The simulator shows a one-dimensional chain of atoms with a partially filled electronic band spontaneously dimerizing at low temperature, opening a gap at the Fermi level and lowering the total electronic energy, while visualizing the accompanying charge density wave and its Fermi-wavevector-set wavelength in real time.
Start with an evenly spaced chain and a chosen band filling, then gradually cool the system using the temperature slider and watch the bond lengths spontaneously alternate into a short-long-short-long pattern once the transition temperature is crossed. Adjust the electron-phonon coupling strength to see how it controls the size of the resulting energy gap and the transition temperature, and switch on the density overlay to watch the charge density wave crest and trough track each dimerized bond pair. Try different filling fractions away from one-half to see the dimerized pattern give way to an incommensurate, non-repeating modulation.
Sliders for temperature, electron-phonon coupling strength, and band filling fraction; a play/pause and cooling-rate control for the temperature sweep; a toggle to overlay the charge density wave on top of the atomic chain; and a readout panel showing the current gap size, bond-length alternation amplitude, and charge density wave wavelength.
Rudolf Peierls first described this instability in his 1955 textbook Quantum Theory of Solids almost as a passing remark, yet it took roughly two more decades before experiments on materials like TTF-TCNQ and NbSe3 confirmed that real quasi-one-dimensional crystals actually undergo exactly the kind of spontaneous, coupling-independent dimerization his argument predicted.
The simulator shows a one-dimensional chain of atoms with a partially filled electronic band spontaneously dimerizing at low temperature, opening a gap at the Fermi level and lowering the total electronic energy, while visualizing the accompanying charge density wave and its Fermi-wavevector-set wavelength in real time.
The simulator shows a one-dimensional chain of atoms with a partially filled electronic band spontaneously dimerizing at low temperature, opening a gap at the Fermi level and lowering the total electronic energy, while visualizing the accompanying charge density wave and its Fermi-wavevector-set wavelength in real time.
Start with an evenly spaced chain and a chosen band filling, then gradually cool the system using the temperature slider and watch the bond lengths spontaneously alternate into a short-long-short-long pattern once the transition temperature is crossed. Adjust the electron-phonon coupling strength to see how it controls the size of the resulting energy gap and the transition temperature, and switch on the density overlay to watch the charge density wave crest and trough track each dimerized bond pair. Try different filling fractions away from one-half to see the dimerized pattern give way to an incommensurate, non-repeating modulation.
Rudolf Peierls first described this instability in his 1955 textbook Quantum Theory of Solids almost as a passing remark, yet it took roughly two more decades before experiments on materials like TTF-TCNQ and NbSe3 confirmed that real quasi-one-dimensional crystals actually undergo exactly the kind of spontaneous, coupling-independent dimerization his argument predicted.