Signatures of Wigner localization in epitaxially grown nanowires

Abstract

It was predicted by Wigner in 1934 that the electron gas will undergo a transition to a crystallized state when its density is very low. Whereas significant progress has been made towards the detection of electronic Wigner states, their clear and direct experimental verification still remains a challenge. Here we address signatures of Wigner molecule formation in the transport properties of InSb nanowire quantum dot systems, where a few electrons may form localized states depending on the size of the dot (i.e. the electron density). By a configuration interaction approach combined with an appropriate transport formalism, we are able to predict the transport properties of these systems, in excellent agreement with experimental data. We identify specific signatures of Wigner state formation, such as the strong suppression of the antiferromagnetic coupling, and are able to detect the onset of Wigner localization, both experimentally and theoretically, by studying different dot sizes.

Formation of defects in multirow Wigner crystals

“…Three equivalent minima at N = 58, N = 116, and N = 174 can be clearly seen. These minima correspond to configurations with defects in the outer-most rows, i.e., the outer rows have less particles than the inner rows, namely N inner = 12 (24,36), and N outer = 11 (22,33), respectively. The corresponding defect density is n 4.85 def = 1 − 11/12 = 0.083.…”

“…The three-dimensional Wigner crystal and its two-dimensional counterpart have been extensively studied, and there exist beautiful experimental realizations of the latter using electrons trapped on the surface of liquid Helium [2][3][4][5] . More recently, Wigner crystallization in one dimension has received renewed interest [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] ; for recent reviews see Refs. 23 and 24.…”

Thermopower as a tool to investigate many-body effects in quantum systems

“…We consider a segment of a nanowire, which is connected to leads on either side via a tunneling barrier. Possible realizations are, e.g., semiconductor nanowires with metal stripes acting as leads and simultaneously providing a Schottky barrier, 16 nanowires with embedded heterostructures, 20 or nanowires defined by cleaved edge overgrowth. 21 The nanowire segment is modeled as a hard-wall cylinder of radius 35 nm.…”

“…[8][9][10] Here, we apply this concept to the Wigner localization 11 in a nanowire. [12][13][14][15][16][17] Wigner localization is a prime example for a pronounced many-body effect, caused by the dominance of the repulsive interaction over the kinetic energy of the electrons in the system. 11,18 Clearly, such spatially correlated quantum states cannot be described by the constant interaction model commonly used for thermal transport simulations, 8 see also Ref.…”

“…Our approach follows Ref. 16, where we probed the Wigner localization by the conductance signal of excited states under finite bias. Using the thermopower signal, these features can be extracted already in linear response as demonstrated in this letter.…”