Surface of K0.9Mo6O17
Daixiang Mou, A. Sapkota, H.-H. Kung, Viktor Krapivin, Yun Wu, A. Kreyssig, Xingjiang Zhou, A. I. Goldman, G. Blumberg, Rebecca Flint, and Adam Kaminski
Phys. Rev. Lett. 116, 196401
 We use angle resolved photoemission spectroscopy, Raman spectroscopy, low energy electron diffraction, and x-ray scattering to reveal an unusual electronically mediated charge density wave (CDW) in K0.9Mo6O17. Not only does K0.9Mo6O17 lack signatures of electron-phonon coupling, but it also hosts an extraordinary surface CDW, with TS_CDW=220  K nearly twice that of the bulk CDW, TB_CDW=115  K. While the bulk CDW has a BCS-like gap of 12 meV, the surface gap is 10 times larger and well in the strong coupling regime. Strong coupling behavior combined with the absence of signatures of strong electron-phonon coupling indicates that the CDW is likely mediated by electronic interactions enhanced by low dimensionality.
• Evidence of an odd-parity hidden order in a spin–orbit coupled correlated iridate
L. Zhao, D. H. Torchinsky, H. Chu, V. Ivanov, R. Lifshitz, R. Flint, T. Qi, G. Cao and D. Hsieh
Nature Physics 12, 32–36 (2016)
 A rare combination of strong spin–orbit coupling and electron–electron correlations makes the iridate Mott insulator Sr2IrO4 a promising host for novel electronic phases of matter. The resemblance of its crystallographic, magnetic and electronic structures to La2CuO4, as well as the emergence on doping of a pseudogap region and a low-temperature d-wave gap, has particularly strengthened analogies to cuprate high-Tc superconductors. However, unlike the cuprate phase diagram, which features a plethora of broken symmetry phases in a pseudogap region that includes charge density wave, stripe, nematic and possibly intra-unit-cell loop-current orders, no broken symmetry phases proximate to the parent antiferromagnetic Mott insulating phase in Sr2IrO4 have been observed so far, making the comparison of iridate to cuprate phenomenology incomplete. Using optical second-harmonic generation, we report evidence of a hidden non-dipolar magnetic order in Sr2IrO4 that breaks both the spatial inversion and rotational symmetries of the underlying tetragonal lattice. Four distinct domain types corresponding to discrete 90°-rotated orientations of a pseudovector order parameter are identified using nonlinear optical microscopy, which is expected from an electronic phase that possesses the symmetries of a magneto-electric loop-current order. The onset temperature of this phase is monotonically suppressed with bulk hole doping, albeit much more weakly than the Néel temperature, revealing an extended region of the phase diagram with purely hidden order. Driving this hidden phase to its quantum critical point may be a path to realizing superconductivity in Sr2IrO4.
• Remarkably Robust and Correlated Coherence and Antiferromagnetism in (Ce1−xLax)Cu2Ge2
H. Hodovanets, S. L. Bud’ko, W. E. Straszheim, V. Taufour, E. D. Mun, H. Kim, R. Flint, and P. C. Canfield
Phys. Rev. Lett. 114, 236601
 We present magnetic susceptibility, resistivity, specific heat, and thermoelectric power measurements on (Ce1−xLax)Cu2Ge2 single crystals (0≤x≤1). With La substitution, the antiferromagnetic temperature TN is suppressed in an almost linear fashion and moves below 0.36 K, the base temperature of our measurements for x>0.8. Surprisingly, in addition to robust antiferromagnetism, the system also shows low temperature coherent scattering below Tcoh up to ∼0.9 of La, indicating a small percolation limit ∼9% of Ce. Tcoh as a function of magnetic field was found to have different behavior for x<0.9 and x>0.9. Remarkably, (Tcoh)2 at H=0 was found to be linearly proportional to TN. The jump in the magnetic specific heat δCm at TN as a function of TK/TN for (Ce1−xLax)Cu2Ge2 follows the theoretical prediction based on the molecular field calculation for the S=1/2 resonant level model.
• Hastatic Order in URu2Si2 : Hybridization with a Twist
Premala Chandra, Piers Coleman and Rebecca Flint
Phys. Rev. B 91, 205103 (2015)
 The broken symmetry that develops below 17.5K in the heavy fermion compound URu2Si2 has long eluded identification. Here we argue that the recent observation of Ising quasiparticles in URu2Si2 results from a spinor hybridization order parameter that breaks double time-reversal symmetry by mixing states of integer and half-integer spin. Such "hastatic order" (hasta:[Latin]spear) hybridizes Kramers conduction electrons with Ising, non-Kramers 5f2 states of the uranium atoms to produce Ising quasiparticles. The development of a spinorial hybridization at 17.5K accounts for both the large entropy of condensation and the magnetic anomaly observed in torque magnetometry. This paper develops the theory of hastatic order in detail, providing the mathematical development of its key concepts. Hastatic order predicts a tiny transverse moment in the conduction sea, a collosal Ising anisotropy in the nonlinear susceptibility anomaly and a resonant energy-dependent nematicity in the tunneling density of states.
• Strong interaction between electrons and collective excitations in the multiband superconductor MgB2
Daixiang Mou, Rui Jiang, Valentin Taufour, Rebecca Flint, S. L. Bud'ko, P. C. Canfield, J. S. Wen, Z. J. Xu, Genda Gu, and Adam Kaminski
Phys. Rev. B 91, 140502(R) (2015)
 We use a tunable laser angle-resolved photoemission spectroscopy to study the electronic properties of the prototypical multiband BCS superconductor MgB2. Our data reveal a strong renormalization of the dispersion (kink) at ∼65meV, which is caused by the coupling of electrons to the E2g phonon mode. In contrast to cuprates, the 65 meV kink in MgB2 does not change significantly across Tc. More interestingly, we observe strong coupling to a second, lower energy collective mode at a binding energy of 10 meV. This excitation vanishes above Tc and is likely a signature of the elusive Leggett mode.
• Molecular Pairing and Fully-Gapped Superconductivity in Yb doped CeCoIn5
Onur Erten, Rebecca Flint and Piers Coleman
Phys. Rev. Lett. 114, 027002
(previous version available at arxiv:1402.7361)
 The recent observation of fully-gapped superconductivity in Yb doped CeCoIn5 poses a paradox, for the disappearance of nodes suggests that they are accidental, yet d-wave symmetry with protected nodes is well established by experiment. Here, we show that composite pairing provides a natural resolution: in this scenario, Yb doping drives a Lifshitz transition of the nodal Fermi surface, forming a fully-gapped d-wave molecular superfluid of composite pairs. The T4 dependence of the penetration depth associated with the sound mode of this condensate is in accord with observation.
• Evolution of the superconducting energy gap structure concomitant with Fermi surface reconstruction in the heavy-fermion superconductor CeCoIn5
Hyunsoo Kim, M. A. Tanatar, R. Flint, C. Petrovic, Rongwei Hu, B. D. White, I. K. Lum, M. B. Maple and R. Prozorov
Phys. Rev. Lett. 114, 027003
(previous version available at arxiv:1404.3700)
 The London penetration depth, lambda(T) was measured in single crystals of Ce1-xRxCoIn5, R=La, Nd and Yb down to Tmin = 50 mK (Tc/Tmin > 50) using a tunnel-diode resonator. In the cleanest samples lambda(T) is best described by the power law, lambda(T) , with n = 1, consistent with line nodes. Substitutions of Ce with La, Nd and Yb lead to similar monotonic suppressions of Tc, however the effects on lambda(T) differ. While La and Nd doping results in an increase of the exponent to n = 2, as expected for a dirty nodal superconductor, Yb doping leads to n>3, inconsistent with nodes, suggesting a change from nodal to nodeless superconductivity where Fermi surface topology changes were reported, implying that the nodal structure and Fermi surface topology are closely linked.
• Ising Quasiparticles and Hidden Order in URu2Si2
Premala Chandra, Piers Coleman and Rebecca Flint
Philosophical Magazine Special Issue (in press)
(previous version available as arXiv:1404.5920)
 The observation of Ising quasiparticles is a signatory feature of the hidden order phase of URu2Si2. In this paper we discuss its nature and the strong constraints it places on current theories of the hidden order. In the hastatic theory such anisotropic quasiparticles are naturally described described by resonant scattering between half-integer spin conduction electrons and integer-spin Ising moments. The hybridization that mixes states of different Kramers parity is spinorial; its role as an symmetry-breaking order parameter is consistent with optical and tunnelling probes that indicate its sudden development at the hidden order transition. We discuss the microscopic origin of hastatic order, identifying it as a fractionalization of three body bound-states into integer spin fermions and half-integer spin bosons. After reviewing key features of hastatic order and their broader implications, we discuss our predictions for experiment and recent measurements. We end with challenges both for hastatic order and more generally for any theory of the hidden order state in URu2Si2.
• Hidden and Hastatic Orders in URu2Si2
Rebecca Flint, Premala Chandra and Piers Coleman
J. Phys. Soc. Jpn. 83, 061003 (2014)
(previous version available as arXiv:1403.3422)
 The hidden order developing below 17.5K in the heavy fermion material URu2Si2 has eluded identification for over twenty five years. This paper will review the recent theory of hastatic order,'' a novel two-component order parameter capturing the hybridization between half-integer spin (Kramers) conduction electrons and the non-Kramers 5f^2 Ising local moments, as strongly indicated by the observation of Ising quasiparticles in de Haas-van Alphen measurements. Hastatic order differs from conventional magnetism as it is a spinor order that breaks both single and double time-reversal symmetry by mixing states of different Kramers parity. The broken time-reversal symmetry simply explains both the pseudo-Goldstone mode between the hidden order and antiferromagnetic phases and the nematic order seen in torque magnetometry. The spinorial nature of the hybridization also explains how the Kondo effect gives a phase transition, with the hybridization gap turning on at the hidden order transition as seen in scanning tunneling microscopy. Hastatic order also has a number of new predictions: a basal-plane magnetic moment of order .01\mu_B, a gap to longitudinal spin fluctuations that vanishes continuously at the first order antiferromagnetic transition and a narrow resonant nematic feature in the scanning tunneling spectra.
• Spins, electrons and broken symmetries: Realizations of two-channel Kondo physics
Rebecca Flint and Piers Coleman
Comptes Rendus Physiques 15, 557 (2014).
(previous version available as arXiv:1403.3422)
 Adding a second Kondo channel to heavy fermion materials reveals new exotic symmetry breaking phases associated with the development of Kondo coherence. In this paper, we review two such phases, the "hastatic order" associated with non-Kramers doublet ground states, where the two-channel nature of the Kondo coupling is guaranteed by virtual valence fluctuations to an excited Kramers doublet, and "composite pair superconductivity," where the two channels differ by charge 2e and can be thought of as virtual valence fluctuations to a pseudo-isospin doublet. The similarities and differences between these two orders will be discussed, along with possible realizations in actinide and rare earth materials like URu2Si2 and NpPd5Al2.
• Emergent honeycomb lattice in LiZn2Mo3O8
Rebecca Flint and Patrick A. Lee
Phys. Rev. Lett. 111, 217201 (2013)
(previous version available as arXiv:1308.2642)
 We introduce the idea of emergent lattices, where a simple lattice decouples into two weakly-coupled lattices as a way to stabilize spin liquids. In LiZn2Mo3O8, the disappearance of 2/3rds of the spins at low temperatures suggests that its triangular lattice decouples into an emergent honeycomb lattice weakly coupled to the remaining spins, and we suggest several ways to test this proposal. We show that these orphan spins act to stabilize the spin-liquid in the J1-J2 honeycomb model and also discuss a possible 3D analogue, Ba2MoYO6 that may form a "depleted fcc lattice." * Editor's suggestion
• Chiral RKKY interaction in Pr2Ir2O7
Rebecca Flint and T. Senthil
Phys. Rev. B 87, 125147 (2013)
(previous version available as arXiv:1301.0815)
 Motivated by the potential chiral spin liquid in the metallic spin ice Pr2Ir2O7, we consider how such a chiral state might be selected from the spin ice manifold. We propose that chiral fluctuations of the conducting Ir moments promote ferro-chiral couplings between the local Pr moments, as a chiral analogue of the magnetic RKKY effect. Pr2Ir2O7 provides an ideal setting to explore such a chiral RKKY effect, given the inherent chirality of the spin-ice manifold. We use a slave-rotor calculation on the pyrochlore lattice to estimate the sign and magnitude of the chiral coupling, and find it can easily explain the 1.5K transition to a ferro-chiral state. * Editor's Suggestion
• Hastatic order in URu2Si2
Premala Chandra, Piers Coleman and Rebecca Flint
Nature 493, 621 (2013)
(previous version available as arXiv:1207.4828)
 The development of collective long-range order via phase transitions occurs by the spontaneous breaking of fundamental symmetries. Magnetism is a consequence of broken time-reversal symmetry while superfluidity results from broken gauge invariance. The broken symmetry that develops below 17.5K in the heavy fermion compound URu2Si2 has long eluded such identification. Here we show that the recent observation of Ising quasiparticles in URu2Si2 results from a spinor order parameter that breaks double time-reversal symmetry, mixing states of integer and half-integer spin. Such hastatic order hybridizes conduction electrons with Ising 5f2 states of the uranium atoms to produce Ising quasiparticles; it accounts for the large entropy of condensation and the magnetic anomaly observed in torque magnetometry. Hastatic order predicts a tiny transverse moment in the conduction sea, a collosal Ising anisotropy in the nonlinear susceptibility anomaly and a resonant energy-dependent nematicity in the tunneling density of states.
• Basal-Plane Nonlinear susceptibility: A Direct Probe of the Single-Ion Physics in URu2Si2
Rebecca Flint, Premala Chandra and Piers Coleman
Phys. Rev. B 86, 155155 (2012)
(also available as arXiv:1207.2433)
 The microscopic nature of the hidden order state in URu2Si2 is dependent on the low-energy configurations of the uranium ions, and there is currently no consensus on whether it is predominantly 5f2 or 5f3. Here we show that measurement of the basal-plane nonlinear susceptibility can resolve this issue; its sign at low-temperatures is a distinguishing factor. We calculate the linear and nonlinear susceptibilities for specific 5f2 and 5f3 crystal-field schemes that are consistent with current experiment. Because of its dual magnetic and orbital character, a Gamma5 magnetic non-Kramers doublet ground-state of the U ion can be identified by chi3ab(T) where we have determined the constant of proportionality for URu2Si2.
• Origin of the Large Anisotropy in the chi3 Anomaly in URu2Si2
Premala Chandra, Piers Coleman and Rebecca Flint
Conference Proceedings for Invited Talk at Materials and Mechanisms of Superconductivity in Washington, D.C. 2012
arXiv:1210.6425 (2012)
 Motivated by recent quantum oscillations experiments on URu2Si2, we discuss the microscopic origin of the large anisotropy observed many years ago in the anomaly of the nonlinear susceptibility in this same material. We show that the magnitude of this anomaly emerges naturally from hastatic order, a proposal for hidden order that is a two-component spinor arising from the hybridization of a non-Kramers Gamma5 doublet with Kramers conduction electrons. A prediction is made for the angular anisotropy of the nonlinear susceptibility anomaly as a test of this proposed order parameter for URu2Si2.
• The symplectic-N t-J model and sÂ± superconductors
Rebecca Flint and Piers Coleman
Phys. Rev. B 86, 184508 (2012)
also available at arXiv:1204.2302
 The possible discovery of sÂ± superconducting gaps in the moderately correlated iron-based superconductors has raised the question of how to properly treat sÂ± gaps in strongly correlated superconductors. Unlike the d-wave cuprates, the Coulomb repulsion does not vanish by symmetry, and a careful treatment is essential. Thus far, only the weak correlation approaches have included this Coulomb pseudopotential, so here we introduce a symplectic N treatment of the t-J model that incorporates the strong Coulomb repulsion through the complete elimination of on-site pairing. Through a proper extension of time-reversal symmetry to the large N limit, symplectic-N is the first superconducting large N solution of the t-J model. For d-wave superconductors, the previous uncontrolled mean field solutions are reproduced, while for sÂ± superconductors, the SU(2) constraint enforcing single occupancy acts as a pair chemical potential adjusting the location of the gap nodes. This adjustment can capture the wide variety of gaps proposed for the iron based superconductors: line and point nodes, as well as two different, but related full gaps on different Fermi surfaces.
• Composite pairing in a mixed-valent two-channel Anderson model
Rebecca Flint, Andriy Nevidomskyy and Piers Coleman
Phys. Rev. B 84, 064514 (2011)
(also available as arxiv 1103.1550)

 Using a two-channel Anderson model, we develop a theory of composite pairing in the 115 family of heavy fermion superconductors that incorporates the effects of f-electron valence fluctuations. Our calculations introduce â€œsymplectic Hubbard operators" an extension of the slave boson Hubbard operators that preserves both spin rotation and time-reversal symmetry in a large N expansion, permitting a unified treatment of anisotropic singlet pairing and valence fluctuations. We find that the development of composite pairing in the presence of valence fluctuations manifests itself as a phase-coherent mixing of the empty and doubly occupied configurations of the mixed valent ion. This effect redistributes the f-electron charge within the unit cell. Our theory predicts a sharp superconducting shift in the nuclear quadrupole resonance frequency associated with this redistribution. We calculate the magnitude and sign of the predicted shift expected in CeCoIn5.
Tandem Pairing in Heavy Fermion Superconductors
Rebecca Flint and Piers Coleman
Phys. Rev. Lett. 105, 246404 (2010)
(also available as arXiv:0912.2339)

 We consider the internal structure of a d-wave heavy-fermion superconducting condensate, showing that it necessarily contains two components condensed in tandem: pairs of quasiparticles on neighboring sites and composite pairs consisting of two electrons bound to a single local moment. These two components draw upon the antiferromagnetic and Kondo interactions to cooperatively enhance the superconducting transition temperature. This tandem condensate is electrostatically active, with an electric quadrupole moment predicted to lead to a superconducting shift in the nuclear quadrupole resonance frequency.
• Heavy electrons and the symplectic symmetry of spin
Rebecca Flint, Maxim Dzero, and Piers Coleman
Nature Physics 4, 643 - 648 (2008)
(also available as arxiv 0710.1126 with supplementary material at arxiv 0710.1128).

 Here, we introduce a new class of large-N expansion that uses symplectic symmetry to protect the odd time-reversal parity of spin and sustain Cooper pairs as well-defined singlets. We show that when a lattice of magnetic ions exchange spin with their metallic environment in two distinct symmetry channels, they can simultaneously satisfy both channels by forming a condensate of composite pairs between local moments and electrons. We then discuss the application of this two channel Kondo model to the heavy fermion superconductors, PuCoGa5 and NpPd5Al2. The inclusion of spin-orbit coupling and the crystal fields predicts a g-wave superconducting order parameter.
• Symplectic N and time reversal in frustrated magnetism
Rebecca Flint and Piers Coleman
Physical Review B 79, 014424(2009)
(also available as arxiv 0810.5144).

 In this paper, we develop a new large N treatment of the Heisenberg model based on symplectic-N, represent the spins by Schwinger bosons, which allows us study the boundaries between short-range and long-range order. This limit treats ferromagnetic and antiferromagnetic correlations simultaneously, exacting an energy cost for frustrating antiferromagnetic bonds. As an example, we treated the two dimensional J1-J2 model, where the symplectic-N phase diagram improves over previous large N treatments both at zero and finite temperatures.
• Magnetization and Spin State Crossover in the Multiferroic Ca3Co2-xMnxO6
Rebecca Flint, Hee-Taek Yi, Premala Chandra, Sang-Wook Cheong, and Valery Kiryukhin
Phys. Rev. B 81, 092402 (2010)
(also available as arXiv 0909.4773).

 Ca3Co2-xMnxO6(x ~ 0.96) is a multiferroic with spin-chains of alternating Co2+ and Mn4+ ions. The spin state of Co2+ remains unresolved, as there is a discrepancy between high temperature X-ray absorption (S= 3/2) and low temperature neutron (S= 1/2) measurements. Here we study the high-field magnetization using magnetic modeling and confirm the small Co moment. With crystal-field analysis, we show that neither spin orbit coupling nor Jahn-Teller distortions yield a small effective moment with large anisotropy at low temperatures within the high spin (S = 3/2) scenario, while the low spin (S=1/2) can explain both the small moment and large anisotropy. In order to unify the experimental results, we propose a spin-state crossover, and make a number of specific predictions for experiment.

### My PhD Thesis

PhD Thesis: Symplectic-N in strongly correlated materials
(Click for explanation of symplectic-N)
 Strongly correlated electrons provide a unique challenge to theorists as they sit at the intersection of the kinetic and potential energy scales, where traditional, perturbative many body techniques fail. To make progress, we must develop non-perturbative methods. One method that has had some success here is large N theory, which generalizes the number of components of the electron spin from 2 to N, providing an artificial perturbation expansion about a strongly correlated state which, if chosen properly, captures the essential physics. Large N has been heavily used in both the Kondo lattice and in frustrated magnetism, where SU(2N) is the traditional generalization of the electron spin group, SU(2). In choosing the large N group, we chose which symmetries to preserve and which to discard. Unfortunately, SU(2N) inadvertently loses the time inversion and charge conjugation properties of SU(2); while some generators invert under time reversal like spins, $\vec{S} \rightarrow -\vec{S}$, and remain neutral under charge conjugation, the others behave more like electric dipoles: neutral under time reversal and flipped by charge conjugation. To treat phenomena like frustrated magnetism and superconductivity, which relies on the formation of Cooper pairs, we must restrict ourselves to the subgroup of spin-like generators, SP(2N), a large N limit we call symplectic-N. This limit differs from the SP(2N) limit introduced by Sachdev and Read, which breaks the SU(2N) symmetry of the Hamiltonian down to SP(2N) in that the interaction Hamiltonian is constricted solely from symplectic spins. Symplectic-N has been successfully applied to frustrated magnetism, where it treats ferromagnetic and antiferromagnetic correlations simultaneously, and to the two channel Kondo model, where it treats the Kondo effect and superconductivity simultaneously. We are currently working to develop symplectic-N Hubbard operators to treat the t-J and Anderson models.

Last updated 21 February 2013