Nematic order on the surface of a three-dimensional topological insulator

Abstract

We study the spontaneous breaking of rotational symmetry in the helical surface state of threedimensional topological insulators due to strong electron-electron interactions, focusing on timereversal invariant nematic order. Owing to the strongly spin-orbit coupled nature of the surface state, the nematic order parameter is linear in the electron momentum and necessarily involves the electron spin, in contrast with spin-degenerate nematic Fermi liquids. For a chemical potential at the Dirac point (zero doping), we find a first-order phase transition at zero temperature between isotropic and nematic Dirac semimetals. This extends to a thermal phase transition that changes from first to second order at a finite-temperature tricritical point. At finite doping, we find a transition between isotropic and nematic helical Fermi liquids that is second order even at zero temperature. Focusing on finite doping, we discuss various observable consequences of nematic order, such as anisotropies in transport and the spin susceptibility, the partial breakdown of spinmomentum locking, collective modes and induced spin fluctuations, and non-Fermi liquid behavior at the quantum critical point and in the nematic phase. arXiv:1702.07364v2 [cond-mat.str-el]

Fermi surface instabilities of symmetry-breaking and topological types on the surface of a three-dimensional topological insulator

“…kF < 0 which implies that the isotropic to nematic transition is a second order phase transition, in agreement with the Ref. [22]. It is worthwhile to point out that in the case of the conventional Landau Fermi liquid, it has been essential to incorporate non-linear terms in the non-interacting dispersion relation to stabilize the nematic quantum critical point [52].…”

“…With sufficiently strong e-e interaction in the l = 2 angular momentum channel the the ground state energy of an HFL is further lowered by spontaneous quadrupolar deformation of the corresponding Fermi surface, leading to a nematic phase [22]. Such spontaneous rotational symmetry breaking in the surface states of 3D-TI has been studied considering the following effective Hamiltonian,…”

“…where the quantity F (q) = (2π) 2 F 2 δ(q − 0) and for nematic instability the value of F 2 is usually taken to be negative [22]. With this choice I now compare the self energy of the above Hamiltonian with the coefficient of the cos(2θ kk ′ ) of the Hartree-Fock self energy corresponding to (10) by using the parametrization (6).…”

“…It is worthwhile to point out that in the case of the conventional Landau Fermi liquid, it has been essential to incorporate non-linear terms in the non-interacting dispersion relation to stabilize the nematic quantum critical point [52]. However, in case of HFL which is strictly valid for finite doping only, µ > 0, the linear dispersion relation corresponding to a single Dirac cone has been sufficient to stabilize the quantum critical point and phase transition becomes continuous in nature even at T = 0 [22].…”

“…The resulting shape deformation instability is renowned as Pomeranchuk Instability (PI) which occurs in a particular angular momentum channel l, when corresponding the Landau parameter F l becomes sufficiently negative [17][18][19][20][21]. For example, in HFL the l = 2 PI leads to a new phase exhibiting nematic order characterized by elongation (contraction) of the Fermi surface along k x (k y ) direction and vice versa, and more interestingly a partial breakdown of spin momentum locking (in the sense that spin and momentum are no-longer orthogonal) [22]. In the case of SU(2)-FL such PIs have been studied in a sufficiently general frame work by taking into account a generic central Fermion-Fermion (e-e) interaction both in two and three dimensions [23,24].…”