Elastic Manipulation and Dynamics of Quantum Materials

Light-matter interaction is a powerful tool to probe the properties of electrons and phonons in correlated materials. A particularly promising technique, known as multidimensional spectroscopy, consists of perturbing the system with a sequence of time-spaced coherent light pulses in the terahertz or optical range. The response of the system to such perturbation is inherently non-linear and yields a multidimensional spectrum by Fourier transforming it with respect to the pulse delays. The spectrum contains features that provide information about the nature, intrinsic lifetimes, and interaction of the quasiparticle excitations that are not easily accessible in linear spectroscopy. In this talk, I will discuss the prospect of using multidimensional spectroscopy to directly detect quantum coherence in many-body systems and differentiate between electronic orders. I will focus on multidimensional Raman spectroscopy and argue that it can be used to uniquely identify an electronic nematic liquid phase that was recently proposed in tetragonal BaNi$_2$As$_2$ [1]. Characterizing this liquid phase can be challenging since linear Raman spectroscopy is also consistent with a solid nematic phase, where tetragonal symmetry is broken but spatial orthorhombic domains coexist and a spatial domain average yields a fourfold symmetric response. In sharp contrast with linear Raman spectroscopy, I will show that the theoretically calculated multidimensional Raman spectrum has unique features associated with a dynamical nematic order parameter that is characteristic of the liquid phase. This allows for an unambiguous distinction between the nematic liquid and the nematic solid phase. [1] Y. Yao, R. Willa, T. Lacmann, S.-M. Souliou, M. Frachet, K. Willa, M. Merz, F. Weber, C. Meingast, R. Heid, A.-A. Haghighirad, J. Schmalian, and M. Le Tacon, Nature Communications 13, 4535 (2022).

From the outset of research into femtomagnetism, the field in which spins are manipulated by light on femtosecond or faster time scales, several questions have arisen and remain highly debated: How does the light interact with spin moments? How is the angular momentum conserved between the nuclei, spin, and angular momentum during this interaction? What causes the ultrafast optical switching of magnetic structures? What is the ultimate time limit on the speed of spin manipulation? What is the impact of nuclear dynamics on the light-spin interaction? In my talk I will advocate a parameter free ab-initio approach to treating ultrafast light-matter interactions, and discuss how this approach has led both to new answers to these old questions but also to the uncovering of novel and hitherto unsuspected early time spin dynamics phenomena [1,2]. In particular I will show that selective excitation of optical phonon modes exert a strong influence on femtosecond demagnetisation, generating an additional loss of moment within 40 femtoseconds [3] in laser pumped materials. Amongst the available modes that could be optically excited, we identify a strong spin-phonon coupled mode that dominates the early spin dynamics. Underpinning this enhanced loss of moment we deduce a new physical mechanism of inter-site charge transfer, dominant in the minority channel. Our finding demonstrates that the nuclear system, typically assumed to play a role of an energy sink aiding remagnetization of the spin system, can play a profound role in controlling femtosecond demagnetization of magnetic materials. In the second part of the talk I address the question of valley control in 2d transition metal dichalcogenides (TMDC), with current understanding that it couples exclusively via circularly polarized light. In our work we show that on femtosecond time scales valley coupling is a much more general effect. We find that two time separated linearly polarized pulses allow almost complete control over valley excitation, with the pulse time difference and polarization vectors emerging as key parameters for valley control. Finally, I discuss how hybrid pulses combining gap tuned circularly polarized light and linearly polarized THz light I show leads to complete control over valley current states in TMDCs. [1] Dewhust et al., Nano Lett. 18, 1842 (2018). [2] Siegrist et al. Nature 571, 240 (2019) [3] Sharma et al. Sci. Advs. 8, eabq2021 (2022) [4] Sharma et al. Optica 9 (8), 947-952 (2022)

Strontium ruthenate Sr${}_2$RuO${}_4$ is an unconventional superconductor whose pairing symmetry has not been fully clarified, despite more than two decades of intensive research. Recent NMR Knight shift experiments have rekindled the Sr${}_2$RuO${}_4$ pairing debate by giving strong evidence against all odd pairings, including chiral $p$-wave pairing that was for a long time the leading pairing candidate. Here, we exclude a large number of possible pairing states by analyzing recent elastocaloric measurements [YS. Li et al., Nature 607, 276-280 (2022)]. Among unconventional even pairings, we find that only superconducting states with large $d_{x^2 - y^2}$-wave or $\{d_{xz} \mid d_{yz}\}$-wave admixtures are able to explain the elastocaloric experiment. Among $\{d_{xz} \mid d_{yz}\}$-wave admixtures, only those that take the form of harmonics specific to body-centered lattices count. Hence $g_{xy(x^2-y^2)}$-wave and $d_{xy}$-wave pairings are excluded as possible dominant even pairing states.

I will discuss how coherent electromagnetic radiation at Tera-Hertz frequencies can be used to drive complex solids periodically, controlling the coupling between their collective excitations. These drives give rise to non-thermal states with unconventional types of microscopic order and new functional properties. Important examples involve the nonlinear control of the crystal lattice, used to induce magnetic order, ferroelectricity and non-equilibrium superconductivity at high temperatures.

One of the apparent difficulties for New Materials Physics is how to identify promising phase spaces to explore or study. In essence, with hundreds of thousands of possible compounds (known and unknown) to consider, how can promising materials be discovered? The design and discovery of new strongly correlated electron systems or quantum materials is essentially a negotiation with Nature. As with any negotiation, it is important to be as flexible as possible while still holding on to the key points that are vital. In this talk I will try to illustrate how desires can be translated into specific new materials growth efforts. For example, how “wanting a low degeneracy, topological non-trivial compound that we could readily study with ARPES” can lead directly to the identification and study of RhBi2. Another example is how a desire to discover new quantum critical materials can be translated into searches near collapsed tetragonal phase transitions or the study of ternary compounds that include an immiscible pair of elements. NOTE: one of the goals of this talk it to provide my theoretical colleagues some insight into how experimentalists translate complex theoretical ideas into very primitive attempts to shave the dice in this cosmic game of craps.

I will discuss the commonalities between superconductivity near the onset of a magnetic order in Bernal bilayer graphene at a finite displacement field and in doped FeSe near the onset of a nematic order. In both cases, I argue that the pairing interaction, mediated by soft fluctuations of the order parameter, is attractive, but, contrary to more known cases, one needs to go beyond PRA to obtain such an interaction. I will argue that, as a consequence, soft-mode-mediated pairing interaction becomes dominant only in a narrow range near an instability. I will also discuss the cases when soft-mode mediate pairing interaction is repulsive. Here, I will argue that superconductivity is induced by either a magnetic field or by a spin-orbit coupling. For doped FeSe, I will argue that the resulting pairing state is rather unconventional. In particular, there is no discontinuity of the specific heat at Tc.

I will present two examples where orbital-dependent transport could account for the strain dependence of transport properties. In Sr$_2$RuO$_4$, uniaxial stress applied along a <100> lattice direction drives the largest Fermi surface through a Lifshitz transition from an electron-like to an open geometry. The Hall effect becomes more electron-like across this transition, opposite to expectations from the change in Fermi surface topology. This result could be explained by a drastic decrease in the electron-electron scattering rate on sections of Fermi surface with xy orbital character. For FeSe, strain tuning was used to obtain the resistive anisotropy within the nematic state, which was found to have a nonmonotonic temperature dependence. The qualitative form is potentially explainable by strong scattering on sections of Fermi surface with yz orbital character.

In two-dimensional electron systems with broken inversion and time-reversal symmetries, a Josephson junction reveals an anomalous response: the supercurrent is nonzero even at zero phase difference between two superconductors. We consider details of this peculiar phenomenon in the planar double-barrier configurations of hybrid circuits, where the noncentrosymmetric normal region is described in terms of the paradigmatic Rashba model of spin-orbit coupling. We analyze this anomalous Josephson effect by means of both the Ginzburg-Landau formalism and the microscopic Green's functions approach in the clean limit. The magnitude of the critical current is calculated for an arbitrary in-plane magnetic field orientation, and anomalous phase shifts in the Josephson current-phase relation are determined in terms of the parameters of the model in several limiting cases.

The superconducting state of Sr2RuO4 emerges from a strongly correlated and very clean Fermi liquid normal state, for which the properties are extraordinarily well characterized. For these reasons, there is a general expectation for full understanding of the mechanism and ground state symmetry. While our recent 17O NMR studies are incompatible with the long-held understanding that Sr2RuO4 is an odd-parity (p-wave) superconductor, several questions about the superconducting state remain unresolved. In this context, we examined the normal and superconducting states of Sr2RuO4 while subjected to variable (B1g) stress. The stress drives the Fermi energy through a van Hove singularity, resulting in a reconstructed Fermi surface. Tuning to the Lifshitz transition manifests in a magnetic response that is strongly nonlinear in field and a logarithmic temperature dependence persisting over 100s K. Nevertheless, a quasiparticle description remains consistent with the observations. At higher stresses, a magnetically ordered ground state is inferred from mu-SR measurements. We employ NMR spectroscopy and relaxation measurements to explore the nature of the magnetic phase, and its possible connection to the nearby superconducting state.

I will present a comparative study of the phonon anomalies and the electronic gap features in the infrared response of the weakly coupled two-leg-ladders in Sr$_{14-x}$Ca$_x$Cu$_{24}$O$_{41}$ (SCCO) and the planar high-$T_c$ superconductor YBa$_2$Cu$_3$O$_{6+x}$ (YBCO). In particular, I will highlight some surprising similarities with respect to the gap features in the electronic response of these seemingly rather different cuprates. The implication for SCCO is that local superconducting pairing correlations occur within the ladders while a macroscopic superconducting state would require a stronger coupling between the ladders (and thus can be induced by applying high pressure). The implication for the planar YBCO is that collective degrees of freedom probably make an important contribution to the low-energy electronic response.

In a metal with multiple Fermi pockets, the formation of s-wave superconductivity can both be conventional due to electron-phonon coupling or unconventional due to spin fluctuations. We analyze the hexagonal diboride CrB2 which is found to be an itinerant antiferromagnet at ambient conditions and turn superconducting upon increasing pressure. While the high pressure behavior of Tc suggests conventional s_++-wave pairing, we find that spin fluctuations mediating unconventional s_+_-wave pairing form a significant contribution in the vicinity of the antiferromagnetic dome. As the symmetry class of the s-wave state is independent of its underlying mechanism, we argue that CrB2 is a realization of a hybrid s-wave superconductor where unconventional and conventional s-wave mechanisms team up to form a joint superconducting dome.

Charge density waves and other forms of nesting-driven order on hexagonal lattices remain an exciting space for studies of correlated electron physics, in some cases, also in the setting of topologically nontrivial band structures. Recent examples range from proposed nematic correlations to orbital antiferromagnetism in kagome lattices with nested saddle points, and, in several of these new examples, the density wave order is accompanied by a near degeneracy of lattice distortion types. In this talk, I will try and motivate several of these new hexagonal compounds as promising platforms for strain-based studies and elastic control of their unusual properties.

I reflect on the current theoretical status quo of electronically mediated vs. phonon-mediated electronic order in kagome metals.

Using a kinetic equation approach we calculate the dynamics of collective amplitude and phase modes in the incommensurate charge-density wave state of K$_{0.3}$MoO$_3$ (``blue bronze''). Our approach goes beyond the random-phase approximation and allows us to calculate also the lifetime of the collective modes. With the exception of the lowest phase mode our theoretical results agree quantitatively with recent experiments using optical pump terahertz-probe spectroscopy.

Soumendra Nath Panja$^1$, Anton Jesche$^1$, Nan Tang$^1$, Bin Shen$^1$, Philipp Gegenwart$^1$ $^1$ Experimental Physics VI, Center for Electronic Correlations and Magnetism, Institute of Physics, University of Augsburg, 86135 Augsburg, Germany Heavy-fermion metals like prototypical YbRh$_2$Si$_2$ (YRS) are governed by the interplay between Kondo- and RKKY interaction, which can be tuned by chemical substitution, pressure or magnetic field. We aim to introduce uniaxial strain (compressive and tensile) as new control parameter for quantum criticality in heavy-fermions. For the case of well-studied YRS, it could potentially reveal important new insights. YRS orders magnetically below 70 mK and the nature of its magnetic field-tuned quantum critical point (QCP) has been controversially discussed. Since hydrostatic/uniaxial pressure enhances T$_N$, volume expansion/tensile strain is required to tune through a zero-field QCP, not realized so far. We report the first electrical resistivity measurements of YRS under compressive and tensile strain and first focus our attention on T$_max$, the temperature of a resistivity maximum, arising above 100 K from the Kondo scattering and crystal electric field splitting. A systematic evolution of T$_max$ by compressive and tensile strain tuning is observed. Comparison with previous data under hydrostatic pressure and negative chemical pressure for Ge-substituted YRS suggests that the Kondo interaction in YRS can be effectively tuned by uniaxial strain. This opens up the possibility to tune pure YbRh2Si2 at zero magnetic field through its quantum critical point and follow in-situ the evolution of non-Fermi liquid behavior and the Hall coefficient.

Different phases of matter can be distinguished by symmetry, order parameters and topological properties. In this talk we will discuss the classification of magnetically ordered crystals according to recently studied spin symmetries [1]. Spin symmetries consider pairs of operations in spin and crystal space and remarkably reveal an unusual magnetic class. This unconventional class, altermagnetism, is distinct from ferromagnets and antiferromagnets. It is characterized by an unusual alternating spin order in electronic momentum space in d, g, i -wave form that breaks time reversal symmetry and is spin-compensated and anisotropic [1,2,3]. In the second part of the talk we will discuss possible non-trivial band topologies and spintronic effects in altermagnetics [1-4] and the first experimental evidence of a Berry phase breaking time-reversal symmetry in ruthenium oxide [5,6]. Finally, we will consider the possibility of elastic tuning of altermagnets due to their strongly entangled crystal and magnetic ordering [1,2]. References [1] Šmejkal, L., Sinova, J., and Jungwirth, T., Phys. Rev. X 12, 031042 (2022), Phys. Rev. X 12, 040501 (2022) [2] Šmejkal, L. et al., Science Advances 6, eaaz8809 (2020), arXiv:1901.00445 [3] Mazin, I.I et al., PNAS 118 (42) e2108924118 (2021) [4] Šmejkal, L., Birk Hellenes, A., Gonzalez-Hernandez, R., et al., Phys. Rev. X, 12, 011028 (2022) [5] Feng, Z., Zhou, X., Šmejkal, L. et al., Nature Electron. 5, 743 (2022). https://doi.org/10.1038/s41928-022-00866-z [6] Šmejkal, L., MacDonald, A.H., Sinova, J., Nakatsuji, S., and Jungwirth, T., Nature Reviews Materials 7, 482–496 (2022)

Superconductivity in low carrier density metals challenges the conventional electron-phonon theory due to the absence of retardation required to over- come Coulomb repulsion. Here we demonstrate that pairing mediated by energy fluctuations, ubiquitously present close to continuous phase transi- tions, occurs in dilute quantum critical polar metals and results in a dome-like dependence of the superconducting Tc on carrier density, characteristic of non-BCS superconductors. In quantum critical polar metals, the Coulomb repulsion is heavily screened, while the critical transverse optical phonons decouple from the electron charge. In the resulting vacuum, long-range attractive interactions emerge from the energy fluctuations of the critical phonons, resembling the gravitational interactions of a chargeless dark matter universe. Our estimates show that this mechanism may explain the critical temperatures observed in doped SrTiO3. We provide predictions for the enhancement of superconductivity near polar quantum criticality in two- and three-dimensional materials that can be used to test our theory. Work carried out by Pavel Volkov, Premi Chandra and Piers Coleman Nature Communications, 13:4599 (2022)

Laser excitation leads to out of equilibrium dynamics of electronic, phononic and spin systems. A major question is the flow of angular momentum and energy between the three subsystems. I will discuss theoretical development to describe out-of-equilibrium electron and phonon populations together with Boltzmann theory that elucidates how energy is transfered from laser-excited hot electrons to which phonons and how non-equilibrium phonons thermalize with one another. Ultrafast laser-excitation of a ferromagnet leads furthermore to a remarkably fast quenching of its equilibrium magnetization on the femtosecond timescale, the origin of which is still being debated. The fast demagnetization offers possible ways to alter the magnetic moments on femtosecond time scales, i.e., much faster than timescales typical for (Landau-Lifshitz-Gilbert) magnetization dynamics. We investigate the ultrafast demagnetization in elemental ferromagnets (Ni, Fe) as well as in FePt, using real-time time-dependent density functional theory (TD-DFT). Specifically, we investigate the influence of spin-orbit coupling, which is shown to play a significant role in the demagnetization. We elucidate how optical excitations can bring about demagnetization and we show that a significant contribution of the demagnetization is due to quenching of the spin angular momentum as compared to the contribution from the orbital angular momentum. To study the transfer of angular momentum to the lattice, i.e., spin-phonon coupling, we include motions of the atoms through Ehrenfest dynamics and search for evidence for non-equilibrium motions of atoms with orbital angular momentum.

Motivated by recent experiments on pump-induced polar ordering in the quantum paraelectric $SrTiO_3$, we study a driven phonon system close to a second order phase transition. Analyzing its classical dynamics, we find that sufficiently strong driving leads to transitions into polar phases whose structures, determined by the light polarization, are not all accessible in equilibrium. In addition, for certain intensity profiles we demonstrate the possibility of two-step transitions as a function of fluence. For even stronger field intensities, the possibility of period-doubling and chaotic behavior is demonstrated. Finally we develop a generalized formalism that allows us to consider quantum corrections to the classical dynamics in a systematic fashion. We predict a shift in the critical pump fluence due to quantum fluctuations with a characteristic dependence on the fluence increase rate, which can be observed in experiments. Talk based on Z. Zhuang, A. Chakraborty, P. Chandra, P. Coleman and P.A. Volkov, arXiv:2301.06161.

Organic charge-transfer salts of the family $\kappa$-(BEDT-TTF)$_2X$ are well known to show a plethora of interesting electronic phases, originating from the interplay of varying degrees of correlations, frustration induced by their triangular lattice geometry as well as electron-lattice coupling. Surprisingly, only little experimental work is available discussing their phase diagrams as a function of uniaxial pressure, even though it would offer a natural way to precisely control the triangular-lattice geometry, characterized by the frustration parameter $t^\prime/t$. In this talk, I will discuss the response of $\kappa$-(BEDT-TTF)$_2$Cu$_2$(CN)$_3$ – a compound which has been discussed for many years as one of the most promising spin-liquid candidate systems – to uniaxial pressure. Using the novel thermodynamic method of elastocaloric effect measurements, we map out its phase diagram as a function of uniaxial pressure for the first time. In our study, we cover a wide range of $t^\prime/t$ values, ranging from $\sim\,$0.75 to the isotropic limit of $t^\prime/t$= 1. The resulting phase diagram will be discussed in the context of the highly-debated question of the ground state of this compound.

Phonons play a crucial role in many properties of solid state systems, such as thermal and electrical conductivity, neutron scattering and associated effects or superconductivity. Hence, it is expected that topological phonons will also lead to rich and unconventional physics and the search of materials hosting topological phonons becomes a priority in the field. In this talk I will present a methodology to identify topological phonons in materials as well as charge-density waves instabilities. In particular, we will focus in some of these instabilities and identify a vdW layered materials as possible candidate for CDW and we explore the coupling of Dirac fermions with it. Finally, we present a theoretical study of light-matter coupling to induce phase transitions by means of non-linear phononics.

The third law of thermodynamics states that the entropy of any system in equilibrium has to vanish at absolute zero temperature. At nonzero temperatures, on the other hand, matter is expected to accumulate entropy near a quantum critical point, where it undergoes a continuous transition from one ground state to another1. We determine, based on general thermodynamic principles, the spatial-dimensional profile of the entropy S near a quantum critical point and its steepest descent in the corresponding multidimensional stress space.We demonstrate this approach for the canonical quantum critical compound CeCu6????xAux near its onset of antiferromagnetic order. We are able to link the directional stress dependence of S to the previously determined geometry of quantum critical fluctuations. Our demonstration of the multidimensional entropy landscape provides the foundation to understand how quantum criticality nucleates novel phases.

At a quantum phase transition, the ground state of a system changes as a function of a non-thermal control parameter. In a solid, the associated quantum critical degrees of freedom generically couple to the crystal lattice. This coupling is potentially able to change the universality class of the quantum critical point. We discuss various scenarios where this is realised. The coupling is necessarily non-perturbative when the order parameter couples bilinearly to strain as it is the case for quantum critical endpoints or nematic quantum criticality. If the strain couples only to the square of the order parameter, it is non-perturbative at weak coupling if the effective dimension d+z, with the spatial dimension d and the dynamical exponent z, is smaller than 2/ν, where ν is the correlation length exponent. We discuss a specific example and show that non-perturbative effects might also arise if this criterion is not fulfilled but the coupling exceeds a critical threshold.

Motivated by the report of superconductivity in bilayer $La_3Ni_2O_7$ at high pressure, we examine the interacting electrons in this system. First-principles many-body theory is utilized to study the normal-state electronic properties. Below 100\,K, a multi-orbital non-Fermi liquid state resulting from loss of Ni-ligand coherence within a flat-band dominated low-energy landscape is uncovered. The incoherent low-temperature Fermi surface displays strong mixing between Ni-$d_{z^2}$ and Ni-$d_{x^2−y^2}$ orbital character. In a model-Hamiltonian picture, spin fluctuations originating mostly from the Ni-$d_{z^2}$ orbital give rise to strong tendencies towards a superconducting instability with $d_{x^2−y^2}$ order parameter. The dramatic enhancement of $T_c$ in pressurized $La_3Ni_2O_7$ is due to stronger Ni-$d_{z^2}$ correlations compared to those in the infinite-layer nickelates.