Elastoresistivity as a probe of electronically driven rotational symmetry breaking and its application to the hidden order state in URu2Si2 [electronic resource]
Keywords: Applied Physics.

Electronic nematic order refers to a phase of matter in which rotational symmetry is broken due to electronic correlations. For a large class of materials (including many cuprate and iron-pnictide superconductors), even though the crystal lattice possesses a certain degree of rotational symmetry at high temperatures, the electronic properties on cooling are much more strongly anisotropic. Such electronic anisotropy generically induces a corresponding structural distortion, however, and it is a challenge to the experimentalist to find appropriate means for differentiating electronically driven phase transitions from other types of structural instabilities. In this thesis, I have advanced a technique (building on earlier work largely driven by our group) which can directly probe the tendency toward electronic nematic order. Since anisotropic strain acts as a conjugate field to nematic order, a central insight is that a divergence in the associated nematic susceptibility (the linear nematic response to an induced anisotropic strain) on approaching the phase boundary can identify a nematic instability. If the physical quantity chosen to characterize the nematic response is the induced resistivity anisotropy, then probing the nematic susceptibility involves measurement of select components of a fourth-rank tensor called the elastoresistivity. Advancing the elastoresistivity technique has comprised two parts. First, I have formalized the mathematical description of the elastoresistivity tensor and elucidated its symmetry properties. This formalism involves the first discussion of elastoresistivity for a non-cubic system, inherently includes the presence of a magnetic field, and directly connects select components of the elastoresistivity tensor to order parameters of continuous phase transitions within a Landau paradigm. Second, given this formalism, I have proposed and demonstrated a new class of elastoresistivity measurements based on transverse resistivity configurations. The transverse elastoresistivity technique confers several experimental advantages over earlier differential longitudinal methods, including direct determination of the induced resistivity anisotropy from a single measurement and minimization of symmetry-admixing errors which complicate symmetry-based statements of an associated order parameter. In addition to describing an appropriate formalism for elastoresistivity and developing appropriate methods to measure specific components of the elastoresistivity tensor, I have also used elastoresistivity to investigate the electronic nematic properties of URu2Si2. This material is a heavy Fermion superconductor whose unconventional superconducting state condenses out of a novel Hidden Order state which has defied comprehensive understanding for over 30 years. Through a series of differential longitudinal and transverse elastoresitivity measurements, I have found evidence that the Hidden Order parameter is a multicomponent vector with a nematic component, the onset of which breaks fourfold rotational symmetry in addition to other symmetries. Preliminary measurements further indicate that this behavior persists to high magnetic fields even as Hidden Order is suppressed to zero temperature. Finally, I have observed a strong dependence of the elastoresistance on sample quality, indicating that while many thermodynamic properties associated with Hidden Order have large experimental signatures, the symmetry properties of Hidden Order are very sensitive to disorder.