ABSTRACT - DRUM - University of Maryland
ABSTRACT - DRUM - University of Maryland
ABSTRACT - DRUM - University of Maryland
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ameter correlations.<br />
It is therefore an important question to understand the fluctuation effects on<br />
the topological aspects, particularly the Majorana zero modes in TSC, since they<br />
do live in one or two dimensions. From a more general perspective, the interplay<br />
between interaction (since fluctuations are essentially caused by interactions) and<br />
topological classification <strong>of</strong> non-interacting systems is a fundamental problem which<br />
we only began to understand quite recently. A remarkable progress is that the topological<br />
classification <strong>of</strong> one-dimensional non-interacting fermionic systems with timereversal<br />
symmetry is dramatically changed by interactions [152, 153, 154]. Several<br />
theoretical studies on the effects <strong>of</strong> interactions on Majorana fermions in proximityinduced<br />
TSC have been performed recently [155, 156, 157, 158], confirming the<br />
stability <strong>of</strong> Majorana fermions against weak and moderate interactions.<br />
In this chapter we present an attempt to understand the fate <strong>of</strong> Majorana<br />
zero modes when quantum fluctuations are strong enough that only quasi-longrange<br />
superconducting order can exist. We consider a generic theoretical model <strong>of</strong><br />
spinless fermions on two-chain ladders.<br />
The model generalizes the simplest onedimensional<br />
TSC, namely spinless fermions with p-wave pairing (also known as Majorana<br />
chain) [28], to interacting two-chain systems. Instead <strong>of</strong> introducing pairing<br />
by proximity effect, the effective field theory includes inter-chain pair tunneling with<br />
inter-chain single-particle tunneling being suppressed. Therefore the fermion parity<br />
on each chain is conserved. When the pair-tunneling interaction drives the system to<br />
strong coupling, localized Majorana zero-energy states are found on the boundaries,<br />
which represents a nontrivial many-body collective state <strong>of</strong> the underlying fermions.<br />
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