Electronic Nematic Phases Andrew Davis Preliminaries Fermi Liquid - - PowerPoint PPT Presentation

Electronic Nematic Phases

Andrew Davis

Preliminaries – Fermi Liquid Theory

• Begin with free Fermi gas – elementary excitations are

particles/holes

• Adiabatically turn on interactions → quasiparticles
• 1-to-1 correspondence between non-interacting and

interacting states

• Quasiparticles have same quantum numbers
• At low T, we have a dilute gas of quasiparticles
• State characterized by 𝜀𝑜𝑞

Preliminaries – Fermi Liquid Theory

• Energy functional for a state 𝜀𝑜𝑞 :

𝐹 = 𝐹0 + ෍

𝑞𝜏

𝜁𝑞𝜀𝑜𝑞 + 1 2 ෍

𝑞𝜏𝑞′𝜏′

𝑔𝑞𝜏𝑞′𝜏′ 𝜀𝑜𝑞𝜏𝜀𝑜𝑞′𝜏′ + ⋯

• Expand interaction in Legendre polynomials:

𝑔𝑞𝐺෠

𝑙,𝑞𝐺෠ 𝑙′ = ෍ 𝑚=0 ∞

𝑄

𝑚(෠

𝑙 ∙ ෠ 𝑙′)𝑔

𝑚

• Feedback mechanism and distortion of Fermi surface
• Nature of feedback depends on the 𝑔

𝑚 Effect of interactions

Preliminaries – Pomeranchuk instabilities

• Feedback may be positive or negative
• Fermi pressure stabilizes the FS
• But if any 𝑔

𝑚 < −(2𝑚 + 1), we get “runaway” feedback

• FS unstable to this deformation
• Fermi Liquid Theory breaks down – new phase

Nematic phases defined

Classical

• Rod-like molecules which break
• rientational symmetry
• Order parameter is a director

Electronic

• The electron fluid breaks the sym. of

the underlying Hamiltonian which interchanges two axes – despite no anisotropy in lattice!

• Resulting anisotropy is in k-space
• Observed through transport

anisotropies, etc.

• Many choices of OP – e.g.

𝜍𝑦𝑦−𝜍𝑧𝑧 𝜍𝑦𝑦+𝜍𝑧𝑧

• Examples: C4 → C2 , C∞ → C2

Fradkin et al. 2010, Nematic Fermi Fluids in Condensed Matter Physics

Two views of nematicity

“Strong coupling” view: a smectic crystal melts “Weak coupling” view – a PI destroys a Fermi liquid Broken orientational sym. Broken translational sym. Broken orientational sym. Restored translational sym. l = 2 channel (quadrupole)

An Example – Sr3Ru2O7

Borzi et al. 2007, Formation of a Nematic Fluid at High Fields in Sr3Ru2O7

Model of an anisotropic system with a dPI

n.n. and n.n.n. hopping Interaction which drives dPI Explicit xy anisotropy Peaked at q = 0

nd 0 is proportional to the order parameter, so μd is the conjugate field.

Yamase 2014, Electron nematic phase transition in the presence of anisotropy

Mean Field Analysis

• Focus on q = 0 contribution
• Order parameter 𝜚 = 𝑕 0 𝑜𝑒 0
• A metanematic transition – discontinuous

jump in 𝜚 when crossing wing

• At the upper tip of the wing 𝜈𝑒 is so large

(≈2) that the system is extremely anisotropic: “the wing interpolates between a two- and (effectively) one-dimensional system”

Beyond Mean-Field

• Analyzed by fRG
• CEL is suppressed so much that the wing

breaks in two – two new QCEPs form

• Crossover region
• Unlike in MFT, a QCEP is accessible at a

very small anisotropy

• The wing is extremely sensitive to

fluctuations

Connection to experiment

• Y-based cuprates
• Weak anisotropy in YBa2Cu3O6.85 and YBa2Cu3O6.6, but strong anisotropy in YBa2Cu3O6.45
• Because of slight orthorhombicity of YBCO, the system may be crossing the first wing by

tuning oxygen concentration

• Ruthenates
• A tetragonal system, but predicts critical behavior when applying a slight strain
• Quasi-1D metals
• Highly anisotropic – could potentially observing crossing of second wing
• Less obvious that anisotropy has a partly nematic origin
• Cold atoms
• Interesting because 𝜈𝑒 can be tuned

References

• Fradkin et al. 2010, Nematic Fermi Fluids in Condensed Matter Physics.

https://arxiv.org/abs/0910.4166

• Borzi et al. 2007, Formation of a Nematic Fluid at High Fields in Sr3Ru2O7.

https://arxiv.org/abs/cond-mat/0612599

• Yamase 2014, Electron nematic phase transition in the presence of anisotropy.

https://arxiv.org/abs/1401.4628

• Yamase, Oganesyan, & Metzner 2005, Mean-field theory for symmetry-breaking

Fermi surface deformations on a square lattice. https://arxiv.org/abs/cond-mat/0502238