We use spectroscopic imaging scanning tunneling microscopy (SI-STM) to visualize the spatial symmetries of the electronic states that occur at the pseudogap energy scale in underdoped cuprates. We find evidence for the local intra-unit-cell electronic nematicity - by which we mean the disordered breaking of C 4v symmetry within each CuO 2 unit cell [1]. We also find that the coexisting incommensurate (smectic) electronic modulations couple to the intra-unit-cell nematicity through their 2π topological defects [2]. © 2012 Elsevier B.V. All rights reserved.

Direct visualization of electronic-structure symmetry within each crystalline unit cell is a new technique for complex electronic matter research (Lawler et al 2010 Nature 466 347-51, Schmidt et al 2011 New J. Phys. 13 065014, Fujita K et al 2012 J. Phys. Soc. Japan 81 011005). By studying the Bragg peaks in Fourier transforms of electronic structure images and particularly by resolving both the real and imaginary components of the Bragg amplitudes, distinct types of intra-unit-cell symmetry breaking can be studied.

One of the key motivations for the development of atomically resolved spectroscopic imaging scanning tunneling microscopy (SI-STM) has been to probe the electronic structure of cuprate high temperature superconductors. In both the d-wave superconducting (dSC) and the pseudogap (PG) phases of underdoped cuprates, two distinct classes of electronic states are observed using SI-STM. The first class consists of the dispersive Bogoliubov quasiparticles of a homogeneous d-wave superconductor.

Motivated by recent experiments on high-Tc cuprate superconductors pointing toward intra-unit-cell (IUC) order in the pseudogap phase, we investigate three distinct intra-unit-cell-ordering possibilities: nematic, nematic-spin-nematic, and current-loop order. The first two are Fermi-surface instabilities involving a spontaneous charge and magnetization imbalance between the two oxygen sites in the unit cell, respectively, while the third describes circulating currents within the unit cell.

We study the coexisting smectic modulations and intra-unit-cell nematicity in the pseudogap states of underdoped Bi 2Sr 2CaCu 2O 8+δ. By visualizing their spatial components separately, we identified 2π topological defects throughout the phase-fluctuating smectic states. Imaging the locations of large numbers of these topological defects simultaneously with the fluctuations in the intra-unit-cell nematicity revealed strong empirical evidence for a coupling between them.

We survey the use of spectroscopic imaging scanning tunneling microscopy (SI-STM) to probe the electronic structure of underdoped cuprates. Two distinct classes of electronic states are observed in both the d-wave superconducting (dSC) and the pseudogap (PG) phases. The first class consists of the dispersive Bogoliubov quasiparticle excitations of a homogeneous d-wave superconductor, existing below a lower energy scale E = Δ0.

We study a theoretical model of virtual scanning tunneling microscopy (VSTM): a proposed application of interlayer tunneling in a bilayer system to locally probe a two-dimensional electron system (2DES) in a semiconductor heterostructure. We consider tunneling for the case where transport in the 2DESs is ballistic and show that the zero-bias anomaly is suppressed by extremely efficient screening. Since such an anomaly would complicate the interpretation of data from VSTM, this result is encouraging for efforts to implement such a microscopy technique.

We study the electronic states of graphene in piecewise constant potentials using the continuum Dirac equation appropriate at low energies and a transfer matrix method. For superlattice potentials, we identify patterns of induced Dirac points that are present throughout the band structure and verify for the special case of a particle-hole symmetric potential their presence at zero energy. We also consider the cases of a single trench and a p-n junction embedded in neutral graphene, which are shown to support confined states.

Ever since its discovery, the electron spin has only been measured or manipulated through the application of an electromagnetic force acting on the associated magnetic moment. In this work, we propose a spin Aharonov-Bohm effect in which the electron spin is controlled by a magnetic flux while no electromagnetic field is acting on the electron.

In the high-transition-temperature (high-Tc) superconductors the pseudogap phase becomes predominant when the density of doped holes is reduced. Within this phase it has been unclear which electronic symmetries (if any) are broken, what the identity of any associated order parameter might be, and which microscopic electronic degrees of freedom are active. Here we report the determination of a quantitative order parameter representing intra-unit-cell nematicity: the breaking of rotational symmetry by the electronic structure within each CuO2 unit cell.