Observation of a nematic quantum Hall liquid on the surface of bismuth

Abstract

Nematic quantum fluids with wavefunctions that break the underlying crystalline symmetry can form in interacting electronic systems. We examine the quantum Hall states that arise in high magnetic fields from anisotropic hole pockets on the Bi(111) surface. Spectroscopy performed with a scanning tunneling microscope shows that a combination of single-particle effects and many-body Coulomb interactions lift the six-fold Landau level (LL) degeneracy to form three valley-polarized quantum Hall states. We image the resulting anisotropic LL wavefunctions and show that they have a different orientation for each broken-symmetry state. The wavefunctions correspond to those expected from pairs of hole valleys and provide a direct spatial signature of a nematic electronic phase. Main text:Nematic electronic states represent an intriguing class of broken-symmetry phases that can spontaneously form as a result of electronic correlations (1, 2). They are characterized by reduced rotational symmetry relative to the underlying crystal lattice and have attracted considerable interest in systems such as two-dimensional electron gases (2DEGs) (3-5), strontium ruthenate (6), and high-temperature superconductors (7)(8)(9)(10)(11)(12). The sensitivity of electronic nematic phases to disorder results in short range ordering and domains, making them difficult to study using global measurements that average over microscopic configurations. The effect of perturbations, such as crystalline strain, may be used to show a propensity for nematic order, i.e. to provide evidence that vestiges of nematic behavior survive even in the presence of material imperfections (1). However, it is difficult to quantitatively correlate the experimental evidence of ordering with a microscopic description of the electronic states and the interactions responsible for nematic behavior. To put the study of nematic electronic phases on more quantitative ground, it is therefore important not only to perform local measurements, but also to find a material system for which theory can fully characterize the underlying broken-symmetry states and the electronic interactions.Multi-valley 2DEGs with anisotropic band structure have been anticipated as a model platform to explore nematic order in the quantum Hall regime (13-17). The key idea is that Coulomb interactions can spontaneously lift the valley degeneracy in materials with low disorder and thereby break rotational symmetry. In contrast to previously studied metallic nematic phases, this leads to a gapped nematic state with quantized Hall conductance. We examine such a 2DEG on the surface of single crystals of bismuth (Bi), which is one of the cleanest electronic systems, with a bulk mean free path reaching 1 mm at low temperatures (18). Interest in Bi has recently been rekindled by bulk measurements showing phase transitions and anisotropic behavior at large magnetic fields, which may be related to nematic electronic phenomena (19)(20)(21)(22). We focus here on the (111) surface of Bi, for which strong R...

Fermi Surfaces of Composite Fermions

“…Fermi contours with shapes similar to those in Fig. 6 have been observed in GaAs systems in a parallel field [17], as well as in the surface states of Sn 1−x Pb x Se [35] and bismuth [36] [37] (though in the latter case the valleys are elongated radially, rather than tangentially). In such systems it is tempting to assume that multiple zero-field Fermi pockets imply that the system can be treated as having a single Fermi pocket and an additional "valley pseudospin" at high field.…”

Two-dimensional Fermi liquid dynamics with density-density and quadrupolar interactions

“…Iron based superconductors are promising compounds 38,39 , which have clear evidences of electronic nematic phases. Moreover, quantum Hall systems at partially filled Landau levels also display spontaneous breakdown of rotational symmetry 5,[40][41][42] , signaling the relevance of the quadrupolar interaction. Since much of the interesting features of our model have signatures for weak interactions, we expect that ultracold Fermionic atoms 43,44 could also be an arena to look for this phenomenology, due to the fact that weak repulsive as well as attractive couplings can be manipulated with great precision in these systems.…”

Topology- and symmetry-protected domain wall conduction in quantum Hall nematics

“…by uniaxial strain [9]. Such a nematic QH liquid was recently observed via high-field scanning tunneling microscopy (STM) experiments on the sixfold valleydegenerate (111) surface of bismuth (Bi) [13]. Orientational symmetry breaking is detected by imaging local density of states (LDOS) modulations near atomic-scale impurities, while energy-resolved measurements clarify the role of interactions.…”

“…Mirror symmetries play the role of C 4 in constraining dispersions. We take λ = 5, and approximate screening crudely via a large dielectric constant ≈ 45, yielding a bulk exchange gap [13] ∆ ex ∼ 535 µeV, and Luttinger liquid parameters u ρ ∼ 0.1∆ ex B , K ρ ∼ 0.1 for Γ ∼ 0.01∆ ex B . For ν = 2 we estimate a charge gap of 120 µeV for small Γ, a sizable fraction of ∆ ex ; this is is consistent with our discussion above and the dichotomy between ν = 1, 2 reported in [1].…”