Many unusual behaviors in complex oxides are deeply associated with the spontaneous emergence of microscopic phase separation. Depending on the underlying mechanism, the competing phases can form ordered or random patterns at vastly different length scales. Using a microwave impedance microscope, we observed an orientation-ordered percolating network in strained Nd0.5Sr0.5MnO3 thin films with a large period of 100 nm. The filamentary metallic domains align preferentially along certain crystal axes of the substrate, suggesting the anisotropic elastic strain as the key interaction in this system. The local impedance maps provide microscopic electrical information of the hysteretic behavior in strained thin film manganites, suggesting close connection between the glassy order and the colossal magnetoresistance effects at low temperatures. PACS numbers:Doped cuprate superconductors and colossal magnetoresistive (CMR) manganites, the two most studied complex oxides, exhibit rich phase diagrams as a result of the simultaneously active charge, spin, orbital, and lattice degrees of freedom [1,2]. Recent work on these strongly correlated materials has shown that multiple states can coexist near certain phase boundaries, a scenario known as microscopic phase separation [1]. The configurations of these spatially inhomogeneous phases reflect the underlying interactions. When the long-range Coulomb interaction prevails, the competing phases usually form nanometer-scale orders, because of the electrostatic energy penalty for macroscopic phase separation [3][4][5][6]. For self-organized patterns at larger length scales, weaker long-range interactions, such as the elastic strain arising from either the cooperative lattice distortions or lattice mismatch between substrates and epitaxial thin films, become the dominant factors [7][8][9]. Finally, the unavoidable quenched disorders in real materials always introduce short-range potential fluctuations, which usually smear out the orders or even result in micrometersized clusters with random shapes [10].Many physical properties affected by the phase separation, such as the local density of states [4-6, 11, 12], the local magnetization [13][14][15], and the atomic displacement [16], can be spatially mapped out by established microscopy tools. For CMR manganites with drastic resistance changes at different temperatures (T) and magnetic fields (H), the local resistivity (ρ) has a large span that makes spatially resolved DC measurements challenging. Imaging with high-frequency AC-coupled local probes is thus desirable. We carried out a microwave impedance microscopy (MIM) study [17,18] on manganite thin films. Unlike other GHz microscopes [19], the cantilever probe is well shielded to reduce the stray fields [18]. In the microwave electronics, the high-Q resonator [20] susceptible to environmental conditions is eliminated so that the system can be implemented under variable temperatures (2-300K) and high magnetic fields (9T). Our cryogenic MIM is therefore a versatile tool to investigat...

This paper presents a detailed modeling and characterization of a microfabricated cantilever-based scanning microwave probe with separated excitation and sensing electrodes. Using finite-element analysis, we model the tip-sample interaction as small impedance changes between the tip electrode and the ground at our working frequencies near 1 GHz. The equivalent lumped elements of the cantilever can be determined by transmission line simulation of the matching network, which routes the cantilever signals to 50 Omega feed lines. In the microwave electronics, the background common-mode signal is canceled before the amplifier stage so that high sensitivity (below 1 aF capacitance changes) is obtained. Experimental characterization of the microwave microscope was performed on ion-implanted Si wafers and patterned semiconductor samples. Pure electrical or topographical signals can be obtained from different reflection modes of the probe.

Ultra-thin topological insulator nanostructures, in which coupling between top and bottom surface states takes place, are of great intellectual and practical importance. Due to the weak Van der Waals interaction between adjacent quintuple layers (QLs), the layered bismuth selenide (Bi 2 Se 3 ), a single Dirac-cone topological insulator with a large bulk gap, can be exfoliated down to a few QLs. In this paper, we report the first controlled mechanical exfoliation of Bi 2 Se 3 nanoribbons (> 50 QLs) by an atomic force microscope (AFM) tip down to a single QL. Microwave impedance microscopy is employed to map out the local conductivity of such ultra-thin nanoribbons, showing drastic difference in sheet resistance between 1~2 QLs and 4~5 QLs. Transport measurement carried out on an exfoliated (≤5 QLs) Bi 2 Se 3 device shows nonmetallic temperature dependence of resistance, in sharp contrast to the metallic behavior seen in thick (>50 QLs) ribbons. These AFM-exfoliated thin nanoribbons afford interesting candidates for studying the transition from quantum spin Hall surface to edge states.Keywords: Topological insulator, Bismuth selenide, Nanoribbon, Mechanical exfoliation, Atomic force microscopy The metallic surface states of 3D topological insulators 1-7 are protected from disorder effects such as crystal defects and non-magnetic impurities, promising realization of dissipationless electron transport in the absence of high magnetic fields 8 . After the initial discovery of the 2D quantum spin Hall effect (QSHE) in HgTe quantum wells 7,9 , three binary compounds -Bi 2 Se 3 , Bi 2 Te 3 , and Sb 2 Te 3 were predicted and later confi rmed by angle-resolved photoemission spectroscopy (ARPES) as 3D topological insulators 10-13 . In particular, Bi 2 Se 3 has been studied due to the relatively large bulk band gap (~0.3 eV) and the simple band structure near the Dirac point. 12-17 Many exotic physical phenomena are predicted to emerge in low dimensional nanostructures of Bi 2 Se 3 . 18,19 For example, ultra-thin Bi 2 Se 3 down to a few (≤5) nanometers is expected to exhibit topologically non-trivial edge states, which serves as a new platform for the 2D QSHE 18 .In addition, tuning of the chemical potential becomes easier than thick Bi 2 Se 3 due to the suppression of bulk contribution. Fortunately, such ultra-thin Bi 2 Se 3 can be naturally obtained due to its layered rhombohedral crystal structure; two Bi and three Se atomic sheets are covalently bonded to form one quintuple layer (QL, ~1 nm thick) (Figure 1b), where adjacent QLs are coupled by relatively weak van der Waals interaction. Such anisotropic bonding structure implies that similar to the case of graphene, 20 low dimensional crystals of Bi 2 Se 3 can be generated by mechanical exfoliation, which has been achieved by several groups [21][22][23] . However, the obtained flakes are usually irregular in shape and the yield of obtaining ultra-thin flakes is low: the typical reported flakes (~10 nm) are still thick compared with the 2D limit where strong coupling betwe...

Driven by interactions due to the charge, spin, orbital, and lattice degrees of freedom, nanoscale inhomogeneity has emerged as a new theme for materials with novel properties near multiphase boundaries. As vividly demonstrated in complex metal oxides 1-5 and chalcogenides 6,7 , these microscopic phases are of great scientific and technological importance for research in hightemperature superconductors 1,2 , colossal magnetoresistance effect 4 , phase-change memories 5,6 , and domain switching operations [7][8][9] . Direct imaging on dielectric properties of these local phases, however, presents a big challenge for existing scanning probe techniques. Here, we report the observation of electronic inhomogeneity in indium selenide (In 2 Se 3 ) nanoribbons 10 by near-field scanning microwave impedance microscopy [11][12][13] . Multiple phases with local resistivity spanning six orders of magnitude are identified as the coexistence of superlattice, simple hexagonal lattice and amorphous structures with ~100nm inhomogeneous length scale, consistent with high-resolution transmission electron microscope studies. The atomic-force-microscope-compatible microwave probe is able to perform quantitative sub-surface electronic study in a noninvasive manner. Finally, the phase change memory function in In 2 Se 3 nanoribbon devices can be locally recorded with big signal of opposite signs. 2While the conventional wisdom on solids largely results from the real-space periodic structures and k-space band theories 14 , recent advances in physics have shown clear evidence that microscopic inhomogeneity, manifested as sub-micron spatial variations of the material properties, could indeed occur under certain conditions. Utilizing various probe-sample coupling mechanisms 15 , spatial inhomogeneity has been observed as nanometer gap variations in high-Tc superconductors 1,2 , coexisting electronic states in VO 2 near the metal-insulator transition 3 , ferromagnetic domains in manganites showing colossal magnetoresistance effect 4 , and in an ever-growing list. Probing these non-uniform phases provides not only much knowledge of the underlying interactions, but also valuable information for applications of the domain structures. In particular, spatially resolved properties are of significant interest for phase change and other switching materials to be on board the nanoelectric era [5][6][7][8][9] .While a number of contrast mechanisms 15 have been employed to visualize the electronic inhomogeneity, established scanning probe techniques do not directly access the low-frequency (f) complex permittivity ε(ω) = ε′ + iσ/ω, where ε′ is the dielectric constant and σ the conductivity, which holds a special position to study the ground state properties of materials. For local electrodynamic response, near-field technique is imperative to resolve spatial variations at length scales well below the radiation wavelength 16 . For this study, the working frequency is set at ~1GHz, i.e., in the microwave regime, to stay below resonant excitation...

Quantitative dielectric and conductivity mapping in the nanoscale is highly desirable for many research disciplines, but difficult to achieve through conventional transport or established microscopy techniques. Taking advantage of the micro-fabrication technology, we have developed cantilever-based near-field microwave probes with shielded structures. Sensitive microwave electronics and finite-element analysis modeling are also utilized for quantitative electrical imaging. The system is fully compatible with atomic force microscope platforms for convenient operation and easy integration of other modes and functions. The microscope is ideal for interdisciplinary research, with demonstrated examples in nano electronics, physics, material science, and biology.