The frequency of the breathing mode of a two-dimensional Fermi gas with zero-range interactions in a harmonic confinement is fixed by the scale invariance of the Hamiltonian. Scale invariance is broken in the quantized theory by introducing the two-dimensional scattering length as a regulator. This is an example of a quantum anomaly in the field of ultracold atoms and leads to a shift of the frequency of the collective breathing mode of the cloud. In this work, we study this anomalous frequency shift for a two component Fermi gas in the strongly interacting regime. We measure significant upwards shifts away from the scale invariant result that show a strong interaction dependence. This observation implies that scale invariance is broken anomalously in the strongly interacting two-dimensional Fermi gas.Symmetries are an indispensable ingredient to any attempt of formulating a fundamental theory of nature. Yet, it is not allways true that one can make accurate predictions about the behaviour of some complex system based on the symmetries of its Hamiltonian alone. The fundamental reason behind this is the concept of symmetry breaking [1]. Symmetry violations often have drastic effects on the state of the system, for example when some metal breaks rotational invariance and becomes ferromagnetic. There are three different mechanisms through which a given system may violate some of the symmetries of its Hamiltonian: explicit, spontaneous and anomalous symmetry breaking [2].Quantum anomalies are violations of an exact symmetry of a classical action in the corresponding quantized theory [3]. They may occur when a cut-off has to be introduced to regularize divergent terms. This regulator may explicitly break some symmetry of the theory. If this symmetry is not restored even after the cut-off is removed at the end of the renormalization procedure, the symmetry is broken anomalously.Quantum anomalies are ubiquitous in quantum field theories and provide, important constraints on physical gauge theories like the standard model [4, 5] or on string theories [6, 7]. Whereas the formalisms of explicit and spontaneous symmetry breaking are frequently applied across many fields in physics [8][9][10], anomalous symmetry breaking is typically associated only with high energy physics. One exception was found in molecular physics [11,12] and here we report an observation of a quantum anomaly in the field of cold atom physics.A particular class of anomalies, called conformal anomalies, break the scale invariance of a theory, that is invariance of the Hamiltonian under r → λr. The most prominent examples are found in field theories like QED or QCD where the renormalized coupling constants depend on the energy scale and thus break scale invariance explicitly. In ordinary quantum mechanics the 1/r 2 -and the δ 2 -potential in 2D are well-known examples of conformal anomalies [13,14].Notably, the δ 2 -potential is used to model contact in-teractions in cold atom gases in two-dimensions as V int ∝ g 0 δ 2 (r i − r j ). Including the kinetic...

We study the effects of finite temperature on normal state properties of a metal near a quantum critical point to an antiferromagnetic or Ising-nematic state. At T ¼ 0, bosonic and fermionic self-energies are traditionally computed within Eliashberg theory, and they obey scaling relations with characteristic power laws. Corrections to Eliashberg theory break these power laws but only at very small frequencies. Quantum Monte Carlo (QMC) simulations have shown that, already at much larger frequencies, there are strong systematic deviations from these predictions, casting doubt on the validity of the theoretical analysis. We extend Eliashberg theory to finite T and argue that in the T range accessible in the QMC simulations above the superconducting transition, the scaling forms for both fermionic and bosonic self-energies are quite different from those at T ¼ 0. We compare finite T results with QMC data and find good agreement for both systems. We argue that this agreement resolves the key apparent contradiction between the theory and the QMC simulations.

The properties of quantum materials are commonly tuned using experimental variables such as pressure, magnetic field and doping. Here we explore a different approach: irreversible, plastic deformation of single crystals. We show for the archetypal unconventional superconductor SrTiO3 that compressive plastic deformation induces lowdimensional superconductivity significantly above the superconducting transition temperature (Tc) of undeformed samples. We furthermore present evidence for unusual normal-state transport behaviour that suggests superconducting correlations at temperatures two orders of magnitude above the bulk Tc. The superconductivity enhancement is correlated with the appearance of structural features related to selforganized dislocation structures, as revealed by diffuse neutron and X-ray scattering.These results suggest that deformed SrTiO3 is a potential high-temperature superconductor, and push the limits of superconductivity in this low-density electronic system. More broadly, we demonstrate the promise of plastic deformation and dislocation engineering as tools to manipulate electronic properties of quantum materials.

Quantum Monte Carlo (QMC) simulations of correlated electron systems provide unbiased information about system behavior at a quantum critical point (QCP) and can verify or disprove the existing theories of non-Fermi liquid (NFL) behavior at a QCP. However, simulations are carried out at a finite temperature, where quantum critical features are masked by finite-temperature effects. Here, we present a theoretical framework within which it is possible to separate thermal and quantum effects and extract the information about NFL physics at T = 0. We demonstrate our method for a specific example of 2D fermions near an Ising ferromagnetic QCP. We show that one can extract from QMC data the zero-temperature form of fermionic self-energy Σ(ω) even though the leading contribution to the self-energy comes from thermal effects. We find that the frequency dependence of Σ(ω) agrees well with the analytic form obtained within the Eliashberg theory of dynamical quantum criticality, and obeys ω2/3 scaling at low frequencies. Our results open up an avenue for QMC studies of quantum critical metals.

We study the dynamic response of a two-dimensional system of itinerant fermions in the vicinity of a uniform (Q = 0) Ising nematic quantum critical point of d−wave symmetry. The nematic order parameter is not a conserved quantity, and this permits a nonzero value of the fermionic polarization in the d−wave channel even for vanishing momentum and finite frequency: Π(q = 0, Ωm) = 0. For weak coupling between the fermions and the nematic order parameter (i.e. the coupling is small compared to the Fermi energy), we perturbatively compute Π(q = 0, Ωm) = 0 over a parametrically broad range of frequencies where the fermionic self-energy Σ(ω) is irrelevant, and use Eliashberg theory to compute Π(q = 0, Ωm) in the non-Fermi liquid regime at smaller frequencies, where Σ(ω) > ω. We find that Π(q = 0, Ω) is a constant, plus a frequency dependent correction that goes as |Ω| at high frequencies, crossing over to |Ω| 1/3 at lower frequencies. The |Ω| 1/3 scaling holds also in a non-Fermi liquid regime. The non-vanishing of Π(q = 0, Ω) gives rise to additional structure in the imaginary part of the nematic susceptibility χ (q, Ω) at Ω > vF q, in marked contrast to the behavior of the susceptibility for a conserved order parameter. This additional structure may be detected in Raman scattering experiments in the d−wave geometry. arXiv:1708.05308v1 [cond-mat.str-el]