University of Pittsburg researchers have been studying orbital degrees of freedom and nano-Kelvin cold atoms in optical lattices (a set of standing wave lasers) to better understand new quantum states of matter. From that research, a surprising topological semimetal has emerged. “We never expected a result like this based on previous studies,” said Liu. “We were surprised to find that such a simple system could reveal itself as a new type of topological state—an insulator that shares the same properties as a quantum Hall state in solid materials.”
“By studying these orbital degrees of freedom, we were able to discover liquid matter that had no origins within solid-state electronic materials,” said Liu.
Liu says this liquid matter could potentially lead toward topological quantum computers and new quantum devices for topological quantum telecommunication. Next, he and his team plan to measure quantities for a cold-atom system to check these predicted quantum-like properties.
The optical lattice shown in equation (S1) at different parameters. The darker (lighter) regions represent areas where the potential is low (high). The dashed line marks one unit cell of the lattice.
Since the discovery of the quantum Hall effect by Klaus Van Klitzing in 1985, researchers like Liu have been particularly interested in studying topological states of matter, that is, properties of space unchanged under continuous deformations or distortions such as bending and stretching. The quantum Hall effect proved that when a magnetic field is applied perpendicular to the direction a current is flowing through a metal, a voltage is developed in the third perpendicular direction. Liu’s work has yielded similar yet remarkably different results.
“This new quantum state is very reminiscent of quantum Hall edge states,” said Liu. “It shares the same surface appearance, but the mechanism is entirely different: This Hall-like state is driven by interaction, not by an applied magnetic field.”
Liu and his collaborators have come up with a specific experimental design of optical lattices and tested the topological semimetal state by loading very cold atoms onto this “checkerboard” lattice. Generally, these tests result in two or more domains with opposite orbital currents; therefore the angular momentum remains at zero. However, in Liu’s study, the atoms formed global rotations, which broke time-reversal symmetry: The momentum was higher, and the currents were not opposite.
Optical lattices have an important role in advancing our understandingof correlated quantum matter. The recent implementation of orbital degrees of freedom in chequerboard and hexagonal optical lattices opens up a new avenue towards discovering novel quantum states of matter that have no prior analogues in solid-state electronic materials. Here, we predict that an exotic topological semimetal emerges as a parity-protected gapless state in the orbital bands of a two-dimensional fermionic optical lattice. This new quantum state is characterized by a parabolic band-degeneracy point with Berry flux 2π, in sharp contrast to the π flux of Dirac points as in graphene. We show that the appearance of this topological liquid is universal for all lattices with D4 point-group symmetry, as long as orbitals with opposite parities hybridize strongly with each other and the band degeneracy is protected by odd parity. Turning on inter-particle repulsive interactions, the system undergoes a phase transition to a topological insulator whose experimental signature includes chiral gapless domain-wall modes, reminiscent of quantum Hall edge states.
Experimental signatures for the topological semimetal and topological insulator in Bragg scattering. On the top row, the experimental setup of Bragg scattering is shown in (a) and the schematic scattering process is shown in (b) along with the formula for ⃗ δq and δω. (c) and (d) demonstrate the scattering processes with small and large δω respectively. The former processes is forbidden, due to the lack of a final state which can satisfy the energy and momentum conservation laws. The threshold for δω above which the scatterings are allowed is shown in Figs. (e)-(g) as a function of the momentum change δq, for a metal, topological semimetal and insulator accordingly.
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