No Arabic abstract
Berry phase plays an important role in determining many physical properties of quantum systems. However, a Berry phase altering energy spectrum of a quantum system is comparatively rare. Here, we report an unusual tunable valley polarized energy spectra induced by continuously tunable Berry phase in Bernal-stacked bilayer graphene quantum dots. In our experiment, the Berry phase of electron orbital states is continuously tuned from about pi to 2pi by perpendicular magnetic fields. When the Berry phase equals pi or 2pi, the electron states in the two inequivalent valleys are energetically degenerate. By altering the Berry phase to noninteger multiples of pi, large and continuously tunable valley polarized energy spectra are detected in our experiment. The observed Berry phase-induced valley splitting, on the order of 10 meV at a magnetic field of 1 T, is about 100 times larger than Zeeman splitting for spin, shedding light on graphene-based valleytronics.
Since its discovery, Berry phase has been demonstrated to play an important role in many quantum systems. In gapped Bernal bilayer graphene, the Berry phase can be continuously tuned from zero to 2pi, which offers a unique opportunity to explore the tunable Berry phase on the physical phenomena. Here, we report experimental observation of Berry phases-induced valley splitting and crossing in moveable bilayer graphene p-n junction resonators. In our experiment, the bilayer graphene resonators are generated by combining the electric field of scanning tunneling microscope tip with the gap of bilayer graphene. A perpendicular magnetic field changes the Berry phase of the confined bound states in the resonators from zero to 2pi continuously and leads to the Berry phase difference for the two inequivalent valleys in the bilayer graphene. As a consequence, we observe giant valley splitting and unusual valley crossing of the lowest bound states. Our results indicate that the bilayer graphene resonators can be used to manipulate the valley degree of freedom in valleytronics.
Understanding how the electron spin is coupled to orbital degrees of freedom, such as a valley degree of freedom in solid-state systems is central to applications in spin-based electronics and quantum computation. Recent developments in the preparation of electrostatically-confined quantum dots in gapped bilayer graphene (BLG) enables to study the low-energy single-electron spectra in BLG quantum dots, which is crucial for potential spin and spin-valley qubit operations. Here, we present the observation of the spin-valley coupling in a bilayer graphene quantum dot in the single-electron regime. By making use of a highly-tunable double quantum dot device we achieve an energy resolution allowing us to resolve the lifting of the fourfold spin and valley degeneracy by a Kane-Mele type spin-orbit coupling of $approx 65~mu$eV. Also, we find an upper limit of a potentially disorder-induced mixing of the $K$ and $K$ states below $20~mu$eV.
Realizations of some topological phases in two-dimensional systems rely on the challenge of jointly incorporating spin-orbit and magnetic exchange interactions. Here, we predict the formation and control of a fully valley-polarized quantum anomalous Hall effect in bilayer graphene, by separately imprinting spin-orbit and magnetic proximity effects in different layers. This results in varying spin splittings for the conduction and valence bands, which gives rise to a topological gap at a single Dirac cone. The topological phase can be controlled by a gate voltage and switched between valleys by reversing the sign of the exchange interaction. By performing quantum transport calculations in disordered systems, the chirality and resilience of the valley-polarized edge state are demonstrated. Our findings provide a promising route to engineer a topological phase that could enable low-power electronic devices and valleytronic applications.
Valley pseudospin, the quantum degree of freedom characterizing the degenerate valleys in energy bands, is a distinct feature of two-dimensional Dirac materials. Similar to spin, the valley pseudospin is spanned by a time reversal pair of states, though the two valley pseudospin states transform to each other under spatial inversion. The breaking of inversion symmetry induces various valley-contrasted physical properties; for instance, valley-dependent topological transport is of both scientific and technological interests. Bilayer graphene (BLG) is a unique system whose intrinsic inversion symmetry can be controllably broken by a perpendicular electric field, offering a rare possibility for continuously tunable valley-topological transport. Here, we used a perpendicular gate electric field to break the inversion symmetry in BLG, and a giant nonlocal response was observed as a result of the topological transport of the valley pseudospin. We further showed that the valley transport is fully tunable by external gates, and that the nonlocal signal persists up to room temperature and over long distances. These observations challenge contemporary understanding of topological transport in a gapped system, and the robust topological transport may lead to future valleytronic applications.
Recent experiments have measured local uniaxial strain fields in twisted bilayer graphene (TBG). Our calculations found that the finite Berry curvature generated by breaking the sublattice symmetry and the band proximity between narrow bands in these TBG induces a giant Berry dipole of order 10,nm or larger. The large Berry dipole leads to transverse topological non-linear charge currents which dominates over the linear bulk valley current at experimentally accessible crossover in-plane electric field of $sim 0.1 {rm mV} / mu rm{m}$. This anomalous Hall effect, due to Berry dipole, is strongly tunable by the strain parameters, electron fillings, gap size, and temperature.