Spring School on Modern Topics in Condensed Matter

Spiral spin liquids are a special kind of paramagnetic state that features a subextensive classical ground-state degeneracy related to a family of spin spirals whose ordering wave vectors form a submanifold of momentum space. As the number of their theoretical and experimental realizations grows, there is cumulative evidence that, under additional perturbations, spiral spin liquids constitute a promising platform for the emergence of exotic phases and excitations, including quantum spin liquids, multiple-$q$ states, and skyrmions. However, little is known about their response to quenched disorder. In this poster, we investigate how various types of defects affect the classical ground-state manifold of a spiral spin liquid on the honeycomb lattice. Among our results, we describe how different order-by-disorder mechanisms can arise, compete among themselves, and lead to spin-glass physics in these systems.

We analyze quantum fluctuation effects at the onset of charge or spin density wave order with a $2k_F$ wave vector ${\bf Q}$ in two-dimensional metals -- for the special case where ${\bf Q}$ connects a pair of hot spots situated at high symmetry points of the Fermi surface with a vanishing Fermi surface curvature. We compute the order parameter susceptibility and the fermion self-energy in one-loop approximation. The susceptibility has a pronounced peak at ${\bf Q}$, and the self-energy displays non-Fermi liquid behavior at the hot spots, with a linear frequency dependence of its imaginary part. The real part of the one-loop self-energy exhibits logarithmic divergences with universal prefactors as a function of both frequency and momentum, which may be interpreted as perturbative signatures of power laws with universal anomalous dimensions. As a result, one obtains a non-Fermi liquid metal with a vanishing quasiparticle weight at the hot spots, and a renormalized dispersion relation with anomalous algebraic momentum dependencies near the hot spots.

Differently from their fully-gapped counterpart, topologically non-trivial phases in nodal systems can only be understood in terms of momentum-dependent topological invariants defined on a submanifold enclosing the nodes. In the case of superconductors with a dx2-y2-gap symmetry, the non-zero winding number of the nodes leads to the appearance of Majorana flat-bands at two-dimensional regions of the (110) surface’s Brillouin zone which are bounded by the projections of the superconducting nodes. The characteristic momentum dependence of these topological bands can be probed by Angle-Resolved Photo-Emission Spectroscopy (ARPES), but the obtainment of a clean (110) surface remains a technical challenge. Hence, we propose a recently established approach to cleave crystals for angle-resolved photoemission studies in which the fracture propagation is controlled by means of micro-notches.

The ability to control the charger carrier density inside the solids is an important factor to realize different phase transitions in materials. This could not only be interesting for technological applications but also provide new insights about the fundamental properties of materials. In particular, inducing high charge carrier density into various two-dimensional materials has led to exotic phenomena such as insulator-metal phase transition and superconductivity [1, 2] . So far, different techniques have been used to achieve this. Meanwhile, electric double layer transistor (EDLT) is a highly promising platform as it can provide high charge carrier density of up to $10^{15}$ $cm^{-2}$ in its channel material. This is two orders of magnitude larger than that in the conventional transistors as a result of using ionic liquids instead of common solid dielectrics [3] . Here, I will first give a brief overview on the EDLTs, then I will present our experimental results of ionic liquid gated p-type tellurium (Te). Our results show the possibility of gate tuning insulator-metal transition and the crossover between weak localization (WL) and weak anti-localization (WAL) into the sample. The WAL becomes more pronounced as we increase the conductivity of the sample. Moreover, temperature-dependence of WAL showed e-e interaction is the main scattering mechanism of quantum decoherence in the material. More interestingly, we have shown the ability of controlling the spin-orbit interaction in Te by changing the applied gate voltage which could be interesting for spintronics application. [1] AM. Goldman, Annual Review of Materials Research 44, 45-63 (2014). [2] D. Costanzo et al., Nature nanotechnology 13, 483-488 (2018). [3] K. Ueno et al., Journal of the Physical Society of Japan 83, 3200 (2014).

We report finite-size topology in the quintessential time-reversal (TR) invariant systems, the quantum spin Hall insulator (QSHI) and the three-dimensional, strong topological insulator (STI): previously-identified helical or Dirac cone boundary states of these phases hybridize in wire or slab geometries with one open boundary condition for finite system size, and additional, topologically-protected, lower-dimensional boundary modes appear for open boundary conditions in two or more directions. For the quasi-one-dimensional (q(2-1)D) QSHI, we find topologically-protected, quasi-zero-dimensional (q(2-2)D) boundary states within the hybridization gap of the helical edge states, determined from q(2-1)D bulk topology characterized by topologically non-trivial Wilson loop spectra. We show this finite-size topology furthermore occurs in 1T'-WTe2 in ribbon geometries with sawtooth edges, based on analysis of a tight-binding model derived from density-functional theory calculations, motivating experimental investigation of our results. In addition, we find quasi-two-dimensional (q(3-1)D) finite-size topological phases occur for the STI, yielding helical boundary modes distinguished from those of the QSHI by a non-trivial magneto-electric polarizability linked to the original 3D bulk STI. Finite-size topological phases therefore exhibit signatures associated with the non-trivial topological invariant of a higher-dimensional bulk. Finally, we find the q(3-2)D STI also exhibits finite-size topological phases, finding the first signs of topologically-protected boundary modes of codimension greater than 1 due to finite-size topology. Finite-size topology of four or higher-dimensional systems is therefore possible in experimental settings without recourse to thermodynamically large synthetic dimensions.

$AgCrSe_2$ is a quasi-2D layered chalcogenide with a structure that alternates Ag layers and $CrSe_6$ octahedral layers. In oxygen-based delafossites, the choice of transition metal/rare earth metal ions has little effect in the band structure. However, replacing the chalcogenide in $AgCrO_2$ with Se to form its sister non-delafossite compound $AgCrSe_2$ promotes correlation effects and leads to the emergence of unconventional transport and magnetism, such as unconventional anomalous Hall Effect [1]. This study reports on transport measurements conducted on bulk single crystal $AgCrSe_2$. The temperature-dependent in-plane resistivity shows metallic behavior from 300 K to around 80 K, followed by an increase in resistivity proportional to -ln (T) below 80 K, which is a hallmark of the Kondo effect. This resistive behavior is suppressed by magnetic field. Additionally, the magnetoresistance curves overlap when scaled by the Kondo temperature, which is consistent with Schlottmann’s scaling theory and another signature of the Kondo effect. In summary, the resistivity and magnetoresistance measurements in $AgCrSe_2$ provide evidence of Kondo-like transport behavior. [1] Haijing Zhang, et al. Unpublished

Elastocaloric effect (ECE) provides people a powerful tool to probe the strain and temperature dependence of entropy. On one hand, with the 100-Sr2RuO4 ECE data, after a proper calibration procedure, is used to generate an entropy map on the temperature-strain plane. The entropy map reproduces the double peak of specific heat near the van Hove singularity point and further gives more information about the potential magnetic order at strain. On the other hand, our recent ECE measurement of 110- Sr2RuO4 samples focuses on a debate on whether the superconducting (SC) order parameter has more than one component. If the superconducting order parameter is degenerate and protected by lattice symmetry, the degeneracy will be lifted when the lattice symmetry is broken. Here we report the latest progress on elastocaloric measurement of Sr2RuO4 crystal with strain applied along <110>. Within our experimental precision, no signal indicating a second phase transition below Tc is observed. Combined with previous ECE measurements with strain applied along <100>, more stringent constraints on the nature of superconducting states at zero strain were placed by the absence of the second transition.

Laughlin states have recently been constructed on fractal lattices and have been shown to be topological in such systems. Some of their properties are, however, quite different from the two-dimensional case. On the Sierpinski triangle, for instance, the entanglement entropy shows oscillations as a function of particle number and does not obey the area law despite being topologically ordered, and the particle density is non-uniform in the bulk. Here, we investigate these deviant properties in greater detail on the Sierpinski triangle, and we also study the properties on the Sierpinski carpet and the T-fractal. We find that the density variations across the fractal are present for all the considered fractal lattices and for most choices of the number of particles. The size of anyons inserted into the lattice Laughlin state also varies with position on the fractal lattice. We observe that quasiholes and quasiparticles have similar sizes and that the size of the anyons typically increases with decreasing Hausdorff dimension. As opposed to periodic lattices in two dimensions, the Sierpinski triangle and carpet have inner edges. We construct trial states for both inner and outer edge states. We find that oscillations of the entropy as a function of particle number are present for the T-fractal, but not for the Sierpinski carpet. Finally, we observe deviations from the area law for several different bipartitions on the Sierpinski triangle.

Recent studies of van der Waals heterostructures have revealed several interesting phenomena, such as strongly correlated states, superconductivity of unknown origin, and 2D ferroelectricity. Information regarding these novel states can be gathered through investigating their signatures in collective modes, including phonons and plasmons. However, because many of these modes are on the few-meV energy scale, such investigation requires probing at Terahertz (THz) frequencies. Traditional far-field THz detection methods are challenging for these systems due to the micron-sized nature of 2D heterostructures. In this work, we drive the shear phonon mode of a thin layer of WTe2, and probe the emitted THz which is coupled into a waveguide using ultrafast transport methods. We track the behavior of the phonon as a function of excitation fluence. This study opens the door for further investigation of other phenomena in gate-tunable heterostructures, such as studying the role of this mode in a 2D ferroelectric material.

Cuprates show a lot of interesting physics (pseudogap phase, strange metal behaviour, unconventional superconductivity etc.) that is not well understood. Past experiments on overdoped cuprates have faced difficulties due to the rarity of high-quality samples compounding the usual issues that arise from surface reconstructions. Here we attempt to study overdoped Tl2201, which can be grown to show quantum oscillations, using recently developed microstructuring techniques to suppress the surface contributions. Focused Ion Beam technology allows us to cut precise geometries with high aspect ratios, thus enhancing the signal to noise ratio, but it introduces inhomogeneities in our samples. We correct this by annealing our devices, using high-temperature resistivity measurements as a probe for sample composition. This method of annealing also enables us to study the entire doping range with a single device, eliminating sample-to-sample variations in our measurements. We can take a further step and use 2D transport measurements to measure the sample resistivity and anisotropy simultaneously on a single device. We study the physics of this clean overdoped cuprate without any sample geometry, compositional variations or high contact resistances influencing our measurements, allowing us to effectively probe the underlying physics.

Using optical methods to investigate a material is a powerful noncontact method to explore fundamental physics. In our experiment, we use optics as a versatile microscope to investigate birefringence as well as thermal transport with micron-scale spatial resolution. It can be combined with an in-situ controllable uniaxial pressure device, which has recently been shown to be a powerful tuning parameter to control lattice symmetries in quantum materials. In this contribution, we present the thermal diffusivity and birefringence of an anisotropic material, Ca$_3$Ru$_2$O$_7$, which has structural domains at room temperature and can be tuned through a structural phase transition by lowering the temperature at ambient pressure.

The thermal Hall effect, defined as a heat current response transversal to an applied temperature gradient, is a central experimental probe of exotic electrically insulating phases of matter. A key question is how the interplay between magnetic and structural degrees of freedom gives rise to a nonzero thermal Hall conductivity (THC). Here, we present evidence for an intrinsic thermal Hall effect in the Heisenberg-Kitaev antiferromagnet and spin-liquid candidate Na$_2$Co$_2$TeO$_6$ brought about by the quantum-geometric Berry curvature of so-called magnon polarons, resulting from magnon-phonon hybridization. At low temperatures, our field- and temperature-dependent measurements show a negative THC for magnetic fields below 10 T and a sign change to positive THC above. Theoretically, the sign and the order of magnitude of the THC cannot be solely explained with magnetic excitations. We demonstrate that, by incorporating spin-lattice coupling into our theoretical calculations, the Berry curvature of magnon polarons counteracts the purely magnonic contribution, reverses the overall sign of the THC, and increases its magnitude, which significantly improves agreement with experimental data. Our work highlights the crucial role of spin-lattice coupling in the thermal Hall effect.

Fractals – objects with noninteger dimensions – occur in manifold settings and length scales in nature. In this work, we identify an emergent dynamical fractal in a disorder-free, stoichiometric, and three-dimensional magnetic crystal in thermodynamic equilibrium. The phenomenon is born from constraints on the dynamics of the magnetic monopole excitations in spin ice, which restrict them to move on the fractal. This observation explains the anomalous exponent found in magnetic noise experiments in the spin ice compound Dy2Ti2O7, and it resolves a long-standing puzzle about its rapidly diverging relaxation time. The capacity of spin ice to exhibit such notable phenomena suggests that there will be further unexpected discoveries in the cooperative dynamics of even simple topological many-body systems.

Sr$_2$RuO$_4$ under uniaxial pressure undergoes a Lifshitz transition [1]. It has recently been shown that the electronic Lifshitz transition results in a pronounced lattice softening which can be observed through measurements of the Young's Modulus [2]. The Young's Modulus has previously been measured using both force and displacement capacitors on the uniaxial pressure cell [3]. We present a new technique using AC stresses and strains which allows for the direct measurement of the Young's Modulus. In addition, the AC stress-strain measurements also allow to determine imaginary part of the Young’s modulus, which can be indicative of slow lattice relaxations. Through these experiments on Sr$_2$RuO$_4$ we prove the viability of this technique. [1] Sunko et al., npj Quantum Mater. 4, 46 (2019) [2] Noad et al., submitted (2023). [3] Barber et al., Review of Scientific Instruments 90, 023904 (2019) Authors: C. I. O’Neil, Z. Hu, N. Kikugawa, D. A. Sokolov, A.P. Mackenzie, H. M. L. Noad, E. Gati

We investigate how an optical cavity can modify electron-phonon coupling by developing a fully quantum-mechanical treatment of the structural and electronic properties of the Su-Schrieffer-Heeger model coupled to quantum light. We perform numerical calculations using the exact diagonalization method, and assess the effects of the cavity for both the ground and excited states. We show how including correlation between all the constituents of the system (electrons, nuclei, and photons) gives rise to so called phonoritons, and we compare our treatment to an approach based on the Peierls substitution method. Our results highlight some important factors to consider when treating light-matter interactions.

A three-level system can be used in a $\Lambda$-type configuration in order to construct a universal set of quantum gates through the use of non-Abelian nonadiabatic geometrical phases. Such construction allows for high-speed operation times which diminish the effects of decoherence. This might be, however, accompanied by a breakdown of the validity of the rotating-wave approximation (RWA) due to the comparable timescale between counter-rotating terms and the pulse length, which greatly affects the dynamics. Here, we investigate the trade-off between dissipative effects and the RWA validity, obtaining the optimal regime for the operation of the holonomic quantum gates.

With the observation of superconductivity in Sr-doped infinite-layer nickelate Nd0.8Sr0.2NiO2 research interest in this material class intensified. We used ozone assisted molecular beam epitaxy to grow RNiO3 thin films (R=La,Pr) and investigated the subsequent topotactic softchemistry reaction, needed to synthesize the square-planar phase, at different stages of reduction by x-ray absorption spectroscopy. We observe the evolution of the Ni oxidation state and that the process is laterally homogeneous down to length scales of 50 nm. To reach the superconducting phase hole doping of the infinite-layer nickelates is required with an optimal doping level around x=0.2. This can be achieved by self-doping in quintuple-layer Ruddlesden-Popper nickelates or alkaline-earth doping, Ca or Sr, in infinite-layer films. Using angle-resolved photoemission spectroscopy (ARPES) we studied changes in the Fermi surface upon alkaline-earth doping in (La,Ca)NiO3.

Fractional excitations produced scattering continua in linear response because they are always created as groups of multiple particles. This makes unambiguous observation challenging, as it is difficult to distinguish such a continuum from the broadening produced by disorder or finite lifetimes. Two-dimensional coherent spectroscopy (2DCS) is a non-linear spectroscopic method which can solve this problem by resolving the continuum into a set of sharp responses. Previous theoretical discussion of the technique has focussed on simplified models; here we propose an experimental setting in which it could be used to probe fractionalised excitations in a real material. In an applied [110] magnetic field, the rare earth pyrochlore $Ce_2Zr_2O_7$ is predicted to exhibit chain-like structures, which are decoupled from one-another at the mean field level. Within this treatment, we can calculate the 2DCS response in terms of anisotropic XYZ spin-1/2 chains, and we demonstrate that clear signatures of fractionalised quasiparticle excitations should be observable in the 2DCS response of $Ce_2Zr_2O_7$.

Dual-unitary circuits are paradigmatic examples of exactly solvable yet chaotic quantum many- body systems, but solvability naturally goes along with a degree of non-generic behaviour. By investigating the effect of weakly broken dual-unitarity on the spreading of local operators we study whether, and how, small deviations from dual-unitarity recover fully generic many-body dynamics. We present a discrete path-integral formula for the out-of-time-order correlator and use it to recover a butterfly velocity smaller than the light-cone velocity, $v_B < v_{LC}$ , and a diffusively broadening operator front, two generic features of ergodic quantum spin chains absent in dual-unitary circuit dynamics. We find that the butterfly velocity and diffusion constant are determined by a small set of microscopic quantities and that the operator entanglement of the gates plays a crucial role.

The ultra-long mean free path in delafossite oxides, which are among the most highly conducting materials known, has enabled the study of new transport regimes [1]. In delafossite oxides, the nearly undisturbed motion of conduction electrons at low temperatures has been established to result from low defect scattering due to the high perfection of the atomic arrangement in the as-grown crystals [2]. More highly conducting metals are found in perovskite and perovskite related structures with, among others, SrMoO3 in the perovskite structure and ReO3 in its related own structure type [3]. Especially SrMoO3 has sparked interest since the first and only so far reported single-crystals show a resistivity as low as 5 μΩ cm at room temperature [4], however, the growth of SrMoO3 single crystals is challenging since the Mo4+ oxidation state is only stable in a very limited window of oxygen partial pressure during synthesis conditions. Here, we present the growth of single-crystals of this fascinating material and first structural characterization. The small dimensions of the grown single-crystals necessitate the fabrication of microstructured devices in order to characterize transport properties of the material. With the help of synthesis effort of new perovskite-related oxides and microstructured transport measurements we aim to establish the origin of ultra-high conductivity in this structural family. [1] Bachmann, Maja D., et al. Nature Physics 18, 7, (2022), 819–24. [2] Sunko, V., P. H. McGuinness, et.al. Physical Review X 10, 2, (2020), 021018. [3] Goodenough, J. B., Reports on Progress in Physics 67, 11, (2004), 1915. [4] Nagai, Ichiro, et al. Applied Physics Letters 87, 2, (2005), 024105.

Will be submitted asap

Recently, there have been experimental indications that in the quantum Hall bilayer at $\nu_T = 1$, interlayer electron-hole pairs form at larger layer separations than expected. Furthermore, a numerical study showed that there is a stable pairing between composite fermion (CF) electrons and holes in different layers; favouring the $s$-wave channel. Here, we formulate a Chern-Simons (CS) theory for CF-electrons in one layer and CF-holes in the other. Calculating an effective action for the CS gauge field fluctuations around the saddle-point yields an effective attraction between the CFs in the two layers. This results in a stable pairing of CF electrons and holes. Contrary to CF electron-electron pairing, the pairing symmetry is the one of an $s$-wave, which can be explained by an emergent time-reversal-symmetry of the CF electron-hole bilayer. In addition, we propose an experiment to distinguish between CF electron-electron and CF electron-hole pairing by introducing a small, charge-conserving imbalance between the layers. Our finding presents a microscopic understanding of the above-mentioned numerical and experimental results, and also introduces a novel means for addressing unresolved questions in quantum Hall bilayers.

GeSn shows promise for a range of optoelectronic device applications because of its tunable band gap and potential for monolithic integration on Si platforms [1]. To evaluate the electrical properties of GeSn:In thin films, we carry out resistivity and Hall effect measurements at temperatures 150-300K and magnetic fields varied between -5T and +5T using the Van der Pauw configuration [2]. GeSn:In was epitaxially grown by Molecular Beam Epitaxy (MBE) on a Ge(001) substrate, of nominal resistivity >30 Ohmcm. The average In concentration in the film was measured to be 1.2E18 $cm^{-3}$ by Secondary Ion Mass Spectroscopy (SIMS). Despite the p-type doping of the GeSn:In film, we obtain a negative Hall coefficient at 300K. We observe a transitional behavior at 275K, and p-type doping, as expected, for lower temperatures. We measure non-linear dependence of the Hall resistance on the magnetic field, which we determine to be due to parallel contributions from the film and Ge substrate. A two-carrier model [3] provides a good fit for the Hall resistance data at temperatures under 250K and indicates the presence of p-type impurities in the Ge substrate contributing to conduction. For temperatures over 250K, we suspect that we also begin to see the effects of intrinsic conduction in the Ge substrate.We aim to perform a three-carrier fit to confirm this [4]. References: [1] J. Zheng et al., J. Semicond. 39, 061006 (2018) [2] L.J. Van der Pauw, Phillips Tech. Rev. 20, 220 (1958) [3] G. Pettinari et al., Appl. Phys. Lett. 101, 222103 (2012) [4] T. Harman et al., J. Phys. and Chem. of Solids, 28 (10), 1995 (1967)

The antiferromagnetic topological insulator phase is a foundational realization of three- dimensional topological phases of matter with magnetic order. It is furthermore an example of an axion insulator and condensed matter platform for realizing exotic axion dynamics of high-energy physics. Experimental evidence of the axion insulator phase in MnBi2Te4 for thin-film samples—a quasi-(3-1)-dimensional (q(3-1)D) geometry—therefore motivates investigation of finite-size topo- logical (FST) phases derived from the axion insulator phase. Here, we show the AFM TI does realize finite-size topological phases for the q(3-1)D geometry, with open-boundary conditions and small system size in one direction. We first characterize the FST phase diagram in the q(3-1)D bulk using Wannier spectral flow. We also confirm the defining response signature of the underly- ing 3D AFM TI phase, due to the topologically non-trivial magnetoelectric polarizability, persists in this geometry but only for the topologically non-trivial finite-size topological regions. We then open boundary conditions in a second direction to confirm the additional bulk-boundary corre- spondence of the finite-size topological phases, finding q(3-2)D topologically-protected, gapless edge modes. The co-existence of the q(3-2)D topologically non-trivial edge states with a topological response associated with the 3D bulk topological invariant, the magnetoelectric polarizability, confirms finite-size AFM topological phases occur and should be sought experimentally for AFM TI candidates MnBi2Te4(Bi2Te3)n in thin film geometries. This further demonstrates that finite-size topology is a generic feature of topological phases and very relevant experimentally.